Templum musicum, or, The musical synopsis of the learned and famous Johannes-Henricus-Alstedius being a compendium of the rudiments both of the mathematical and practical part of musick, of which subject not any book is extant in our English tongue / faithfully translated out of Latin by John Birchensha ...
         Elementale mathematicum. VI, Musica. English
         Alsted, Johann Heinrich, 1588-1638.
      
       
         
           1664
        
      
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         59254
         
           
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         Transcribed from: (Early English Books Online ; image set 59254)
         Images scanned from microfilm: (Early English books, 1641-1700 ; 198:9)
      
       
         
           
             Templum musicum, or, The musical synopsis of the learned and famous Johannes-Henricus-Alstedius being a compendium of the rudiments both of the mathematical and practical part of musick, of which subject not any book is extant in our English tongue / faithfully translated out of Latin by John Birchensha ...
             Elementale mathematicum. VI, Musica. English
             Alsted, Johann Heinrich, 1588-1638.
             Birchensha, John, fl. 1664-1672.
          
           [15], 93 [i.e. 94] p. : ill., music.
           
             Printed by Will. Godbid for Peter Dring ...,
             London :
             1664.
          
           
             A translation of one part, Elementale musicum, of: Elementale mathematicum. Frankfort, 1611.
             "Imprimatur, Feb. 5. 1663. Roger L'Estrange"
             Errata: p. [15].
             Reproduction of original in Harvard University Libraries.
          
        
      
    
     
       
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         eng
      
       
         
           Music theory -- History -- 17th century.
        
      
    
     
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           To
           Musicks
           sacred
           Temple
           ,
           Mercurie
           .
        
         
           And
           Orpheiis
           dedicate
           their
           Harmonie
        
         
           From
           thence
           proceeding
           .
           Whose
           faire
           Handmaids
           an
        
         
           Myster'ous
           Numbers
           :
           which
           ,
           if
           you
           compare
           .
        
         
           The
           Rat'on
           of
           proport'ons
           you
           will
           find
           .
        
         
           These
           please
           the
           Eare
           ,
           and
           satisfie
           the
           mind
           .
        
         
           For
           nothing
           ,
           more
           ,
           the
           Soule
           and
           sense
           contents
           .
        
         
           Then
           Sounds
           express'd
           by
           voice
           ,
           and
           Instruments
           .
        
         
           Io.
           Dir.
           Iohn
           Chantry
           ●
        
         
           sould
           by
           Peter
           Dring
           at
           the
           Sun
           in
           the
           Poultry
           :
        
      
       
         
         
           TEMPLVM
           MVSICVM
           :
           OR
           THE
           MUSICAL
           SYNOPSIS
           ,
           OF
           The
           Learned
           and
           Famous
           Johannes
           -
           Henricus
           -
           Alstedius
           ,
           BEING
           A
           Compendium
           of
           the
           Rudiments
           both
           of
           the
           Mathematical
           and
           Practical
           Part
           of
           MUSICK
           :
           Of
           which
           Subject
           not
           any
           Book
           is
           extant
           in
           our
           English
           Tongue
           .
        
         
           Faithfully
           translated
           out
           of
           Latin
           By
           
             John
             Birchensha
             .
             Philomath
          
           .
        
         
           ●mprimatur
           ,
           Feb.
           5.
           1663.
           
           Roger
           L'Estrange
           .
        
         
           London
           ,
           Printed
           by
           
             Will
             ,
             Godbid
          
           for
           
             Peter
             Dring
          
           at
           〈◊〉
           Sun
           in
           the
           Poultrey
           next
           Dore
           to
           the
           Rose-Tavern
           .
           1664.
           
        
      
       
         
         
         
           To
           the
           Right
           Honourable
           EDVVARD
           Lord
           MONTAGU
           Earl
           of
           Sandwich
           ,
           &c.
           
           Knight
           of
           the
           
             most
             Noble
             Order
          
           of
           the
           Garter
           ,
           and
           One
           of
           His
           Majesties
           most
           Honourable
           Privy-Council
           .
        
         
           
             SIR
             ,
          
        
         
           WHen
           I
           considered
           the
           Excellency
           of
           the
           Subject
           of
           this
           Book
           ,
           and
           deserved
           Fame
           of
           the
           learned
           Author
           ,
           I
           thought
           it
           not
           necessary
           to
           crave
           a
           Protection
           
           for
           this
           Treatise
           by
           a
           Dedication
           of
           it
           unto
           any
           :
           being
           in
           it self
           far
           above
           the
           reach
           of
           detracting
           Calumniators
           .
           Yet
           I
           have
           made
           bold
           ,
           humbly
           ,
           to
           present
           it
           to
           your
           Honour
           as
           a
           pleasant
           and
           delightful
           Divertisement
           from
           your
           many
           and
           great
           Imployments
           .
           In
           all
           Ages
           Musick
           hath
           been
           acceptable
           to
           the
           wisest
           ,
           greatest
           ,
           and
           most
           Learned
           men
           ,
           of
           whom
           many
           have
           been
           famous
           for
           their
           great
           Ability
           and
           Knowledge
           in
           this
           Science
           and
           Art.
           It
           was
           no
           dispraise
           to
           David
           that
           he
           plaid
           skilfully
           on
           the
           Harp
           ,
           and
           Sang
           well
           :
           the
           
           Compositions
           of
           divers
           German
           Princes
           are
           extant
           :
           neither
           is
           it
           the
           least
           of
           those
           Virtues
           which
           are
           eminent
           in
           your
           Lordship
           ,
           that
           you
           are
           both
           a
           Lover
           of
           Musick
           ,
           and
           a
           good
           Musician
           .
           The
           renowned
           Alstedius
           in
           this
           Compendium
           (
           not
           much
           differing
           in
           his
           Judgement
           from
           the
           Opinion
           of
           the
           Generality
           of
           modern
           musical
           Classic's
           )
           does
           present
           the
           world
           with
           a
           great
           Light
           and
           Discovery
           of
           this
           Art
           ,
           with
           the
           
             Subject
             ,
             Principle
          
           and
           Affections
           thereof
           ,
           with
           the
           curious
           Symmetry
           of
           Proportions
           :
           the
           proportional
           Dimensions
           of
           
           Sounds
           :
           the
           Variety
           of
           Diastems
           :
           the
           admirable
           Series
           of
           musical
           Voices
           :
           the
           usefulnesse
           of
           Tetrachords
           :
           the
           several
           Genus's
           of
           Musick
           :
           and
           harmonical
           Moods
           ,
           which
           being
           expressed
           by
           Voice
           or
           Instrument
           or
           both
           ,
           do
           operate
           ineredibly
           upon
           the
           Affections
           .
           Wherefore
           I
           hope
           that
           this
           Book
           will
           be
           accepted
           both
           by
           your
           Honour
           ,
           and
           all
           ingenuous
           Lovers
           and
           Professors
           of
           this
           Art
           ,
           and
           the
           Errors
           thereof
           favourably
           pardoned
           by
           your
           Lordship
           and
           them
           .
           The
           Reason
           which
           moved
           me
           to
           undertake
           this
           Translation
           ,
           was
           ,
           because
           
           I
           desired
           a
           Discovery
           might
           be
           made
           of
           some
           Principles
           of
           the
           Mathematical
           part
           of
           Musick
           ,
           unto
           those
           ingenuous
           Lovers
           of
           this
           Science
           ,
           who
           understand
           only
           our
           own
           Language
           ,
           to
           the
           End
           that
           by
           this
           means
           the
           transcendent
           Virtue
           and
           Excellency
           that
           is
           comprehended
           in
           the
           due
           proportions
           of
           musical
           Sounds
           may
           be
           known
           unto
           them
           ;
           which
           will
           give
           Satisfaction
           unto
           their
           Reason
           aswell
           as
           to
           their
           Sence
           .
           I
           do
           not
           think
           this
           unworthy
           my
           labour
           ,
           because
           that
           many
           skilful
           Musicians
           have
           not
           thought
           it
           any
           Disparagement
           
           to
           publish
           their
           Translations
           of
           the
           Works
           of
           famous
           Men
           ,
           who
           did
           write
           of
           the
           Art
           which
           they
           themselves
           professed
           .
           As
           Meibomius
           Translated
           some
           Fragments
           of
           
             Baccheus
             ,
             Alyppius
             ,
             Nichomachus
          
           ,
           and
           others
           :
           the
           never
           to
           be
           forgotten
           Franchinus
           ,
           the
           Commentaries
           of
           
             Briennius
             ,
             Aristides
             ,
             Ptolomy
          
           ,
           and
           others
           :
           and
           our
           
             English
             Douland
          
           ,
           the
           Introduction
           of
           Ornithoparcus
           .
           In
           the
           Author's
           last
           Edition
           of
           his
           universal
           Encyclopaedia
           ,
           I
           met
           with
           an
           Appendix
           to
           his
           Musical
           Synopsis
           ,
           taken
           out
           of
           the
           writings
           of
           
             Erycius
             Puteanus
          
           ;
           but
           not
           finding
           
           any
           thing
           new
           in
           it
           ,
           only
           an
           
             ABCdary
             Repetition
          
           of
           the
           first
           Elements
           of
           Musick
           ,
           formerly
           but
           more
           judiciously
           and
           largely
           handled
           in
           this
           Compendium
           :
           and
           also
           some
           few
           Questions
           started
           by
           Cardanus
           ,
           which
           are
           ,
           for
           the
           most
           part
           more
           fully
           and
           Satisfactorily
           resolved
           by
           the
           Author
           ;
           I
           did
           forbear
           the
           Translation
           thereof
           ;
           not
           being
           willing
           to
           weary
           the
           Reader
           with
           the
           unnecessary
           recital
           of
           those
           things
           ,
           nor
           your
           Lordship
           with
           too
           tedious
           an
           Epistle
           ,
           which
           I
           here
           conclude
           ,
           humbly
           craving
           pardon
           for
           my
           boldnesse
           ,
           and
           your
           Honours
           
           favourable
           Acceptation
           of
           this
           Mite
           from
           your
           Lordships
        
         
           
             
               Most
               humble
               and
               devoted
               Servant
            
             ,
             JOHN
             BIRCHENSHA
             .
          
        
      
       
         
         
           To
           all
           ingenious
           LOVERS
           of
           MUSICK
           .
        
         
           
             GENTLEMEN
             ,
          
        
         
           IT
           was
           for
           your
           Profit
           and
           Benefit
           that
           I
           undertook
           this
           Translation
           :
           and
           that
           you
           might
           thereby
           understand
           the
           Rudiments
           and
           Principles
           both
           of
           the
           Mathematical
           and
           Practical
           Parts
           of
           this
           Science
           .
           We
           know
           that
           there
           is
           some
           light
           into
           the
           Mathematical
           Part
           of
           all
           other
           Arts
           ;
           but
           little
           discovery
           of
           that
           Part
           of
           the
           Theory
           of
           Musick
           hath
           been
           made
           in
           our
           Language
           ;
           therefore
           I
           did
           suppose
           that
           this
           work
           would
           be
           gratefully
           accepted
           by
           you
           ,
           the
           Author
           having
           more
           fully
           discovered
           the
           Precepts
           ,
           Rules
           ,
           and
           Axioms
           of
           this
           Science
           ,
           then
           any
           other
           whose
           Works
           I
           have
           seen
           .
        
         
           Since
           the
           Rumour
           of
           this
           Translation
           hath
           been
           spred
           abroad
           ,
           I
           have
           by
           diverse
           been
           demanded
           ,
           
             What
             Benefit
             and
             Advantage
             the
             Knowledge
             of
             the
             Mathematical
             Part
             of
             Musick
             does
             contribute
             to
             the
             completing
             of
             a
             Musician
             ?
          
           To
           which
           I
           answer
           ,
           That
           it
           is
           as
           necessary
           for
           a
           perfect
           and
           complete
           Musician
           to
           
           understand
           the
           Proportion
           of
           Sounds
           ,
           as
           for
           a
           curious
           Painter
           ,
           exactly
           to
           know
           the
           Symmetry
           of
           every
           part
           o●
           a
           Body
           :
           that
           so
           he
           may
           rightly
           understand
           the
           ground
           and
           foundation
           of
           the
           Art
           he
           does
           profess
           ,
           which
           is
           ,
           the
           nature
           of
           Sounds
           ,
           and
           their
           due
           Proportion
           ,
           in
           respect
           of
           their
           Ration
           ,
           Habitude
           ,
           Quality
           ,
           Difference
           ,
           Excess
           ,
           Dimension
           ,
           and
           Magnitude
           .
           For
           this
           I
           dare
           boldly
           affirm
           ,
           and
           if
           ●ccasion
           be
           offered
           :
           undertake
           to
           prove
           it
           :
           That
           such
           Rules
           may
           be
           yet
           further
           ,
           and
           are
           already
           ,
           in
           part
           ,
           contrived
           (
           drawn
           from
           the
           Mathematical
           Principles
           of
           Musick
           ,
           by
           which
           ,
           musical
           Consonants
           and
           Dissonants
           (
           artificially
           applied
           and
           disposed
           ,
           according
           to
           the
           nature
           of
           their
           Proportions
           ,
           and
           by
           the
           forementioned
           Canons
           )
           may
           afford
           ,
           in
           
             2
             ,
             3
             ,
             4
             ,
             5
             ,
             6
             ,
             7
             ,
          
           or
           more
           parts
           ,
           as
           go●d
           Musick
           ,
           that
           is
           ,
           as
           agreeable
           ,
           artificial
           ,
           and
           formal
           ,
           as
           can
           be
           composed
           by
           the
           help
           of
           any
           Instrument
           .
           Yet
           until
           such
           Rules
           be
           known
           ,
           it
           is
           commendable
           in
           any
           to
           use
           such
           helps
           as
           may
           Advantage
           their
           Compositions
           .
           But
           for
           any
           Musician
           to
           unde●
           value
           or
           speak
           slightly
           of
           the
           Mathematical
           part
           of
           Musick
           ,
           is
           to
           repro●ch
           the
           Common
           Parent
           from
           whom
           the
           Art
           h●
           professeth
           rec●ived
           a
           Being
           .
           I
           k●ow
           that
           all
           Ingenuous
           persons
           who
           are
           Artists
           ,
           will
           acknowledge
           that
           it
           is
           a
           more
           noble
           way
           to
           work
           by
           Rules
           and
           Pr●c●pts
           in
           any
           Art
           ,
           then
           mechanically
           ;
           And
           so
           to
           work
           in
           this
           Art.
           
             i.
             e.
          
           to
           compose
           regularly
           ,
           will
           be
           found
           m●re
           advantagious
           then
           any
           other
           way
           in
           these
           Respects
           .
           For
           by
           such
           a
           way
           of
           Operation
           the
           Composer
           shall
           work
           more
           certain●y
           ,
           firmly
           ,
           readily
           ,
           and
           with
           more
           facility
           then
           by
           any
           other
           way
           .
        
         
           If
           Musick
           be
           an
           Art
           ,
           then
           it
           may
           be
           contracted
           
           and
           collected
           into
           certain
           Rules
           which
           may
           discover
           all
           those
           Mysteries
           that
           are
           contained
           in
           that
           Science
           ,
           by
           which
           a
           man
           may
           become
           an
           excellent
           Musician
           ,
           and
           expert
           ,
           both
           in
           the
           Theorical
           and
           Practical
           Parts
           thereof
           .
           To
           the
           Completeing
           of
           such
           forcible
           Rules
           I
           have
           contributed
           my
           Mite
           ,
           whose
           Certainty
           and
           Reality
           has
           been
           Experienced
           by
           divers
           ,
           and
           may
           likewise
           be
           further
           known
           unto
           others
           ,
           if
           they
           please
           or
           desire
           to
           understand
           them
           .
        
         
           I
           know
           that
           all
           Virtuoso's
           will
           encourage
           those
           things
           which
           conduce
           to
           the
           Improvement
           of
           any
           ingenious
           Art
           :
           but
           what
           shall
           be
           spoken
           against
           such
           things
           by
           persons
           rude
           ,
           envious
           ,
           or
           that
           do
           pass
           their
           Judgement
           rashly
           upon
           things
           which
           they
           know
           not
           ,
           having
           neither
           seen
           ,
           heard
           ,
           nor
           understood
           them
           ,
           is
           not
           to
           be
           valued
           .
           And
           I
           do
           assure
           my self
           that
           there
           is
           not
           any
           person
           in
           this
           Nation
           ,
           that
           is
           a
           true
           Lover
           of
           this
           Science
           ;
           or
           a
           Professour
           thereof
           ,
           who
           does
           truely
           honour
           and
           understand
           this
           Art
           ,
           but
           could
           cordially
           wish
           such
           an
           Improvement
           thereof
           ,
           that
           those
           things
           which
           in
           Musick
           are
           concealed
           and
           mysterious
           ,
           might
           be
           fully
           discovered
           :
           those
           which
           are
           imperfect
           ,
           completed
           :
           those
           which
           are
           doubtful
           and
           disputable
           ,
           cleared
           by
           evident
           Demonstration
           :
           those
           which
           are
           not
           to
           be
           done
           without
           great
           trouble
           ,
           facilitated
           :
           those
           many
           Observations
           which
           burthen
           the
           Memory
           ,
           made
           few
           and
           plain
           :
           and
           those
           whose
           Operation
           and
           Experience
           do's
           require
           the
           study
           and
           Expence
           of
           many
           years
           ,
           might
           be
           performed
           without
           any
           difficulty
           in
           a
           few
           Weeks
           ,
           or
           Months
           at
           the
           farthest
           .
           And
           that
           this
           way
           is
           found
           out
           and
           effected
           in
           a
           great
           measure
           ,
           I
           say
           ,
           many
           persons
           of
           Worth
           and
           Quality
           are
           able
           experimentally
           to
           testifie
           .
        
         
         
           Musick
           hath
           already
           flowed
           to
           a
           great
           ●eighth
           in
           this
           Nation
           ,
           for
           I
           am
           perswaded
           that
           there
           is
           as
           much
           Exc●llency
           in
           the
           Musick
           which
           hath
           been
           ,
           and
           is
           now
           c●mposed
           in
           England
           ,
           as
           in
           any
           part
           of
           the
           World
           for
           Ayre
           ,
           variety
           and
           Substance
           .
           ●ut
           I
           heartily
           wish
           ,
           that
           af●er
           this
           great
           Spring
           and
           ●lood
           ,
           there
           be
           not
           in
           our
           succ●eding
           Generations
           )
           as
           low
           an
           Ebb.
           For
           if
           the
           serious
           and
           substantial
           part
           of
           Harmony
           be
           neglected
           ,
           and
           the
           mercurial
           only
           used
           :
           It
           will
           prove
           volatile
           ,
           evaporate
           ,
           and
           come
           to
           nothing
           .
           But
           ,
           Gentlemen
           ,
           I
           woul●
           not
           willingly
           weary
           your
           patience
           ,
           and
           sinc●●he
           Temple
           is
           so
           small
           ,
           I
           will
           not
           make
           the
           ●ate
           too
           bigg
           ;
           But
           subscribe
           my self
           as
           it
           is
           known
           I
           am
           )
           a
           true
           Lover
           of
           Musick
           ,
           and
        
         
           
             Your
             Servant
             
               J.
               B.
            
             
          
        
      
       
         
           I
           Have
           endevoured
           fa●thfully
           to
           translate
           the
           Origin●l
           ,
           in
           wh●ch
           I
           find
           some
           mistakes
           ,
           which
           I
           dare
           not
           impute
           to
           the
           Author
           ,
           of
           which
           I
           would
           have
           thee
           take
           no●ice
           .
           And
           also
           one
           Erratum
           in
           this
           Impression
           .
        
         
           1.
           
           
             Fol.
             20.
          
           the
           greater
           Sem●tone
           exceedeth
           the
           lesser
           by
           the
           lesser
           Diesis
           :
           whereas
           it
           exceedeth
           it
           but
           by
           a
           Comma
           ,
           as
           appeareth
           
             fol.
             18.
          
           where
           the
           Author
           saith
           thus
           ,
           
             The
             Comma
             is
             the
             difference
             between
             the
             Semitone
             m●jor
             and
             minus
             .
          
        
         
           2.
           
           
             Fol.
             31.
          
           almost
           ten
           parallel
           Lines
           ;
           the
           Word
           almost
           should
           be
           left
           out
           ,
           for
           the
           greater
           System
           is
           ten
           parallel
           Lines
           .
        
         
           3.
           
           
             Fol.
             44
          
           for
           
             d
             moll
          
           .
           read
           
             b
             moll
          
           .
        
      
    
     
       
         
         
           TEMPLUM
           MUSICUM
           .
        
         
           
             CHAP.
             I.
             Of
             the
             Subject
             of
             MUSICK
             .
          
           
             
               PRECEPTS
               .
            
             
               MUSICK
               is
               the
               Science
               of
               Singing
               well
               ,
               otherwise
               called
               Harmonical
               :
               and
               Musathena
               .
            
             
               The
               parts
               thereof
               are
               two
               :
               the
               general
               and
               the
               special
               .
            
             
               The
               general
               part
               doth
               treat
               of
               the
               Subject
               of
               Musick
               ;
               and
               both
               of
               the
               Principles
               and
               Affections
               of
               the
               Subject
               .
            
             
               The
               Subject
               of
               Musick
               is
               an
               harmonical
               Song
               .
               And
               this
               is
               the
               Subject
               of
               Tractation
               .
               The
               Subject
               of
               Information
               ,
               
               is
               the
               Faculty
               of
               Singing
               :
               and
               the
               Subject
               of
               Operation
               ,
               is
               the
               matter
               to
               which
               harmonical
               Musick
               may
               be
               applied
               .
            
          
           
             
               RULES
               .
            
             
               
                 1.
                 
                 Musick
                 is
                 a
                 Mathematical
                 Science
                 ,
                 subalternate
                 to
                 Arithmetick
                 .
              
               
                 For
                 as
                 Arithmetick
                 doth
                 treat
                 of
                 Number
                 ,
                 so
                 Musick
                 of
                 the
                 number
                 of
                 Sounds
                 :
                 Or
                 as
                 others
                 of
                 numerous
                 Sound
                 .
                 For
                 as
                 the
                 
                   Optick
                   Science
                
                 is
                 called
                 a
                 certain
                 special
                 Geometrie
                 ,
                 so
                 Musick
                 may
                 be
                 called
                 a
                 certain
                 special
                 Arithmetick
                 :
                 But
                 whereas
                 some
                 contend
                 that
                 Musick
                 is
                 both
                 a
                 
                   Science
                   ,
                   Prudence
                
                 ,
                 and
                 Art
                 ,
                 because
                 it
                 doth
                 instruct
                 both
                 skilfully
                 ,
                 or
                 scientifically
                 ,
                 and
                 prudently
                 ,
                 and
                 artificially
                 to
                 compose
                 an
                 harmonical
                 Song
                 ,
                 it
                 is
                 not
                 so
                 accurate
                 .
                 For
                 it
                 is
                 not
                 here
                 Queried
                 ,
                 whether
                 
                   Science
                   ,
                   Prudence
                
                 ,
                 and
                 Art
                 may
                 concur
                 in
                 Practise
                 :
                 but
                 whether
                 Musick
                 being
                 considered
                 as
                 a
                 Discipline
                 either
                 habitual
                 or
                 systematical
                 ,
                 be
                 a
                 
                   Science
                   ,
                   Prudence
                
                 ,
                 or
                 Art.
                 But
                 that
                 it
                 is
                 a
                 Science
                 it
                 doth
                 thus
                 app●ar
                 ,
                 because
                 it
                 hath
                 
                   Subject
                   ,
                   Principles
                
                 ,
                 and
                 Affections
                 ;
                 which
                 three
                 thin●s
                 are
                 required
                 unto
                 the
                 complete
                 Ration
                 of
                 a
                 Science
                 .
              
            
             
               
               
                 2.
                 
                 An
                 Harmonical
                 Song
                 ,
                 is
                 a
                 concinnous
                 multitude
                 of
                 Sounds
                 ,
                 rightly
                 composed
                 according
                 to
                 the
                 Text.
                 
              
               
                 The
                 Subject
                 of
                 Explication
                 in
                 Musick
                 is
                 a
                 Song
                 ,
                 whose
                 chief
                 Force
                 lieth
                 in
                 this
                 ,
                 〈◊〉
                 accommodated
                 to
                 the
                 Text
                 and
                 Affections
                 〈◊〉
              
               
                 But
                 if
                 the
                 same
                 Sound
                 may
                 be
                 accommodated
                 to
                 divers
                 and
                 contrary
                 things
                 and
                 Affections
                 ,
                 then
                 the
                 Musick
                 is
                 inept
                 and
                 irrational
                 ;
                 because
                 it
                 is
                 contrary
                 to
                 the
                 Scope
                 and
                 Principle
                 of
                 that
                 most
                 laudable
                 Discipline
                 ,
                 which
                 will
                 ,
                 That
                 Melodie
                 be
                 applied
                 both
                 to
                 Things
                 and
                 Affections
                 .
              
               
                 If
                 therefore
                 
                   v.
                   g.
                
                 in
                 any
                 Psalm
                 of
                 David
                 ,
                 three
                 Parts
                 do
                 occur
                 ,
                 
                   viz.
                   Lamentation
                   ,
                   Consolation
                
                 ,
                 and
                 giving
                 of
                 Thanks
                 :
                 there
                 ,
                 three
                 Tones
                 ought
                 to
                 be
                 .
              
            
             
               
                 3.
                 
                 The
                 Subject
                 of
                 Operation
                 in
                 Musick
                 are
                 Things
                 sacred
                 and
                 liberal
                 .
                 By
                 which
                 it
                 appeareth
                 that
                 the
                 usefulnesse
                 of
                 it
                 is
                 very
                 great
                 .
              
               
                 Things
                 sacred
                 ,
                 as
                 the
                 Psalms
                 and
                 Songs
                 in
                 the
                 Bible
                 ,
                 and
                 of
                 other
                 things
                 wholly
                 Divine
                 .
              
               
                 Things
                 liberal
                 ,
                 as
                 pathetical
                 matters
                 in
                 things
                 Philosophical
                 ,
                 and
                 which
                 doth
                 altogether
                 concern
                 the
                 common
                 Life
                 of
                 Man.
                 For
                 Musick
                 doth
                 penetrate
                 
                 the
                 In●eriors
                 of
                 the
                 mind
                 ,
                 it
                 moveth
                 Affections
                 ,
                 promoveth
                 Contemplation
                 ,
                 expelleth
                 ●orrow
                 ,
                 di●solveth
                 bad
                 Humours
                 ,
                 exhilerateth
                 the
                 animal
                 Spirits
                 :
                 and
                 so
                 is
                 beneficial
                 to
                 the
                 Life
                 of
                 Men
                 in
                 general
                 ,
                 to
                 the
                 Pious
                 for
                 Devotion
                 ,
                 to
                 the
                 Contemplative
                 Life
                 for
                 Science
                 ,
                 to
                 the
                 Solitary
                 for
                 Recreation
                 ,
                 to
                 the
                 domestick
                 and
                 publick
                 Life
                 for
                 Moderation
                 of
                 mind
                 ,
                 to
                 the
                 Healt●
                 〈◊〉
                 the
                 temperament
                 of
                 their
                 Body
                 ,
                 and
                 to
                 the
                 〈◊〉
                 for
                 Delight
                 ;
                 As
                 excellently
                 saith
                 that
                 famous
                 Musician
                 Lippius
                 in
                 his
                 Musical
                 Synopsis
                 .
                 Hence
                 it
                 is
                 that
                 the
                 Divel
                 hateth
                 Musick
                 liberal
                 ,
                 and
                 on
                 the
                 contrary
                 is
                 delighted
                 with
                 filthy
                 Musick
                 and
                 illiberal
                 ,
                 which
                 he
                 useth
                 as
                 his
                 Vehicle
                 ,
                 by
                 which
                 he
                 slideth
                 himself
                 into
                 the
                 minds
                 of
                 men
                 ,
                 who
                 take
                 Pleasure
                 in
                 such
                 Diabolical
                 Musick
                 .
                 On
                 the
                 contrary
                 ,
                 the
                 holy
                 Angels
                 are
                 delighted
                 with
                 Musick
                 liberal
                 ,
                 not
                 because
                 corporal
                 Harmony
                 doth
                 affect
                 them
                 ,
                 but
                 because
                 all
                 Harmony
                 ,
                 especially
                 that
                 which
                 is
                 conjoyned
                 with
                 the
                 Affection
                 of
                 a
                 pious
                 Will
                 ,
                 is
                 grateful
                 to
                 those
                 chast
                 Spirits
                 .
                 Hence
                 it
                 is
                 ,
                 that
                 the
                 Heroes
                 ,
                 holy
                 Men
                 ,
                 and
                 Lovers
                 of
                 Virtue
                 of
                 all
                 times
                 ,
                 have
                 magnified
                 Musick
                 :
                 as
                 appeareth
                 by
                 these
                 Scriptures
                 ;
                 Exod.
                 15.
                 
                 Judg.
                 5.1
                 .
                 1
                 Sam.
                 16.23
                 .
                 2
                 Sam.
                 6
                 5.
                 2
                 
                 Kings
                 3.15
                 .
                 1
                 Chron.
                 23.5
                 .
                 Judith
                 16.1
                 ,
                 2
                 ,
                 
                   &c.
                   Syrach
                
                 23.5
                 ,
                 6
                 ,
                 &
                 39.20
                 .
                 &
                 44.5
                 .
                 Matth.
                 26.30
                 .
                 Luke
                 1.46
                 .
                 &
                 2.13
                 .
                 Eph.
                 5.18
                 ,
                 19.
                 
                 Col.
                 3.16
                 .
                 Apoc.
                 5.9
                 .
                 &
                 14.2
                 ,
                 ●
                 .
              
            
          
        
         
           
           
             CHAP.
             II.
             Of
             the
             Principles
             of
             Cognition
             in
             Musick
             .
          
           
             
               PRECEPTS
               .
            
             
               THE
               Principles
               of
               an
               Harmonical
               Song
               are
               those
               things
               upon
               which
               it
               doth
               depend
               :
               And
               those
               are
               either
               the
               Principles
               of
               the
               Cognition
               or
               Constitution
               thereof
               .
            
             
               Those
               are
               complex
               :
               these
               incomplex
               .
            
             
               The
               Principles
               of
               Cognition
               are
               those
               by
               which
               an
               harmonical
               Song
               is
               known
               .
               And
               they
               are
               either
               internal
               or
               external
               .
               Those
               are
               taken
               from
               the
               Science
               it self
               ,
               these
               from
               Philosophy
               ,
               partly
               theoretical
               ,
               and
               partly
               practical
               .
            
          
           
             
             
               RULES
               .
            
             
               
                 1.
                 
                 The
                 internal
                 or
                 domestical
                 Principles
                 of
                 Cognition
                 are
                 here
                 and
                 there
                 spread
                 through
                 the
                 whole
                 Body
                 of
                 Musick
                 .
              
               
                 Wherefore
                 it
                 were
                 not
                 worth
                 while
                 to
                 treat
                 of
                 them
                 in
                 this
                 place
                 .
              
            
             
               
                 2.
                 
                 The
                 theoretical
                 Principles
                 which
                 Musick
                 doth
                 use
                 ,
                 or
                 is
                 built
                 upon
                 ,
                 are
                 either
                 remote
                 or
                 proximate
                 .
              
               
                 The
                 remote
                 are
                 such
                 as
                 are
                 taken
                 from
                 the
                 Metaphysicks
                 and
                 Physicks
                 .
                 And
                 indeed
                 from
                 the
                 Metaphysicks
                 ,
                 there
                 are
                 taken
                 Principles
                 of
                 Unity
                 ,
                 Goodnesse
                 ,
                 Pulchritude
                 ,
                 Perfection
                 ,
                 Order
                 ,
                 Opposition
                 ,
                 Quantity
                 ,
                 Quality
                 ,
                 and
                 the
                 like
                 .
                 And
                 from
                 the
                 Physicks
                 ,
                 tho●e
                 that
                 treat
                 of
                 the
                 Quantity
                 ,
                 Quality
                 ,
                 Motion
                 ,
                 Place
                 ,
                 and
                 Time
                 of
                 a
                 natural
                 Body
                 :
                 Al●o
                 of
                 Air
                 ,
                 an●
                 Sound
                 ,
                 and
                 of
                 its
                 propagation
                 ,
                 multiplication
                 ,
                 differences
                 ,
                 and
                 perception
                 :
                 And
                 lastly
                 of
                 Affections
                 ,
                 as
                 Love
                 ,
                 Joy
                 ,
                 Sorrow
                 ,
                 and
                 the
                 like
                 .
                 The
                 proximate
                 principles
                 are
                 Axioms
                 ,
                 Assumptions
                 ,
                 Questions
                 ,
                 Theorems
                 ,
                 Problems
                 ,
                 and
                 Consectaries
                 mathematical
                 ;
                 and
                 those
                 pa●tly
                 arithmetical
                 ,
                 partly
                 geometrical
                 :
                 but
                 chiefly
                 a●ithmatical
                 ;
                 especially
                 those
                 which
                 concern
                 the
                 Proprieties
                 
                 of
                 Simple
                 Numbers
                 ,
                 and
                 also
                 their
                 proportion
                 ;
                 
                   viz.
                   dupla
                   ,
                   tripla
                   ,
                   sesquialtera
                   ,
                
                 and
                 the
                 like
                 ,
                 of
                 which
                 in
                 my
                 Arithmeticks
                 :
                 But
                 here
                 let
                 these
                 Axioms
                 be
                 observed
                 .
                 1.
                 
                 That
                 Proportion
                 of
                 Equality
                 is
                 radically
                 between
                 one
                 and
                 one
                 :
                 And
                 this
                 is
                 the
                 Radix
                 of
                 all
                 Proportion
                 .
                 2.
                 
                 Dupla
                 Proportion
                 is
                 radically
                 between
                 two
                 and
                 one
                 ,
                 tripla
                 between
                 three
                 and
                 one
                 ,
                 quadrupla
                 between
                 four
                 and
                 one
                 ,
                 and
                 so
                 forward
                 .
                 Obse●ve
                 ,
                 that
                 radical
                 proportio●s
                 are
                 in
                 Nine
                 Simple
                 Numbers
                 ,
                 from
                 1.
                 to
                 9.
                 because
                 these
                 are
                 the
                 Radixes
                 of
                 all
                 Numbers
                 .
                 3.
                 
                 Sesquialtera
                 Proportion
                 is
                 between
                 three
                 and
                 two
                 ,
                 Sesquitertia
                 between
                 four
                 and
                 three
                 ,
                 
                   Superbipartiens
                   tertias
                
                 ,
                 is
                 radically
                 between
                 five
                 and
                 three
                 ,
                 and
                 
                   Supertripartiens
                   quintas
                
                 is
                 between
                 eight
                 and
                 five
                 .
                 And
                 these
                 are
                 simple
                 proportions
                 ,
                 in
                 which
                 such
                 an
                 order
                 of
                 perfection
                 is
                 observed
                 ,
                 that
                 after
                 a
                 proportion
                 of
                 Equality
                 ,
                 a
                 proportion
                 of
                 inequality
                 followeth
                 :
                 First
                 Dupla
                 ,
                 afterward
                 Sesquialtera
                 ,
                 then
                 Sesquitertia
                 ,
                 afterward
                 Sesquiquarta
                 ,
                 and
                 Sesquiquinta
                 ,
                 then
                 
                   Superbipartiens
                   tertias
                
                 ,
                 an●
                 
                   Supertripartiens
                   quintas
                
                 .
                 To
                 these
                 succeed
                 com●ound●d
                 P●opo●tions
                 ,
                 as
                 Dupla-Sesquialtera
                 b●tween
                 5
                 ,
                 and
                 2.
                 
                 〈◊〉
                 Sesquitertia
                 between
                 10
                 ,
                 and
                 3.
                 
                 
                   Dupla-Superbipartiens
                   tertias
                
                 ,
                 as
                 between
                 8
                 ,
                 and
                 3.
                 and
                 so
                 forward
                 .
                 4.
                 
                 Proportions
                 are
                 numbred
                 by
                 Division
                 logistical
                 ,
                 as
                 the
                 proportion
                 which
                 is
                 between
                 3
                 ,
                 2.
                 appeareth
                 by
                 Division
                 .
                 For
                 if
                 3.
                 be
                 divided
                 by
                 2.
                 it
                 will
                 produce
                 1.
                 
                 ½
                 .
                 5.
                 
                 Proportions
                 are
                 added
                 by
                 vulgar
                 multiplication
                 ,
                 as
                 3
                 /
                 2
                 :
                 2
                 /
                 1
                 :
                 make
                 6
                 /
                 2
                 :
                 2
                 /
                 1
                 :
                 6.
                 
                 Proportions
                 are
                 substracted
                 by
                 Multiplication
                 crucial
                 ;
                 as
                 
                 
                 7.
                 
                 Proportions
                 are
                 multiplied
                 or
                 coupled
                 when
                 they
                 are
                 written
                 without
                 Intermission
                 ,
                 and
                 the
                 antecedent
                 number
                 of
                 the
                 latter
                 proportion
                 is
                 multiplied
                 into
                 the
                 Consequent
                 of
                 the
                 former
                 ,
                 or
                 contrarily
                 .
                 Also
                 when
                 the
                 Consequent
                 of
                 the
                 former
                 is
                 multiplied
                 into
                 the
                 Consequent
                 of
                 the
                 latter
                 .
                 Or
                 lastly
                 ,
                 when
                 the
                 Antecedent
                 of
                 the
                 former
                 is
                 multiplied
                 into
                 the
                 antecedent
                 of
                 the
                 posterior
                 .
                 As
                 2.1
                 ,
                 3
                 ,
                 2.
                 
                 Here
                 ,
                 once
                 three
                 ,
                 give
                 three
                 :
                 and
                 once
                 two
                 ,
                 give
                 two
                 ,
                 and
                 twice
                 three
                 ,
                 give
                 six
                 .
                 8.
                 
                 Proportions
                 are
                 radicated
                 in
                 greater
                 numbers
                 ,
                 and
                 in
                 numberss
                 compounded
                 one
                 with
                 another
                 by
                 Mediation
                 logistical
                 ▪
                 as
                 16-8
                 .
                 First
                 they
                 are
                 reduced
                 to
                 8-4
                 .
                 then
                 to
                 4-2
                 .
                 lastly
                 to
                 2-1
                 .
                 And
                 thus
                 radical
                 Proportions
                 by
                 course
                 are
                 easily
                 reduced
                 to
                 their
                 greater
                 Terms
                 by
                 logistical
                 Duplation
                 ;
                 as
                 1-2
                 .
                 to
                 2-4
                 .
                 thence
                 to
                 4-8
                 .
                 then
                 to
                 8-16
                 .
                 and
                 so
                 forward
                 .
                 9.
                 
                 Every
                 Dupla
                 Proportion
                 doth
                 consist
                 of
                 a
                 Sesquialtera
                 and
                 Sesquitertia
                 .
                 10.
                 
                 If
                 a
                 Sesquialtera
                 be
                 taken
                 away
                 from
                 a
                 Dupla
                 ,
                 a
                 Sesquitertia
                 will
                 only
                 remain
                 ,
                 and
                 so
                 consequently
                 .
              
            
             
               
                 3.
                 
                 Practical
                 Principles
                 which
                 Musick
                 useth
                 ,
                 are
                 chiefly
                 taken
                 from
                 the
                 Ethicks
                 ,
                 Oeconomicks
                 ,
                 Politicks
                 ,
                 and
                 Poeticks
                 .
              
               
                 From
                 the
                 Ethick●
                 are
                 taken
                 Principles
                 of
                 Virtue
                 ,
                 and
                 moral
                 Beatitude
                 ;
                 from
                 the
                 Oeconomicks
                 of
                 Act●ons
                 
                 domestick
                 ;
                 from
                 Politicks
                 Principles
                 of
                 virtue
                 ,
                 and
                 civil
                 Beatitude
                 ;
                 and
                 from
                 Poetrie
                 Principles
                 concerning
                 Rhyme
                 and
                 Verse
                 :
                 which
                 have
                 ●uch
                 Affinity
                 with
                 Musick
                 ,
                 that
                 by
                 some
                 Mus●ck
                 is
                 divided
                 into
                 Harmonical
                 ,
                 Rhythmical
                 ,
                 and
                 Metrical
                 .
              
            
          
        
         
           
             CHAP.
             III.
             Of
             the
             Efficient
             and
             End
             of
             an
             Harmonical
             Song
             .
          
           
             
               PRECEPTS
               .
            
             
               THE
               Principles
               of
               Constitution
               are
               those
               by
               which
               an
               harmonical
               Song
               is
               constituted
               .
            
             
               And
               they
               are
               either
               external
               or
               internal
               .
            
             
               The
               external
               are
               the
               Efficient
               and
               End.
               The
               Efficient
               Cause
               of
               a
               Song
               is
               either
               the
               first
               or
               second
               .
            
             
               The
               first
               Cause
               is
               GOD
               the
               Author
               of
               all
               Symphony
               .
            
             
               The
               second
               is
               partly
               Nature
               ,
               the
               Mother
               
               of
               all
               Sounds
               :
               partly
               Art
               perfecting
               the
               Rudiment
               of
               Nature
               .
            
             
               The
               ultimate
               End
               is
               GOD
               that
               Archetype
               of
               Harmony
               .
            
             
               The
               subordinate
               End
               is
               Motion
               ,
               and
               the
               impulse
               of
               Man
               to
               the
               hatred
               of
               Uice
               ,
               and
               study
               of
               Uirtue
               .
            
          
           
             
               RULES
               .
            
             
               
                 1.
                 
                 God
                 is
                 the
                 Author
                 and
                 Maintainer
                 of
                 all
                 Harmony
                 ,
              
               
                 Seeing
                 Harmony
                 is
                 Order
                 ,
                 and
                 tendeth
                 to
                 Unity
                 ;
                 for
                 God
                 is
                 the
                 Author
                 and
                 Maintainer
                 of
                 all
                 Order
                 ,
                 and
                 the
                 greatest
                 Unity
                 .
                 Furthe●more
                 ,
                 God
                 is
                 the
                 chief
                 and
                 unspeakable
                 Joy
                 ,
                 therefore
                 they
                 who
                 rightly
                 rejoyce
                 come
                 nigher
                 unto
                 God.
                 Hence
                 the
                 Rabbins
                 say
                 ,
                 
                   the
                   Holy
                   Ghost
                   doth
                   sing
                   by
                   reason
                   of
                   Joy.
                
                 And
                 Philosophers
                 say
                 ,
                 
                   That
                   the
                   Soul
                   of
                   a
                   Wise
                   man
                   doth
                   alwayes
                   rejoyce
                
                 ;
                 For
                 joy
                 as
                 it
                 is
                 pure
                 Harmony
                 cannot
                 but
                 be
                 excited
                 and
                 maintained
                 by
                 Musical
                 Harmony
                 .
              
            
             
               
               
                 2.
                 
                 The
                 Exemplary
                 Cause
                 of
                 Harmonical
                 Musick
                 ;
                 is
                 that
                 Musick
                 which
                 is
                 called
                 mundane
                 .
              
               
                 This
                 is
                 discerned
                 in
                 the
                 Order
                 ,
                 Disposition
                 ,
                 and
                 admirable
                 proportion
                 which
                 doth
                 occur
                 in
                 the
                 Celestial
                 ,
                 and
                 ●ubcelestial
                 Region
                 ;
                 partly
                 among
                 the
                 St●rs
                 ,
                 partly
                 among
                 the
                 Elements
                 ,
                 partly
                 among
                 all
                 things
                 compounded
                 of
                 the
                 Elements
                 ;
                 and
                 lastly
                 ,
                 among
                 all
                 tho●e
                 things
                 which
                 are
                 compa●ed
                 one
                 with
                 another
                 :
                 of
                 which
                 Musick
                 and
                 Harmony
                 we
                 have
                 spoken
                 in
                 our
                 Physicks
                 .
                 This
                 Harmony
                 being
                 such
                 and
                 so
                 great
                 ,
                 when
                 ancient
                 men
                 did
                 diligently
                 consider
                 it
                 ,
                 they
                 supposed
                 that
                 there
                 was
                 the
                 like
                 Proportion
                 not
                 only
                 in
                 Numbers
                 and
                 Lines
                 ,
                 but
                 also
                 in
                 the
                 Voice
                 ;
                 especially
                 when
                 they
                 did
                 discern
                 that
                 Proportion
                 in
                 the
                 various
                 Sound
                 of
                 various
                 Bodies
                 .
              
            
             
               
                 3.
                 
                 Musick
                 receiveth
                 his
                 greatest
                 Perfection
                 from
                 the
                 End.
                 
              
               
                 That
                 Perfection
                 doth
                 not
                 only
                 depend
                 upon
                 matter
                 and
                 Form
                 ,
                 but
                 also
                 upon
                 the
                 ●nd
                 we
                 have
                 formerly
                 shewn
                 in
                 our
                 Metaphysicks
                 and
                 Logicks
                 .
                 In
                 Musick
                 certainly
                 this
                 is
                 most
                 manifest
                 :
                 for
                 unlesse
                 it
                 be
                 referred
                 to
                 the
                 Glory
                 of
                 God
                 ,
                 and
                 the
                 pious
                 Recreation
                 of
                 Man
                 it
                 cannot
                 but
                 equivocally
                 be
                 called
                 Musick
                 .
                 Hence
                 it
                 is
                 apparent
                 that
                 those
                 simple
                 men
                 who
                 abuse
                 Vocal
                 and
                 Instrumental
                 Musick
                 to
                 
                 nourish
                 the
                 pleasures
                 of
                 this
                 World
                 ,
                 whilst
                 they
                 si●g
                 Songs
                 highly
                 obscene
                 ,
                 are
                 nothing
                 lesse
                 then
                 Musicians
                 .
                 For
                 although
                 the
                 Form
                 of
                 a
                 Song
                 occur
                 there
                 ,
                 yet
                 the
                 End
                 which
                 perfecteth
                 the
                 Instrument
                 ,
                 is
                 not
                 there
                 discerned
                 :
                 The●efore
                 in
                 such
                 Musick
                 there
                 is
                 the
                 first
                 perfection
                 but
                 not
                 the
                 ultimate
                 ;
                 which
                 necess●rily
                 is
                 ●equired
                 in
                 an
                 Instrument
                 ,
                 because
                 the
                 Virtue
                 ther●of
                 is
                 placed
                 in
                 the
                 use
                 .
              
            
          
        
         
           
             CHAP.
             IV.
             Of
             the
             quantity
             of
             a
             Musical
             Song
             .
          
           
             
               PRECEPTS
               .
            
             
               THE
               internal
               Principles
               of
               an
               harmonical
               Song
               are
               Matter
               and
               Form.
               
            
             
               Matter
               comprehendeth
               the
               integral
               parts
               of
               which
               an
               Harmonical
               Song
               is
               made
               .
            
             
               Of
               the
               parts
               thereof
               ,
               the
               one
               is
               Simple
               ,
               and
               the
               other
               is
               compounded
               .
            
             
             
               The
               simple
               part
               is
               called
               Sound
               :
               also
               a
               Musical
               Monad
               .
               in
               Greek
               Tonos
               .
            
             
               A
               Musical
               Sound
               is
               considered
               in
               respect
               of
               his
               Quantity
               and
               Signs
               .
            
             
               The
               Doctrine
               of
               that
               is
               called
               theoretical
               Musick
               ,
               and
               of
               this
               Signatory
               .
            
             
               Quantity
               is
               threefold
               ,
               Longitude
               ,
               Latitude
               ,
               and
               Crassitude
               .
            
             
               The
               Longitude
               of
               a
               Musical
               Sound
               ,
               is
               that
               which
               is
               discerned
               in
               the
               motion
               and
               duration
               thereof
               :
               and
               measured
               by
               a
               Musical
               Touch
               or
               Tact.
               
            
             
               The
               Latitude
               of
               a
               Musical
               Sound
               is
               that
               which
               is
               discerned
               in
               the
               tenuous
               and
               asperous
               spirit
               .
            
             
               The
               Crassitude
               of
               a
               Musical
               Sound
               is
               that
               which
               is
               discerned
               in
               the
               Profundity
               and
               Altitude
               thereof
               .
            
             
               By
               reason
               of
               this
               Crassitude
               a
               Musical
               Sound
               is
               equal
               or
               unequal
               .
            
             
               The
               equal
               Sound
               is
               the
               Simple
               Unison
               .
            
             
               The
               unequal
               Sound
               doth
               bring
               forth
               a
               Distance
               or
               an
               Interval
               of
               a
               sonorous
               Crassitude
               :
               which
               is
               called
               a
               Musical
               Interval
               .
            
             
             
               A
               Musical
               Interval
               is
               seen
               in
               Proportion
               and
               Intention
               .
            
             
               By
               reason
               of
               Proportion
               ,
               an
               Interval
               is
               simple
               or
               compounded
               :
               that
               is
               called
               radical
               ,
               this
               radicated
               .
            
             
               A
               Simple
               Interval
               is
               either
               Just
               ,
               or
               not
               Just.
               
            
             
               A
               Just
               Interval
               is
               that
               which
               is
               neither
               defective
               nor
               redundant
               :
               as
               an
               
                 Octave
                 Fifth
                 ,
                 &c.
              
               
            
             
               An
               Interval
               not
               Just
               is
               that
               which
               is
               defective
               or
               redundant
               :
               as
               a
               
                 Semioctave
                 ,
                 &c.
              
               
            
             
               A
               compounded
               Interval
               is
               that
               which
               doth
               consist
               of
               simple
               Intervals
               :
               as
               a
               
                 double
                 Octave
              
               ,
               a
               
                 triple
                 Octave
              
               ,
               a
               
                 quadruple
                 Octave
              
               ,
               and
               so
               
                 ad
                 infinitum
              
               .
            
             
               By
               reason
               of
               Intention
               it
               is
               a
               Scale
               ,
               called
               Musical
               ;
               and
               it
               is
               the
               various
               disposition
               of
               acute
               and
               grave
               Sounds
               .
            
          
           
             
             
               RULES
               .
            
             
               
                 1.
                 
                 Every
                 Sound
                 is
                 Quantus
                 .
              
               
                 For
                 in
                 every
                 Body
                 that
                 hath
                 Quantity
                 ,
                 there
                 is
                 an
                 audible
                 Quality
                 .
                 That
                 Quantity
                 is
                 numbred
                 by
                 Division
                 ,
                 and
                 not
                 barely
                 considered
                 ,
                 as
                 it
                 is
                 a
                 magnitude
                 .
                 So
                 that
                 the
                 most
                 accurate
                 Lippius
                 might
                 rightly
                 say
                 ,
                 every
                 Sound
                 is
                 continual
                 or
                 discrete
                 ,
                 or
                 explainable
                 by
                 number
                 .
                 But
                 a
                 Sound
                 is
                 Quantus
                 ,
                 by
                 complete
                 Quantity
                 .
                 
                   i.
                   e.
                
                 So
                 that
                 it
                 have
                 a
                 trine
                 Dimension
                 ,
                 and
                 therefore
                 Longitude
                 ,
                 Latitude
                 ,
                 and
                 Crassitude
                 .
              
            
             
               
                 2.
                 
                 Every
                 Sound
                 is
                 long
                 numerably
                 .
              
               
                 For
                 seeing
                 every
                 Sound
                 doth
                 continue
                 so
                 long
                 ,
                 or
                 not
                 so
                 long
                 ,
                 this
                 temporal
                 duration
                 thereof
                 may
                 be
                 numbred
                 .
                 And
                 it
                 is
                 numbred
                 by
                 a
                 Musical
                 Touch
                 ,
                 which
                 ,
                 according
                 to
                 the
                 motion
                 of
                 the
                 Heart
                 ,
                 in
                 this
                 Science
                 ought
                 to
                 be
                 observed
                 .
                 This
                 Touch
                 doth
                 consist
                 of
                 Depression
                 and
                 Elevation
                 ,
                 according
                 to
                 a
                 certain
                 Proportion
                 ,
                 but
                 especially
                 a
                 Dupla
                 :
                 And
                 it
                 is
                 either
                 more
                 simple
                 ,
                 more
                 natural
                 ,
                 and
                 more
                 ●ommon
                 ,
                 which
                 is
                 finished
                 in
                 two
                 equal
                 parts
                 ,
                 and
                 may
                 be
                 called
                 Spondaic
                 ,
                 as
                 
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                
                 :
                 or
                 lesse
                 simple
                 ,
                 and
                 more
                 unusual
                 ,
                 which
                 doth
                 consist
                 of
                 unequal
                 parts
                 ,
                 th●
                 one
                 greater
                 ,
                 and
                 the
                 other
                 lesser
                 ,
                 and
                 may
                 be
                 call●d
                 Tr●chaic
                 .
                 as
                 
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                   〈◊〉
                
              
            
             
               
               
                 3.
                 
                 Every
                 Sound
                 is
                 numerably
                 broad
                 .
              
               
                 For
                 every
                 Sound
                 besides
                 the
                 length
                 thereof
                 ,
                 is
                 also
                 tenuous
                 or
                 gentle
                 ,
                 flat
                 ,
                 submi●s
                 ,
                 small
                 ;
                 or
                 sharp
                 ,
                 ha●sh
                 ,
                 clear
                 ,
                 full
                 ,
                 as
                 consisting
                 of
                 a
                 tenuous
                 and
                 a●perous
                 Spirit
                 .
              
            
             
               
                 4.
                 
                 Every
                 Sound
                 is
                 numerably
                 thick
                 .
              
               
                 Besides
                 the
                 length
                 and
                 breadth
                 ,
                 every
                 Sound
                 is
                 al●o
                 thick
                 ;
                 and
                 so
                 it
                 is
                 either
                 deep
                 or
                 high
                 .
                 That
                 ,
                 is
                 called
                 grave
                 ,
                 and
                 this
                 ,
                 acute
                 .
                 And
                 we
                 measure
                 this
                 magnitude
                 of
                 a
                 Sound
                 by
                 Proportions
                 of
                 numbers
                 ,
                 especially
                 ra●ical
                 ,
                 as
                 they
                 are
                 applied
                 to
                 the
                 Monochord
                 .
              
            
             
               
                 5.
                 
                 The
                 Simple
                 Vnison
                 is
                 the
                 Principal
                 and
                 Radix
                 of
                 all
                 Musical
                 Intervals
                 .
              
               
                 As
                 in
                 numbers
                 there
                 is
                 one
                 proportion
                 of
                 Equality
                 ,
                 and
                 another
                 of
                 Inequality
                 :
                 So
                 also
                 in
                 Sounds
                 ,
                 one
                 is
                 equal
                 ,
                 and
                 another
                 is
                 unequal
                 .
                 And
                 again
                 as
                 in
                 numbers
                 ,
                 the
                 Proportion
                 of
                 ●quality
                 is
                 the
                 Radix
                 of
                 all
                 the
                 rest
                 :
                 So
                 in
                 Sounds
                 ,
                 the
                 Simple
                 Unison
                 is
                 the
                 principal
                 and
                 Radix
                 o●
                 all
                 Musical
                 Intervals
                 .
                 For
                 the
                 Simple
                 Uni●on
                 doth
                 consist
                 of
                 a
                 proportion
                 of
                 Equality
                 ,
                 which
                 is
                 radical●y
                 between
                 1.
                 and
                 1.
                 as
                 may
                 be
                 seen
                 in
                 a
                 Mon●ch●rd
                 .
                 Therefore
                 a
                 Simple
                 Unison
                 is
                 not
                 a
                 musical
                 I●terval
                 ,
                 but
                 the
                 original
                 thereof
                 .
              
            
             
               
               
                 6.
                 
                 Vnequal
                 Sounds
                 do
                 make
                 a
                 Musical
                 Intervall
                 .
              
               
                 Unequal
                 Sounds
                 do
                 make
                 a
                 Diastem
                 or
                 Distance
                 ,
                 which
                 is
                 called
                 a
                 Musical
                 Intervall
                 ,
                 in
                 which
                 the
                 grave
                 Sound
                 is
                 profound
                 and
                 greater
                 :
                 and
                 the
                 acute
                 ,
                 high
                 and
                 lesser
                 .
                 Of
                 this
                 Intervall
                 these
                 Theorems
                 are
                 noted
                 .
                 1.
                 
                 
                   He
                   that
                   knoweth
                   a
                   simple
                   Intervall
                   ,
                   may
                   easily
                   know
                   a
                   compounded
                   Intervall
                   .
                
                 That
                 ,
                 as
                 they
                 say
                 ,
                 is
                 radical
                 :
                 this
                 ,
                 radicated
                 .
                 2.
                 
                 
                   There
                   are
                   seventeen
                   simple
                   Intervals
                   or
                   Diastems
                   in
                   this
                   order
                   .
                
                 The
                 first
                 ,
                 an
                 Octave
                 ,
                 to
                 wit
                 ,
                 a
                 voice
                 ,
                 in
                 Greek
                 a
                 Diapason
                 ,
                 which
                 is
                 of
                 a
                 Dupla
                 Proportion
                 ,
                 between
                 2.
                 and
                 1.
                 where
                 one
                 Sound
                 as
                 the
                 greater
                 and
                 graver
                 ,
                 doth
                 contain
                 another
                 ,
                 as
                 the
                 lesser
                 and
                 acuter
                 ,
                 twice
                 in
                 it self
                 ;
                 Therefore
                 is
                 the
                 Unison
                 composed
                 from
                 Letter
                 to
                 Letter
                 ,
                 
                   v.
                   g.
                
                 from
                 G.
                 to
                 
                   g.
                   &c.
                
                 
                 The
                 second
                 ,
                 a
                 Fifth
                 ,
                 or
                 Diapente
                 ,
                 which
                 is
                 of
                 a
                 Sesquialtera
                 Proportion
                 ;
                 between
                 3.
                 and
                 2.
                 
                 The
                 third
                 ,
                 a
                 Fourth
                 ,
                 or
                 Diatessaron
                 ,
                 which
                 is
                 of
                 a
                 Sesquitertian
                 Proportion
                 between
                 4.
                 and
                 3.
                 
                 The
                 fourth
                 ,
                 a
                 greater
                 Third
                 or
                 Ditone
                 ,
                 which
                 is
                 of
                 Sesquiquarta
                 Proportion
                 ,
                 between
                 5.
                 and
                 4.
                 
                 The
                 fifth
                 ,
                 a
                 
                   Third
                   minor
                
                 ,
                 or
                 Hemiditone
                 ,
                 which
                 is
                 of
                 Sesquiquinta
                 Proportion
                 ,
                 betwe●n
                 6
                 a●d
                 5.
                 
                 The
                 sixth
                 ,
                 a
                 ma●or●or
                 ●or
                 greater
                 Sixth
                 ]
                 or
                 fourth
                 with
                 the
                 greater
                 thi●d
                 ,
                 which
                 is
                 of
                 a
                 
                   Superbipartiens
                   tertias
                
                 Proportion
                 ,
                 as
                 between
                 5.
                 and
                 3
                 7.
                 
                 A
                 
                   Sexta
                   minor
                
                 or
                 fourth
                 with
                 the
                 lesser
                 Third
                 ,
                 which
                 is
                 of
                 a
                 
                   Supertripartiens
                   quintas
                
                 Proportion
                 ,
                 between
                 8.
                 and
                 5.
                 
                 The
                 eigth
                 ,
                 is
                 the
                 
                   major
                   Second
                
                 ,
                 or
                 whole
                 Tone
                 ,
                 which
                 
                 is
                 of
                 a
                 Sesquioctave
                 Proportion
                 ,
                 between
                 9.
                 and
                 8.
                 
                 The
                 ninth
                 ,
                 is
                 the
                 
                   minor
                   Second
                
                 ,
                 or
                 
                   minor
                   Tone
                
                 ,
                 of
                 a
                 Sesquinona
                 Proportion
                 ,
                 between
                 10.
                 and
                 9.
                 
                 The
                 tenth
                 ,
                 is
                 the
                 
                   major
                   Semitone
                
                 ,
                 of
                 the
                 Proportion
                 of
                 16.
                 and
                 15.
                 
                 The
                 eleventh
                 ,
                 is
                 the
                 
                   minor
                   Semitone
                
                 ,
                 of
                 a
                 
                   Sesquivicefima
                   quarta
                
                 Proportion
                 ,
                 between
                 25.
                 and
                 24.
                 
                 The
                 twelfth
                 ,
                 the
                 
                   Diesis
                   minor
                
                 ,
                 of
                 a
                 
                   supertripartiens
                   centesimas
                   vigesimas
                   quintas
                
                 Proportion
                 between
                 128.
                 and
                 125.
                 
                 The
                 thirteenth
                 ,
                 a
                 Comma
                 which
                 is
                 the
                 difference
                 between
                 the
                 
                   Semitone
                   majus
                
                 ,
                 and
                 minus
                 ,
                 of
                 a
                 Sesqui●ctogesima
                 Proportion
                 ,
                 between
                 81.
                 and
                 80.
                 
                 The
                 fourteenth
                 ,
                 a
                 Schisma
                 which
                 is
                 the
                 half
                 of
                 a
                 Comma
                 ,
                 or
                 half
                 of
                 the
                 Difference
                 between
                 the
                 
                   Semitone
                   majus
                
                 and
                 minus
                 .
                 The
                 fifteenth
                 ,
                 is
                 the
                 fifth
                 with
                 a
                 
                   tertia
                   major
                
                 ,
                 or
                 greater
                 Seventh
                 ,
                 which
                 is
                 of
                 a
                 
                   Superseptipartiens
                   octavas
                
                 Proportion
                 ,
                 as
                 between
                 15.
                 and
                 8.
                 
                 The
                 sixteenth
                 ,
                 is
                 the
                 lesser
                 Seventh
                 ,
                 or
                 
                   quinta
                   cum
                   tertia
                   minore
                
                 ,
                 which
                 is
                 a
                 
                   Superquadripartiens
                   quintas
                
                 Proportion
                 ,
                 between
                 9.
                 and
                 5.
                 
                 The
                 seventeenth
                 ,
                 are
                 Intervalls
                 not
                 just
                 ,
                 which
                 are
                 either
                 deficient
                 or
                 redundant
                 ,
                 chiefly
                 by
                 the
                 lesser
                 Semitone
                 ,
                 or
                 Comma
                 ,
                 or
                 both
                 together
                 :
                 as
                 the
                 Semioctave
                 deficient
                 and
                 abounding
                 Fifth
                 :
                 the
                 minute
                 and
                 superfluous
                 fourth
                 which
                 is
                 named
                 a
                 Tritone
                 ,
                 and
                 such
                 like
                 .
                 3.
                 
                 
                   Intervalls
                   compounded
                   of
                   simple
                   Diastems
                   may
                   be
                   infinite
                   .
                
                 But
                 it
                 is
                 proper
                 to
                 Musick
                 to
                 bound
                 that
                 Infinity
                 of
                 gross
                 Sounds
                 .
                 (
                 which
                 is
                 such
                 only
                 potentially
                 .
                 )
                 Notwithstanding
                 let
                 us
                 take
                 notice
                 of
                 certain
                 compounded
                 Intervalls
                 .
                 First
                 ,
                 such
                 as
                 are
                 once
                 compounded
                 ,
                 as
                 a
                 Disdiapason
                 ,
                 double
                 Octave
                 ,
                 or
                 Fifteenth
                 ,
                 which
                 is
                 of
                 a
                 quadrupla
                 Proportion
                 ,
                 between
                 4.
                 and
                 1.
                 
                 Also
                 a
                 Diapason
                 
                 with
                 a
                 Diapente
                 ,
                 an
                 Octave
                 ,
                 with
                 a
                 Fifth
                 ,
                 or
                 Twelfth
                 ,
                 of
                 a
                 triple
                 Proportion
                 ,
                 between
                 3.
                 and
                 1.
                 
                 Also
                 a
                 Diapason
                 with
                 a
                 Diatessaron
                 ,
                 an
                 Octave
                 with
                 a
                 Fourth
                 ,
                 or
                 Eleventh
                 ,
                 of
                 a
                 
                   dupla
                   superbipartiens
                   tertias
                
                 Proportion
                 ,
                 between
                 8.
                 and
                 3.
                 
                 Al●o
                 others
                 are
                 twice
                 compounded
                 ,
                 as
                 a
                 
                   Trisdiapason
                   ,
                   Triple
                   Octave
                
                 ,
                 or
                 two
                 and
                 twentieth
                 of
                 an
                 Octupla
                 Proportion
                 ,
                 between
                 8.
                 and
                 1.
                 &c.
                 
                 Thirdly
                 ,
                 others
                 are
                 thrice
                 compounded
                 ,
                 as
                 a
                 
                   Tetradiapason
                   ,
                   quadrupla
                   Octave
                
                 ,
                 or
                 nine
                 and
                 twentieth
                 of
                 a
                 sedecupla
                 Proportion
                 ,
                 between
                 16.
                 and
                 1.
                 
                 Others
                 are
                 four
                 times
                 compounded
                 ,
                 and
                 so
                 
                   ad
                   infinitum
                
                 .
                 4.
                 
                 
                   An
                   Octave
                   is
                   the
                   most
                   simple
                   ,
                   perfect
                   ,
                   and
                   prime
                   musical
                   Intervall
                   .
                
                 5.
                 
                 
                   An
                   Octave
                   divided
                   be
                   gets
                   all
                   other
                   simple
                   Diastems
                   .
                
                 Therefore
                 from
                 the
                 Division
                 of
                 the
                 0ctave
                 ,
                 the
                 Harmonies
                 of
                 every
                 Genus
                 do
                 flow
                 .
                 For
                 every
                 Octave
                 being
                 divided
                 two
                 wayes
                 ,
                 begetteth
                 two
                 Moods
                 of
                 it self
                 .
                 6.
                 
                 
                   An
                   Octave
                   is
                   first
                   divided
                   into
                   a
                   fifth
                   and
                   fourth
                   ,
                   of
                   which
                   it
                   doth
                   consist
                   :
                   and
                   that
                   either
                   by
                   harmonical
                   or
                   arithmetical
                   Division
                   .
                   That
                   is
                   called
                   the
                   harmonical
                   Medium
                   of
                   an
                   Octave
                   ,
                   when
                   the
                   fifth
                   is
                   beneath
                   the
                   fourth
                   :
                   and
                   that
                   the
                   arithmetical
                   ,
                   when
                   the
                   fourth
                   is
                   beneath
                   the
                   fifth
                   .
                
                 Let
                 this
                 be
                 the
                 Example
                 of
                 Harmonical
                 Division
                 .
              
               
                 But
                 I
                 suppose
                 the
                 Author
                 meaneth
                 thus
                 :
                 
              
               
               
                 Division
                 Arithmetical
                 is
                 thus
                 :
                 
              
               
                 Therfore
                 in
                 the
                 harmonical
                 Division
                 of
                 an
                 Octave
                 the
                 fifth
                 remaining
                 immoveable
                 ,
                 the
                 fourth
                 is
                 placed
                 above
                 the
                 fifth
                 :
                 in
                 the
                 arithmetical
                 Division
                 ,
                 the
                 fifth
                 remaining
                 immoveable
                 ,
                 the
                 fourth
                 is
                 put
                 beneath
                 the
                 fifth
                 .
                 7.
                 
                 
                   If
                   a
                   Fifth
                   be
                   taken
                   from
                   an
                   Eighth
                   ,
                   there
                   remaineth
                   a
                   Fourth
                   ,
                
                 and
                 so
                 on
                 the
                 contrary
                 .
                 8.
                 
                 
                   A
                   Fifth
                   is
                   divided
                   into
                   a
                   Ditone
                   ,
                   and
                   Semiditone
                   .
                
                 9.
                 
                 
                   A
                   Ditone
                   is
                   compounded
                   of
                   the
                   greater
                   and
                   lesser
                   Tone
                
                 10.
                 
                 The
                 Tonus
                 major
                 
                   is
                   disp●sed
                   into
                   the
                
                 Semitone
                 majus
                 and
                 minus
                 .
                 11.
                 
                 
                   The
                   D●tone
                   is
                   more
                   then
                   the
                   Semiditone
                   by
                   the
                
                 Semitone
                 minus
                 .
                 12.
                 
                 
                   A
                   Fourth
                   exceedeth
                   a
                   Ditone
                   by
                   the
                
                 major
                 Semitone
                 .
                 13.
                 
                 
                   A
                   Fifth
                   is
                   more
                   then
                   a
                   fourth
                   by
                   the
                   greater
                   Tone
                   .
                
                 14.
                 
                 
                   The
                   lesser
                   Tone
                   is
                   excceded
                   by
                   the
                   greater
                   by
                   a
                
                 Comma
                 .
                 15.
                 
                 
                   The
                   greater
                   Semitone
                   exceedeth
                   the
                   lesser
                   by
                
                 〈…〉
                 .
                 16.
                 
                 
                   A
                   Sixth
                   is
                   made
                   of
                   a
                   Fourth
                   and
                   a
                   Th●rd
                   ,
                   the
                   greater
                   of
                   the
                   greater
                   ,
                   and
                   lesser
                   of
                   the
                   lesser
                   ,
                   or
                   the
                   greater
                   of
                   a
                   fifth
                   and
                   lesser
                   Tone
                   ,
                   and
                   the
                   lesser
                   of
                   the
                
                 Semitone
                 major
                 .
                 17.
                 
                 
                   The
                   seventh
                
                 major
                 ,
                 
                   is
                   made
                   of
                   a
                   Fifth
                   and
                   greater
                   Third
                   ,
                   the
                
                 minor
                 ,
                 
                   of
                   the
                
                 minor
                 .
                 18.
                 
                 
                   The
                   greater
                   Tone
                   doth
                   contain
                   almost
                   ten
                   Comma's
                   ,
                   the
                   lesser
                   almost
                   nine
                   ;
                   the
                   greater
                   Semitone
                   almost
                   five
                   ,
                   and
                   the
                   lesser
                   a
                   most
                   four
                   .
                
                 19.
                 
                 
                   A
                   fifth
                   doth
                   contain
                   two
                   greater
                   T●nes
                   ,
                   one
                   lesser
                   ,
                   and
                   the
                
                 Semitone
                 majus
                 :
                 
                   A
                   fourth
                   
                   one
                   greater
                   and
                   lesser
                   Tone
                   ,
                   and
                
                 the
                 Semitone
                 majus
                 .
                 Therefore
                 an
                 Octave
                 hath
                 in
                 it self
                 six
                 Tones
                 three
                 major
                 ,
                 and
                 three
                 minor
                 ,
                 with
                 the
                 lesser
                 D●esis
                 :
                 to
                 wit
                 ,
                 five
                 Tones
                 ,
                 three
                 greater
                 ,
                 and
                 two
                 lesser
                 ,
                 with
                 two
                 
                   major
                   Semitones
                
                 ,
                 and
                 so
                 it
                 doth
                 comprehend
                 more
                 then
                 fifty
                 Comma's
                 .
                 20.
                 
                 
                   Compounded
                   Intervalls
                   do
                   imitate
                   the
                   nature
                   of
                   their
                   simple
                   .
                
                 A
                 Disdiapason
                 ariseth
                 from
                 two
                 Octaves
                 ,
                 an
                 Octave
                 with
                 a
                 Fifth
                 comprehendeth
                 eight
                 Tones
                 ,
                 five
                 major
                 ,
                 three
                 minor
                 ,
                 and
                 three
                 greater
                 Semitones
                 .
                 A
                 Trisdiapason
                 is
                 divided
                 into
                 three
                 Octaves
                 ,
                 and
                 so
                 of
                 the
                 rest
                 .
                 These
                 Propositions
                 are
                 demonstrated
                 by
                 propositions
                 arithmetical
                 of
                 proportions
                 added
                 ,
                 substracted
                 ,
                 coupled
                 ,
                 
                   &c.
                   v.
                   gr
                
                 .
                 An
                 Octave
                 is
                 of
                 a
                 dupla
                 proportion
                 ,
                 a
                 Fifth
                 of
                 a
                 Sesquialtera
                 ,
                 a
                 Fourth
                 of
                 a
                 Sesquitertia
                 .
                 Therefore
                 an
                 Octave
                 doth
                 consist
                 of
                 a
                 Fifth
                 and
                 a
                 Fourth
                 .
                 This
                 whole
                 matter
                 is
                 demonstrated
                 in
                 a
                 Monochord
                 :
                 How
                 these
                 things
                 may
                 be
                 vulgarly
                 propounded
                 ,
                 you
                 may
                 see
                 hereafter
                 in
                 the
                 last
                 Chapter
                 and
                 last
                 Rule
                 .
              
            
             
               
                 7.
                 
                 The
                 Scale
                 of
                 Musick
                 is
                 explained
                 in
                 these
                 Theorems
                 .
              
               
                 1.
                 
                 
                   The
                   Series
                   of
                   Intension
                   and
                   Remission
                   :
                
                 or
                 of
                 Ascension
                 from
                 a
                 grave
                 Sound
                 into
                 an
                 Acute
                 ,
                 and
                 of
                 the
                 Descension
                 from
                 an
                 acute
                 into
                 a
                 grave
                 ,
                 is
                 called
                 the
                 
                   Scale
                   of
                   Musick
                
                 .
                 2.
                 
                 
                   The
                   Scale
                   of
                   Musick
                   doth
                   vary
                   both
                   according
                   to
                   ancient
                   and
                   modern
                   Musicians
                   .
                
                 For
                 the
                 Scale
                 of
                 the
                 most
                 ancient
                 Musicians
                 ,
                 was
                 only
                 
                 of
                 one
                 Diapason
                 for
                 radical
                 Simplicity
                 .
                 The
                 Scale
                 of
                 the
                 Pythagorians
                 was
                 of
                 a
                 Disdiapason
                 ,
                 for
                 the
                 keeping
                 of
                 Mediocrity
                 .
                 And
                 now
                 it
                 is
                 of
                 a
                 Tris
                 ,
                 and
                 Tetra-Diapason
                 ,
                 for
                 the
                 grateful
                 variety
                 of
                 vocal
                 and
                 Instrumental
                 Musick
                 .
                 The
                 Scale
                 also
                 is
                 either
                 Simple
                 :
                 and
                 that
                 either
                 old
                 as
                 the
                 
                   enharmonic
                   ,
                   chromatic
                
                 ,
                 and
                 diatonic
                 ;
                 or
                 new
                 as
                 the
                 Syntonic
                 :
                 or
                 mixed
                 ,
                 which
                 is
                 compounded
                 of
                 simple
                 [
                 Intervalls
                 ]
                 Of
                 these
                 the
                 enharmonic
                 and
                 chromatic
                 ,
                 in
                 respect
                 of
                 their
                 Difficulty
                 and
                 imperfection
                 are
                 not
                 used
                 in
                 Solitary
                 Musick
                 .
                 3.
                 
                 
                   The
                   Syntonian
                   Scale
                   is
                   of
                   all
                   others
                   the
                   most
                   harmonical
                   ,
                   to
                   which
                   the
                   Diaton
                   Scale
                   may
                   aptly
                   be
                   mixed
                   :
                
                 as
                 it
                 may
                 be
                 seen
                 in
                 a
                 Clavichord
                 ,
                 and
                 wind
                 Instrument
                 ,
                 
                   i.
                   e.
                
                 an
                 Organ
                 ;
                 where
                 the
                 white
                 Keyes
                 do
                 proceed
                 in
                 the
                 Syntonian
                 Scale
                 ;
                 which
                 is
                 somewhat
                 moderated
                 by
                 the
                 Diaton
                 .
                 The
                 Syntonian
                 Scale
                 proceedeth
                 by
                 the
                 great
                 Tone
                 ,
                 the
                 lesser
                 Tone
                 ,
                 and
                 the
                 greater
                 Semitone
                 which
                 ariseth
                 from
                 the
                 minor
                 Tone
                 :
                 the
                 diatonic
                 or
                 diaton
                 proceedeth
                 by
                 two
                 Tones
                 and
                 a
                 Semitone
                 .
                 To
                 these
                 the
                 
                   enharmonic
                   Scale
                
                 is
                 added
                 ,
                 proceeding
                 by
                 two
                 Dieses
                 ,
                 the
                 greater
                 and
                 lesser
                 ,
                 and
                 an
                 immediate
                 Ditone
                 in
                 his
                 Tetrachords
                 .
                 Also
                 the
                 chromatic
                 proceedeth
                 by
                 two
                 Semitones
                 ,
                 the
                 greater
                 and
                 the
                 lesser
                 ,
                 and
                 an
                 immediate
                 Semiditone
                 .
                 So
                 the
                 black
                 Keyes
                 proceed
                 with
                 the
                 white
                 in
                 the
                 chromatic
                 :
                 from
                 whence
                 they
                 are
                 called
                 fict
                 in
                 the
                 Syntonian
                 .
                 Hence
                 also
                 ariseth
                 the
                 Scale
                 irregular
                 or
                 flat
                 ,
                 which
                 differeth
                 not
                 from
                 the
                 regular
                 or
                 dural
                 ,
                 but
                 by
                 accidental
                 Transposition
                 ,
                 or
                 by
                 the
                 fourth
                 above
                 ,
                 or
                 by
                 the
                 fifth
                 beneath
                 .
                 And
                 this
                 is
                 the
                 Disposition
                 of
                 the
                 old
                 
                   diatonic
                   Scale
                
                 .
              
               
                 
                 
                   1.
                   
                   
                     The
                     greater
                     Tone
                  
                   .
                   9.8
                   .
                
                 
                   2.
                   
                   
                     The
                     greater
                     Tone
                  
                   .
                   9.8
                   .
                
                 
                   3.
                   
                   
                     The
                     lesser
                     Semitone
                     from
                     the
                     greater
                     Tone
                  
                   256.243
                
                 
                   4.
                   
                   
                     The
                     greater
                     Tone
                  
                   .
                   9.8
                   .
                
                 
                   5.
                   
                   
                     The
                     greater
                     Tone
                  
                   .
                   9.8
                   .
                
                 
                   6.
                   
                   
                     The
                     greater
                     Tone
                  
                   .
                   9.8
                   .
                
                 
                   7.
                   
                   
                     The
                     lesser
                     Semitone
                  
                   .
                   256.243
                   .
                
                 
                   8.
                   
                   
                     The
                     greater
                     Tone
                  
                   .
                   9.8
                   .
                   and
                   so
                   on
                   through
                   the
                   Octaves
                   below
                   and
                   above
                   .
                
              
               
                 
                   But
                   the
                   Disposition
                   of
                   the
                   new
                   and
                   perfect
                   Syntonian
                   Scale
                   is
                   as
                   followeth
                
                 ;
                 
                   
                     1.
                     
                     
                       The
                       greater
                       Tone
                    
                     .
                     9.8
                     .
                  
                   
                     2.
                     
                     
                       The
                       lesser
                       Tone
                    
                     .
                     10.9
                     .
                  
                   
                     3.
                     
                     
                       The
                       greater
                       Semitone
                    
                     .
                     16.15
                     .
                  
                   
                     4.
                     
                     
                       The
                       greater
                       Tone
                    
                     .
                     9.8
                     .
                  
                   
                     5.
                     
                     
                       The
                       lesser
                       Tone
                    
                     .
                     10.9
                     .
                  
                   
                     6.
                     
                     
                       The
                       greater
                       Tone
                    
                     .
                     9.8
                     .
                  
                   
                     7.
                     
                     
                       The
                       greater
                       Semitone
                    
                     .
                     16.15
                     .
                  
                   
                     8.
                     
                     
                       The
                       greater
                       Tone
                    
                     .
                     9.8
                     .
                     And
                     so
                     on
                     through
                     the
                     Octaves
                     above
                     and
                     below
                     .
                     Compare
                     these
                     things
                     with
                     the
                     antecedent
                     Rule
                     ,
                     and
                     following
                     Chapters
                     .
                  
                
              
            
          
        
         
           
           
             CHAP.
             V.
             Of
             the
             Signs
             of
             a
             Musical
             Sound
             .
          
           
             
               PRECEPTS
               .
            
             
               THE
               Signs
               of
               a
               Musical
               Sound
               do
               follow
               .
            
             
               And
               those
               are
               of
               a
               Sound
               either
               broad
               ,
               long
               ,
               or
               thick
               .
            
             
               The
               signes
               of
               a
               long
               Sound
               do
               note
               the
               duration
               thereof
               :
               and
               they
               are
               either
               principal
               or
               lesse
               principal
               .
            
             
               The
               principal
               Signes
               are
               a
               Note
               and
               a
               Pause
               .
            
             
               A
               Note
               is
               a
               signe
               of
               a
               present
               and
               positive
               sound
               :
               and
               containeth
               Touch
               ,
               and
               that
               either
               whole
               or
               not
               whole
               .
            
             
               It
               containeth
               the
               whole
               Touch
               either
               eight
               times
               as
               a
               Large
               ,
               or
               four
               times
               as
               a
               Long
               ,
               or
               twice
               as
               a
               Breve
               ,
               or
               once
               as
               a
               Semibreve
               .
            
             
               The
               rest
               do
               contain
               not
               the
               whole
               ,
               but
               
               part
               of
               a
               Touch
               ,
               and
               that
               either
               the
               half
               part
               as
               a
               Minim
               ,
               or
               the
               fourth
               part
               as
               a
               Crotchet
               ,
               or
               the
               eigth
               part
               as
               a
               Quaver
               ,
               or
               the
               sixteenth
               part
               as
               a
               Semiquaver
               .
            
             
               A
               Pause
               is
               the
               Index
               of
               a
               privitive
               or
               absent
               Sound
               ,
               that
               is
               of
               silence
               :
               and
               it
               answereth
               either
               to
               a
               Large
               ,
               or
               Long
               ,
               or
               
                 Breve
                 ,
                 &c.
              
               
            
             
               Signes
               lesse
               principal
               are
               a
               semicircle
               with
               a
               Center
               ,
               Custos
               ,
               or
               the
               like
               .
            
             
               Signes
               of
               a
               broad
               sound
               ,
               are
               a
               prick
               of
               Augmentation
               ,
               breathing
               ,
               and
               Syncope
               :
               of
               which
               ,
               Syncope
               ,
               is
               a
               certain
               loosing
               of
               the
               Touch
               ;
               Notes
               ,
               or
               Pauses
               ;
               breathing
               answereth
               a
               
                 Semi
                 Minim
              
               .
            
             
               The
               Signes
               of
               a
               Crasse
               Sound
               are
               parallel
               Lines
               ,
               whereof
               the
               place
               and
               name
               do
               occur
               .
            
             
               The
               place
               is
               a
               Musical
               System
               ,
               and
               that
               greater
               or
               lesser
               .
            
             
               The
               greater
               System
               for
               the
               most
               part
               doth
               consist
               of
               ten
               Lines
               :
               and
               serveth
               for
               the
               Composing
               of
               a
               Song
               ,
               called
               otherwise
               a
               conjoyned
               System
               .
            
             
               The
               lesser
               System
               doth
               consist
               of
               five
               Lines
               ,
               and
               serveth
               chiefly
               to
               a
               Song
               pricked
               out
               .
               This
               is
               otherwise
               called
               a
               simple
               System
               .
            
             
             
               The
               Name
               is
               aswell
               a
               Letter
               as
               a
               Uoice
               ,
               or
               as
               others
               will
               ,
               a
               Musical
               Syllable
               .
            
             
               A
               Letter
               is
               as
               a
               Key
               by
               which
               the
               Song
               is
               opened
               ,
               therefore
               called
               Clavis
               .
               Such
               letters
               are
               seven
               .
               
                 A.
                 B.
                 C.
                 D.
                 E.
                 F.
                 G.
                 
              
            
             
               The
               musical
               Uoices
               or
               Syllables
               are
               six
               ,
               
                 ut
                 ,
                 re
                 ,
                 mi
                 ,
                 fa
                 ,
                 sol
                 ,
                 la.
                 
              
            
             
               These
               are
               found
               in
               a
               Musical
               Scale
               either
               continued
               or
               discontinued
               .
            
             
               There
               ,
               there
               is
               no
               need
               of
               Mutation
               :
               but
               here
               otherwise
               .
            
          
           
             
               RULES
               .
            
             
               
                 1.
                 
                 The
                 most
                 certain
                 and
                 ready
                 Signs
                 of
                 Sounds
                 are
                 Cyphers
                 of
                 Numbers
                 .
              
               
                 Because
                 a
                 Sound
                 can
                 neither
                 by
                 any
                 Man
                 be
                 written
                 in
                 Paper
                 ,
                 nor
                 kept
                 in
                 his
                 Mind
                 ,
                 neither
                 only
                 nor
                 alwayes
                 ;
                 therefore
                 it
                 standeth
                 in
                 need
                 of
                 certain
                 Signs
                 ,
                 by
                 which
                 the
                 Quantity
                 and
                 Quality
                 thereof
                 may
                 be
                 represented
                 .
                 For
                 because
                 in
                 the
                 Numbers
                 and
                 Proportions
                 of
                 these
                 ,
                 all
                 the
                 Dimensions
                 of
                 Sound
                 have
                 their
                 assigned
                 Essence
                 ;
                 the
                 most
                 sure
                 and
                 ready
                 Signs
                 are
                 Cyphers
                 of
                 Numbers
                 placed
                 according
                 
                 to
                 their
                 
                   Longitude
                   ,
                   Latitude
                
                 ,
                 and
                 Profundity
                 .
                 For
                 according
                 to
                 Longitude
                 .
                 1.2.3.4.8
                 .
                 ½
                 1
                 /
                 3
                 ¼
                 may
                 note
                 the
                 stay
                 of
                 one
                 Touch
                 ,
                 two
                 ,
                 three
                 ,
                 or
                 four
                 ,
                 &c.
                 
                 According
                 to
                 Latitude
                 in
                 like
                 manner
                 ;
                 and
                 according
                 to
                 Crassitude
                 the
                 g●eater
                 Numbers
                 may
                 signifie
                 the
                 grave
                 Sound
                 ;
                 and
                 the
                 lesser
                 Numbers
                 ,
                 the
                 acute
                 Sound
                 .
                 But
                 it
                 behoveth
                 here
                 to
                 retain
                 vulgar
                 Signs
                 ,
                 because
                 they
                 are
                 most
                 used
                 .
              
            
             
               
                 2.
                 
                 The
                 Doctrine
                 of
                 Notes
                 is
                 contained
                 in
                 these
                 Rules
                 .
              
               
                 1.
                 
                 Notes
                 are
                 either
                 simple
                 or
                 compounded
                 .
                 And
                 those
                 are
                 either
                 whole
                 or
                 broken
                 .
                 These
                 are
                 called
                 bound
                 .
                 Simple
                 Notes
                 are
                 placed
                 without
                 any
                 joyning
                 of
                 either
                 :
                 Compounded
                 ,
                 contrarily
                 .
                 Whole
                 Notes
                 are
                 measured
                 by
                 whole
                 Times
                 ;
                 broken
                 Notes
                 ,
                 by
                 parts
                 of
                 Time.
                 Whole
                 Sounds
                 consist
                 either
                 of
                 one
                 Time
                 ,
                 as
                 a
                 Semibreve
                 :
                 or
                 of
                 more
                 ,
                 and
                 those
                 either
                 of
                 two
                 ,
                 as
                 a
                 Breve
                 :
                 four
                 ,
                 as
                 a
                 Long
                 :
                 or
                 eight
                 ,
                 as
                 a
                 Large
                 .
                 The
                 broken
                 Notes
                 do
                 contain
                 either
                 the
                 second
                 part
                 of
                 a
                 Time
                 ,
                 as
                 a
                 Minim
                 :
                 or
                 the
                 fourth
                 ,
                 as
                 a
                 Crotchet
                 :
                 or
                 the
                 eighth
                 ,
                 as
                 a
                 Quaver
                 :
                 or
                 the
                 Sixteenth
                 ,
                 as
                 a
                 Semiquaver
                 .
                 According
                 to
                 the
                 following
                 Scheme
                 .
              
               
               
                 
                   
                     
                       Names
                       .
                    
                     
                       Figure
                       .
                    
                     
                       Value
                       .
                    
                  
                   
                     
                       Large
                       .
                    
                     
                       𝆶
                       Excessus
                       .
                    
                     
                       8.
                       
                    
                  
                   
                     
                       Long.
                       
                    
                     
                       𝆷
                       Excessus
                       .
                    
                     
                       4.
                       
                    
                  
                   
                     
                       Breve
                       .
                    
                     
                       𝆸
                       Excessus
                       .
                    
                     
                       2.
                       
                    
                  
                   
                     
                       Semibreve
                       .
                    
                     
                       𝆹
                       Medium
                       .
                    
                     
                       1.
                       
                    
                  
                   
                     
                       Minim
                       .
                    
                     
                       톹텥
                       톹텥
                       Defectus
                       .
                    
                     
                       ½
                    
                  
                   
                     
                       Crotchet
                       .
                    
                     
                       톺텥
                       톺텥
                       Defectus
                       .
                    
                     
                       ¼
                    
                  
                   
                     
                       Quaver
                       .
                    
                     
                       톼텮
                       톼텮
                       Defectus
                       .
                    
                     
                       ⅛
                    
                  
                   
                     
                       Semiquaver
                       .
                    
                     
                       톼텯
                       톼텯
                       Defectus
                       .
                    
                     
                       1
                       /
                       16
                    
                  
                
              
               
                 Although
                 more
                 Notes
                 of
                 Longitude
                 may
                 be
                 given
                 ,
                 as
                 well
                 greater
                 or
                 lesser
                 ,
                 potentially
                 infinite
                 :
                 yet
                 the●e
                 notwithstanding
                 do
                 suffice
                 ,
                 which
                 were
                 invented
                 by
                 Musicians
                 of
                 former
                 Ages
                 .
                 2.
                 
                 
                   Notes
                   are
                   varied
                   according
                   to
                   the
                   Augmentation
                   or
                   Diminution
                   of
                   their
                   value
                   ,
                   or
                   according
                   to
                   both
                   together
                   .
                
                 Either
                 all
                 or
                 some
                 are
                 augmented
                 by
                 the
                 half
                 part
                 ;
                 and
                 truely
                 ,
                 all
                 are
                 augmented
                 either
                 by
                 the
                 Opposition
                 of
                 a
                 Semicircle
                 .
                 𝇋
                 .
                 𝇍
                 .
                 and
                 a
                 Prick
                 ,
                 of
                 which
                 this
                 is
                 the
                 Rule
                 :
                 A
                 Prick
                 put
                 after
                 Notes
                 doth
                 add
                 the
                 half
                 part
                 of
                 the
                 time
                 above
                 their
                 proper
                 value
                 ,
                 as
                 
                   
                     
                       12.
                       
                    
                     
                       6.
                       
                    
                     
                       3.
                       
                    
                     
                       3
                       /
                       2
                    
                     
                       ¾
                    
                  
                   
                     
                       𝆶
                       .
                    
                     
                       𝆷
                       .
                    
                     
                       𝆸
                       .
                    
                     
                       𝆹
                       .
                    
                     
                       톹텥
                       .
                    
                  
                
                 
                 Thus
                 a
                 Prick
                 after
                 a
                 𝆸
                 .
                 is
                 a
                 Monotone
                 ,
                 or
                 𝆹
                 .
                 after
                 a
                 Semibreve
                 is
                 a
                 Minim
                 ,
                 or
                 톹텥
                 .
                 Some
                 Notes
                 are
                 only
                 augmented
                 by
                 prefixing
                 a
                 Circle
                 𝇈
                 .
                 as
                 a
                 
                   Large
                   ,
                   Long
                   ,
                   Breve
                
                 .
                 Notes
                 are
                 diminished
                 by
                 a
                 Trochaic
                 Touch
                 in
                 a
                 certain
                 proportion
                 ,
                 either
                 Tripla
                 or
                 Sesquialtera
                 .
                 Where
                 the
                 Signs
                 are
                 either
                 Number
                 or
                 Colour
                 :
                 as
                 3
                 /
                 1
                 is
                 tripla
                 ,
                 3
                 /
                 2
                 is
                 sesquialtera
                 .
                 Notes
                 are
                 partly
                 augmented
                 and
                 partly
                 diminished
                 ,
                 chiefly
                 by
                 the
                 ligation
                 and
                 obliquation
                 of
                 a
                 Breve
                 ,
                 which
                 is
                 done
                 for
                 the
                 extending
                 of
                 one
                 Syllable
                 .
                 And
                 a
                 Long
                 also
                 with
                 a
                 Breve
                 is
                 counted
                 for
                 a
                 Semibreve
                 ;
                 and
                 also
                 in
                 like
                 manner
                 a
                 Breve
                 with
                 a
                 Breve
                 .
                 But
                 this
                 kind
                 of
                 ligation
                 and
                 obliquation
                 is
                 now
                 wholly
                 omitted
                 ,
                 as
                 not
                 necessary
                 in
                 the
                 least
                 .
              
            
             
               
                 3.
                 
                 Pauses
                 measuring
                 Silence
                 do
                 answer
                 to
                 those
                 musical
                 Notes
                 whereof
                 they
                 are
                 Privations
                 .
              
               
                 For
                 a
                 Pause
                 (
                 which
                 is
                 noted
                 by
                 a
                 little
                 Line
                 )
                 doth
                 answer
                 either
                 to
                 a
                 Large
                 ,
                 or
                 Long
                 ,
                 or
                 Breve
                 ,
                 or
                 other
                 Note
                 :
                 as
                 in
                 the
                 Type
                 .
                 
                 8.
                 4.
                 2.
                 1.
                 
                 ½
                 ¼
              
               
               
                 A
                 double
                 Breathing
                 doth
                 answer
                 to
                 a
                 Quaver
                 :
                 a
                 Triple
                 to
                 a
                 Semiquaver
                 .
                 Hitherto
                 do
                 pertain
                 the
                 
                   Neuma
                   ,
                   Custos
                
                 ,
                 and
                 the
                 like
                 .
                 As
                 
                 Neuma
                 .
                 Custos
                 .
              
            
             
               
                 4.
                 
                 Signs
                 of
                 a
                 broad
                 Sound
                 are
                 by
                 Artists
                 expressed
                 less
                 carefully
                 .
              
               
                 The
                 Sign
                 of
                 a
                 broad
                 Sound
                 ought
                 to
                 shew
                 the
                 Latitude
                 of
                 it
                 according
                 to
                 the
                 asperous
                 ,
                 harsh
                 ,
                 clear
                 ,
                 full
                 ,
                 soft
                 ,
                 flat
                 ,
                 and
                 small
                 Spirit
                 thereof
                 ,
                 as
                 the
                 nature
                 of
                 the
                 Text
                 requireth
                 .
                 But
                 Musicians
                 do
                 less
                 weigh
                 the
                 Latitude
                 of
                 a
                 Sound
                 ,
                 and
                 do
                 leave
                 it
                 to
                 the
                 Text
                 ,
                 and
                 to
                 the
                 things
                 themselves
                 that
                 are
                 to
                 be
                 sung
                 ,
                 and
                 are
                 content
                 with
                 few
                 Signs
                 ,
                 chiefly
                 using
                 breathing
                 and
                 Syncopation
                 .
                 Breathing
                 doth
                 answer
                 to
                 the
                 Crotchet
                 :
                 Syncope
                 or
                 Syncopation
                 is
                 a
                 certain
                 Luxation
                 ,
                 that
                 is
                 ,
                 a
                 fraction
                 ,
                 and
                 Contraction
                 of
                 Touch
                 ,
                 Notes
                 ,
                 and
                 Pauses
                 .
                 
                   e.
                   gr
                
                 .
                 
              
            
             
               
                 5.
                 
                 The
                 Sign
                 of
                 a
                 Crass
                 Sound
                 is
                 a
                 crossed
                 Line
                 ,
                 as
                 they
                 call
                 it
                 .
              
               
                 The
                 Sign
                 signifying
                 Crassitude
                 of
                 gravity
                 and
                 acutenesse
                 
                 measurable
                 by
                 proportionable
                 Numbers
                 ,
                 is
                 a
                 perpendicular
                 Line
                 ,
                 which
                 a
                 right
                 line
                 doth
                 cut
                 ;
                 thus
                 ,
                 +
                 .
                 The●e
                 Lines
                 are
                 called
                 Seats
                 of
                 crass
                 Sounds
                 or
                 Musical
                 Intervalls
                 .
                 Also
                 a
                 Musical
                 System
                 which
                 is
                 twofold
                 ,
                 the
                 greater
                 and
                 the
                 lesser
                 .
                 In
                 both
                 there
                 are
                 perpendicular
                 and
                 parallel
                 Lines
                 ;
                 indeed
                 in
                 the
                 greater
                 there
                 are
                 〈◊〉
                 ten
                 parallel
                 Lines
                 ,
                 in
                 the
                 lesser
                 alwayes
                 five
                 .
                 The
                 greater
                 serveth
                 for
                 the
                 composing
                 of
                 a
                 Song
                 ;
                 where
                 the
                 perpendicular
                 Lines
                 are
                 cut
                 by
                 the
                 distance
                 of
                 one
                 or
                 two
                 Touches
                 :
                 But
                 the
                 lesser
                 doth
                 serve
                 for
                 Melody
                 ,
                 which
                 is
                 to
                 be
                 extracted
                 and
                 noted
                 .
              
               
                 Let
                 this
                 be
                 the
                 Type
                 of
                 the
                 greater
                 System
                 .
                 
              
               
                 Let
                 this
                 be
                 the
                 Type
                 of
                 the
                 lesser
                 System
                 .
                 
              
               
                 Both
                 these
                 Systems
                 are
                 put
                 in
                 a
                 Chart
                 ,
                 or
                 Melopoetick
                 Abacus
                 ,
                 or
                 Compositary
                 as
                 they
                 call
                 it
                 .
                 The
                 first
                 is
                 convenient
                 to
                 a
                 young
                 Beginner
                 :
                 the
                 latter
                 ,
                 
                 for
                 a
                 longer
                 Practitioner
                 :
                 but
                 others
                 would
                 rather
                 draw
                 more
                 simple
                 Systems
                 in
                 an
                 Abacus
                 ;
                 Thus
                 ,
                 
              
            
             
               
                 6.
                 
                 Of
                 Letters
                 and
                 Voices
                 Musical
                 ,
                 as
                 they
                 call
                 them
                 ,
                 these
                 are
                 the
                 Theorems
                 .
              
               
                 1.
                 
                 The
                 radical
                 Letters
                 are
                 seven
                 ,
                 in
                 this
                 order
                 ,
                 
                   a.
                   b.
                   c.
                   d.
                   e.
                   f.
                   g.
                
                 which
                 do
                 moderate
                 Sounds
                 in
                 the
                 
                   Diato●ic
                   Scale
                
                 of
                 a
                 Diapason
                 .
                 These
                 are
                 usually
                 called
                 Keyes
                 ,
                 because
                 that
                 by
                 them
                 a
                 ●ong
                 is
                 ,
                 as
                 it
                 were
                 ,
                 opened
                 .
                 They
                 were
                 invented
                 by
                 
                   Guido
                   Aretine
                
                 ;
                 at
                 this
                 time
                 they
                 are
                 insufficient
                 .
                 2.
                 
                 Letters
                 or
                 Keyes
                 are
                 either
                 
                   capital
                   ,
                   minute
                
                 ,
                 or
                 
                   geminate
                   .
                   Capital
                
                 are
                 they
                 which
                 are
                 written
                 with
                 Capital
                 ,
                 that
                 is
                 with
                 great
                 Letters
                 .
                 Thus
                 Γ.
                 
                   A.
                   B.
                   C.
                   D.
                   E.
                   F.
                   G.
                
                 of
                 which
                 Γ.
                 
                   A.
                   B.
                   C.
                
                 are
                 called
                 grave
                 ,
                 because
                 they
                 emit
                 a
                 grave
                 Sound
                 in
                 respect
                 of
                 the
                 rest
                 :
                 the
                 rest
                 ,
                 as
                 
                   D.
                   E.
                   F.
                   G.
                
                 are
                 called
                 finals
                 ,
                 because
                 every
                 Song
                 regularly
                 doth
                 end
                 in
                 these
                 Keyes
                 .
                 We
                 have
                 only
                 
                 Γ
                 from
                 the
                 School
                 of
                 the
                 Greeks
                 .
                 The
                 minute
                 Keys
                 are
                 in
                 number
                 seven
                 ,
                 so
                 called
                 because
                 they
                 are
                 written
                 with
                 little
                 Letters
                 .
                 Of
                 these
                 
                   a.
                   b.
                   c.
                   d.
                
                 are
                 called
                 asfinal
                 ,
                 because
                 in
                 these
                 Keyes
                 the
                 transposed
                 Song
                 doth
                 end
                 :
                 oth●rwise
                 call●d
                 acute
                 ,
                 because
                 they
                 do
                 emit
                 a
                 more
                 acute
                 Sound
                 .
                 The
                 other
                 are
                 called
                 Superacute
                 because
                 they
                 are
                 put
                 above
                 the
                 acute
                 ,
                 as
                 e.f.g.
                 The
                 geminate
                 Keyes
                 are
                 commonly
                 five
                 in
                 n●mber
                 .
                 
                   aa
                   bb
                   .
                   cc.
                   dd
                   .
                   ee
                   .
                
                 So
                 called
                 because
                 they
                 are
                 written
                 with
                 double
                 Letters
                 .
                 Otherwise
                 called
                 excelling
                 ;
                 because
                 in
                 their
                 Sound
                 they
                 transcend
                 all
                 others
                 .
                 But
                 because
                 the
                 number
                 of
                 Keys
                 is
                 not
                 sufficient
                 ;
                 therefore
                 latter
                 Musicians
                 under
                 the
                 great
                 Latin
                 Letters
                 have
                 put
                 seven
                 German
                 Letters
                 :
                 and
                 the
                 double
                 Letters
                 they
                 do
                 fully
                 recite
                 ,
                 and
                 more-over
                 they
                 add
                 unto
                 them
                 triplicated
                 Letters
                 .
                 Thus
                 
                   
                     1.
                     
                     
                       A
                       B
                       C
                       D
                       E
                       F
                       G.
                       
                    
                  
                   
                     2.
                     
                     
                       A
                       B
                       C
                       D
                       E
                       F
                       G.
                       
                    
                  
                   
                     3.
                     
                       a
                       b
                       c
                       d
                       e
                       f
                       g.
                       
                    
                  
                   
                     4.
                     
                       aa
                       bb
                       cc
                       dd
                       ee
                       ff
                       gg
                       .
                    
                  
                   
                     5.
                     
                       aaa
                       bbb
                       ccc
                       ddd
                       eee
                       fff
                       ggg
                       .
                    
                  
                
                 3.
                 
                 Keyes
                 are
                 signed
                 ,
                 or
                 understood
                 ,
                 or
                 not
                 signed
                 .
                 The
                 signed
                 Keyes
                 are
                 three
                 which
                 are
                 distant
                 one
                 from
                 another
                 by
                 a
                 Fifth
                 ,
                 and
                 they
                 are
                 
                   g.
                   c.
                   f.
                
                 thus
                 
              
               
               
                 These
                 in
                 the
                 conjoyned
                 System
                 are
                 thus
                 put
                 ,
                 and
                 are
                 distant
                 from
                 one
                 another
                 by
                 a
                 Diapente
                 .
                 
              
               
                 In
                 a
                 simple
                 System
                 they
                 are
                 variously
                 placed
                 by
                 reason
                 of
                 the
                 Profundity
                 and
                 Altitude
                 of
                 a
                 Song
                 ;
                 As
                 ,
                 
              
               
                 But
                 Keyes
                 not
                 signed
                 are
                 known
                 by
                 the
                 signed
                 .
              
               
                 4.
                 
                 
                   Out
                   of
                   these
                   seven
                   Keyes
                   there
                   is
                   a
                   double
                
                 b.
                 
                   viz.
                   flat
                   and
                   sharp
                
                 .
                 These
                 two
                 Letters
                 in
                 the
                 signing
                 are
                 distant
                 by
                 the
                 lesser
                 half
                 Note
                 .
                 So
                 that
                 the
                 regular
                 or
                 dural
                 Scale
                 beginneth
                 in
                 C.
                 and
                 the
                 irregular
                 or
                 flat
                 Scale
                 in
                 
                   F.
                   b
                
                 dural
                 is
                 thus
                 marked
                 ♯
                 and
                 is
                 called
                 
                   b.
                   quadrate
                
                 .
              
               
                 5.
                 
                 
                   Besides
                   b.
                   molle
                   ,
                   as
                   they
                   call
                   it
                   ,
                   there
                   is
                   need
                   of
                   Cancells
                   ♯
                   .
                   and
                   cis
                   ,
                   dis
                   ,
                   fis
                   ,
                   gis
                   :
                
                 which
                 are
                 called
                 fict
                 Letters
                 by
                 instrumental
                 Musicians
                 .
                 But
                 
                   David
                   Mostar●
                
                 so
                 accommodateth
                 the
                 Musical
                 Keyes
                 to
                 ●even
                 n●w
                 Vo●ces
                 .
                 Four
                 Keyes
                 in
                 the
                 whole
                 are
                 
                 here
                 to
                 be
                 held
                 .
                 The
                 first
                 is
                 C.
                 in
                 which
                 he
                 will
                 alwayes
                 have
                 bo
                 sung
                 .
                 The
                 second
                 is
                 G.
                 five
                 Tones
                 below
                 and
                 four
                 above
                 G
                 ,
                 he
                 alwayes
                 singeth
                 bo
                 .
                 The
                 third
                 is
                 F.
                 and
                 four
                 above
                 ,
                 and
                 five
                 Tones
                 below
                 
                   F.
                   bo
                
                 .
                 is
                 alwayes
                 sung
                 .
                 Also
                 five
                 Notes
                 above
                 
                   B.
                   molle
                
                 ,
                 and
                 four
                 under
                 
                   B.
                   molle
                   ,
                   bo
                
                 .
                 is
                 alwayes
                 to
                 be
                 sung
                 .
                 6.
                 
                 
                   Musical
                   Voices
                   are
                   one
                   way
                   rehearsed
                   by
                   the
                   Ancients
                   ,
                   and
                   another
                   way
                   by
                   later
                   Musicians
                   .
                
                 The
                 ancient
                 Musicians
                 did
                 constitute
                 these
                 six
                 
                   ut
                   ,
                   re
                   ,
                   mi
                   ,
                   fa
                   ,
                   sol
                   ,
                   la.
                
                 To
                 these
                 six
                 Voices
                 some
                 do
                 add
                 the
                 seventh
                 Si
                 ,
                 lest
                 there
                 should
                 be
                 need
                 of
                 some
                 Mutation
                 .
                 Concerning
                 this
                 thing
                 
                   Erycius
                   Puteanus
                
                 in
                 his
                 Musathena
                 doth
                 so
                 for
                 the
                 most
                 part
                 play
                 the
                 Philosopher
                 .
                 
                   Guido
                   Aretine
                
                 (
                 lived
                 under
                 Henry
                 the
                 third
                 Emperour
                 )
                 for
                 his
                 Skill
                 in
                 Musick
                 among
                 the
                 prime
                 of
                 his
                 Age
                 ,
                 and
                 delighted
                 with
                 the
                 perfection
                 of
                 the
                 Senary
                 Number
                 ,
                 introduced
                 these
                 six
                 Syllabic
                 Notes
                 ,
                 
                   ut
                   ,
                   re
                   ,
                   mi
                   ,
                   fa
                   ,
                   sol
                   ,
                   la.
                
                 which
                 he
                 borrowed
                 and
                 translated
                 out
                 of
                 the
                 Hymne
                 .
                 
                   
                     Ut
                     queant
                     laxis
                     Resonare
                     fibris
                     ,
                  
                   
                     MIra
                     gestorum
                     FAmuli
                     tuorum
                     ,
                  
                   
                     SOLve
                     pollutum
                     LAbij
                     reatum
                     .
                  
                   
                     Sancte
                     Johannes
                     .
                  
                
              
               
                 These
                 six
                 Notes
                 so
                 invented
                 ,
                 do
                 shew
                 their
                 use
                 every
                 where
                 among
                 Musicians
                 ,
                 but
                 very
                 slow
                 and
                 difficult
                 .
                 For
                 what
                 impediment
                 is
                 there
                 of
                 Mutations
                 ,
                 confusion
                 of
                 Keyes
                 ,
                 substitution
                 of
                 Voices
                 ?
                 You
                 may
                 see
                 most
                 (
                 whether
                 with
                 Indignation
                 or
                 no
                 )
                 to
                 have
                 spent
                 a
                 good
                 part
                 of
                 their
                 Age
                 upon
                 this
                 Art
                 ,
                 
                 and
                 yet
                 to
                 have
                 profited
                 very
                 little
                 ,
                 though
                 perfect
                 many
                 years
                 before
                 in
                 the
                 Lection
                 thereof
                 .
                 But
                 the
                 D●fficulty
                 doth
                 hinder
                 ,
                 and
                 make
                 it
                 a
                 remora
                 to
                 most
                 .
                 Which
                 some
                 do
                 thus
                 take
                 away
                 by
                 joyning
                 si
                 .
                 to
                 the●e
                 six
                 received
                 Not●s
                 .
                 For
                 which
                 Note
                 you
                 may
                 put
                 Bi.
                 out
                 of
                 the
                 ●aid
                 Hymne
                 .
                 
                   Solve
                   polluti
                   la
                   BI
                   .
                   i.
                   reatum
                   .
                
              
               
                 This
                 therefore
                 shall
                 be
                 the
                 order
                 of
                 Notes
                 ,
                 
                   ut
                   ,
                   re
                   ,
                   mi
                   ,
                   fa
                   ,
                   sol
                   ,
                   la
                   ▪
                   bi
                   ,
                
                 for
                 th●s
                 Heptade
                 these
                 following
                 Rea●ons
                 are
                 brought
                 .
                 1.
                 
                 Whereas
                 Notes
                 are
                 the
                 Index's
                 of
                 Vo●ces
                 ,
                 and
                 as
                 certain
                 Signs
                 ,
                 it
                 is
                 of
                 necessity
                 that
                 there
                 should
                 be
                 as
                 many
                 Notes
                 as
                 Voices
                 .
                 But
                 there
                 are
                 seven
                 distinct
                 voices
                 stablished
                 in
                 that
                 half
                 verse
                 
                   septem
                   discrimina
                   vocum
                
                 .
                 Therefore
                 there
                 are
                 seven
                 Notes
                 .
                 For
                 by
                 voices
                 are
                 understood
                 those
                 sev●n
                 Sounds
                 ,
                 which
                 are
                 distinguished
                 by
                 certain
                 Intervalls
                 .
                 Those
                 Intervalls
                 or
                 Diastems
                 are
                 called
                 Tones
                 .
                 Therefore
                 a
                 Sound
                 ,
                 and
                 Tone
                 or
                 Intervall
                 do
                 differ
                 .
                 A
                 Sound
                 is
                 the
                 Voice
                 it self
                 ,
                 which
                 being
                 formed
                 by
                 the
                 Mouth
                 ,
                 is
                 brought
                 by
                 the
                 Air
                 to
                 the
                 Ears
                 .
                 A
                 Tone
                 is
                 a
                 Space
                 circumscribed
                 by
                 two
                 Sounds
                 :
                 or
                 ,
                 the
                 distance
                 of
                 a
                 grave
                 and
                 acute
                 Sound
                 :
                 So
                 that
                 Tones
                 are
                 tho●e
                 Intervals
                 ,
                 which
                 are
                 placed
                 between
                 the
                 first
                 and
                 secon●●ound
                 ,
                 the
                 second
                 and
                 third
                 ,
                 the
                 third
                 and
                 fourth
                 ,
                 the
                 fourth
                 and
                 fifth
                 ,
                 the
                 fifth
                 and
                 sixth
                 ,
                 the
                 sixth
                 and
                 seventh
                 .
                 But
                 this
                 Hep●ade
                 of
                 Voices
                 ,
                 Ptolomy
                 in
                 his
                 eleventh
                 Book
                 concern●ng
                 Musick
                 doth
                 confirm
                 ;
                 saying
                 ,
                 
                   that
                   by
                   nature
                   Voices
                   can
                   be
                   made
                   neither
                   more
                   nor
                   fewer
                   then
                   seven
                   .
                
                 2.
                 
                 The
                 Aegyptians
                 and
                 Grecians
                 have
                 approved
                 
                 the
                 seven
                 Voyces
                 by
                 the
                 number
                 of
                 seven
                 Vowells
                 .
                 For
                 the
                 Egyptians
                 as
                 
                   Demetrius
                   Phalereus
                
                 doth
                 testifie
                 ,
                 did
                 commend
                 their
                 Gods
                 by
                 the
                 modulated
                 enunciation
                 of
                 seven
                 vowels
                 .
                 And
                 Plutarch
                 doth
                 accommodate
                 the
                 Greeks
                 seven
                 Vowels
                 to
                 so
                 many
                 Voices
                 of
                 Musick
                 .
                 3.
                 
                 The
                 
                   Lyre
                   ,
                   Cithren
                
                 ,
                 and
                 certain
                 other
                 musical
                 Instruments
                 which
                 are
                 strung
                 with
                 strings
                 ,
                 were
                 anciently
                 of
                 seven
                 strings
                 ,
                 without
                 doubt
                 ,
                 by
                 reason
                 of
                 the
                 seven
                 Voices
                 .
                 The
                 Chords
                 of
                 the
                 Lyre
                 were
                 of
                 old
                 in
                 this
                 order
                 ,
                 and
                 by
                 these
                 Names
                 ,
                 
                   Hypate
                   ,
                   Parhypate
                   ,
                   Hypermese
                   ,
                   Mese
                   ,
                   Paramese
                   ,
                   Paranete
                   ,
                   Ne●e
                   .
                
                 The
                 first
                 is
                 called
                 Hypate
                 ,
                 not
                 only
                 for
                 the
                 acutenesse
                 of
                 the
                 Voice
                 ,
                 but
                 for
                 a
                 certain
                 excellency
                 and
                 virtue
                 .
                 For
                 Hypatos
                 as
                 it
                 were
                 Hypertatos
                 ,
                 doth
                 signifie
                 a
                 degree
                 of
                 Eminency
                 and
                 Dignity
                 .
                 Nete
                 ,
                 as
                 Neate
                 ,
                 that
                 is
                 ,
                 the
                 last
                 or
                 ultimate
                 .
                 Neither
                 have
                 the
                 Chords
                 been
                 only
                 by
                 these
                 Names
                 ,
                 but
                 also
                 the
                 Sounds
                 themselves
                 ,
                 nigh
                 this
                 manner
                 .
                 Hypate
                 hath
                 to
                 himself
                 Bi.
                 and
                 soundeth
                 acutely
                 :
                 
                   Parhypate
                   ,
                   la
                
                 ,
                 and
                 doth
                 lullaby
                 :
                 
                   Hypermese
                   ,
                   sol
                
                 ,
                 and
                 doth
                 sound
                 sweetly
                 :
                 
                   Mese
                   ,
                   fa
                
                 ,
                 and
                 doth
                 sound
                 temperately
                 :
                 
                   Paramese
                   ,
                   mi
                
                 ,
                 and
                 doth
                 delight
                 pleasantly
                 :
                 
                   Paranete
                   ,
                   re
                
                 ,
                 and
                 doth
                 grate
                 tremulously
                 :
                 
                   Nete
                   ,
                   ut
                
                 ,
                 and
                 doth
                 ,
                 as
                 it
                 were
                 low
                 hoarfly
                 .
                 Furthermore
                 the
                 Ancients
                 did
                 attribute
                 the
                 seven
                 Planets
                 to
                 so
                 many
                 Chords
                 of
                 the
                 Lyre
                 ,
                 in
                 this
                 Order
                 .
                 To
                 
                   Saturn
                   ,
                   Hypate
                
                 :
                 to
                 
                   Jupiter
                   ,
                   Parhypate
                
                 :
                 to
                 
                   Mars
                   ,
                   Hypermese
                
                 :
                 to
                 
                   Sol
                   ,
                   Mese
                
                 :
                 to
                 
                   Venus
                   ,
                   Paramese
                
                 :
                 to
                 
                   Mercury
                   ,
                   Paranete
                
                 :
                 and
                 to
                 
                   Luna
                   ,
                   Nete
                
                 .
                 In
                 which
                 Comparation
                 the
                 acutenesse
                 and
                 gravity
                 of
                 the
                 Chords
                 and
                 Planets
                 do
                 respond
                 exactly
                 .
                 Although
                 others
                 invert
                 
                 the
                 order
                 ,
                 and
                 attribute
                 to
                 
                   Saturn
                   Nete
                
                 ,
                 and
                 to
                 
                   Luna
                   Hypate
                
                 .
                 Which
                 Comparation
                 although
                 it
                 may
                 consist
                 :
                 Yet
                 notwithstanding
                 the
                 first
                 is
                 more
                 allowed
                 :
                 because
                 Saturn
                 doth
                 proceed
                 in
                 a
                 mundane
                 motion
                 most
                 quickly
                 ,
                 Luna
                 most
                 slowly
                 .
                 Look
                 Cicero
                 in
                 his
                 Dream
                 .
                 From
                 the
                 Chords
                 to
                 the
                 Notes
                 we
                 transfer
                 this
                 Comparation
                 ,
                 and
                 ascribe
                 to
                 
                   Luna
                   ,
                   vt
                
                 ;
                 to
                 
                   Mercury
                   ,
                   re
                
                 ;
                 to
                 
                   Venus
                   ,
                   mi
                
                 ;
                 to
                 
                   sol
                   ,
                   fa
                
                 ;
                 to
                 
                   Jupiter
                   ,
                   la
                
                 ;
                 to
                 
                   Saturn
                   ,
                   bi
                
                 .
                 For
                 surely
                 as
                 the
                 Planet's
                 do
                 run
                 round
                 the
                 Week
                 ,
                 or
                 the
                 Septenary
                 Circle
                 of
                 dayes
                 in
                 their
                 Term
                 or
                 gliding
                 Course
                 ,
                 and
                 each
                 of
                 them
                 by
                 a
                 certain
                 diurnal
                 vicissitude
                 of
                 Government
                 do's
                 obtain
                 the
                 primacy
                 :
                 So
                 these
                 seven
                 Notes
                 do
                 complete
                 the
                 universal
                 harmonical
                 Lection
                 ,
                 divided
                 by
                 Musicians
                 into
                 seven
                 Types
                 .
                 These
                 Types
                 are
                 certain
                 and
                 appointed
                 Progressions
                 of
                 Notes
                 ,
                 distinguished
                 by
                 iudicial
                 Letters
                 .
                 4.
                 
                 These
                 seven
                 Voices
                 do
                 render
                 all
                 Musick
                 very
                 facile
                 ,
                 aswell
                 in
                 the
                 Theory
                 as
                 in
                 the
                 Practise
                 ,
                 thus
                 .
                 All
                 Musick
                 is
                 accomplished
                 by
                 Voices
                 .
                 The
                 Voices
                 being
                 known
                 ,
                 Notes
                 are
                 adhibited
                 :
                 To
                 the
                 Notes
                 Characters
                 of
                 Letters
                 ;
                 as
                 appeareth
                 by
                 this
                 Diagram
                 .
              
               
                 
                   
                     In
                     a
                     Flat
                     Song
                     .
                  
                   
                     
                       Between
                    
                     
                       A
                    
                     
                       and
                    
                     
                       B
                    
                     
                       also
                    
                     
                       mi
                    
                     
                       and
                    
                     
                       fa
                    
                     
                       Hemiton●
                    
                  
                   
                     
                       B
                    
                     
                       C
                    
                     
                       fa
                    
                     
                       sol
                    
                     
                       Tone
                    
                  
                   
                     
                       C
                    
                     
                       D
                    
                     
                       sol
                    
                     
                       la
                    
                     
                       Tone
                    
                  
                   
                     
                       D
                    
                     
                       E
                    
                     
                       la
                    
                     
                       bi
                    
                     
                       Tone
                    
                  
                   
                     
                       E
                    
                     
                       F
                    
                     
                       bi
                    
                     
                       vt
                    
                     
                       Hemitone
                    
                  
                   
                     
                       F
                    
                     
                       G
                    
                     
                       vt
                    
                     
                       re
                    
                     
                       Tone
                    
                  
                
              
               
               
                 
                   
                     In
                     a
                     sharp
                     Song
                     .
                  
                   
                     
                       Between
                    
                     
                       A
                    
                     
                       and
                    
                     
                       B
                    
                     
                       also
                    
                     
                       la
                    
                     
                       and
                    
                     
                       bi
                    
                     
                       Tone
                    
                  
                   
                     
                       B
                    
                     
                       C
                    
                     
                       bi
                    
                     
                       vt
                    
                     
                       Hemitone
                    
                  
                   
                     
                       C
                    
                     
                       D
                    
                     
                       vt
                    
                     
                       re
                    
                     
                       Tone
                    
                  
                   
                     
                       D
                    
                     
                       E
                    
                     
                       re
                    
                     
                       mi
                    
                     
                       Tone
                    
                  
                   
                     
                       E
                    
                     
                       F
                    
                     
                       mi
                    
                     
                       fa
                    
                     
                       Hemitone
                    
                  
                   
                     
                       F
                    
                     
                       G
                    
                     
                       fa
                    
                     
                       sol
                    
                     
                       Tone
                    
                  
                
                 Therefore
                 in
                 a
                 Flat
                 Song
                 ,
                 A
                 hath
                 mi
                 conjoyned
                 with
                 it
                 ,
                 
                   B
                   fa
                   ,
                   C
                   sol
                   ,
                   D
                   la
                   ,
                   E
                   bi
                   ,
                   F
                   vt
                   ,
                   G
                   re
                   .
                
                 In
                 a
                 sharp
                 Song
                 ,
                 A
                 hath
                 la
                 ascribed
                 to
                 it
                 ,
                 
                   B
                   bi
                   ,
                   C
                   vt
                   ,
                   D
                   re
                   ,
                   E
                   mi
                   ,
                   F
                   fa
                   ,
                   G
                   sol
                   .
                
                 Which
                 difference
                 the
                 variated
                 Disposition
                 of
                 the
                 Hemitones
                 hath
                 begotten
                 .
                 Moreover
                 of
                 these
                 Letters
                 only
                 four
                 are
                 expressed
                 ,
                 
                   B
                   ,
                   C
                   ,
                   F
                   ,
                   G.
                
                 Nor
                 yet
                 those
                 together
                 or
                 conjoynedly
                 ,
                 but
                 one
                 or
                 two
                 in
                 the
                 beginning
                 of
                 Lines
                 .
                 The
                 other
                 Letters
                 not
                 noted
                 ,
                 you
                 may
                 know
                 by
                 these
                 four
                 .
                 If
                 you
                 ascend
                 from
                 the
                 
                   Index
                   Letter
                
                 ,
                 number
                 the
                 first
                 seven
                 according
                 to
                 the
                 Order
                 of
                 the
                 Alphabet
                 ,
                 but
                 if
                 you
                 go
                 further
                 ,
                 then
                 iterate
                 the
                 same
                 :
                 but
                 if
                 you
                 descend
                 ,
                 proceed
                 by
                 a
                 retrograde
                 Order
                 ,
                 from
                 the
                 Line
                 to
                 the
                 Intervall
                 ,
                 and
                 from
                 the
                 Intervall
                 to
                 the
                 Line
                 .
                 Then
                 you
                 may
                 rightly
                 find
                 out
                 the
                 Letters
                 ;
                 by
                 the
                 Letters
                 ,
                 the
                 Notes
                 ;
                 by
                 the
                 Notes
                 ,
                 the
                 Voices
                 ;
                 which
                 is
                 the
                 Summe
                 of
                 Musick
                 .
                 Therefore
                 see
                 that
                 you
                 be
                 most
                 exactly
                 skilled
                 in
                 the
                 ascending
                 and
                 descending
                 Order
                 of
                 the
                 Notes
                 :
                 and
                 that
                 the
                 Tones
                 and
                 Semitones
                 being
                 observed
                 ,
                 you
                 may
                 rise
                 and
                 fall
                 with
                 your
                 Voice
                 .
                 After
                 that
                 ,
                 a
                 Song
                 being
                 proposed
                 ,
                 you
                 
                 may
                 pass
                 from
                 the
                 Sign
                 and
                 Letter
                 noted
                 ,
                 to
                 the
                 Note
                 answering
                 it
                 :
                 from
                 hence
                 ,
                 omitting
                 the
                 ●etters
                 ,
                 to
                 the
                 other
                 Notes
                 .
                 And
                 this
                 tr●el●
                 is
                 easie
                 in
                 a
                 flat
                 Song
                 ,
                 when
                 B.
                 is
                 marked
                 in
                 the
                 begining
                 of
                 the
                 Lines
                 ,
                 there
                 it
                 sheweth
                 that
                 ●a
                 is
                 ●o
                 be
                 sung
                 .
                 But
                 in
                 a
                 sharp
                 Song
                 the
                 difference
                 is
                 of
                 these
                 three
                 Letters
                 ,
                 
                   C.
                   F.
                   G.
                
                 of
                 which
                 by
                 that
                 you
                 may
                 know
                 Sol
                 ,
                 by
                 that
                 fa
                 ,
                 lastly
                 b●
                 this
                 Sol
                 Ther●fore
                 every
                 where
                 con●ult
                 the
                 Signed
                 Letter
                 ,
                 find
                 out
                 the
                 Note
                 ,
                 and
                 call
                 it
                 by
                 its
                 proper
                 Vo●ce
                 ,
                 and
                 so
                 proceed
                 from
                 thence
                 by
                 ascending
                 and
                 d●scen●ing
                 :
                 but
                 if
                 in
                 Singing
                 a
                 Note
                 do
                 occur
                 ,
                 which
                 hath
                 a
                 peculiar
                 Letter
                 prefixed
                 ,
                 the
                 Tone
                 is
                 to
                 be
                 changed
                 ,
                 and
                 the
                 Note
                 of
                 the
                 Letter
                 sung
                 .
                 Therefore
                 if
                 you
                 have
                 rightly
                 accommodated
                 the
                 seven
                 Notes
                 ,
                 you
                 may
                 mixe
                 any
                 Concent
                 ,
                 or
                 read
                 any
                 Melody
                 that
                 you
                 would
                 ,
                 whether
                 it
                 be
                 the
                 simple
                 Aeolian
                 ,
                 or
                 the
                 various
                 Asian
                 ,
                 or
                 the
                 querulous
                 Lydian
                 ,
                 or
                 the
                 religious
                 Phrygian
                 ,
                 or
                 Warlike
                 Dorian
                 .
                 But
                 you
                 will
                 say
                 that
                 Songs
                 are
                 not
                 concluded
                 in
                 those
                 Seven
                 Voices
                 ,
                 but
                 rise
                 higher
                 .
                 The
                 Answer
                 is
                 ready
                 ;
                 As
                 in
                 numbers
                 when
                 we
                 rise
                 from
                 the
                 Monade
                 to
                 the
                 Denary
                 ,
                 the
                 first
                 is
                 the
                 chief
                 of
                 numbers
                 ,
                 and
                 by
                 iterating
                 and
                 compounding
                 them
                 we
                 proceed
                 
                   in
                   infinitum
                
                 .
                 So
                 in
                 these
                 Voices
                 after
                 every
                 seventh
                 Sound
                 ,
                 it
                 returneth
                 to
                 the
                 first
                 ,
                 but
                 more
                 subtile
                 ;
                 and
                 after
                 every
                 seventh
                 Note
                 the
                 first
                 :
                 and
                 so
                 also
                 afterward
                 the
                 second
                 of
                 Notes
                 doth
                 agree
                 with
                 the
                 ninth
                 ;
                 the
                 third
                 ,
                 with
                 the
                 tenth
                 ;
                 the
                 fourth
                 ,
                 with
                 the
                 eleventh
                 ;
                 the
                 fifth
                 ,
                 with
                 the
                 twelfth
                 ;
                 the
                 sixth
                 ,
                 with
                 the
                 thirteenth
                 ;
                 the
                 seventh
                 ▪
                 with
                 the
                 fourteenth
                 ,
                 &c.
                 
                 Of
                 Sounds
                 there
                 is
                 the
                 same
                 Judgement
                 .
                 From
                 a
                 
                 Musical
                 Instrument
                 ,
                 which
                 by
                 way
                 of
                 Eminency
                 is
                 so
                 called
                 ,
                 you
                 may
                 take
                 the
                 Experience
                 of
                 your
                 Ears
                 .
                 But
                 in
                 these
                 Notes
                 observe
                 a
                 double
                 order
                 of
                 Intension
                 and
                 
                   Rem●ssion
                   .
                   Intension
                
                 (
                 by
                 the
                 
                   Greeks
                   Epitasis
                
                 )
                 is
                 the
                 commotion
                 of
                 the
                 Voice
                 ,
                 from
                 the
                 graver
                 place
                 to
                 an
                 acute
                 :
                 Remission
                 (
                 by
                 the
                 
                   Greeks
                   Anesis
                
                 )
                 from
                 an
                 acuter
                 to
                 a
                 grave
                 .
                 But
                 it
                 is
                 worth
                 the
                 pains
                 ,
                 that
                 here
                 some
                 Director
                 or
                 Ruler
                 of
                 the
                 Voice
                 (
                 as
                 Tertullian
                 speaks
                 )
                 go
                 before
                 and
                 lead
                 .
                 Hitherto
                 Puteanus
                 ,
                 with
                 whom
                 worketh
                 
                   David
                   Mostart
                   in
                   his
                   Introduction
                   of
                   Musick
                   ,
                
                 as
                 indeed
                 he
                 proveth
                 the
                 Septenary
                 of
                 Voices
                 .
                 But
                 he
                 doth
                 substitute
                 other
                 Voices
                 in
                 this
                 manner
                 ,
                 
                   bo
                   ,
                   ce
                   ,
                   di
                   ,
                   ga
                   ,
                   lo
                   ,
                   ma
                   ,
                   ni
                   .
                
                 But
                 so
                 that
                 in
                 C
                 of
                 a
                 sharp
                 Song
                 bo
                 is
                 sung
                 .
                 Also
                 in
                 F.
                 of
                 a
                 flat
                 ,
                 
                   bo
                   .
                   e.
                   gr
                
                 .
                 
                 
              
               
                 But
                 let
                 Mostart
                 himself
                 be
                 heard
                 .
                 Who
                 saith
                 thus
                 ,
                 
                   It
                   is
                   worth
                   our
                   labour
                   seriously
                   to
                   invent
                   such
                   Musical
                   Voices
                   as
                   exhibite
                   unto
                   us
                   a
                   perfect
                   Octave
                   ,
                   
                   so
                   that
                   it
                   be
                   the
                   Consequence
                   of
                   eight
                   Tones
                   or
                   Notes
                   :
                   by
                   which
                   Connexion
                   and
                   Series
                   the
                   perfection
                   of
                   any
                   Melody
                   may
                   be
                   performed
                   ,
                   without
                   any
                   Mutation
                   :
                   which
                   indeed
                   is
                   the
                   torture
                   of
                   tender
                   wits
                   .
                
                 And
                 the
                 Series
                 is
                 this
                 ,
                 
                   bo
                   ,
                   ce
                   ,
                   di
                   ,
                   ga
                   ,
                   lo
                   ,
                   ma
                   ,
                   ni
                   .
                   bo
                
                 Which
                 Abridgement
                 if
                 it
                 should
                 be
                 admitted
                 ,
                 those
                 old
                 vulgar
                 Keyes
                 should
                 be
                 abolished
                 ,
                 the
                 Letters
                 of
                 those
                 seven
                 Syllables
                 being
                 only
                 retained
                 in
                 every
                 Song
                 ,
                 
                   viz.
                   b.
                   c.
                   d.
                   g.
                   l.
                   m.
                   n.
                   
                
              
               
                 For
                 Example
                 sake
                 .
                 
              
               
                 Therefore
                 Mostart
                 rejecteth
                 the
                 six
                 Voices
                 of
                 the
                 Ancients
                 ;
                 becau●e
                 they
                 complete
                 not
                 an
                 Octave
                 ,
                 and
                 for
                 that
                 Cause
                 require
                 Mutation
                 ,
                 which
                 is
                 the
                 torture
                 of
                 the
                 Ingenious
                 :
                 and
                 also
                 the
                 seven
                 Voices
                 of
                 latter
                 Musicians
                 ,
                 because
                 they
                 do
                 not
                 respond
                 to
                 the
                 seven
                 Letters
                 or
                 Keyes
                 .
                 But
                 because
                 those
                 Voices
                 of
                 the
                 Ancients
                 be
                 much
                 used
                 in
                 Schools
                 ,
                 therefore
                 let
                 us
                 see
                 their
                 use
                 .
                 For
                 1.
                 
                 Some
                 of
                 those
                 Voices
                 are
                 superiour
                 ,
                 by
                 which
                 a
                 Song
                 descendeth
                 ,
                 
                   viz.
                   la
                   ,
                   sol
                   ,
                   fa
                   ,
                
                 and
                 others
                 are
                 inferiour
                 ,
                 by
                 which
                 it
                 ascendeth
                 ,
                 as
                 
                   ut
                   ,
                   re
                   ,
                   mi.
                
                 2.
                 
                 All
                 those
                 Voices
                 are
                 equally
                 distant
                 one
                 from
                 another
                 by
                 a
                 Tone
                 ,
                 besides
                 mi
                 and
                 fa
                 which
                 are
                 distant
                 by
                 a
                 Semitone
                 .
                 3.
                 
                 Of
                 these
                 
                 
                   Voices
                   ,
                   vt
                
                 and
                 fa
                 sound
                 flatly
                 ;
                 mi
                 and
                 la
                 sharply
                 ;
                 the
                 rest
                 ,
                 meanly
                 .
                 But
                 concerning
                 this
                 thing
                 others
                 speaks
                 thus
                 ,
                 vt
                 and
                 sol
                 denote
                 Sweetnesse
                 ,
                 re
                 and
                 la
                 gravity
                 ,
                 mi
                 Lamentation
                 ,
                 fa
                 threatnings
                 .
                 Lastly
                 ,
                 others
                 consider
                 these
                 Voices
                 thus
                 .
                 Vt
                 and
                 fa
                 are
                 flat
                 Voices
                 by
                 
                   b
                   moll
                
                 ,
                 because
                 they
                 emit
                 a
                 flat
                 and
                 effeminate
                 Sound
                 :
                 re
                 and
                 la
                 natural
                 ,
                 because
                 they
                 afford
                 a
                 natural
                 and
                 middle
                 Sound
                 :
                 mi
                 and
                 
                   la
                   b
                
                 durales
                 ,
                 because
                 they
                 make
                 a
                 sharp
                 and
                 manlike
                 Sound
                 .
                 According
                 to
                 these
                 Verses
                 ;
                 
                   
                     Vt
                     cum
                     fa
                     mollis
                     vox
                     est
                     ;
                     quia
                     Cantica
                     mollit
                     :
                  
                   
                     Mi
                     cum
                     la
                     dura
                     est
                     ,
                     Nam
                     duras
                     efficit
                     odas
                     .
                  
                   
                     Sol
                     naturalis
                     (
                     quoniam
                     neutras
                     facit
                     )
                     &
                     re
                     .
                  
                
              
               
                 4.
                 
                 
                   Certain
                   Voices
                   do
                   answer
                   all
                   Keyes
                   .
                
                 Thus
                 
                   
                     
                       A
                    
                     
                       la
                    
                     
                       mi
                    
                     
                       re
                    
                  
                   
                     
                       B
                    
                     
                       fa
                    
                     
                       mi
                    
                     
                        
                    
                  
                   
                     
                       C
                    
                     
                       sol
                    
                     
                       fa
                    
                     
                       vt
                    
                  
                   
                     
                       D
                    
                     
                       la
                    
                     
                       sol
                    
                     
                       re
                    
                  
                   
                     
                       E
                    
                     
                       la
                    
                     
                       mi
                    
                     
                        
                    
                  
                   
                     
                       F
                    
                     
                       fa
                    
                     
                       vt
                    
                     
                        
                    
                  
                   
                     
                       G
                    
                     
                       sol
                    
                     
                       re
                    
                     
                       vt
                    
                  
                
              
               
                 5.
                 
                 These
                 Voices
                 are
                 circumscribed
                 in
                 certain
                 parallel
                 Lines
                 ,
                 so
                 that
                 in
                 a
                 Song
                 we
                 may
                 ascend
                 and
                 descend
                 ;
                 and
                 that
                 in
                 a
                 progression
                 either
                 continued
                 ,
                 or
                 discontinued
                 .
                 Continued
                 Progression
                 is
                 that
                 which
                 observeth
                 the
                 natural
                 Order
                 of
                 Voices
                 ,
                 and
                 is
                 called
                 a
                 natural
                 Song
                 ;
                 As
                 ,
                 
                 
              
               
                 Discontinued
                 Progression
                 is
                 the
                 Mutation
                 of
                 a
                 Voice
                 ,
                 which
                 is
                 considered
                 either
                 in
                 the
                 minor
                 or
                 greater
                 
                   System
                   .
                   Mutation
                
                 in
                 the
                 lesser
                 System
                 ,
                 is
                 made
                 for
                 the
                 Paucity
                 of
                 Voices
                 :
                 and
                 it
                 is
                 either
                 Vocal
                 or
                 mental
                 .
                 That
                 is
                 called
                 explicite
                 ,
                 this
                 implicite
                 .
                 And
                 both
                 is
                 diverse
                 in
                 a
                 flat
                 Song
                 ,
                 and
                 in
                 a
                 sharp
                 .
                 In
                 a
                 flat
                 Song
                 Mutation
                 is
                 made
                 in
                 
                   d.
                   a.
                   g.
                
                 whose
                 memorial
                 Note
                 is
                 dag
                 .
                 In
                 a
                 sha●p
                 Song
                 Mutation
                 is
                 made
                 in
                 
                   d.
                   a.
                   e.
                
                 Whose
                 Voice
                 of
                 remembrance
                 is
                 dea
                 .
                 In
                 the
                 greater
                 System
                 Mutation
                 is
                 made
                 according
                 to
                 the
                 
                   triple
                   Scale
                
                 .
                 The
                 first
                 is
                 
                   b
                   dural
                   Scale
                
                 ;
                 which
                 is
                 the
                 Progression
                 of
                 Musical
                 Voices
                 ,
                 rising
                 from
                 a.
                 into
                 b.
                 sharply
                 ,
                 that
                 is
                 ,
                 by
                 the
                 
                   Voice
                   mi.
                
                 The
                 second
                 is
                 
                   b
                   moll
                
                 ;
                 which
                 is
                 the
                 progression
                 of
                 Musical
                 Voices
                 ,
                 rising
                 from
                 a.
                 into
                 
                   b
                   moll
                
                 ,
                 that
                 is
                 the
                 
                   Voice
                   fa.
                
                 The
                 third
                 is
                 the
                 fict
                 Scale
                 ,
                 which
                 in
                 every
                 Key
                 admitteth
                 a
                 strange
                 Voice
                 .
                 And
                 hence
                 it
                 is
                 called
                 
                   fict
                   Musick
                
                 :
                 because
                 modulated
                 by
                 feigned
                 Voices
                 .
                 
                   i.
                   e.
                
                 by
                 such
                 as
                 are
                 sung
                 in
                 any
                 Key
                 ,
                 in
                 which
                 essentially
                 they
                 are
                 not
                 contained
                 .
                 As
                 vt
                 in
                 
                   e.
                   re
                
                 .
                 in
                 f.
                 and
                 so
                 on
                 .
              
               
               
                 This
                 is
                 the
                 Type
                 of
                 the
                 
                   Triple
                   Scale
                
                 .
                 
                   
                     
                       5.
                       Tetrachord
                    
                     
                       ee
                    
                     
                       b
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       la
                    
                  
                   
                     
                       dd
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       la
                    
                     
                       sol
                    
                  
                   
                     
                       cc
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       sol
                    
                     
                       fa
                    
                  
                   
                     
                       bb
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       fa
                    
                     
                       mi
                    
                  
                   
                     
                       4.
                       
                       
                         Tetrachord
                         of
                         excellents
                      
                       .
                    
                     
                       aa
                    
                     
                       b
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       la
                    
                     
                       mi
                    
                     
                       re
                    
                  
                   
                     
                       g
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       sol
                    
                     
                       re
                    
                     
                       vt
                    
                  
                   
                     
                       f
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       fa
                    
                     
                       vt
                    
                     
                        
                    
                  
                   
                     
                       e
                    
                     
                       b
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       la
                    
                     
                       mi
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       3.
                       
                       
                         Tetrachord
                         of
                         Superiors
                      
                       .
                    
                     
                       d
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       la
                    
                     
                       sol
                    
                     
                       re
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       c
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                       sol
                    
                     
                       fa
                    
                     
                       vt
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       b
                    
                     
                       b
                    
                     
                        
                    
                     
                        
                    
                     
                       fa
                    
                     
                       mi
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       a
                    
                     
                        
                    
                     
                        
                    
                     
                       la
                    
                     
                       mi
                    
                     
                       re
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       2.
                       
                       
                         Tetrachord
                         of
                         Finals
                      
                       .
                    
                     
                       G
                    
                     
                        
                    
                     
                        
                    
                     
                       sol
                    
                     
                       re
                    
                     
                       vt
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       F
                    
                     
                        
                    
                     
                        
                    
                     
                       fa
                    
                     
                       vt
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       E
                    
                     
                       b
                    
                     
                       la
                    
                     
                       mi
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       D
                    
                     
                        
                    
                     
                       sol
                    
                     
                       re
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       1.
                       
                       
                         Tetrachord
                         of
                         grave
                         Sounds
                      
                       .
                    
                     
                       C
                    
                     
                        
                    
                     
                       fa
                    
                     
                       vt
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       B
                    
                     
                       b
                    
                     
                       mi
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       A
                    
                     
                       b
                    
                     
                       re
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                   
                     
                       Γ
                    
                     
                        
                    
                     
                       vt
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                     
                        
                    
                  
                
              
               
               
               
                 In
                 this
                 Table
                 musical
                 Sounds
                 are
                 so
                 contained
                 ,
                 that
                 first
                 there
                 is
                 the
                 
                   Simple
                   Vnison
                
                 .
                 2.
                 
                 The
                 
                   Tonus
                   minor
                
                 .
                 3.
                 
                 The
                 
                   Tonus
                   major
                
                 .
                 4.
                 
                 The
                 
                   greater
                   Semitone
                
                 .
                 5.
                 
                 The
                 Semiditone
                 .
                 6.
                 
                 The
                 Ditone
                 .
                 7.
                 
                 The
                 Fourth
                 .
                 8.
                 
                 The
                 Fifth
                 .
                 9.
                 
                 The
                 
                   lesser
                   Sixth
                
                 .
                 10.
                 
                 The
                 
                   greater
                   Sixth
                
                 .
                 11.
                 
                 The
                 
                   lesser
                   Seventh
                
                 .
                 12.
                 
                 The
                 
                   greater
                   Seventh
                
                 .
                 13.
                 
                 The
                 Octave
                 .
                 And
                 this
                 is
                 the
                 Cyclus
                 or
                 Compass
                 of
                 the
                 Diapason
                 .
                 Concerning
                 the
                 Proportions
                 of
                 all
                 these
                 Sounds
                 ,
                 look
                 into
                 the
                 former
                 Chap.
                 thus
                 
                   v.
                   gr
                
                 .
                 To
                 the
                 Octave
                 ascribe
                 1.2
                 .
                 to
                 the
                 Septima
                 8.15
                 .
                 and
                 so
                 of
                 others
                 :
                 So
                 that
                 the
                 lesser
                 number
                 be
                 applied
                 to
                 the
                 upper
                 Note
                 in
                 the
                 Scale
                 .
                 The
                 significates
                 of
                 the
                 Letters
                 .
                 
                   B.
                   L.
                   b.l.bb.
                
                 are
                 a
                 little
                 before
                 called
                 
                   bo
                   .
                   ce.di.ga.lo.ma.ni
                
                 .
              
            
          
        
         
           
             CHAP.
             VI.
             Of
             the
             Musical
             DYAS
             .
          
           
             
               PRECEPTS
               .
            
             
               HItherto
               of
               the
               simple
               part
               of
               an
               harmonical
               Song
               :
               the
               compounded
               part
               thereof
               followeth
               ;
               whose
               tractation
               is
               called
               practical
               or
               Melopoetical
               Musick
               ,
               if
               the
               form
               of
               the
               Song
               be
               added
               .
            
             
               The
               compounded
               part
               of
               an
               harmonical
               
               Song
               ,
               is
               that
               which
               ariseth
               from
               musical
               sounds
               or
               Monads
               conjoyned
               according
               to
               three
               Dimensions
               .
            
             
               And
               it
               is
               either
               primary
               or
               secondary
               .
            
             
               The
               primary
               is
               called
               harmony
               and
               consonancy
               ,
               which
               doth
               arise
               from
               grave
               and
               acute
               sounds
               united
               by
               such
               a
               proportion
               ,
               that
               it
               may
               delight
               the
               hearing
               .
            
             
               The
               secondary
               is
               dissonancy
               or
               Anarmosty
               ,
               which
               ariseth
               from
               such
               a
               proportion
               of
               grave
               and
               acute
               Sounds
               ,
               that
               it
               offendeth
               the
               hearing
               .
            
             
               And
               this
               double
               part
               is
               either
               a
               musical
               Dyas
               ,
               or
               Tryas
               ,
               of
               which
               the
               one
               is
               perfect
               ,
               and
               the
               other
               imperfect
               .
            
             
               A
               musical
               Dyas
               ,
               is
               that
               which
               ariseth
               from
               two
               sounds
               :
               consonant
               and
               harmonical
               from
               Consonants
               ,
               and
               dissonant
               from
               Dissonants
               .
            
             
               And
               it
               is
               more
               simple
               ,
               or
               more
               compounded
               .
               That
               is
               called
               radical
               ,
               this
               radicated
               .
            
             
               The
               simple
               Consonant
               Dyads
               ,
               are
               seven
               ,
               viz.
               An
               
                 Octave
                 ,
                 Fifth
                 ,
                 Fourth
                 ,
                 Ditone
                 ,
                 Semiditone
                 ,
                 greater
                 Sixth
                 ,
              
               and
               
                 lesser
                 Sixth
              
               :
               the
               dissonant
               Dyads
               are
               the
               other
               simple
               Intervalls
               ,
               as
               the
               
                 Tone
                 major
              
               and
               minor
               ,
               the
               
                 Semitone
                 greater
              
               and
               lesser
               ,
               the
               
                 Seventh
                 
                 greater
              
               and
               lesser
               ;
               and
               lastly
               ,
               all
               sim●le
               Intervalls
               not
               Just
               ,
               as
               the
               
                 Semioctave
                 ,
                 Semififth
                 ,
                 &c.
              
               
            
             
               The
               Dyas
               more
               compounded
               is
               that
               which
               ariseth
               from
               the
               simple
               Dyas
               :
               and
               that
               again
               is
               either
               consonant
               or
               dissonant
               :
               and
               both
               compounded
               either
               once
               ,
               twice
               ,
               thrice
               ,
               or
               so
               forward
               .
               In
               Dyads
               once
               compounded
               the
               double
               Octave
               ,
               also
               the
               Octave
               with
               a
               Fifth
               ,
               the
               Octave
               with
               a
               Fourth
               ,
               and
               Octave
               with
               a
               Ditone
               do
               consonate
               :
               but
               the
               Octave
               with
               both
               tones
               ,
               with
               a
               Semitone
               ,
               and
               with
               an
               Intervall
               not
               just
               doth
               dissonate
               .
               In
               Dyads
               twice
               compounded
               the
               
                 triple
                 Octave
              
               ,
               and
               double
               Octave
               ,
               with
               a
               Fifth
               do
               consonate
               :
               but
               the
               double
               Octave
               with
               both
               tones
               ,
               with
               the
               Semitone
               ,
               and
               so
               forwards
               ;
               doth
               dissonate
               .
            
          
           
             
               RULES
               .
            
             
               
                 1.
                 
                 There
                 are
                 two
                 Arbiters
                 of
                 congruous
                 and
                 incongruous
                 Proportions
                 .
              
               
                 The
                 first
                 is
                 superior
                 ,
                 which
                 doth
                 judge
                 of
                 Proportions
                 
                 
                   à
                   priori
                
                 ,
                 to
                 wit
                 ,
                 Logos
                 :
                 the
                 other
                 is
                 inferior
                 ,
                 which
                 doth
                 exactly
                 judge
                 of
                 Sounds
                 
                   à
                   posteriori
                
                 ,
                 to
                 wit
                 ,
                 the
                 Hearing
                 .
                 And
                 there
                 is
                 a
                 necessity
                 that
                 both
                 these
                 Judges
                 should
                 concur
                 ,
                 as
                 Ptolomy
                 doth
                 rightly
                 teach
                 :
                 but
                 falsly
                 Pythagoras
                 ,
                 who
                 doth
                 think
                 that
                 nothing
                 here
                 is
                 to
                 be
                 attributed
                 to
                 the
                 hearing
                 ;
                 and
                 falsly
                 Aristoxenus
                 ,
                 that
                 supposeth
                 nothing
                 here
                 is
                 to
                 be
                 attributed
                 to
                 Ration
                 .
                 But
                 the
                 nature
                 of
                 Proportions
                 is
                 demonstrated
                 by
                 the
                 Monochord
                 :
                 for
                 that
                 in
                 it
                 all
                 Musical
                 Diastems
                 are
                 contained
                 .
              
            
             
               
                 2.
                 
                 The
                 Simple
                 Vnison
                 is
                 the
                 Radix
                 of
                 all
                 Consonancy
                 and
                 Dissonancy
                 .
              
               
                 Vulgarly
                 they
                 imagine
                 that
                 the
                 Unison
                 doth
                 both
                 consonate
                 and
                 dissonate
                 .
                 But
                 they
                 erre
                 ;
                 for
                 the
                 Unison
                 doth
                 equisonate
                 only
                 ,
                 because
                 it
                 hath
                 the
                 proportion
                 of
                 Equality
                 ,
                 and
                 is
                 the
                 principal
                 of
                 every
                 Interval
                 .
                 
                   e.
                   gr
                
                 .
                 
              
               
                 Rightly
                 therefore
                 the
                 simple
                 Vnison
                 is
                 made
                 the
                 Radix
                 of
                 Consonancy
                 and
                 Dissonancy
                 .
              
            
             
               
               
                 3.
                 
                 The
                 Simple
                 Consonant
                 Dyads
                 are
                 in
                 number
                 Seven
                 ,
                 and
                 may
                 be
                 called
                 Simple
                 Concordancies
                 .
              
               
                 Vulgarly
                 they
                 thus
                 rehear●e
                 the
                 Simple
                 Concordancies
                 .
                 There
                 are
                 twelve
                 Concordancies
                 ,
                 the
                 1.3.5.6.8.10.12.13.15.17.19.20
                 .
                 And
                 these
                 are
                 divided
                 two
                 waves
                 .
                 First
                 ,
                 there
                 are
                 Simple
                 ,
                 replicated
                 or
                 triplicated
                 .
                 The
                 
                   Simple
                   Concordances
                
                 are
                 the
                 1.3.5.6
                 .
                 which
                 are
                 also
                 called
                 primary
                 .
                 The
                 Replicated
                 are
                 such
                 as
                 are
                 equisonant
                 to
                 the
                 former
                 ,
                 conceived
                 by
                 a
                 double
                 Dimension
                 ,
                 as
                 the
                 8.10.12.13
                 .
                 Otherwise
                 called
                 Secondary
                 .
                 For
                 in
                 Sound
                 the
                 Octave
                 doth
                 associate
                 with
                 the
                 Vnison
                 ,
                 the
                 tenth
                 with
                 the
                 third
                 ,
                 the
                 twelfth
                 with
                 the
                 fifth
                 ,
                 and
                 the
                 thirteenth
                 with
                 the
                 sixth
                 .
                 The
                 
                   triplicated
                   Consonants
                
                 are
                 the
                 15.17.19.20
                 .
                 otherwi●e
                 called
                 tertiaries
                 .
                 Of
                 these
                 the
                 15.
                 is
                 coequated
                 in
                 Sound
                 with
                 the
                 Octave
                 and
                 the
                 first
                 :
                 the
                 seventeenth
                 with
                 the
                 tenth
                 and
                 third
                 ,
                 and
                 the
                 nineteenth
                 with
                 the
                 twelfth
                 and
                 fifth
                 ,
                 and
                 the
                 twentieth
                 doth
                 equisonate
                 with
                 the
                 thirteenth
                 and
                 sixth
                 ,
                 According
                 to
                 this
                 Type
                 .
              
               
                 
                   
                     
                       1.
                       
                    
                     
                       3.
                       
                    
                     
                       5.
                       
                    
                     
                       6.
                       
                    
                  
                   
                     
                       8.
                       
                    
                     
                       10.
                       
                    
                     
                       12.
                       
                    
                     
                       13.
                       
                    
                  
                   
                     
                       15.
                       
                    
                     
                       17.
                       
                    
                     
                       19.
                       
                    
                     
                       20.
                       
                    
                  
                
              
               
                 Lastly
                 ,
                 There
                 are
                 Concordances
                 perfect
                 ,
                 or
                 imperfect
                 .
                 The
                 Perfect
                 are
                 those
                 which
                 can
                 stand
                 by
                 themselves
                 ,
                 that
                 is
                 ,
                 begin
                 and
                 terminate
                 a
                 Song
                 :
                 as
                 
                 the
                 1.5.8
                 .
                 The
                 imperfect
                 are
                 those
                 which
                 may
                 concur
                 in
                 Counterpoint
                 ,
                 as
                 the
                 3.6.10
                 .
                 The
                 Discordances
                 are
                 nine
                 ,
                 viz.
                 the
                 2.4.7.9.11.14.16.18.21
                 .
                 Others
                 also
                 do
                 number
                 the
                 
                   perfect
                   Concordances
                
                 thus
                 ,
                 the
                 1.3.5.8
                 .
                 because
                 they
                 respond
                 to
                 the
                 
                   Pythogorical
                   Quaternary
                
                 .
                 But
                 it
                 behoveth
                 them
                 to
                 play
                 the
                 Philosophers
                 of
                 Concordances
                 more
                 acurately
                 .
                 There
                 are
                 seven
                 Concordances
                 or
                 simple
                 Consonances
                 .
                 Of
                 which
                 the
                 Octave
                 is
                 the
                 first
                 ,
                 which
                 is
                 of
                 a
                 dupla
                 proportion
                 between
                 2.
                 and
                 1.
                 
                 In
                 his
                 Terms
                 the
                 most
                 simple
                 Conveniency
                 is
                 diverse
                 ,
                 as
                 is
                 between
                 the
                 whole
                 and
                 the
                 half
                 .
                 The
                 Fifth
                 doth
                 obtain
                 the
                 second
                 place
                 ;
                 then
                 followeth
                 the
                 fourth
                 ;
                 then
                 the
                 Ditone
                 or
                 third
                 in
                 a
                 sharp
                 Song
                 ;
                 then
                 the
                 Semiditonus
                 ,
                 which
                 is
                 the
                 third
                 in
                 a
                 flat
                 Song
                 ;
                 in
                 the
                 last
                 place
                 save
                 one
                 is
                 the
                 
                   Sexta
                   major
                
                 in
                 a
                 sharp
                 Song
                 ;
                 and
                 in
                 the
                 last
                 place
                 ,
                 the
                 
                   Sexta
                   minor
                
                 in
                 a
                 flat
                 Song
                 .
                 And
                 this
                 is
                 the
                 Order
                 of
                 Perfection
                 .
                 For
                 although
                 every
                 Simple
                 Consonancy
                 is
                 perfect
                 in
                 his
                 degree
                 ;
                 yet
                 notwithstanding
                 in
                 respect
                 of
                 another
                 ,
                 it
                 is
                 either
                 more
                 perfect
                 or
                 imperfect
                 ;
                 yet
                 so
                 as
                 the
                 first
                 and
                 most
                 perfect
                 is
                 the
                 Octave
                 ,
                 that
                 compounded
                 Unison
                 ;
                 the
                 most
                 imperf●ct
                 and
                 last
                 ,
                 is
                 the
                 lesser
                 Sixth
                 ;
                 the
                 intermediate
                 are
                 measurably
                 as
                 the
                 most
                 perfect
                 or
                 most
                 imperfect
                 are
                 nearer
                 .
                 Here
                 Musicians
                 do
                 wonder
                 ,
                 why
                 the
                 Septinary
                 begetteth
                 no
                 Consonancy
                 ,
                 when
                 as
                 it
                 numbereth
                 all
                 simple
                 Consonances
                 .
                 And
                 this
                 is
                 the
                 Scheme
                 of
                 those
                 seven
                 simple
                 Consonances
                 .
                 
              
               
               
                 Of
                 these
                 the
                 first
                 three
                 are
                 perfect
                 ,
                 the
                 four
                 latter
                 are
                 imperfect
                 .
                 And
                 indeed
                 principally
                 the
                 Octave
                 ,
                 in
                 respect
                 of
                 his
                 excellent
                 perfection
                 doth
                 equisonate
                 and
                 unisonate
                 after
                 the
                 Vnison
                 an●●imple
                 Equison
                 .
                 After
                 it
                 the
                 Fifth
                 for
                 its
                 perfection
                 doth
                 consonate
                 by
                 his
                 most
                 grateful
                 ,
                 firm
                 ,
                 and
                 masculine
                 Sound
                 .
                 After
                 it
                 the
                 Ditone
                 or
                 greater
                 Third
                 by
                 his
                 sweet
                 Imperfection
                 doth
                 concent
                 but
                 more
                 cheerfully
                 ,
                 strongly
                 ,
                 and
                 lively
                 .
                 Then
                 the
                 Semiditone
                 or
                 lesser
                 Third
                 also
                 by
                 his
                 sweet
                 Imperfection
                 doth
                 concent
                 more
                 softly
                 ,
                 remisly
                 ,
                 and
                 heavily
                 .
                 Then
                 the
                 greater
                 Sixth
                 by
                 his
                 Imperfection
                 doth
                 circumsonate
                 as
                 it
                 were
                 more
                 high
                 and
                 pleasantly
                 .
                 Last
                 of
                 all
                 the
                 lesser
                 Sixth
                 doth
                 also
                 so
                 circumsonate
                 but
                 more
                 slowly
                 ,
                 flatly
                 ,
                 and
                 weakly
                 .
                 These
                 four
                 latter
                 Consonances
                 were
                 not
                 used
                 by
                 the
                 Ancients
                 in
                 their
                 
                   Diatone
                   Scale
                
                 :
                 but
                 now
                 they
                 are
                 used
                 most
                 chiefly
                 ,
                 naturally
                 ,
                 and
                 artificially
                 in
                 the
                 
                   Syntonian
                   Scale
                
                 .
                 And
                 this
                 is
                 the
                 Order
                 of
                 Perfection
                 in
                 the
                 seven
                 simple
                 Consonances
                 .
                 The
                 Order
                 of
                 the
                 Crassitude
                 of
                 Sound
                 ,
                 or
                 of
                 Intension
                 and
                 Remission
                 is
                 this
                 ,
                 which
                 is
                 firmly
                 contrary
                 to
                 the
                 first
                 .
                 After
                 the
                 simple
                 Unison
                 is
                 the
                 Semiditone
                 ,
                 then
                 the
                 Ditone
                 ,
                 then
                 the
                 
                   Fourth
                   ,
                   Fifth
                   ,
                   Sixth
                   minor
                   ,
                   Sixth
                   major
                   ,
                
                 and
                 Octave
                 .
                 From
                 these
                 it
                 is
                 an
                 easie
                 thing
                 to
                 Judge
                 of
                 
                   Simple
                   Dissonances
                
                 ,
                 to
                 wit
                 ,
                 because
                 they
                 are
                 all
                 Tones
                 placed
                 without
                 the
                 Septinary
                 of
                 Consonances
                 ;
                 as
                 the
                 greater
                 and
                 lesser
                 Tone
                 ;
                 the
                 greater
                 and
                 lesser
                 Semitone
                 ;
                 the
                 greater
                 and
                 lesser
                 Seventh
                 ,
                 and
                 lastly
                 Intervalls
                 not
                 just
                 deficient
                 .
                 For
                 in
                 these
                 are
                 disagreeing
                 Proportions
                 ,
                 whose
                 extreme
                 Sounds
                 do
                 but
                 ill
                 agree
                 ,
                 and
                 therefore
                 if
                 they
                 be
                 put
                 together
                 ,
                 they
                 offend
                 the
                 Ears
                 .
              
            
             
               
               
                 4.
                 
                 Compounded
                 Dyads
                 do
                 imitate
                 the
                 nature
                 of
                 Simple
                 .
              
               
                 This
                 is
                 true
                 both
                 of
                 compounded
                 Concordances
                 and
                 Discordances
                 ,
                 according
                 to
                 that
                 elegant
                 Axiom
                 of
                 
                   Musicians
                   .
                   Of
                   Octaves
                   there
                   is
                   the
                   same
                   and
                   like
                   Judgement
                   .
                
                 And
                 that
                 for
                 the
                 essential
                 Similitude
                 of
                 
                   dupla
                   ,
                   quadrupla
                   ,
                   octupla
                
                 ,
                 and
                 sedecupla
                 Proportion
                 ,
                 as
                 16.8.4.2.1
                 .
                 Also
                 of
                 compounded
                 Dyads
                 the
                 Order
                 of
                 perfection
                 and
                 Crassitude
                 ,
                 is
                 like
                 unto
                 the
                 Order
                 of
                 their
                 simple
                 Dyads
                 .
                 Otherwise
                 although
                 the
                 Composition
                 of
                 perfect
                 Concordances
                 might
                 proceed
                 
                   in
                   infinitum
                
                 :
                 yet
                 notwithstanding
                 because
                 they
                 are
                 not
                 the
                 same
                 Terms
                 of
                 Sound
                 and
                 Hearing
                 (
                 which
                 thing
                 therefore
                 obtaineth
                 in
                 the
                 rest
                 of
                 the
                 Senses
                 )
                 it
                 is
                 necessary
                 that
                 we
                 be
                 mindful
                 of
                 Mediocrity
                 ,
                 lest
                 we
                 create
                 trouble
                 to
                 the
                 Eare
                 ,
                 by
                 any
                 Sound
                 too
                 great
                 or
                 too
                 acute
                 .
              
            
             
               
                 5.
                 
                 It
                 behoveth
                 us
                 alwayes
                 to
                 have
                 in
                 our
                 Eye
                 the
                 Radixes
                 of
                 Simple
                 Dyads
                 .
              
               
                 As
                 it
                 is
                 very
                 compendious
                 ,
                 to
                 observe
                 simple
                 only
                 and
                 radical
                 Dyads
                 both
                 consonant
                 and
                 dissonant
                 ,
                 and
                 then
                 by
                 those
                 to
                 judge
                 of
                 compounded
                 Dyads
                 :
                 so
                 also
                 it
                 is
                 very
                 compendious
                 to
                 consider
                 the
                 Roots
                 of
                 those
                 simple
                 Dyads
                 ,
                 according
                 to
                 this
                 Type
                 .
              
               
               
                 
                   
                     
                       Bo.
                       
                    
                     
                       ni
                       .
                    
                     
                       ma.
                       
                    
                     
                       lo.
                       
                    
                     
                       ga
                       .
                    
                     
                       di
                       .
                    
                     
                       ce
                       .
                    
                  
                   
                     
                       90.
                       
                    
                     
                       96.
                       
                    
                     
                       108.
                       
                    
                     
                       120.
                       
                    
                     
                       135.
                       
                    
                     
                       144.
                       
                    
                     
                       160.
                       
                    
                  
                   
                     
                       1.2.4.8
                       .
                    
                     
                        
                    
                     
                        
                    
                     
                       3.6
                       .
                    
                     
                        
                    
                     
                       5.
                       
                    
                     
                        
                    
                  
                
              
               
                 See
                 before
                 in
                 the
                 
                   Syntonic
                   Table
                
                 .
                 Here
                 ,
                 between
                 the
                 Consonances
                 of
                 the
                 Octave
                 and
                 fourth
                 ,
                 the
                 Radix
                 is
                 the
                 Fifth
                 :
                 of
                 both
                 Sixes
                 ,
                 both
                 Thirds
                 .
                 Therefore
                 the
                 Octave
                 and
                 fourth
                 may
                 be
                 reduced
                 to
                 the
                 Fifth
                 ;
                 and
                 the
                 sixth
                 to
                 the
                 third
                 .
                 The
                 Root
                 of
                 simple
                 Dissonant
                 Dyads
                 is
                 the
                 second
                 ,
                 to
                 which
                 both
                 Sevenths
                 may
                 be
                 reduced
                 .
              
            
          
        
         
           
             CHAP.
             VII
             .
             Of
             the
             Musical
             TRIAS
             .
          
           
             
               PRECEPTS
               .
            
             
               THE
               Musical
               Trias
               is
               that
               which
               doth
               arise
               from
               three
               sounds
               and
               as
               many
               Dyads
               :
               otherwise
               called
               the
               
                 unitrisonous
                 Radix
              
               .
            
             
               And
               it
               is
               either
               consonant
               or
               dissonant
               .
            
             
               The
               consonant
               Trias
               is
               that
               in
               which
               a
               third
               and
               a
               fifth
               doth
               concur
               ,
               yet
               so
               as
               
               that
               it
               ariseth
               from
               two
               thirds
               .
            
             
               The
               dissonant
               Tryas
               is
               that
               which
               ariseth
               from
               seconds
               .
            
          
           
             
               RULES
               .
            
             
               
                 1.
                 
                 The
                 Harmonical
                 Tryas
                 is
                 the
                 Root
                 of
                 all
                 the
                 Harmony
                 that
                 can
                 be
                 invented
                 ,
              
               
                 And
                 may
                 be
                 called
                 the
                 
                   unitrisonous
                   Radix
                
                 :
                 because
                 it
                 doth
                 consist
                 of
                 three
                 Monads
                 or
                 Sounds
                 ,
                 and
                 as
                 many
                 Dyads
                 :
                 all
                 of
                 them
                 in
                 that
                 whole
                 Tryas
                 ,
                 and
                 every
                 one
                 most
                 sweetly
                 concenting
                 one
                 with
                 another
                 ,
                 because
                 they
                 are
                 joyned
                 together
                 in
                 a
                 certain
                 Order
                 by
                 just
                 Proportions
                 .
                 Those
                 Sounds
                 or
                 Monads
                 being
                 three
                 in
                 number
                 ,
                 and
                 as
                 many
                 Dyads
                 ,
                 making
                 this
                 Trias
                 ,
                 are
                 these
                 .
                 First
                 ,
                 the
                 two
                 Extremes
                 are
                 distant
                 one
                 from
                 another
                 by
                 a
                 Diapente
                 ,
                 which
                 is
                 of
                 a
                 Sesquialtera
                 Proportion
                 .
                 Then
                 there
                 is
                 one
                 middle
                 ,
                 which
                 by
                 his
                 softer
                 sweetnesse
                 doth
                 joyn
                 those
                 two
                 Extremes
                 ,
                 concenting
                 together
                 by
                 a
                 perfect
                 and
                 masculine
                 Sound
                 ,
                 and
                 is
                 distant
                 from
                 one
                 of
                 them
                 by
                 a
                 Ditone
                 ,
                 and
                 from
                 the
                 other
                 by
                 a
                 Semiditone
                 .
                 There
                 is
                 the
                 Proportion
                 of
                 a
                 Sesquiquarta
                 ,
                 here
                 of
                 a
                 
                   Sesquiquinta
                   .
                   e.
                   gr
                
                 .
                 
                 
              
               
                 Here
                 4.
                 and
                 5.
                 then
                 4.
                 and
                 6.
                 then
                 lastly
                 5.
                 and
                 6.
                 do
                 conspire
                 .
                 This
                 
                   unitrisonous
                   Radix
                
                 is
                 the
                 Rule
                 and
                 Measure
                 of
                 all
                 Consonances
                 ,
                 and
                 is
                 alwayes
                 in
                 one
                 manner
                 .
                 Yet
                 this
                 only
                 is
                 the
                 difference
                 ,
                 that
                 in
                 a
                 flat
                 Song
                 it
                 is
                 more
                 imperfect
                 and
                 soft
                 ,
                 but
                 in
                 a
                 sharp
                 Song
                 ,
                 more
                 
                   natural
                   ,
                   perfect
                   ,
                   nobler
                
                 ,
                 and
                 sweet
                 .
                 The
                 first
                 hath
                 the
                 Ditone
                 above
                 the
                 Semiditone
                 ,
                 the
                 latter
                 hath
                 the
                 Ditone
                 beneath
                 the
                 Semiditone
                 .
                 Moreover
                 this
                 Radix
                 is
                 either
                 increased
                 or
                 diffused
                 .
                 The
                 increased
                 ,
                 is
                 that
                 which
                 hath
                 the
                 Octave
                 for
                 his
                 Companion
                 ,
                 to
                 excite
                 the
                 more
                 various
                 and
                 fuller
                 Harmony
                 .
                 The
                 diffused
                 is
                 that
                 ,
                 who●e
                 radical
                 parts
                 or
                 voices
                 are
                 not
                 so
                 near
                 unto
                 one
                 another
                 ,
                 because
                 dispersed
                 into
                 various
                 Octaves
                 .
                 For
                 the
                 nearer
                 the
                 Voices
                 are
                 one
                 to
                 another
                 ,
                 the
                 more
                 excellent
                 is
                 the
                 Symphony
                 .
                 The
                 best
                 Disposition
                 of
                 all
                 look
                 above
                 Chap.
                 5.
                 
                 Rule
                 6.
                 where
                 I
                 do
                 write
                 of
                 signed
                 Keyes
                 .
              
            
             
               
                 2.
                 
                 The
                 Musical
                 Trias
                 doth
                 arise
                 both
                 from
                 Arithmetical
                 and
                 Geometrical
                 Proportion
                 .
              
               
                 Proportion
                 is
                 threefold
                 :
                 First
                 arithmetical
                 ,
                 which
                 
                 is
                 ,
                 when
                 the
                 numbers
                 are
                 distant
                 one
                 from
                 another
                 by
                 an
                 equal
                 Difference
                 ,
                 and
                 that
                 either
                 continued
                 ;
                 as
                 1.2.3.4
                 .
                 or
                 dis-joyned
                 ,
                 as
                 3.6.8.11
                 .
                 The●e
                 the
                 Difference
                 is
                 an
                 unity
                 ,
                 here
                 a
                 ternary
                 .
                 Secondly
                 ,
                 Geometrical
                 ;
                 which
                 is
                 ,
                 when
                 there
                 is
                 the
                 same
                 Ration
                 of
                 more
                 Terms
                 compared
                 with
                 one
                 another
                 :
                 and
                 it
                 is
                 either
                 continued
                 ,
                 as
                 4.8.16
                 .
                 or
                 dis-joyned
                 ,
                 as
                 2.4.8.16
                 .
                 Thirdly
                 ,
                 musical
                 or
                 harmonical
                 Proportion
                 ,
                 ariseth
                 from
                 arithmetical
                 and
                 geometrical
                 :
                 and
                 it
                 is
                 no
                 other
                 ,
                 then
                 a
                 Symmetry
                 of
                 Concents
                 ,
                 which
                 is
                 discerned
                 in
                 the
                 most
                 perfect
                 musical
                 Triade
                 ;
                 which
                 Lippius
                 therefore
                 calleth
                 the
                 
                   chiefest
                   ,
                   sweetest
                   ,
                   and
                   plainest
                   Compendium
                   of
                   Melopoetical
                   Musick
                   .
                
                 But
                 let
                 us
                 pursue
                 these
                 things
                 further
                 .
                 Musical
                 or
                 Harmonical
                 Proportion
                 is
                 the
                 Symetry
                 or
                 Equality
                 of
                 Concents
                 which
                 doth
                 arise
                 from
                 Proportion
                 arithmetical
                 and
                 geometrical
                 ;
                 so
                 that
                 three
                 Terms
                 being
                 put
                 ,
                 even
                 as
                 the
                 greatest
                 is
                 to
                 the
                 least
                 ,
                 so
                 is
                 the
                 Differ●nce
                 of
                 the
                 middle
                 ,
                 and
                 the
                 greatest
                 to
                 the
                 Difference
                 of
                 the
                 middle
                 and
                 least
                 .
                 As
                 3.4.6
                 .
                 Here
                 ,
                 as
                 Six
                 are
                 the
                 Duplum
                 to
                 three
                 :
                 so
                 two
                 (
                 which
                 is
                 the
                 Difference
                 between
                 4.
                 and
                 6.
                 )
                 are
                 the
                 Duplum
                 to
                 the
                 Unity
                 ,
                 which
                 is
                 the
                 Difference
                 between
                 3.
                 and
                 4.
                 
                 Such
                 is
                 the
                 proportion
                 in
                 the
                 
                   unitrisonus
                   Radix
                
                 .
                 1.3.5
                 .
                 Also
                 between
                 6.8.12
                 .
                 For
                 three
                 Terms
                 musically
                 proportional
                 are
                 found
                 from
                 three
                 arithmetically
                 proportional
                 ,
                 if
                 the
                 first
                 arithmetically
                 proportional
                 be
                 multiplied
                 into
                 the
                 second
                 and
                 third
                 ,
                 and
                 the
                 second
                 into
                 the
                 third
                 .
                 So
                 from
                 these
                 three
                 arithmetically
                 proportional
                 2.4.6
                 .
                 are
                 found
                 these
                 three
                 musically
                 proportional
                 .
                 8.12.24
                 .
                 But
                 that
                 numbers
                 are
                 musically
                 
                 proportional
                 ,
                 is
                 hence
                 manifest
                 ,
                 if
                 in
                 them
                 those
                 three
                 Proportions
                 are
                 found
                 ,
                 on
                 which
                 all
                 Musick
                 doth
                 depend
                 :
                 to
                 wit
                 ,
                 Dupla
                 ,
                 or
                 Diapason
                 ,
                 which
                 doth
                 constitute
                 an
                 
                   Octave
                   :
                   Sesquialtera
                
                 ,
                 or
                 Diapente
                 ,
                 which
                 doth
                 constitute
                 a
                 Fifth
                 :
                 and
                 Sesquitertia
                 ,
                 or
                 Diatessaron
                 ,
                 which
                 doth
                 constitute
                 a
                 Fourth
                 .
                 So
                 in
                 these
                 Numbers
                 6.4.3
                 .
                 between
                 6.
                 and
                 3.
                 is
                 dupla
                 :
                 between
                 6.
                 and
                 4.
                 sesquialtera
                 :
                 between
                 4.
                 and
                 3.
                 sesquitertia
                 .
                 I
                 say
                 ,
                 three
                 to
                 four
                 ,
                 are
                 in
                 the
                 
                   sesquitertian
                   Ration
                
                 ,
                 as
                 the
                 
                   Diatessaron
                   System
                   :
                   four
                
                 to
                 six
                 are
                 in
                 the
                 
                   Sesquialtera
                   Ration
                
                 ,
                 as
                 the
                 
                   Diapente
                   :
                   three
                
                 to
                 six
                 are
                 in
                 the
                 
                   dupla
                   Ration
                
                 ,
                 as
                 the
                 
                   Diapason
                   System
                
                 .
                 And
                 of
                 these
                 the
                 rest
                 a●e
                 compounded
                 ,
                 viz.
                 the
                 
                   Disdiapason
                   ,
                   &c.
                
                 
                 This
                 also
                 is
                 of
                 force
                 in
                 
                   Organical
                   Musick
                
                 .
                 For
                 if
                 two
                 Strings
                 equally
                 thick
                 and
                 stretched
                 differ
                 in
                 Longitude
                 by
                 a
                 
                   Sesquialtera
                   Ration
                
                 ,
                 benig
                 struck
                 ,
                 they
                 will
                 equally
                 Sound
                 the
                 Harmony
                 of
                 a
                 Diapente
                 :
                 if
                 they
                 differ
                 in
                 Longitude
                 by
                 a
                 
                   Sesquitertiae
                   Ration
                
                 ,
                 a
                 Diatessaron
                 :
                 if
                 by
                 a
                 dupla
                 ,
                 a
                 Diapason
                 ,
                 which
                 vulgarly
                 they
                 call
                 an
                 Octave
                 ,
                 as
                 a
                 Diapente
                 a
                 fifth
                 ,
                 and
                 a
                 Diatessaron
                 a
                 Fourth
                 .
                 The
                 same
                 is
                 in
                 Hollownesse
                 ,
                 or
                 in
                 Whistles
                 .
                 From
                 this
                 Operation
                 alwayes
                 except
                 the
                 
                   unitrisonous
                   Radix
                
                 ,
                 because
                 it
                 is
                 the
                 foundation
                 of
                 other
                 musical
                 proportions
                 .
              
            
          
        
         
           
           
             CHAP.
             VIII
             .
             Of
             the
             Forme
             of
             an
             Harmonical
             Song
             .
          
           
             
               PRECEPTS
               .
            
             
               THus
               much
               concerning
               the
               matter
               of
               an
               harmonical
               Song
               :
               now
               of
               the
               Forme
               thereof
               ,
               which
               is
               the
               artificial
               disposition
               of
               
                 Musical
                 Monads
                 ,
                 Dyads
              
               ,
               and
               Tryads
               ,
               according
               to
               the
               Text
               ,
               and
               this
               is
               called
               Melodie
               .
            
             
               Melodie
               is
               simple
               ,
               or
               compounded
               .
               That
               is
               called
               Monodie
               ,
               this
               Symphony
               .
            
             
               
                 Simple
                 Melodie
              
               is
               that
               which
               is
               content
               with
               one
               onely
               Series
               of
               musical
               voices
               :
               as
               is
               discerned
               in
               
                 Choral
                 Musick
              
               ,
               called
               Unicinium
               .
            
             
               Compounded
               Melodie
               is
               that
               which
               doth
               conjoyne
               more
               simple
               Melodies
               between
               themselves
               :
               and
               is
               usually
               called
               Counterpoint
               ;
               as
               is
               discerned
               in
               figural
               
               Musick
               .
               To
               which
               appertaine
               Songs
               of
               two
               ,
               three
               ,
               and
               four
               voices
               ,
               &c.
               
            
             
               Counterpoint
               is
               either
               simple
               or
               coloured
               .
            
             
               Simple
               Counterpoint
               is
               that
               which
               hath
               least
               of
               Artifice
               :
               and
               may
               be
               called
               pure
               Composition
               ,
               whose
               Rules
               or
               Ornaments
               are
               the
               Sounds
               of
               Longitude
               ,
               Latitude
               ,
               or
               Crassitude
               .
            
             
               Counterpoint
               coloured
               is
               that
               which
               hath
               more
               of
               Art
               :
               and
               may
               be
               called
               adorned
               Composition
               ,
               whose
               Rules
               or
               Ornaments
               do
               respect
               the
               Longitude
               ,
               Latitude
               ,
               and
               Crassitude
               of
               a
               Sound
               .
            
          
           
             
               RULES
               .
            
             
               
                 1.
                 
                 A
                 Musical
                 Text
                 doth
                 give
                 as
                 it
                 were
                 a
                 Soul
                 to
                 an
                 Harmonical
                 Song
                 ,
                 as
                 to
                 the
                 Image
                 thereof
                 .
              
               
                 Wherefore
                 seeing
                 the
                 Image
                 is
                 such
                 as
                 is
                 the
                 Archetype
                 ,
                 the
                 practical
                 Musician
                 or
                 Composer
                 as
                 they
                 call
                 him
                 ,
                 is
                 to
                 take
                 care
                 that
                 he
                 understand
                 aright
                 the
                 nature
                 of
                 his
                 Text
                 ,
                 in
                 respect
                 of
                 things
                 and
                 words
                 .
                 For
                 an
                 Harmonical
                 Song
                 ought
                 to
                 be
                 accommodated
                 both
                 to
                 things
                 and
                 words
                 .
                 The
                 things
                 may
                 be
                 all
                 divine
                 
                 and
                 humane
                 matters
                 ,
                 but
                 chiefly
                 practical
                 ,
                 which
                 concern
                 the
                 active
                 felicity
                 of
                 man
                 ;
                 the
                 mean
                 to
                 acquire
                 which
                 ,
                 is
                 virtue
                 moderating
                 the
                 Affections
                 ,
                 which
                 do
                 depend
                 upon
                 things
                 or
                 objects
                 either
                 great
                 ,
                 or
                 low
                 ,
                 or
                 mean
                 :
                 and
                 those
                 again
                 either
                 pleasant
                 or
                 delightful
                 ,
                 or
                 unpleasant
                 and
                 sorrowful
                 ,
                 or
                 moderate
                 .
                 Words
                 may
                 be
                 either
                 of
                 prose
                 or
                 verse
                 ,
                 yet
                 so
                 as
                 that
                 they
                 be
                 like
                 unto
                 things
                 practical
                 ,
                 even
                 ,
                 and
                 congruous
                 .
                 So
                 that
                 he
                 ought
                 to
                 know
                 the
                 nature
                 of
                 all
                 Letters
                 ,
                 (
                 of
                 which
                 in
                 my
                 
                   Rhetoricks
                   .
                
                 )
                 Moreover
                 ,
                 an
                 harmonical
                 Song
                 will
                 rightly
                 express
                 the
                 Text
                 ,
                 if
                 the
                 Musician
                 give
                 heed
                 to
                 the
                 
                   trine
                   Dimension
                
                 of
                 Sound
                 ,
                 viz.
                 
                   Longitude
                   ,
                   Latitude
                
                 ,
                 and
                 Crassitude
                 .
                 For
                 things
                 grave
                 are
                 rightly
                 expressed
                 by
                 long
                 and
                 profound
                 Sounds
                 :
                 light
                 things
                 by
                 short
                 and
                 acute
                 Sounds
                 :
                 Masculine
                 things
                 by
                 sharp
                 Sounds
                 :
                 soft
                 things
                 by
                 flat
                 ●ounds
                 :
                 pleasant
                 things
                 by
                 lively
                 and
                 quick
                 Sounds
                 :
                 Sad
                 things
                 by
                 languid
                 and
                 slow
                 Sounds
                 :
                 and
                 mean
                 things
                 by
                 mean
                 Sounds
                 ;
                 as
                 we
                 see
                 it
                 falleth
                 out
                 in
                 Poesy
                 .
              
            
             
               
                 2.
                 
                 More
                 Simple
                 Melody
                 ,
                 which
                 is
                 called
                 Monadie
                 ,
                 is
                 first
                 to
                 be
                 composed
                 .
              
               
                 A
                 young
                 Composer
                 should
                 first
                 compose
                 the
                 most
                 simple
                 Melodies
                 ,
                 which
                 arise
                 not
                 from
                 Musical
                 Dyads
                 and
                 Tryads
                 ,
                 but
                 from
                 Monads
                 ,
                 or
                 a
                 simple
                 Disposition
                 of
                 musical
                 Voices
                 .
                 
                   e.
                   gr
                
                 .
                 Let
                 this
                 be
                 the
                 Subject
                 ,
                 
                   Laudate
                   Dominum
                
                 ,
                 which
                 may
                 be
                 sung
                 with
                 this
                 Melodie
                 .
                 
                 
              
               
                 Or
                 after
                 the
                 new
                 manner
                 ,
                 which
                 Lippius
                 hath
                 ,
                 which
                 dependeth
                 upon
                 the
                 Syntonick
                 Table
                 ,
                 in
                 the
                 5
                 Chapter
                 before
                 mentioned
                 .
              
               
                 
                   
                     
                       288.
                       
                    
                     
                       320.
                       
                    
                     
                       288.
                       
                    
                     
                       270.
                       
                    
                     
                       270.
                       
                    
                     
                       288.
                       
                    
                  
                   
                     
                       Lau
                    
                     
                       da
                    
                     
                       ●e
                    
                     
                       do
                    
                     
                       mi
                    
                     
                       num
                       .
                    
                  
                   
                     
                       2.
                       
                    
                     
                       1
                       1
                       /
                       2
                    
                     
                       ½
                    
                     
                       ½
                    
                     
                       ½
                    
                     
                       2.
                       
                    
                  
                
              
               
                 Here
                 the
                 Numbers
                 placed
                 above
                 the
                 Text
                 do
                 shew
                 the
                 Notes
                 of
                 the
                 Syntonic
                 Table
                 :
                 and
                 the
                 numbers
                 underneath
                 do
                 expresse
                 the
                 measure
                 of
                 the
                 Touch.
                 Therefore
                 such
                 will
                 be
                 the
                 Series
                 according
                 to
                 this
                 new
                 Mode
                 .
                 
              
            
             
               
                 3.
                 
                 Compounded
                 Melodie
                 doth
                 respect
                 either
                 two
                 ,
                 three
                 ,
                 or
                 four
                 Simple
                 Melodies
                 ,
                 cardinal
                 and
                 radical
                 .
              
               
                 Of
                 these
                 the
                 Composition
                 and
                 Connexion
                 of
                 four
                 
                 Melodies
                 is
                 most
                 perfect
                 .
                 For
                 as
                 a
                 body
                 mixed
                 of
                 four
                 Elements
                 ,
                 is
                 a
                 temperament
                 of
                 four
                 humours
                 :
                 So
                 every
                 harmonical
                 Polyphony
                 doth
                 arise
                 from
                 four
                 simple
                 Melodies
                 .
                 Of
                 these
                 two
                 are
                 extreme
                 ,
                 the
                 Bass
                 which
                 is
                 the
                 gravest
                 ;
                 and
                 the
                 Discantus
                 which
                 is
                 the
                 acutest
                 :
                 and
                 two
                 are
                 intermediate
                 ;
                 the
                 one
                 is
                 nearer
                 to
                 the
                 Bass
                 ,
                 which
                 is
                 the
                 Tenor
                 ;
                 and
                 the
                 other
                 is
                 nearer
                 to
                 the
                 Discantus
                 ,
                 which
                 is
                 the
                 Altus
                 ,
                 according
                 to
                 the
                 Disposition
                 of
                 the
                 four
                 Elements
                 ,
                 
                   Earth
                   ,
                   Water
                   ,
                   Air
                
                 ,
                 and
                 Fire
                 .
                 Of
                 which
                 ,
                 two
                 are
                 extreme
                 ,
                 and
                 as
                 many
                 Median
                 ,
                 as
                 is
                 noted
                 in
                 our
                 Physicks
                 .
                 And
                 this
                 is
                 the
                 Musical
                 Tetras
                 ,
                 in
                 which
                 the
                 Melody
                 of
                 the
                 Bass
                 is
                 fundamental
                 ▪
                 whence
                 its
                 name
                 is
                 from
                 Basis
                 a
                 foundation
                 :
                 or
                 Bassus
                 profound
                 :
                 the
                 Melodie
                 of
                 the
                 Tenor
                 and
                 Discantus
                 (
                 whose
                 vicissitude
                 is
                 very
                 elegant
                 )
                 is
                 principal
                 or
                 regal
                 .
                 Lastly
                 the
                 Melodie
                 of
                 the
                 Altus
                 is
                 explemental
                 .
                 This
                 Tetras
                 ,
                 or
                 Song
                 of
                 four
                 voices
                 ,
                 doth
                 comprehend
                 both
                 musical
                 
                   Monads
                   ,
                   Dyads
                
                 ,
                 and
                 Tryads
                 ,
                 aswell
                 Simple
                 as
                 Compounded
                 ,
                 and
                 is
                 the
                 Radix
                 of
                 all
                 perfect
                 Musical
                 Composition
                 .
                 This
                 therefore
                 is
                 the
                 Order
                 in
                 Musicks
                 .
                 The
                 Musical
                 Monade
                 is
                 the
                 Radix
                 of
                 one
                 Melodie
                 ,
                 or
                 Song
                 of
                 one
                 Voice
                 :
                 the
                 Dya●
                 of
                 two
                 :
                 the
                 Trias
                 of
                 three
                 :
                 and
                 the
                 Tetras
                 of
                 four
                 :
                 Moreover
                 this
                 Composition
                 is
                 called
                 Counterpoint
                 ,
                 because
                 point
                 is
                 put
                 against
                 point
                 .
              
            
             
               
                 4.
                 
                 Pure
                 Composition
                 ,
                 or
                 Simple
                 Counterpoint
                 ;
                 hath
                 this
                 Artifice
                 .
              
               
                 1.
                 
                 Pure
                 Composition
                 doth
                 make
                 the
                 four
                 Melodies
                 ,
                 
                 more
                 simple
                 ,
                 plain
                 ,
                 and
                 easie
                 :
                 yet
                 so
                 that
                 it
                 keepeth
                 the
                 
                   trine
                   Dimension
                
                 of
                 Sound
                 .
                 2.
                 
                 
                   This
                   is
                   the
                   Rule
                   of
                   the
                   Longitude
                   of
                   a
                   Sound
                   .
                
                 Every
                 one
                 of
                 the
                 four
                 
                   radical
                   Melodies
                
                 doth
                 so
                 proceed
                 by
                 his
                 Monads
                 ,
                 that
                 Notes
                 of
                 more
                 simple
                 value
                 may
                 be
                 added
                 ,
                 the
                 Touch
                 being
                 every
                 where
                 equal
                 .
                 3.
                 
                 The
                 Rules
                 of
                 Latitude
                 is
                 this
                 .
                 1.
                 
                 All
                 the
                 members
                 of
                 all
                 the
                 Melodies
                 do
                 make
                 a
                 Consonancy
                 ;
                 which
                 doth
                 depend
                 upon
                 that
                 
                   unitrosonous
                   harmonical
                   Radix
                
                 ,
                 of
                 which
                 mention
                 is
                 made
                 in
                 the
                 foregoing
                 Chapter
                 .
                 And
                 because
                 the
                 parts
                 and
                 productions
                 of
                 that
                 Triade
                 are
                 various
                 ,
                 the
                 Consonancys
                 may
                 be
                 mingled
                 among
                 themselves
                 ,
                 yet
                 so
                 as
                 that
                 the
                 peculiar
                 Ration
                 of
                 the
                 perfecter
                 of
                 them
                 be
                 kept
                 :
                 for
                 in
                 every
                 Genus
                 that
                 which
                 is
                 most
                 perfect
                 is
                 the
                 measure
                 of
                 the
                 rest
                 .
                 2.
                 
                 All
                 melodies
                 should
                 be
                 compared
                 with
                 themselves
                 most
                 diligently
                 .
                 viz.
                 The
                 Bass
                 with
                 the
                 Tenor
                 ,
                 the
                 Tenor
                 with
                 the
                 Altus
                 ,
                 the
                 Altus
                 with
                 the
                 Discantus
                 ,
                 the
                 Bass
                 with
                 the
                 Altus
                 ,
                 the
                 Tenor
                 with
                 the
                 Discantus
                 ,
                 lastly
                 ,
                 the
                 Bass
                 with
                 the
                 Discantus
                 .
                 Or
                 more
                 briefly
                 ,
                 the
                 Tenor
                 with
                 the
                 Bass
                 ,
                 the
                 A●tus
                 with
                 the
                 Tenor
                 and
                 Bass
                 ,
                 the
                 Discantus
                 with
                 the
                 
                   Altus
                   ,
                   Tenor
                
                 ,
                 and
                 Bass.
                 For
                 so
                 every
                 one
                 compared
                 with
                 another
                 will
                 make
                 six
                 times
                 an
                 excellent
                 Song
                 of
                 two
                 Parts
                 :
                 So
                 that
                 every
                 part
                 of
                 the
                 Melody
                 will
                 be
                 adorned
                 with
                 some
                 harmonical
                 Dyade
                 .
                 And
                 also
                 in
                 those
                 Dyades
                 ,
                 varietie
                 is
                 to
                 be
                 used
                 ,
                 yet
                 so
                 that
                 the
                 perfecter
                 do
                 rule
                 .
                 3.
                 
                 
                   Consonant
                   Dyades
                
                 by
                 ascending
                 and
                 descending
                 together
                 may
                 all
                 mutually
                 antecede
                 and
                 follow
                 one
                 another
                 ,
                 if
                 they
                 be
                 of
                 divers
                 species
                 :
                 but
                 if
                 of
                 the
                 same
                 ,
                 as
                 the
                 three
                 perfect
                 Consonancies
                 with
                 the
                 simple
                 unison
                 ,
                 they
                 may
                 
                 not
                 ,
                 but
                 the
                 other
                 imperfect
                 Dyads
                 may
                 .
                 But
                 more
                 briefly
                 ,
                 two
                 simple
                 Unisons
                 may
                 not
                 be
                 put
                 together
                 ascending
                 or
                 descending
                 :
                 nor
                 two
                 Octaves
                 ,
                 nor
                 two
                 Fifths
                 ,
                 nor
                 two
                 Fourths
                 .
                 4.
                 
                 
                   Those
                   Dyads
                   which
                   are
                   nearer
                   in
                   Crassitude
                   ,
                   will
                   better
                   precede
                   and
                   succeed
                   ,
                   then
                   those
                   which
                   are
                   more
                   remote
                   .
                
                 To
                 which
                 purpose
                 is
                 that
                 saying
                 of
                 
                   Musicians
                   ,
                   By
                   how
                   much
                   nearer
                   Voices
                   are
                   to
                   one
                   another
                   ,
                   by
                   so
                   much
                   they
                   make
                   the
                   better
                   Symphony
                   .
                
                 5.
                 
                 
                   Monads
                   should
                   be
                   applied
                   so
                   in
                   all
                   Melodies
                   ,
                   that
                   every
                   one
                   should
                   elegantly
                   walk
                   in
                   his
                   own
                   Region
                   ,
                
                 and
                 commonly
                 of
                 one
                 Octave
                 ,
                 or
                 Diapason
                 .
                 6.
                 
                 
                   Let
                   the
                   Bass
                   always
                   take
                   the
                   lower
                   part
                   or
                   foundation
                   of
                   the
                   harmonical
                   Triade
                   in
                   the
                   place
                   of
                   the
                   gravest
                   :
                   but
                   the
                   Tenor
                   in
                   the
                   place
                   of
                   the
                   graver
                   ,
                   the
                   Altus
                   of
                   the
                   acuter
                   ,
                   and
                   the
                   Discantus
                   of
                   acutest
                   Monads
                   :
                
                 So
                 let
                 them
                 take
                 all
                 three
                 parts
                 of
                 the
                 harmonical
                 
                   Triade
                   ,
                   viz.
                
                 The
                 lowest
                 or
                 first
                 ,
                 the
                 middle
                 and
                 last
                 .
                 But
                 in
                 augmentation
                 and
                 multiplication
                 the
                 first
                 of
                 the
                 Triade
                 is
                 chiefly
                 to
                 be
                 repeated
                 ,
                 the
                 last
                 more
                 rarely
                 ,
                 the
                 middle
                 seldomest
                 .
                 7.
                 
                   ●et
                   Melodies
                   associate
                   by
                   gradual
                   ,
                   not
                   by
                   skipping
                   motion
                   .
                
                 For
                 if
                 every
                 Melodie
                 do
                 proceed
                 rather
                 by
                 degrees
                 ,
                 then
                 flie
                 violently
                 by
                 greater
                 Intervalls
                 and
                 Leaps
                 ,
                 it
                 will
                 be
                 more
                 grateful
                 to
                 the
                 Ears
                 ;
                 yet
                 the
                 Bass
                 is
                 allowed
                 to
                 move
                 by
                 Leaps
                 .
                 8.
                 
                 
                   Let
                   the
                   Bass
                   be
                   first
                   composed
                   .
                
                 Because
                 it
                 is
                 the
                 foundation
                 of
                 the
                 Triads
                 .
                 Hereto
                 belongeth
                 th●s
                 Rule
                 .
                 Better
                 is
                 that
                 harmonical
                 Triade
                 who●e
                 Basis
                 is
                 lowest
                 ,
                 then
                 those
                 whose
                 Basis
                 is
                 in
                 an
                 hi●her
                 place
                 .
                 But
                 now
                 let
                 us
                 see
                 an
                 Example
                 .
                 Let
                 the
                 Text
                 be
                 
                   Laudate
                   Dominum
                
                 .
                 And
                 this
                 you
                 may
                 thus
                 express
                 in
                 a
                 pure
                 Song
                 .
                 Go
                 to
                 the
                 
                 Syntonian
                 Table
                 ,
                 and
                 from
                 thence
                 pick
                 out
                 Consonancies
                 after
                 this
                 manner
                 .
              
               
                 
                   
                     
                        
                    
                     
                       2.
                       
                    
                     
                       1
                       1
                       /
                       2
                    
                     
                       ½
                    
                     
                       ½
                    
                     
                       ½
                    
                     
                       2.
                       
                    
                  
                   
                     
                       Discantus
                       .
                    
                     
                       180
                    
                     
                       192
                    
                     
                       180
                    
                     
                       180
                    
                     
                       180
                    
                     
                       180.
                       
                    
                  
                   
                     
                        
                    
                     
                       Altus
                       .
                    
                     
                       240
                    
                     
                       240
                    
                     
                       240
                    
                     
                       216
                    
                     
                       216
                    
                     
                       240.
                       
                    
                  
                   
                     
                        
                    
                     
                       Tenor.
                       
                    
                     
                       288
                    
                     
                       320
                    
                     
                       288
                    
                     
                       270
                    
                     
                       270
                    
                     
                       288.
                       
                    
                  
                   
                     
                        
                    
                     
                       Bassus
                       .
                    
                     
                       360
                    
                     
                       480
                    
                     
                       360
                    
                     
                       540
                    
                     
                       540
                    
                     
                       720.
                       
                    
                  
                   
                     
                        
                    
                     
                       Lau
                    
                     
                       da
                    
                     
                       te
                    
                     
                       do
                    
                     
                       mi
                    
                     
                       num
                       .
                    
                  
                
              
               
                 
                   These
                   Consonancies
                   you
                   may
                   thus
                   transfer
                   into
                   the
                   great
                   System
                   .
                   
                   Lau╌da╌te
                   —
                   do╌mi╌num
                   .
                
              
               
                 Or
                 if
                 you
                 had
                 rather
                 you
                 may
                 thus
                 write
                 the
                 several
                 *
                 Touches
                 in
                 several
                 Cells
                 .
              
               
                 *
                 Touch
                 is
                 that
                 which
                 Musicians
                 call
                 Tactus
                 ,
                 or
                 the
                 stroke
                 of
                 the
                 hand
                 by
                 which
                 Time
                 is
                 measured
                 .
                 Or
                 it
                 is
                 the
                 successive
                 Motion
                 of
                 the
                 hand
                 ,
                 directing
                 by
                 equal
                 measure
                 the
                 Quantity
                 of
                 all
                 Notes
                 and
                 Pauses
                 in
                 a
                 Song
                 ,
                 according
                 to
                 the
                 variety
                 of
                 Signes
                 and
                 Proportions
                 .
                 The
                 parts
                 thereof
                 are
                 Elevation
                 and
                 Depression
                 ;
                 or
                 the
                 Fall
                 and
                 Rise
                 of
                 the
                 hand
                 .
                 
                 
                 
                   Be╌ne
                   dic╌a╌ni╌ma╌me╌a
                   —
                   Je╌ho╌vae
                
                 .
              
               
                 In
                 the
                 latter
                 Example
                 you
                 may
                 observe
                 the
                 Tenor
                 to
                 have
                 the
                 same
                 Voice
                 with
                 the
                 Bass
                 in
                 the
                 first
                 Cell
                 :
                 and
                 in
                 the
                 Sixth
                 and
                 Seventh
                 ,
                 two
                 Minums
                 put
                 for
                 one
                 Semibreve
                 .
              
            
             
               
                 V.
                 Adorned
                 Composition
                 ,
                 or
                 Coloured
                 Counterpoint
                 ,
                 is
                 contained
                 in
                 these
                 Rules
                 .
              
               
                 1.
                 
                 Adorned
                 Composition
                 doth
                 constitute
                 a
                 Song
                 ●armonical
                 more
                 
                   broken
                   ,
                   florid
                
                 ,
                 and
                 coloured
                 ,
                 there●ore
                 more
                 difficult
                 and
                 effectual
                 .
                 Therefore
                 this
                 doth
                 as
                 it
                 were
                 garnish
                 these
                 three
                 Dimensions
                 of
                 a
                 Song
                 with
                 various
                 Gems
                 and
                 flowers
                 :
                 so
                 that
                 pure
                 Composition
                 may
                 rightly
                 be
                 compared
                 to
                 Grammer
                 ,
                 which
                 teach●th
                 to
                 ●peak
                 purely
                 :
                 and
                 adorned
                 Composition
                 to
                 Rhetorick
                 ,
                 which
                 teacheth
                 to
                 speak
                 Elegantl●
                 .
                 2.
                 
                 
                   Artificial
                   Licenses
                
                 are
                 used
                 in
                 adorned
                 Compos●tion
                 .
                 For
                 as
                 there
                 are
                 allowed
                 Poetical
                 
                 Licenses
                 ,
                 which
                 do
                 beautifie
                 Art
                 ,
                 and
                 not
                 destroy
                 it
                 :
                 so
                 also
                 there
                 are
                 Melopoetical
                 Licenses
                 ,
                 by
                 which
                 the
                 pure
                 and
                 simple
                 Dimensions
                 of
                 a
                 Song
                 are
                 beautified
                 .
                 3.
                 
                 These
                 are
                 the
                 Orn●ments
                 of
                 Longitude
                 .
                 1.
                 
                 An
                 harmonical
                 Song
                 is
                 adorned
                 with
                 the
                 varietie
                 of
                 a
                 Spondaic
                 ,
                 and
                 trochaic
                 Touch
                 :
                 and
                 of
                 unequal
                 Notes
                 ,
                 especially
                 Syncopated
                 .
                 So
                 the
                 Bass
                 doth
                 move
                 more
                 slowly
                 ,
                 and
                 the
                 other
                 Melodies
                 with
                 coloured
                 celeritie
                 ;
                 which
                 is
                 that
                 in
                 Musick
                 ,
                 as
                 flourishing
                 is
                 in
                 Writing
                 .
                 2.
                 
                 An
                 harmonical
                 Song
                 according
                 to
                 the
                 Nature
                 of
                 the
                 Text
                 ,
                 is
                 distinguished
                 by
                 Rests
                 and
                 Closes
                 .
                 For
                 even
                 as
                 Speech
                 is
                 distinguished
                 by
                 
                   Comma's
                   ,
                   Colons
                
                 ,
                 and
                 due
                 Periods
                 ;
                 so
                 ought
                 an
                 harmonical
                 Song
                 ,
                 according
                 to
                 the
                 nature
                 of
                 the
                 Text
                 ,
                 to
                 be
                 distinguished
                 by
                 greater
                 and
                 lesser
                 Rests
                 ;
                 also
                 by
                 
                   Closes
                   native
                   ,
                   primarie
                   ,
                   secondarie
                   ,
                   tertiarie
                   ,
                   peregrine
                   ,
                
                 more
                 perfect
                 ,
                 or
                 more
                 imperfect
                 .
                 A
                 perfect
                 Close
                 doth
                 consist
                 of
                 three
                 Voices
                 ;
                 the
                 
                   antepenult
                   ,
                   penult
                
                 ,
                 and
                 last
                 :
                 by
                 which
                 the
                 Close
                 is
                 chiefly
                 known
                 ,
                 and
                 which
                 is
                 to
                 arise
                 out
                 of
                 an
                 harmonical
                 
                   Triade
                   .
                   e.
                   g.
                
                 
                 
              
               
                 The
                 
                   Primarie
                   Close
                
                 is
                 that
                 whose
                 last
                 is
                 the
                 first
                 ;
                 the
                 secondary
                 ,
                 the
                 supreme
                 ;
                 the
                 tertiarie
                 the
                 middle
                 of
                 the
                 Triade
                 ;
                 but
                 of
                 these
                 in
                 the
                 following
                 Chapter
                 .
                 4.
                 
                 The
                 Ornaments
                 of
                 Latitude
                 are
                 these
                 .
                 An
                 harmonical
                 Song
                 should
                 be
                 so
                 expressed
                 by
                 Voice
                 or
                 I●strument
                 ,
                 or
                 both
                 together
                 ;
                 that
                 according
                 to
                 the
                 
                 Condition
                 of
                 the
                 Text
                 ,
                 an
                 asperous
                 ,
                 sharp
                 ,
                 swift
                 ,
                 full
                 ,
                 gentle
                 ,
                 flat
                 ,
                 submiss
                 ,
                 or
                 small
                 Spirit
                 ,
                 &c.
                 should
                 be
                 heard
                 .
                 5.
                 
                 The
                 Ornaments
                 of
                 Crassitude
                 have
                 these
                 Axioms
                 .
                 1.
                 
                 Varietie
                 should
                 chiefly
                 rule
                 in
                 an
                 harmonical
                 Song
                 ;
                 I
                 say
                 varietie
                 of
                 Dyad's
                 and
                 Triads
                 ,
                 more
                 grave
                 ,
                 more
                 mean
                 ,
                 more
                 acute
                 ,
                 simple
                 and
                 compounded
                 ,
                 diffused
                 and
                 augmented
                 ,
                 more
                 perfect
                 ,
                 and
                 more
                 imperfect
                 ,
                 natural
                 and
                 fict
                 .
                 Hence
                 is
                 a
                 various
                 Licence
                 :
                 for
                 in
                 the
                 Bass
                 it
                 is
                 lawful
                 to
                 use
                 the
                 last
                 and
                 middle
                 Monade
                 of
                 an
                 
                   Unitrisonous
                   Radix
                
                 :
                 and
                 Dyads
                 prohibited
                 ,
                 may
                 antecede
                 and
                 follow
                 one
                 another
                 ;
                 and
                 a
                 Dias
                 and
                 a
                 Trias
                 also
                 anarmonical
                 may
                 be
                 used
                 .
                 All
                 which
                 things
                 are
                 done
                 either
                 covertly
                 or
                 openly
                 .
                 Covertly
                 ,
                 either
                 by
                 greater
                 Rests
                 ,
                 or
                 by
                 Sounds
                 not
                 offending
                 by
                 reason
                 of
                 their
                 swiftnesse
                 ,
                 or
                 by
                 contrary
                 made
                 Sounds
                 ;
                 or
                 by
                 an
                 excuseing
                 Polyphonie
                 ,
                 or
                 by
                 Syncope
                 .
                 Openly
                 for
                 the
                 texts
                 sake
                 ,
                 and
                 singular
                 Artifice
                 .
                 
                   v.
                   gr
                
                 .
                 If
                 the
                 Text
                 command
                 ,
                 and
                 as
                 it
                 were
                 compel
                 to
                 manifest
                 some
                 Discord
                 .
                 According
                 to
                 that
                 of
                 the
                 Logicians
                 ;
                 Contraries
                 placed
                 nigh
                 themselves
                 are
                 the
                 more
                 clearly
                 illustrated
                 .
                 When
                 therefore
                 in
                 Singing
                 some
                 harsh
                 sound
                 is
                 heard
                 ,
                 which
                 presently
                 passeth
                 into
                 a
                 sweet
                 harmony
                 ,
                 the
                 hearing
                 is
                 therewith
                 more
                 affected
                 ,
                 than
                 if
                 there
                 were
                 a
                 current
                 of
                 perpetual
                 Harmony
                 .
                 2.
                 
                 When
                 the
                 whole
                 harmonical
                 Song
                 is
                 rendred
                 more
                 beautiful
                 by
                 the
                 ornament
                 of
                 Celerity
                 and
                 Syncope
                 ;
                 then
                 chiefly
                 the
                 Close
                 should
                 be
                 artificial
                 .
                 3.
                 
                 Polyphony
                 or
                 multiplication
                 of
                 
                   cardinal
                   melodies
                
                 do
                 very
                 much
                 ●dorn
                 Singing
                 .
                 
                   e.
                   gr
                
                 .
                 As
                 if
                 there
                 be
                 two
                 ,
                 three
                 ,
                 or
                 more
                 
                   Basses
                   ,
                   Tenor
                   's
                   ,
                   Altus's
                   ,
                   Discant's
                   ,
                
                 
                 and
                 those
                 placed
                 in
                 certain
                 Quires
                 ,
                 according
                 to
                 the
                 Text
                 and
                 Circumstances
                 .
                 4.
                 
                 The
                 various
                 manner
                 and
                 motion
                 of
                 ascending
                 and
                 descending
                 ,
                 is
                 granted
                 to
                 principle
                 Melodies
                 and
                 sometimes
                 out
                 of
                 their
                 Proper
                 Regions
                 ;
                 as
                 for
                 the
                 Bass
                 to
                 invade
                 the
                 Confines
                 of
                 the
                 Tenor
                 ,
                 or
                 the
                 Tenor
                 of
                 the
                 Altus
                 .
                 5.
                 
                 The
                 ornament
                 of
                 musical
                 ornaments
                 is
                 that
                 which
                 they
                 call
                 a
                 Fuge
                 .
                 This
                 Ornament
                 at
                 this
                 day
                 is
                 most
                 excellent
                 ,
                 difficult
                 ,
                 ingenuous
                 ,
                 efficacious
                 ,
                 and
                 full
                 of
                 Liberty
                 .
                 And
                 this
                 Fuge
                 is
                 nothing
                 else
                 then
                 a
                 more
                 artificial
                 repetition
                 and
                 imitation
                 of
                 certain
                 Parts
                 :
                 to
                 which
                 a
                 more
                 Simple
                 Repetition
                 and
                 Imitation
                 is
                 opposed
                 ,
                 which
                 also
                 hath
                 his
                 Commendations
                 amongst
                 Musicians
                 .
                 And
                 this
                 is
                 the
                 Example
                 of
                 a
                 Fuge
                 in
                 the
                 Unison
                 after
                 two
                 Times
                 .
                 
                 
                 
                   Unum
                   est
                   necessarium
                
                 .
                 
                 
              
               
               
                 *
                 I
                 suppose
                 that
                 this
                 Example
                 was
                 mistaken
                 or
                 rather
                 mis-placed
                 by
                 the
                 Printer
                 or
                 some
                 other
                 ,
                 for
                 I
                 cannot
                 imagine
                 that
                 the
                 Learned
                 Authour
                 would
                 give
                 the
                 Reader
                 Four
                 parts
                 of
                 Simple
                 Counter-point
                 ,
                 for
                 an
                 Example
                 of
                 a
                 Fuge
                 in
                 the
                 Unison
                 after
                 two
                 Minims
                 .
                 Of
                 which
                 let
                 this
                 be
                 an
                 Example
                 .
                 
              
               
                 And
                 thus
                 the
                 Composer
                 may
                 continue
                 his
                 Fuge
                 as
                 long
                 as
                 he
                 pleaseth
                 .
              
               
                 6.
                 
                 The
                 Exercise
                 of
                 a
                 Fuge
                 is
                 to
                 begin
                 in
                 an
                 Harmonical
                 Tryade
                 onely
                 .
                 For
                 so
                 other
                 forms
                 and
                 species
                 of
                 Fuges
                 may
                 more
                 easily
                 be
                 apprehended
                 .
                 And
                 for
                 Examples
                 you
                 may
                 look
                 amongst
                 those
                 Principal
                 and
                 Heroick
                 practical
                 Musicians
                 ,
                 as
                 Orlandus
                 and
                 Marentius
                 .
                 Of
                 which
                 two
                 ,
                 the
                 one
                 in
                 his
                 Mottets
                 ,
                 and
                 the
                 other
                 in
                 his
                 Madrigals
                 ,
                 hath
                 brought
                 Melopoesie
                 to
                 his
                 highest
                 pitch
                 .
                 There
                 are
                 latter
                 Imitators
                 of
                 these
                 principal
                 Melopoets
                 ,
                 who
                 notwithstanding
                 ought
                 to
                 have
                 their
                 due
                 praise
                 .
              
            
          
        
         
           
           
             CHAP.
             IX
             .
             Of
             the
             Affections
             of
             an
             Harmonicall
             Song
             .
          
           
             
               PRECEPTS
               .
            
             
               IN
               the
               last
               place
               the
               Affections
               of
               a
               musicall
               Song
               do
               follow
               ,
               wherewith
               it
               is
               affected
               and
               perfected
               .
            
             
               And
               they
               are
               either
               material
               or
               formal
               .
            
             
               The
               material
               Affection
               of
               a
               Song
               ,
               is
               that
               which
               floweth
               from
               the
               matter
               thereof
               .
               And
               it
               is
               a
               certain
               Genus
               of
               Modulation
               .
            
             
               The
               formal
               Affection
               of
               a
               Song
               ,
               is
               that
               which
               floweth
               from
               the
               Form
               thereof
               :
               and
               is
               called
               a
               musical
               Trope
               or
               Mood
               ;
               which
               is
               a
               Rule
               ,
               according
               to
               which
               we
               direct
               the
               course
               of
               a
               Song
               .
               Otherwise
               called
               Nomus
               and
               Tonus
               .
               And
               it
               is
               the
               same
               in
               Musick
               ,
               as
               a
               certain
               kind
               of
               verse
               is
               in
               Poetry
               .
            
             
             
               A
               musical
               Mood
               is
               either
               simple
               or
               compounded
               .
            
             
               The
               simple
               is
               primarie
               or
               secondarie
               .
               That
               is
               called
               Authentick
               ,
               and
               this
               Plagal
               .
            
             
               The
               primarie
               mood
               is
               either
               legitimate
               or
               spurious
               .
            
             
               The
               legitimate
               is
               either
               more
               natural
               in
               a
               sharp
               Scale
               ,
               or
               more
               soft
               in
               a
               flat
               Scale
               .
               And
               both
               is
               threefold
               ;
               the
               
                 Ionick
                 ,
                 Lydian
                 ,
                 Mixolydian
                 ,
                 Dorian
                 ,
                 Phrygian
                 ,
              
               and
               Aeolian
               .
            
             
               The
               spurious
               ,
               bastard
               ,
               ●or
               illegitimate
               Mood
               is
               the
               Hyper-Aeolian
               ,
               and
               Hyper-Phrygian
               .
            
             
               The
               secondary
               or
               Plagal
               Mood
               is
               also
               called
               remisse
               and
               submisse
               :
               and
               it
               is
               
                 Hypo-Ionic
                 ,
                 Hypo-Doric
                 ,
                 Hypo-Phrygian
                 ,
                 Hypo
                 Lydian
                 ,
                 Hypo-Mixolydian
                 ,
              
               and
               Hypo-Aeolic
               .
            
             
               The
               compounded
               or
               connex
               Mood
               ,
               is
               that
               which
               doth
               arise
               from
               simple
               Moods
               :
               when
               the
               Authent
               is
               joyned
               with
               the
               Plagal
               Mood
               :
               whence
               it
               is
               called
               the
               Plagiosyntactical-Trope
               .
            
          
           
             
             
               RULES
               .
            
             
               
                 1.
                 
                 The
                 mixed
                 Genus
                 of
                 Modulation
                 is
                 now
                 for
                 the
                 most
                 part
                 in
                 use
                 .
              
               
                 The
                 Genus
                 of
                 Modulation
                 is
                 certain
                 ,
                 according
                 unto
                 which
                 the
                 Song
                 doth
                 proceed
                 in
                 his
                 Melodies
                 in
                 a
                 certain
                 Musical
                 Scale
                 .
                 Therefore
                 as
                 the
                 Scale
                 of
                 Musick
                 is
                 simple
                 ,
                 or
                 mixed
                 ,
                 and
                 that
                 old
                 or
                 new
                 :
                 (
                 also
                 the
                 old
                 Scale
                 is
                 either
                 Enharmonic
                 ,
                 or
                 chromatic
                 ,
                 or
                 diatonic
                 :
                 the
                 new
                 ,
                 Syntonic
                 )
                 So
                 also
                 the
                 Genus
                 of
                 Modulation
                 is
                 simple
                 ,
                 or
                 mix'd
                 ,
                 or
                 compounded
                 :
                 the
                 simple
                 is
                 old
                 or
                 new
                 :
                 Again
                 the
                 old
                 is
                 
                   enharmonic
                   ,
                   chromatic
                
                 ,
                 or
                 dia●onic
                 .
                 And
                 is
                 also
                 called
                 
                   Enharmonisme
                   ,
                   Chromatisme
                
                 ,
                 and
                 Diatonisme
                 .
                 The
                 new
                 is
                 Syntonic
                 or
                 Syntonisme
                 .
                 The
                 mixed
                 Genus
                 of
                 Modulation
                 is
                 that
                 which
                 is
                 variously
                 compounded
                 of
                 the
                 Simple
                 .
                 Of
                 the
                 Simple
                 ,
                 at
                 this
                 Day
                 ,
                 Enharmonisme
                 and
                 Chromatisme
                 (
                 to
                 wit
                 alone
                 :
                 )
                 partly
                 for
                 their
                 Imperfection
                 ,
                 partly
                 for
                 their
                 Difficulty
                 are
                 not
                 in
                 use
                 ;
                 but
                 the
                 Syntonian-Diatonisme
                 ,
                 or
                 Diaton-Syntonisme
                 ,
                 yet
                 so
                 ,
                 that
                 chromatisme
                 be
                 often
                 mixed
                 ,
                 and
                 sometimes
                 also
                 Enharmonisme
                 ,
                 if
                 there
                 be
                 need
                 ,
                 according
                 to
                 the
                 force
                 and
                 acuracy
                 of
                 the
                 Text.
                 
              
            
             
               
               
                 2.
                 
                 A
                 Musical
                 Mood
                 is
                 the
                 most
                 certain
                 Rule
                 of
                 a
                 Song
                 .
              
               
                 A
                 musical
                 Mood
                 is
                 that
                 ,
                 according
                 to
                 which
                 a
                 musical
                 Song
                 is
                 limited
                 ,
                 and
                 without
                 it
                 would
                 be
                 too
                 ample
                 and
                 wandring
                 .
                 The
                 Mood
                 therefore
                 doth
                 contain
                 Melody
                 with
                 certain
                 Limits
                 ,
                 and
                 as
                 it
                 were
                 Bounds
                 of
                 an
                 ha●mon●cal
                 Trias
                 ,
                 in
                 the
                 Compass
                 of
                 an
                 Octave
                 or
                 Diapason
                 ;
                 so
                 that
                 wholly
                 it
                 doth
                 continually
                 proceed
                 in
                 a
                 due
                 order
                 ,
                 from
                 the
                 beginning
                 ,
                 by
                 the
                 middle
                 ,
                 to
                 the
                 end
                 ,
                 for
                 the
                 artificial
                 expressing
                 unto
                 ,
                 and
                 imprinting
                 upon
                 the
                 hearers
                 the
                 virtue
                 of
                 the
                 Text.
                 
              
            
             
               
                 3.
                 
                 The
                 Doctrine
                 of
                 Moods
                 is
                 contained
                 in
                 these
                 Rules
                 .
              
               
                 1.
                 
                 
                   We
                   cannot
                   moderate
                   or
                   modulate
                   any
                   Song
                   ,
                   unlesse
                   we
                   first
                   know
                   the
                   Tone
                   thereof
                   .
                
                 The
                 Tone
                 is
                 known
                 by
                 the
                 end
                 ,
                 according
                 to
                 Rule
                 :
                 in
                 the
                 end
                 it
                 is
                 seen
                 of
                 what
                 Tone
                 it
                 is
                 .
                 The
                 end
                 also
                 of
                 a
                 Song
                 is
                 judged
                 by
                 the
                 musical
                 Mood
                 ,
                 which
                 therefore
                 by
                 some
                 is
                 called
                 a
                 Tone
                 ,
                 according
                 to
                 this
                 Diversity
                 of
                 Tones
                 ,
                 there
                 are
                 also
                 divers
                 Melodies
                 .
                 For
                 as
                 one
                 Tone
                 is
                 in
                 vt
                 ,
                 and
                 another
                 in
                 re
                 :
                 So
                 also
                 are
                 the
                 Melodies
                 .
                 Yet
                 here
                 you
                 must
                 remember
                 ,
                 that
                 every
                 Tone
                 or
                 ●ood
                 may
                 not
                 only
                 be
                 known
                 by
                 the
                 end
                 ,
                 but
                 also
                 by
                 the
                 beginning
                 ,
                 and
                 middle
                 or
                 Division
                 thereof
                 :
                 al●o
                 by
                 his
                 skipping
                 .
                 2.
                 
                 
                   A
                   musical
                   Mood
                   ,
                   is
                   an
                   
                   Octave
                   mediated
                   by
                   his
                   neighbouring
                   voice
                   .
                
                 Otherwise
                 it
                 is
                 defined
                 to
                 be
                 the
                 Species
                 of
                 a
                 Diapason
                 ,
                 which
                 is
                 made
                 up
                 of
                 a
                 Diatesseron
                 and
                 Diapente
                 .
                 3.
                 
                 
                   The
                   Simple
                   Mood
                   is
                   that
                   in
                   which
                   one
                   harmonical
                   Triade
                   only
                   doth
                   rule
                   with
                   his
                   Octave
                   ,
                
                 in
                 respect
                 of
                 the
                 Text
                 and
                 more
                 simple
                 Affection
                 .
                 4.
                 
                 
                   All
                   the
                   Moods
                   are
                   six
                
                 ,
                 even
                 as
                 there
                 are
                 six
                 voices
                 .
                 
                   vt
                   .
                   re
                   .
                   mi.
                   fa.
                   sol
                   .
                   la.
                
                 The
                 Ancients
                 had
                 only
                 four
                 Moods
                 ,
                 the
                 first
                 ,
                 second
                 ,
                 third
                 ,
                 and
                 fourth
                 :
                 to
                 which
                 now
                 the
                 four
                 final
                 Voices
                 do
                 respond
                 .
                 
                   re
                   .
                   mi.
                   fa.
                   sol
                
                 .
                 These
                 four
                 Moods
                 the
                 Grecians
                 call
                 Authentic
                 ,
                 and
                 the
                 
                   Latines
                   herile
                
                 or
                 Clamous
                 .
                 For
                 they
                 have
                 ,
                 as
                 I
                 may
                 so
                 speak
                 ,
                 a
                 greater
                 Authority
                 of
                 ascending
                 then
                 the
                 rest
                 .
                 But
                 the
                 Latines
                 more
                 narrowly
                 considering
                 the
                 ascension
                 and
                 descension
                 of
                 every
                 Tone
                 ,
                 have
                 constituted
                 to
                 every
                 Mood
                 a
                 subjugal
                 Mood
                 ;
                 and
                 those
                 four
                 they
                 call
                 Plagal
                 ;
                 also
                 subjugal
                 ,
                 servile
                 ,
                 and
                 the
                 like
                 .
                 And
                 these
                 descend
                 more
                 then
                 the
                 first
                 .
                 And
                 hence
                 arise
                 the
                 eight
                 Moods
                 ,
                 by
                 which
                 every
                 Song
                 is
                 governed
                 
                   per
                   Arsin
                   &
                   Thesin
                
                 ,
                 by
                 rising
                 or
                 falling
                 .
                 But
                 our
                 Latter
                 Musicians
                 more
                 diligently
                 considering
                 the
                 variety
                 of
                 Tones
                 ,
                 have
                 constituted
                 twelve
                 legitimate
                 
                   Tones
                   .
                   viz.
                
                 six
                 Authent
                 ,
                 and
                 as
                 many
                 Plagal
                 .
                 For
                 as
                 there
                 are
                 six
                 Voices
                 .
                 
                   vt
                   .
                   re
                   .
                   mi.
                   fa.
                   sol
                   .
                   la.
                
                 so
                 also
                 there
                 are
                 six
                 Authent
                 ,
                 and
                 as
                 many
                 Plagal
                 ,
                 which
                 are
                 vulgarly
                 named
                 by
                 strange
                 Names
                 of
                 Nations
                 :
                 I
                 say
                 ,
                 of
                 those
                 Nations
                 who
                 commonly
                 were
                 delighted
                 with
                 them
                 .
                 And
                 to
                 these
                 twelve
                 legimate
                 Tones
                 ,
                 two
                 illegitimate
                 were
                 added
                 .
                 Unto
                 all
                 which
                 ,
                 various
                 mixed
                 Moods
                 may
                 be
                 added
                 .
                 5.
                 
                 
                   An
                   Authent
                   Mood
                   is
                   primary
                   ,
                   the
                   Plagal
                   secondary
                   ,
                
                 and
                 this
                 doth
                 not
                 differ
                 from
                 that
                 ,
                 
                 but
                 in
                 respect
                 of
                 subjection
                 ,
                 when
                 it
                 is
                 called
                 Hypotropus
                 ,
                 remiss
                 and
                 submiss
                 ,
                 because
                 the
                 harmonical
                 Mediation
                 of
                 the
                 Octave
                 ,
                 which
                 doth
                 agree
                 with
                 the
                 primary
                 ,
                 is
                 changed
                 into
                 the
                 arithmetical
                 ,
                 by
                 the
                 inversion
                 of
                 the
                 fourth
                 beneath
                 the
                 fifth
                 with
                 the
                 Triade
                 .
                 6.
                 
                 
                   Concerning
                   the
                   Excellency
                   and
                   Efficacy
                   of
                   the
                   musical
                   Moods
                   ,
                
                 there
                 are
                 diverse
                 opinions
                 .
                 
                   Casus
                   in
                   politicis
                
                 lib.
                 8.
                 chap.
                 5.
                 saith
                 thus
                 ,
                 
                   Musick
                   is
                   various
                   and
                   manifold
                   .
                   One
                   kind
                   is
                   humble
                   and
                   remiss
                   ,
                   as
                   the
                
                 Lydian
                 ;
                 
                   another
                   is
                   vehement
                   and
                   more
                   moved
                   ,
                   as
                   the
                
                 Phrygian
                 ;
                 
                   another
                   is
                   more
                   moderate
                   and
                   mean
                   which
                   is
                   called
                   the
                
                 Doric
                 ;
                 and
                 a
                 little
                 after
                 ,
                 
                   that
                   grave
                   ,
                   divine
                   ,
                   and
                   oraculous
                   Musick
                   ,
                   called
                   the
                
                 Doric
                 ,
                 
                   allureth
                   the
                   mind
                   to
                   the
                   study
                   of
                   Wisdome
                   and
                   true
                   Piety
                   .
                
                 This
                 ,
                 both
                 the
                 heathen
                 of
                 old
                 used
                 in
                 their
                 Synagogues
                 ,
                 and
                 Christians
                 now
                 use
                 in
                 their
                 Churches
                 .
                 For
                 in
                 it
                 there
                 is
                 a
                 certain
                 imitation
                 of
                 Celestial
                 Harmony
                 ,
                 by
                 which
                 as
                 by
                 a
                 sweet
                 and
                 wholsome
                 Medicine
                 ,
                 the
                 Diseases
                 of
                 the
                 mind
                 are
                 cured
                 ,
                 Vices
                 are
                 dissipated
                 ,
                 Cares
                 are
                 lessened
                 :
                 and
                 th●
                 Dew
                 of
                 Divine
                 Grace
                 is
                 leisurely
                 ,
                 and
                 by
                 little
                 and
                 little
                 distilled
                 .
                 And
                 in
                 the
                 end
                 of
                 the
                 Chapter
                 ,
                 he
                 saith
                 ,
                 
                   that
                   the
                
                 Doric
                 
                   Musick
                   hath
                   respect
                   unto
                   Virtues
                   ,
                   and
                   divine
                   Inspiration
                   ;
                   and
                   that
                   it
                   forceth
                   men
                   into
                   Extasie
                   of
                   mind
                   ,
                   and
                   oblivion
                   of
                   the
                   world
                   ;
                   so
                   that
                   it
                   driveth
                   away
                   evil
                   Spirits
                   ,
                   which
                   he
                   proveth
                   by
                   the
                   Example
                   of
                
                 Saul
                 .
                 Lippius
                 in
                 his
                 musical
                 Synopsis
                 ,
                 saith
                 thus
                 :
                 
                   the
                   most
                   natural
                   and
                   chief
                   of
                   all
                   the
                   Moods
                   in
                   these
                   times
                   ,
                   is
                   the
                
                 Ionic
                 ,
                 
                   with
                   his
                   secundary
                   the
                
                 Hypo
                 Ionic
                 .
                 (
                 against
                 which
                 many
                 ancient
                 and
                 modern
                 Musicians
                 do
                 speak
                 .
                 )
                 But
                 let
                 us
                 look
                 upon
                 the
                 nature
                 of
                 the
                 Moods
                 in
                 Specie
                 .
                 7.
                 
                 
                   The
                   nature
                   
                   of
                   the
                   Authent
                   Moods
                   is
                   this
                   .
                
                 The
                 
                   Authent
                   Mood
                
                 hath
                 his
                 final
                 Key
                 in
                 the
                 Diapente
                 below
                 ,
                 and
                 is
                 divided
                 harmonically
                 .
                 And
                 that
                 is
                 called
                 harmonical
                 Division
                 ,
                 where
                 the
                 Octave
                 hath
                 the
                 Fifth
                 beneath
                 the
                 Fourth
                 ,
                 thus
                 ;
                 First
                 the
                 Ionic
                 doth
                 occur
                 ,
                 which
                 is
                 by
                 Lucian
                 called
                 
                   Glaphyrus
                   .
                   i.
                   e.
                
                 pleasant
                 :
                 and
                 by
                 Apuleius
                 wanton
                 .
                 And
                 now
                 it
                 is
                 much
                 used
                 .
                 It
                 runneth
                 between
                 C.
                 and
                 c.
                 is
                 divided
                 in
                 G.
                 and
                 endeth
                 in
                 c.
                 In
                 a
                 flat
                 Song
                 it
                 runneth
                 between
                 F.
                 and
                 f.
                 and
                 is
                 divided
                 in
                 C.
                 and
                 endeth
                 in
                 f.
                 It
                 is
                 most
                 agreeable
                 to
                 Iambic's
                 and
                 Trochaic's
                 .
                 Then
                 the
                 Dorian
                 Mood
                 runneth
                 between
                 D.
                 and
                 d.
                 and
                 is
                 divided
                 in
                 a.
                 ending
                 in
                 d.
                 but
                 raised
                 ,
                 or
                 in
                 a
                 flat
                 Song
                 ,
                 hath
                 his
                 course
                 between
                 g.
                 and
                 gg
                 .
                 and
                 is
                 divided
                 in
                 d.
                 and
                 endeth
                 in
                 gg
                 .
                 By
                 Lucian
                 it
                 is
                 called
                 grave
                 ,
                 and
                 by
                 Apuleius
                 warlike
                 .
                 It
                 is
                 most
                 fit
                 to
                 sing
                 to
                 heroick
                 Verse
                 :
                 for
                 it
                 hath
                 wonderful
                 Gravity
                 with
                 Alacrity
                 .
                 The
                 Phrygian
                 Mood
                 hath
                 his
                 course
                 between
                 E.
                 and
                 e.
                 and
                 is
                 divided
                 in
                 mi
                 which
                 is
                 in
                 b.
                 ending
                 in
                 e.
                 In
                 a
                 flat
                 Song
                 it
                 runneth
                 between
                 a.
                 and
                 aa
                 .
                 and
                 is
                 divided
                 in
                 e.
                 and
                 endeth
                 in
                 
                   a
                   a.
                   Lucian
                
                 calleth
                 it
                 
                   Entheus
                   ,
                   Apuleius
                
                 religious
                 .
                 For
                 it
                 hath
                 the
                 severe
                 Insultation
                 of
                 an
                 angry
                 man
                 ,
                 whence
                 it
                 is
                 called
                 Scolius
                 .
                 It
                 is
                 impetuous
                 ,
                 accommodated
                 to
                 warlike
                 Affairs
                 .
                 It
                 is
                 also
                 Iambic
                 and
                 tragic
                 ;
                 distracting
                 and
                 ravishing
                 the
                 mind
                 ,
                 putting
                 it
                 as
                 it
                 were
                 out
                 of
                 it self
                 ,
                 as
                 Aristotle
                 saith
                 ,
                 8.
                 
                   pol.
                   c.
                
                 5.
                 and
                 Plato
                 3.
                 
                   de
                   Instit.
                
                 The
                 Lydian
                 Mood
                 doth
                 take
                 his
                 course
                 between
                 F.
                 and
                 f.
                 is
                 divided
                 in
                 c.
                 and
                 endeth
                 in
                 f.
                 in
                 a
                 flat
                 Song
                 it
                 runneth
                 between
                 b.
                 and
                 bb
                 .
                 and
                 is
                 divided
                 in
                 f.
                 and
                 endeth
                 in
                 bb
                 .
                 It
                 is
                 harsh
                 ,
                 threatning
                 ,
                 and
                 merry
                 .
                 As
                 Plato
                 3.
                 
                   dial
                   .
                   de
                   rep
                
                 .
                 who
                 
                 condemneth
                 the
                 Lydian
                 and
                 
                   Ionic
                   Harmony
                
                 as
                 sottish
                 .
                 This
                 Mood
                 is
                 sharp
                 ,
                 and
                 according
                 to
                 Apuleius
                 ,
                 threatning
                 :
                 and
                 to
                 
                   Lucian
                   Bacchicus
                   .
                   q.
                
                 raging
                 .
                 The
                 Mixolydian
                 Mood
                 runneth
                 between
                 g.
                 and
                 gg
                 .
                 and
                 is
                 divided
                 in
                 d.
                 and
                 endeth
                 in
                 gg
                 .
                 In
                 a
                 flat
                 Song
                 it
                 runneth
                 between
                 c.
                 and
                 cc.
                 and
                 is
                 divided
                 in
                 gg
                 .
                 And
                 endeth
                 in
                 cc.
                 
                 It
                 moveth
                 the
                 Affections
                 ,
                 and
                 rendreth
                 them
                 sorrowful
                 and
                 contracted
                 ;
                 because
                 it
                 is
                 mingled
                 with
                 the
                 Dorick
                 gravity
                 .
                 Lastly
                 ,
                 the
                 Aeolian
                 Mood
                 runneth
                 between
                 a.
                 and
                 aa
                 .
                 and
                 is
                 divided
                 in
                 e.
                 and
                 endeth
                 in
                 aa
                 .
                 being
                 raised
                 up
                 ,
                 it
                 runneth
                 between
                 d.
                 and
                 dd
                 .
                 and
                 is
                 divided
                 in
                 aa
                 .
                 and
                 endeth
                 in
                 dd
                 .
                 It
                 is
                 mild
                 and
                 very
                 sweet
                 ,
                 being
                 sung
                 to
                 Lyrick
                 Verses
                 .
                 8.
                 
                 
                   The
                   nature
                   of
                   the
                   Plagal
                   Moods
                   is
                   this
                   .
                
                 This
                 Mood
                 is
                 called
                 Plagal
                 ,
                 as
                 if
                 we
                 should
                 say
                 oblique
                 or
                 inver●ed
                 ;
                 which
                 hath
                 its
                 final
                 Key
                 in
                 the
                 lowest
                 part
                 of
                 the
                 fifth
                 ,
                 but
                 above
                 the
                 fourth
                 :
                 and
                 is
                 divided
                 arithmetically
                 .
                 That
                 Division
                 is
                 by
                 Musicians
                 called
                 arithmetical
                 ,
                 Where
                 the
                 Octave
                 hath
                 the
                 fourth
                 beneath
                 the
                 fifth
                 ;
                 which
                 is
                 the
                 more
                 unpleasant
                 .
                 This
                 Mood
                 borroweth
                 his
                 name
                 from
                 the
                 Authent
                 ,
                 Hypo
                 being
                 prefixed
                 thereunto
                 .
                 First
                 the
                 Hypoionic
                 Mood
                 runneth
                 between
                 Γ.
                 and
                 g.
                 and
                 divideth
                 and
                 endeth
                 in
                 C.
                 being
                 raised
                 up
                 ,
                 it
                 runneth
                 between
                 C.
                 and
                 c.
                 it
                 is
                 divided
                 in
                 F.
                 In
                 this
                 Mood
                 ,
                 the
                 Molity
                 of
                 the
                 Ionic
                 Mood
                 is
                 rectified
                 .
                 The
                 Hypodorian
                 Mood
                 runneth
                 between
                 A.
                 and
                 a.
                 is
                 divided
                 and
                 endeth
                 in
                 D.
                 being
                 raised
                 up
                 between
                 D.
                 and
                 d.
                 is
                 divided
                 and
                 endeth
                 in
                 g.
                 It
                 hath
                 a
                 harsh
                 kind
                 of
                 Gravity
                 ,
                 and
                 flattereth
                 not
                 .
                 The
                 Hypophrigian
                 Mood
                 runneth
                 between
                 
                   B
                   sharp
                
                 ,
                 and
                 
                   b
                   sharp
                
                 ,
                 is
                 divided
                 and
                 ended
                 in
                 E.
                 being
                 raised
                 up
                 ,
                 it
                 runneth
                 between
                 
                 E.
                 and
                 e.
                 is
                 divided
                 and
                 ended
                 in
                 a.
                 This
                 Mood
                 is
                 humble
                 ,
                 and
                 inclineth
                 to
                 weeping
                 ,
                 as
                 making
                 a
                 sorrowful
                 Complaining
                 and
                 pitiful
                 Lamentation
                 .
                 The
                 Hypolydian
                 Mood
                 runneth
                 between
                 C.
                 and
                 c.
                 is
                 divided
                 and
                 ended
                 in
                 F.
                 being
                 raised
                 up
                 it
                 runneth
                 between
                 F.
                 and
                 f.
                 is
                 divided
                 and
                 ended
                 in
                 
                   b
                   flat
                
                 .
                 It
                 expresseth
                 a
                 kind
                 of
                 sorrowful
                 Continency
                 ,
                 and
                 is
                 called
                 the
                 pious
                 ,
                 and
                 as
                 it
                 were
                 puling
                 Mood
                 ;
                 and
                 stirreth
                 up
                 tears
                 .
                 The
                 Hypomixolydian
                 Mood
                 runneth
                 between
                 D.
                 and
                 d.
                 is
                 divided
                 and
                 ended
                 in
                 g.
                 being
                 raised
                 ,
                 it
                 runneth
                 between
                 G.
                 and
                 g.
                 is
                 divided
                 and
                 ended
                 in
                 c.
                 In
                 it
                 there
                 is
                 a
                 certain
                 natural
                 jollity
                 .
                 The
                 
                   Hypo
                   Aeolian
                
                 Mood
                 runneth
                 between
                 E.
                 and
                 e.
                 is
                 divided
                 and
                 ended
                 in
                 a.
                 being
                 raised
                 up
                 ,
                 it
                 runneth
                 between
                 a.
                 and
                 aa
                 .
                 and
                 is
                 divided
                 in
                 d.
                 9.
                 
                 
                   This
                   is
                   the
                   nature
                   of
                   the
                   illegitimate
                   Moods
                   .
                
                 An
                 illegitimate
                 or
                 bastard
                 Mood
                 ,
                 is
                 that
                 ,
                 which
                 cannot
                 aptly
                 be
                 divided
                 into
                 the
                 fifth
                 and
                 fourth
                 :
                 but
                 into
                 the
                 Tritone
                 and
                 Semidiapente
                 .
                 And
                 it
                 is
                 eithe●
                 the
                 
                   Hyper
                   Aeolian
                
                 Mood
                 ,
                 or
                 the
                 Hyperphrygian
                 .
                 The
                 
                   Hyper
                   Aeolian
                
                 Mood
                 is
                 the
                 illegitimate
                 of
                 the
                 Authent
                 ;
                 which
                 runneth
                 between
                 b.
                 and
                 bb
                 .
                 having
                 below
                 a
                 Semidiapente
                 ,
                 and
                 above
                 a
                 Tritone
                 .
                 The
                 Hyperphrygian
                 is
                 the
                 Bastard
                 of
                 the
                 Plagal
                 Mood
                 ,
                 which
                 runneth
                 between
                 F.
                 and
                 f.
                 having
                 a
                 Tritone
                 below
                 ,
                 and
                 a
                 Semidiapente
                 above
                 .
                 10.
                 
                 
                   Every
                   simple
                   Mood
                   ,
                   out
                   of
                   his
                   own
                   proper
                   harmonical
                   Triade
                   ,
                   doth
                   give
                   to
                   every
                   harmonical
                   Song
                   ,
                   peculiar
                   Ornaments
                   .
                
                 To
                 wit
                 ,
                 Fuges
                 and
                 Closes
                 proper
                 ,
                 primary
                 ,
                 secundary
                 ,
                 and
                 tertiary
                 .
                 Unto
                 which
                 ,
                 strange
                 Closes
                 from
                 a
                 strange
                 Triad
                 may
                 be
                 added
                 ;
                 if
                 they
                 be
                 well
                 taken
                 .
                 The
                 primary
                 Fuge
                 ,
                 and
                 also
                 the
                 
                 Close
                 is
                 from
                 the
                 first
                 of
                 his
                 proper
                 ●riaede
                 :
                 the
                 Secondary
                 from
                 the
                 highest
                 :
                 and
                 the
                 ●ertiat
                 from
                 the
                 middle
                 .
                 11.
                 
                 
                   Every
                   Mood
                   in
                   respect
                   of
                   his
                   Effect
                   and
                   Affection
                   ,
                   doth
                   follow
                   his
                   Radix
                   .
                   i.
                   e.
                
                 his
                 
                   Monads
                   ,
                   Dyads
                
                 ,
                 and
                 Trias
                 of
                 which
                 he
                 doth
                 consist
                 .
                 
                   Hence
                   it
                   is
                
                 (
                 saith
                 Lippius
                 )
                 
                   that
                   one
                   Mo●d
                   is
                   very
                   cheerful
                   and
                   lively
                
                 ;
                 as
                 the
                 Ionic
                 very
                 much
                 ,
                 the
                 Lydian
                 devoutly
                 ;
                 the
                 M●xolydian
                 moderately
                 ;
                 another
                 flat
                 ,
                 soft
                 ,
                 sorrowful
                 ,
                 and
                 grave
                 ,
                 as
                 the
                 Doric
                 meanly
                 ;
                 the
                 Aeolian
                 lesse
                 ;
                 and
                 the
                 Phrygian
                 exceedingl●
                 .
                 12.
                 
                 
                   A
                   compounded
                   Mood
                   doth
                   proceed
                   from
                   simple
                   Moods
                   ,
                   and
                   from
                   it
                   a
                   Song
                   is
                   called
                   mixed
                   .
                
                 A
                 Mood
                 is
                 compounded
                 of
                 Moods
                 neer
                 unto
                 him
                 ,
                 as
                 the
                 Ionic
                 and
                 Hyper-Ionic
                 which
                 is
                 often
                 seen
                 :
                 or
                 of
                 Moods
                 wholly
                 diverse
                 ,
                 as
                 the
                 Ionic
                 and
                 Doric
                 ;
                 which
                 is
                 lesse
                 used
                 .
                 This
                 mixture
                 dependeth
                 more
                 or
                 lesse
                 upon
                 the
                 affected
                 Text.
                 13.
                 
                 
                   The
                   Mood
                   in
                   instrumental
                   Musick
                   ,
                   by
                   the
                   Mediation
                   of
                   Chromatisme
                   ,
                   is
                   transposed
                   either
                   to
                   the
                   fourth
                   above
                   ;
                   or
                   ,
                
                 which
                 is
                 the
                 same
                 ,
                 
                   to
                   the
                   fifth
                   beneath
                
                 .
                 Hence
                 ,
                 from
                 a
                 regular
                 or
                 sharp
                 Mood
                 ,
                 an
                 irregular
                 Mood
                 is
                 made
                 ,
                 which
                 is
                 called
                 mollis
                 .
                 It
                 is
                 transposed
                 also
                 to
                 the
                 second
                 ,
                 third
                 ,
                 or
                 other
                 Interval
                 :
                 So
                 that
                 one
                 Mood
                 is
                 changed
                 into
                 the
                 nature
                 of
                 another
                 ;
                 as
                 the
                 Lydian
                 ,
                 into
                 the
                 Ionic
                 :
                 the
                 Hypolydian
                 into
                 the
                 Hypo-Ionic
                 .
                 14.
                 
                 
                   Alwayes
                   the
                   two
                   proximate
                   Moods
                
                 (
                 the
                 Authent
                 with
                 his
                 Plagal
                 )
                 
                   have
                   the
                   same
                   fifth
                   ,
                   and
                   the
                   same
                   fourth
                   .
                
                 Thus
                 ,
                 
                 
                   
                     
                       1
                       &
                       2.
                       
                    
                     
                       Quartam
                       .
                    
                     
                       
                         re
                         sol
                      
                       .
                    
                  
                   
                     
                       Quintam
                       .
                    
                     
                       
                         re
                         la.
                      
                       
                    
                  
                   
                     
                       3
                       &
                       4.
                       
                    
                     
                       Quartam
                       .
                    
                     
                       
                         mi
                         la.
                      
                       
                    
                  
                   
                     
                       Quintam
                       .
                    
                     
                       
                         mi
                         mi.
                      
                       
                    
                  
                   
                     
                       5
                       &
                       6.
                       
                    
                     
                       Quartam
                       .
                    
                     
                       
                         vt
                         fa.
                      
                       
                    
                  
                   
                     
                       Quintam
                       .
                    
                     
                       
                         fa
                         fa.
                      
                       
                    
                  
                   
                     
                       7
                       &
                       8.
                       
                    
                     
                       Quartam
                       .
                    
                     
                       
                         re
                         sol
                      
                       .
                    
                  
                   
                     
                       Quintam
                       .
                    
                     
                       
                         vt
                         sol
                      
                       .
                    
                  
                   
                     
                       9
                       &
                       10.
                       
                    
                     
                       Quartam
                       .
                    
                     
                       
                         re
                         sol
                      
                       .
                    
                  
                   
                     
                       Quintam
                       .
                    
                     
                       
                         re
                         la.
                      
                       
                    
                  
                   
                     
                       11
                       &
                       12.
                       
                    
                     
                       Quartam
                       .
                    
                     
                       
                         vt
                         fa.
                      
                       
                    
                  
                   
                     
                       Quintam
                       .
                    
                     
                       
                         vt
                         sol
                      
                       .
                    
                  
                
                 But
                 here
                 let
                 us
                 place
                 Schemes
                 to
                 illustrate
                 this
                 thing
                 .
              
               
                 
                   Authent
                   Moods
                   in
                   a
                   sharp
                   Song
                   .
                
              
               
                 
                   Authent
                   Moods
                   in
                   a
                   Flat
                   Song
                   .
                
              
               
                 
                   Plagal
                   Moods
                   in
                   a
                   Sharp
                   Song
                   .
                
              
               
                 
                   Of
                   the
                   Plagal
                   Mood
                   in
                   a
                   Flat
                   Song
                   .
                
              
               
                 By
                 these
                 Tables
                 it
                 doth
                 appear
                 that
                 the
                 Plagal
                 Mood
                 differeth
                 not
                 from
                 the
                 Anthent
                 but
                 by
                 remission
                 into
                 the
                 fourth
                 :
                 when
                 in
                 the
                 Authent
                 here
                 is
                 an
                 Elevation
                 into
                 the
                 fi●th
                 
                   v.
                   g.
                
                 if
                 in
                 the
                 Ionic
                 Mood
                 it
                 be
                 
                   vt
                   ,
                   sol
                
                 ,
                 in
                 the
                 Hypolonic
                 ,
                 it
                 will
                 be
                 
                   vt
                   .
                   fa.
                
                 hence
                 also
                 the
                 Compass
                 of
                 all
                 Moods
                 may
                 easily
                 be
                 found
                 .
                 
                 
                   v.
                   gr
                
                 .
                 the
                 Compass
                 of
                 the
                 Ionic
                 Mood
                 in
                 a
                 sharp
                 Song
                 ,
                 is
                 
                   sol
                   .
                   vt
                
                 .
                 in
                 a
                 flat
                 Song
                 
                   fa.
                   vt
                
                 .
                 the
                 Compass
                 of
                 the
                 Dorian
                 Mood
                 in
                 a
                 sharp
                 Song
                 is
                 
                   re
                   .
                   la.
                
                 in
                 a
                 flat
                 Song
                 
                   re
                   .
                   sol
                
                 .
                 and
                 so
                 of
                 the
                 rest
                 .
              
            
          
        
         
           
             CHAP.
             X.
             Of
             Special
             Musick
             .
          
           
             
               PRECEPTS
               .
            
             
               THus
               far
               of
               the
               general
               part
               of
               Musick
               :
               the
               special
               remaineth
               ,
               concerning
               the
               various
               kinds
               of
               Musick
               ,
               which
               are
               taken
               eith●r
               from
               the
               matter
               :
               or
               the
               Character
               of
               the
               matter
               :
               or
               the
               Organical
               Cause
               :
               or
               Artifice
               of
               Musick
               .
            
             
               First
               ,
               From
               the
               Matter
               ,
               Musick
               is
               either
               sacred
               or
               civil
               .
            
             
               Secondly
               ,
               From
               the
               Character
               ,
               Musick
               is
               either
               great
               ,
               or
               mean
               ,
               or
               humble
               .
            
             
               Thirdly
               ,
               From
               the
               Organical
               Cause
               ,
               Musick
               is
               vocal
               ,
               instrumental
               ,
               or
               mixed
               .
               That
               is
               made
               by
               the
               voice
               of
               man
               ,
               the
               next
               by
               divers
               Instruments
               ,
               and
               this
               
               by
               the
               Uoice
               and
               Instrument
               together
               .
            
             
               Fourthly
               ,
               From
               Artifice
               ,
               Musick
               is
               either
               Choral
               or
               Figural
               .
               That
               doth
               in
               his
               Notes
               observe
               an
               equal
               measure
               ,
               and
               from
               the
               Author
               is
               called
               Gregorian
               :
               and
               this
               is
               either
               old
               or
               plaine
               .
            
             
               This
               is
               such
               whose
               unequal
               Notes
               do
               vary
               their
               measure
               ,
               and
               from
               the
               Author
               is
               called
               Ambrosian
               .
            
             
               Also
               mensural
               ,
               and
               new
               Musick
               .
            
          
           
             
               RULES
               .
            
             
               
                 1.
                 
                 The
                 asper
                 Artery
                 
                   [
                   or
                   Windpipe
                
                 ]
                 of
                 a
                 man
                 ,
                 Vocal
                 by
                 the
                 Tongue
                 ,
                 is
                 the
                 Law
                 of
                 all
                 Musical
                 Instruments
                 .
              
               
                 Lively
                 or
                 Vocal
                 Musick
                 as
                 they
                 call
                 it
                 ,
                 seeing
                 it
                 is
                 the
                 Cause
                 of
                 Instrumental
                 Musick
                 ,
                 without
                 Controversie
                 is
                 the
                 noblest
                 of
                 all
                 .
                 And
                 if
                 it
                 be
                 joyned
                 with
                 instrumental
                 Musick
                 ,
                 it
                 is
                 an
                 incredible
                 Means
                 of
                 moving
                 the
                 Affections
                 and
                 Sences
                 .
                 Also
                 Vocal
                 Musick
                 is
                 called
                 the
                 Exemplary
                 or
                 paradigmatical
                 Cause
                 of
                 Instrumental
                 Musick
                 :
                 whatsoever
                 they
                 talk
                 of
                 Pythagoras
                 ,
                 that
                 he
                 found
                 out
                 Musick
                 by
                 the
                 striking
                 of
                 divers
                 Hammers
                 upon
                 an
                 Anvile
                 .
              
            
             
               
               
                 2.
                 
                 A
                 Song
                 which
                 may
                 be
                 sung
                 both
                 by
                 Voice
                 and
                 Instrument
                 ,
                 is
                 various
                 .
              
               
                 To
                 this
                 belongeth
                 a
                 
                   Mottet
                   ,
                   Madrigal
                   ,
                   Intrade
                
                 ,
                 and
                 bound
                 Fuge
                 :
                 and
                 this
                 of
                 one
                 harmonical
                 Triade
                 only
                 ,
                 or
                 of
                 more
                 .
                 Also
                 the
                 
                   unisonous
                   Simply
                
                 ,
                 or
                 multisonous
                 ,
                 and
                 that
                 through
                 the
                 
                   eight
                   ,
                   fifth
                   ,
                   third
                
                 ,
                 &c.
                 
                 Also
                 to
                 these
                 may
                 be
                 referred
                 Songs
                 of
                 one
                 ,
                 two
                 ,
                 three
                 ,
                 four
                 ,
                 or
                 five
                 Voices
                 ,
                 and
                 likewise
                 Songs
                 of
                 many
                 Voices
                 ,
                 or
                 Polyphoniacs
                 :
                 which
                 for
                 their
                 perfection
                 may
                 swell
                 to
                 forty
                 or
                 more
                 Melodies
                 .
                 Of
                 these
                 the
                 Song
                 for
                 one
                 Voice
                 is
                 an
                 harmonical
                 Song
                 potentially
                 :
                 the
                 Song
                 for
                 two
                 Voices
                 ,
                 is
                 the
                 first
                 harmonical
                 Song
                 ,
                 in
                 Act
                 ;
                 but
                 more
                 imperfect
                 :
                 but
                 the
                 Song
                 for
                 three
                 Voices
                 is
                 perfecter
                 :
                 and
                 the
                 Song
                 of
                 four
                 voices
                 most
                 perfect
                 .
              
            
             
               
                 3.
                 
                 Musical
                 Instruments
                 may
                 conveniently
                 be
                 reduced
                 to
                 these
                 two
                 kinds
                 .
              
               
                 For
                 some
                 are
                 called
                 Pshelaphetus
                 :
                 and
                 others
                 are
                 called
                 Pneumatic
                 :
                 and
                 these
                 are
                 called
                 Crosta's
                 ,
                 which
                 only
                 by
                 striking
                 do
                 make
                 a
                 Concent
                 ,
                 and
                 by
                 others
                 are
                 called
                 Entata
                 .
                 These
                 are
                 also
                 called
                 Empneusta
                 ,
                 and
                 they
                 are
                 moved
                 with
                 the
                 Fingers
                 and
                 Wind.
                 Various
                 kinds
                 of
                 Instruments
                 are
                 comprehended
                 under
                 these
                 .
                 As
                 the
                 
                   Whistle
                   ,
                   Pipe
                   ,
                   Cornet
                   ,
                   Sackbut
                   ,
                   Trumpet
                   ,
                   Bagpipe
                   ,
                
                 and
                 the
                 like
                 ,
                 which
                 are
                 blown
                 .
                 Also
                 the
                 
                   Clavichord
                   ,
                   Psaltery
                   ,
                   Pandore
                   ,
                   
                   Cithren
                   ,
                
                 and
                 the
                 like
                 ,
                 which
                 are
                 struck
                 with
                 strings
                 :
                 So
                 also
                 the
                 
                   Lute
                   ,
                   Harp
                   ,
                   Lyre
                   ,
                   Tabor
                   ,
                
                 and
                 other
                 Instruments
                 struck
                 with
                 strings
                 .
                 The
                 
                   Cymbal
                   ,
                   great
                   Bell
                
                 ,
                 and
                 others
                 struck
                 with
                 Brass
                 .
                 Also
                 the
                 musical
                 Triangle
                 struck
                 with
                 Iron
                 or
                 Steel
                 .
                 Or
                 the
                 Wooden
                 Craticle
                 (
                 by
                 the
                 Germans
                 called
                 
                   einstrofiedel
                   '
                   item
                   ein
                   holtzerngelachter
                
                 )
                 struck
                 with
                 Wood.
                 And
                 lastly
                 the
                 great
                 Wind
                 Instrument
                 or
                 Organ
                 which
                 is
                 both
                 blown
                 and
                 struck
                 together
                 .
                 And
                 here
                 it
                 will
                 be
                 necessary
                 to
                 lay
                 down
                 certain
                 Aphorismes
                 concerning
                 musical
                 Instruments
                 .
                 1.
                 
                 
                   The
                   Canon
                   ,
                   Mother
                   ,
                   and
                   Radix
                   of
                   all
                   Instruments
                   ,
                   is
                   the
                   Monochord
                   :
                
                 which
                 is
                 an
                 Instrument
                 most
                 simple
                 ,
                 and
                 intire
                 ,
                 made
                 of
                 one
                 or
                 more
                 
                   unisonous
                   Chords
                
                 ;
                 and
                 may
                 be
                 divided
                 into
                 how
                 many
                 ,
                 or
                 how
                 great
                 parts
                 you
                 please
                 ,
                 according
                 to
                 radical
                 numbers
                 by
                 the
                 
                   bipartition
                   ,
                   tripartition
                   ,
                   quadripartition
                
                 ,
                 &c.
                 thereof
                 .
                 And
                 we
                 may
                 observe
                 fully
                 in
                 this
                 Instrument
                 ,
                 all
                 the
                 proportions
                 of
                 all
                 musical
                 numbers
                 .
                 And
                 this
                 will
                 be
                 the
                 most
                 simple
                 Example
                 of
                 a
                 Monochord
                 ,
                 if
                 you
                 shall
                 put
                 one
                 Chord
                 upon
                 a
                 fit
                 pe●ce
                 of
                 Wood
                 ;
                 into
                 so
                 many
                 parts
                 as
                 you
                 shall
                 divide
                 the
                 Wood
                 ,
                 certain
                 Notes
                 being
                 added
                 ,
                 so
                 many
                 distinct
                 Sounds
                 there
                 will
                 be
                 ,
                 if
                 you
                 apply
                 your
                 finger
                 to
                 the
                 Chord
                 .
                 2.
                 
                 
                   The
                   Wooden
                   Craticle
                   is
                   next
                   in
                   plainesse
                   unto
                   the
                   Monochord
                   .
                
                 This
                 is
                 made
                 ready
                 without
                 any
                 trouble
                 ,
                 if
                 a
                 Wooden
                 stick
                 being
                 very
                 drie
                 ,
                 be
                 proportionably
                 divided
                 into
                 many
                 parts
                 ;
                 which
                 according
                 to
                 the
                 Order
                 of
                 Proportions
                 ,
                 being
                 bound
                 together
                 by
                 links
                 made
                 of
                 a
                 string
                 ,
                 do
                 afford
                 harmonical
                 Sounds
                 ,
                 if
                 they
                 be
                 struck
                 with
                 a
                 stick
                 ,
                 and
                 put
                 to
                 straw
                 bound
                 together
                 .
                 3.
                 
                 
                   The
                   Lute
                   is
                   the
                   chiefest
                   of
                   all
                   Instruments
                   
                   of
                   Musick
                   .
                
                 For
                 no
                 Invention
                 of
                 ancient
                 or
                 modern
                 Musicians
                 did
                 ever
                 make
                 a
                 more
                 grateful
                 concent
                 .
                 4.
                 
                 
                   In
                   Clavichords
                   and
                   the
                   like
                   Instruments
                   there
                   is
                   the
                   most
                   evident
                   Reason
                   of
                   the
                   Scale
                   of
                   Musick
                   .
                
                 Those
                 Instruments
                 do
                 consist
                 of
                 certain
                 Tetrachords
                 ,
                 which
                 are
                 double
                 ,
                 ordinary
                 ,
                 and
                 extraordinary
                 .
                 The
                 ordinary
                 Tetrachords
                 are
                 four
                 .
                 The
                 first
                 is
                 called
                 
                   Hypaton
                   i.
                   e.
                
                 of
                 greater
                 and
                 gravest
                 Chords
                 :
                 from
                 B.
                 to
                 E.
                 and
                 this
                 is
                 the
                 Bass.
                 The
                 Second
                 is
                 
                   Meson
                   ,
                   i.
                   e.
                
                 of
                 Means
                 :
                 from
                 E.
                 to
                 a.
                 and
                 this
                 is
                 the
                 Tenor.
                 It
                 is
                 called
                 Meson
                 ,
                 because
                 in
                 old
                 time
                 when
                 there
                 were
                 only
                 three
                 Tetrachords
                 ,
                 (
                 the
                 
                   Tetrachord
                   Hyperboloeon
                
                 not
                 being
                 added
                 )
                 it
                 was
                 in
                 the
                 midst
                 .
                 The
                 third
                 is
                 Diezeugmenon
                 of
                 distinct
                 Chords
                 ,
                 which
                 is
                 disjoyned
                 from
                 a.
                 by
                 a
                 Tone
                 ,
                 which
                 is
                 from
                 b.
                 to
                 e.
                 and
                 this
                 is
                 the
                 Altus
                 .
                 The
                 fourth
                 is
                 
                   Hyperboloeon
                   i.
                   e.
                
                 of
                 excellent
                 or
                 most
                 acute
                 Chords
                 :
                 from
                 e.
                 to
                 aa
                 .
                 and
                 this
                 is
                 the
                 Discantus
                 .
                 The
                 extraordinary
                 Tetrachord
                 is
                 
                   Synemmenon
                   .
                   i.
                   e.
                
                 of
                 connexed
                 Chords
                 ;
                 so
                 called
                 because
                 it
                 is
                 joyned
                 with
                 a.
                 and
                 it
                 extendeth
                 from
                 a.
                 to
                 d.
                 There
                 is
                 also
                 a
                 threefold
                 progression
                 of
                 these
                 Tetrachords
                 ,
                 viz.
                 
                   diatonic
                   ,
                   enharmonic
                
                 ,
                 and
                 chromatic
                 .
                 The
                 diatonic
                 progression
                 is
                 by
                 a
                 Ditonus
                 and
                 lesser
                 Semitone
                 .
                 The
                 enharmonic
                 by
                 a
                 Ditonus
                 and
                 two
                 
                   Dieses
                   ,
                   viz
                
                 ,
                 the
                 greater
                 and
                 lesser
                 
                   Diesis
                   .
                   i.e.
                
                 the
                 half
                 of
                 the
                 lesser
                 Semitone
                 .
                 And
                 the
                 chromatic
                 progression
                 is
                 made
                 by
                 the
                 Semiditone
                 ,
                 and
                 greater
                 and
                 lesser
                 
                   Semitones
                   .
                   (
                   vide
                   triple
                   Scale
                   chap.
                
                 5.
                 )
                 This
                 Doctrine
                 will
                 be
                 clearer
                 ,
                 if
                 the
                 Doctrine
                 of
                 Sounds
                 ,
                 or
                 musical
                 Intervalls
                 ,
                 or
                 Moods
                 (
                 as
                 they
                 vulgarly
                 call
                 them
                 )
                 be
                 rightly
                 propounded
                 .
                 For
                 there
                 are
                 in
                 all
                 Ten
                 Moods
                 according
                 to
                 a
                 known
                 
                 Song
                 .
                 
                   The
                   Moods
                   are
                   three
                   times
                   three
                   ,
                   and
                   one
                   ,
                   by
                   which
                   every
                   Song
                   is
                   made
                   .
                
                 sc.
                 
                   The
                   Unison
                   ,
                   Semitone
                   ,
                   Tone
                   ,
                   Semiditone
                   ,
                   Ditone
                   ,
                   Diatessaron
                   ,
                   Diapente
                   ,
                   Semitone
                   with
                   a
                   Diapente
                   ,
                   Tone
                   with
                   a
                   Diapente
                   ,
                   Diapason
                   .
                
                 And
                 whosoever
                 shall
                 diligently
                 consider
                 these
                 Moods
                 ,
                 shall
                 easily
                 know
                 the
                 Ration
                 of
                 musical
                 Intervalls
                 ,
                 and
                 so
                 of
                 all
                 Harmony
                 .
                 And
                 the
                 Artificial
                 Division
                 of
                 these
                 Moods
                 is
                 this
                 .
                 A
                 Mood
                 ,
                 or
                 rather
                 a
                 Sound
                 ,
                 is
                 an
                 Intervall
                 or
                 Distance
                 from
                 another
                 ,
                 and
                 that
                 is
                 either
                 equal
                 or
                 unlike
                 .
                 An
                 equal
                 Mood
                 is
                 that
                 which
                 is
                 in
                 the
                 same
                 Degree
                 ,
                 and
                 is
                 called
                 the
                 unison
                 or
                 Basis.
                 Also
                 an
                 Unison
                 is
                 the
                 conjunction
                 of
                 two
                 or
                 more
                 Notes
                 in
                 the
                 same
                 place
                 .
                 
                   c.
                   gr
                
                 .
                 if
                 sol
                 be
                 ●epeated
                 in
                 the
                 same
                 Key
                 ,
                 or
                 la
                 ,
                 the
                 Mood
                 is
                 unlike
                 ,
                 in
                 which
                 there
                 is
                 both
                 Arsis
                 and
                 
                   Thesis
                   .
                   i.
                   e.
                
                 Elevation
                 and
                 Demission
                 of
                 the
                 Sound
                 .
                 And
                 this
                 is
                 either
                 continued
                 or
                 interrupted
                 .
                 A
                 continued
                 Sound
                 is
                 a
                 Tone
                 or
                 Semitone
                 .
                 A
                 Tone
                 is
                 the
                 skipping
                 of
                 a
                 Voice
                 from
                 a
                 Voice
                 by
                 a
                 perfect
                 Second
                 sounding
                 strongly
                 .
                 Hence
                 it
                 is
                 called
                 a
                 Second
                 .
                 In
                 the
                 progression
                 of
                 six
                 musical
                 Voices
                 ,
                 every
                 next
                 is
                 distant
                 from
                 his
                 next
                 by
                 a
                 
                   Tone
                   .
                   e.
                   gr
                   .
                   vt
                   re
                   .
                
                 except
                 
                   mi
                   fa
                
                 joyned
                 together
                 ;
                 which
                 Connexion
                 is
                 called
                 a
                 Semitone
                 ,
                 which
                 is
                 the
                 skipping
                 of
                 the
                 Voice
                 into
                 a
                 Voice
                 by
                 an
                 imperfect
                 Second
                 ,
                 sounding
                 flatly
                 :
                 as
                 is
                 the
                 Leaping
                 from
                 mi
                 into
                 fa
                 ,
                 and
                 again
                 from
                 fa
                 into
                 
                   mi.
                   scil
                
                 .
                 the
                 next
                 .
                 By
                 the
                 Greeks
                 it
                 is
                 called
                 Hemitone
                 :
                 and
                 by
                 Musicians
                 the
                 lesser
                 Semitone
                 .
                 The
                 interrupted
                 Mood
                 is
                 discrete
                 by
                 certain
                 Intervalls
                 .
                 The
                 first
                 is
                 Diaphonus
                 ,
                 as
                 the
                 Ditonus
                 and
                 Semiditonus
                 .
                 The
                 Ditonus
                 is
                 a
                 sharp
                 and
                 perfect
                 third
                 :
                 and
                 doth
                 consist
                 of
                 two
                 Tones
                 ,
                 as
                 is
                 between
                 
                   vt
                   mi.
                   fa
                   la.
                
                 otherwise
                 
                 called
                 the
                 Third
                 .
                 The
                 Semiditonus
                 is
                 the
                 Intervall
                 of
                 the
                 Voice
                 from
                 a
                 Voice
                 by
                 a
                 flat
                 and
                 imperfect
                 Third
                 As
                 between
                 
                   re
                   fa.
                   mi
                   sol
                
                 .
                 The
                 Second
                 is
                 Paraphonus
                 .
                 As
                 a
                 Diatessaron
                 and
                 a
                 Diapente
                 .
                 A
                 Diatessaron
                 is
                 the
                 leaping
                 from
                 a
                 Voice
                 into
                 a
                 Voice
                 by
                 a
                 fourth
                 .
                 As
                 is
                 between
                 
                   vt
                   fa.
                   re
                   sol
                
                 .
                 and
                 
                   mi
                   la.
                
                 otherwise
                 called
                 a
                 fourth
                 .
                 The
                 Diapente
                 is
                 the
                 skipping
                 of
                 a
                 Voice
                 from
                 a
                 Voice
                 by
                 a
                 Fifth
                 :
                 called
                 vulgarly
                 Quadrimode
                 and
                 Quinta
                 .
                 As
                 between
                 
                   vt
                   sol
                   .
                   re
                   la.
                   mi
                   mi.
                   fa
                   fa.
                
                 And
                 again
                 a
                 Fifth
                 is
                 either
                 compounded
                 with
                 a
                 Tone
                 or
                 a
                 Semitone
                 .
                 Hence
                 a
                 Tone
                 with
                 a
                 Diapente
                 is
                 a
                 perfect
                 Sixth
                 ,
                 as
                 is
                 between
                 vt
                 from
                 c
                 to
                 la
                 in
                 a.
                 The
                 Semitone
                 with
                 a
                 Diapente
                 is
                 the
                 imperfect
                 Sixth
                 .
                 As
                 between
                 mi
                 from
                 e
                 to
                 fa
                 in
                 c.
                 and
                 contrarily
                 .
                 The
                 Third
                 is
                 Antiphonus
                 .
                 as
                 the
                 Diapason
                 :
                 which
                 is
                 the
                 Distance
                 of
                 a
                 Voice
                 from
                 a
                 Voice
                 by
                 an
                 Eighth
                 ;
                 whence
                 it
                 is
                 called
                 an
                 Octave
                 .
                 And
                 it
                 is
                 made
                 seven
                 wayes
                 
                   i.
                   e.
                
                 from
                 every
                 Letter
                 to
                 his
                 like
                 ;
                 as
                 from
                 A
                 to
                 a.
                 from
                 a
                 to
                 aa
                 .
                 &c.
                 To
                 these
                 Moods
                 or
                 Intervalls
                 there
                 are
                 four
                 prohibited
                 Intervalls
                 opposed
                 by
                 vulgar
                 Musicians
                 .
                 1.
                 
                 A
                 Tritone
                 which
                 containeth
                 three
                 Tones
                 ,
                 and
                 is
                 made
                 from
                 fa
                 to
                 mi.
                 2.
                 
                 A
                 Semidiapente
                 which
                 passeth
                 from
                 mi
                 to
                 fa.
                 containing
                 two
                 Tones
                 and
                 as
                 many
                 Semitones
                 .
                 3.
                 
                 A
                 Semidiapason
                 ,
                 which
                 is
                 an
                 Octave
                 containing
                 three
                 Semitones
                 and
                 four
                 Tones
                 ,
                 reaching
                 from
                 mi
                 to
                 fa.
                 4.
                 
                 A
                 Disdiapason
                 ,
                 which
                 is
                 an
                 Intervall
                 by
                 a
                 Fifteenth
                 ;
                 within
                 which
                 there
                 is
                 a
                 Limit
                 appointed
                 to
                 the
                 Voice
                 :
                 beyond
                 which
                 it
                 may
                 not
                 wander
                 ;
                 and
                 if
                 it
                 wander
                 it
                 is
                 but
                 feigned
                 ;
                 For
                 if
                 more
                 Distances
                 then
                 a
                 Diapason
                 occur
                 ,
                 they
                 will
                 equisonate
                 with
                 the
                 former
                 Distances
                 in
                 the
                 Octave
                 .
              
            
          
        
         
           
           
             Conclusion
             .
          
           
             AND
             this
             is
             the
             
               MVSICAL
               TEMPLE
            
             ,
             whose
             Foundation
             is
             Harmony
             ,
             or
             Concord
             :
             whose
             Covering
             is
             honest
             Pleasure
             :
             whose
             Wood
             and
             Stones
             are
             the
             Harmonical
             
               Monads
               ,
               Dyads
            
             ,
             and
             Tryads
             .
             That
             thou
             mayest
             not
             only
             enter
             this
             Temple
             ,
             but
             build
             thy self
             ;
             after
             the
             diligent
             reading
             of
             this
             Synopsis
             which
             we
             here
             present
             thee
             with
             :
             Consider
             those
             
               melopoetic
               Classic's
            
             and
             prime
             Musicians
             ,
             Orlandus
             and
             Marentius
             .
             But
             chiefly
             exercise
             thy self
             in
             the
             Analysis
             of
             many
             examples
             ;
             and
             then
             from
             that
             betake
             thy self
             to
             the
             musical
             Synthesis
             .
          
           
             FINIS
             .