A philosophical essay of musick directed to a friend. Guilford, Francis North, Baron, 1637-1685. 1677 Approx. 68 KB of XML-encoded text transcribed from 19 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2005-03 (EEBO-TCP Phase 1). A42318 Wing G2216 ESTC R38780 18112159 ocm 18112159 106827 This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. Early English books online. (EEBO-TCP ; phase 1, no. A42318) Transcribed from: (Early English Books Online ; image set 106827) Images scanned from microfilm: (Early English books, 1641-1700 ; 1124:17) A philosophical essay of musick directed to a friend. Guilford, Francis North, Baron, 1637-1685. 25 [i.e. 35] p., [1] folded leaf of plates : ill. Printed for John Martyn ..., London : 1677. Attributed to Guilford by Wing and NUC pre-1956 imprints. "Feb. 3d 1676/7. Imprimatur, Guil. Sill." Folded plate not photographed. Page 35 numbered 25. Errata: inserted at end. Imperfect: cropped, with loss of print. Reproduction of the original in the Cambridge University Library. Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford. Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. 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Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements). Keying and markup guidelines are available at the Text Creation Partnership web site . eng Music -- Acoustics and physics. Music theory -- History -- 17th century. 2004-10 TCP Assigned for keying and markup 2004-10 Aptara Keyed and coded from ProQuest page images 2004-11 Andrew Kuster Sampled and proofread 2004-11 Andrew Kuster Text and markup reviewed and edited 2005-01 pfs Batch review (QC) and XML conversion A Philosophical ESSAY OF MUSICK Directed to a FRIEND . Imprimatur , Feb. 3 d 1676 / 7 Guil. Sill. LONDON , Printed for John Martyn , Printer to the Royal Society ; at the Bell in Saint Paul's Church-Yard , 1677. SIR , HAving often tyred you with Discourses of several Parts of Musick , wherein you desired to receive satisfaction , without obtaining the Effect I proposed to my self ; I reflected upon the saying , That no man understands that which he cannot so express as to make another understand it , and doubted whether the Hypothesis I entertained were not founded upon Errours , which I had swallowed without any due examination . I resolved for tryal of it , to trace my Notions as near their Principles as I could , and set them down in method , that I might discover whether they were well deduced from one another , and from such Experiments as I had in memory . Having done this I send them to you , as the severest judge I know : It has not been your custome to flatter me , and now I desire your censure , if I may impose it upon you to give it in writing , wherein you will be obliged to quote what I say truly , before you object to it , and to stand to those Allegations and Inferences you will set down for your own , in both which respects I had great disadvantage in Discourse . I shall prevent you in condemning the stile , for being too contracted and obscure ; and you must take the fault to your self when you know it does not proceed from the aversion I have to Philologie , but that I thought it would be labour lost to enlarge , when writing to so great a Philosopher and Musician as you are , I cannot fail of being understood . In other things I expose it to you ; and if I shall receive plain Confutations , it will not much disappoint or mortifie me : for I have hardly in my whole Life made one set experiment upon this Subject , nor know many of the Instruments I have spoken of : But what I heard from others , or occasionally observed , I laid up in mind , and established this Systeme , which I shall be glad to lose , if I may improve my Knowledge by your Discoveries . This may seem strange to you , considering how fond men are of their own Inventions : At the worst , I hope for this fruit of my pains , that you will make such Experiments as your Curiosity will suggest whilst you read this , and let me know the success of them ; though I may thereby be driven out of his Hypothesis , perhaps I shall receive light towards another , which you may believe I shall take as much pleasure in making , as you , or any body else can to destroy . I am , SIR , Your most Faithfull Friend and Servant . Of SOUND . MY design being to explain the nature of Musick it will not be improper to enquire first , concerning the cause of Sound ; and here though I cannot hope to give full satisfaction , because our Senses want subtilty to discover the motions of the minute parts of the Air whereupon it depends , yet perhaps I may assign a possible cause for the producing of Sound , the knowledge whereof will give some ease to the wondring Philosopher ; and if I have the good fortune to shew a probable cause , the Curious will acquiesce from any farther enquiry , which is all the benefit they can have by speculations of this nature . The Phaenomena of Sound which I think considerable are these , 1. It may be produced in the Torricellian vacuity . 2. It causes motion in solid bodies . 3. It is diminished by interposition of solid bodies , and 4. If the bodies interposed are very thick , its passage is wholly obstructed . 5. It seems to come to the Ear in strait lines when the object is so scituated that it cannot come in a straight line to the Ear. 6. When the air is not in motion its extent is sphaerical . 7. When there is a wind , the sphaere is enlarged on that part to which the wind blows , and diminished on the contrary part . 8. That it arrives not to the Ear in an instant but considerably slower than sight . 9. That it comes as quick against the wind as with it , though not so loud nor so far . There are many other observable Appearances , and more will daily occurre to the Curious upon Experiments , but the consideration of these qualities of Sound and the visible actions that produce it , hath made me entertain the following Hypothesis . I suppose the air we breath in to be a mixture of divers minute bodies which are of different sorts and sizes , though all of them are so small as to escape our senses : the grosser of them are elastical , and are resisted by solid bodies , which are in no sort pervious to them ; the smaller parts pass through solid bodies , but not with that ease but that upon a sudden and violent start of them , they shock the parts of solid bodies that stand in their way , and also the grosser parts of the air ; and there may be another degree of most subtil Ethereal parts with which the interstices of these and all other bodies are repleat , which find freer passage every where , and are capable of no compression , and consequently be the medium and cause of the immediate communication of sight . The middle sort of these I esteem the medium and cause of Sound , and that at any time when the grosser air is driven off any space and leaves it to be possest by these and other more subtil bodies , and returns by its elasticity to its former place , then are these parts extruded with violence as from the center of that space , and communicate their motion as far as the sound is heard . Or when any solid body is moved with a sudden and violent motion , these parts must be affected thereby : for as these parts are so much resisted by solid bodies as to shock them , so on the contrary they must needs be moved by the sudden starting of solid bodies . So that sound may be caused by the tremble of solid bodies without the presence of gross Air , and also by the restitution of gross Air when it has been divided with any violence . We see a Bell will sound in the Torricellian space : and when the Air is divided with any sudden force , as by the end of a Whip having all the motion of the Whip contracted in it , and by a sudden turn throwing off the Air ; by accension , as in Thunder and Guns ; or by any impression of force carrying it where other Air cannot so forcibly follow , as upon compressing of Air in a bladder till it breaks , or in a Potgun , a sudden crack will be caused . I shall leave others to apply this Hypothesis to the afore mentioned Phaenomena ( which they may easily do ) and proceed to the discourse of Musick , where I am in its due place to shew how this action that causes sound is performed by the several instruments of Musick . Of a TONE . A Tone is the repetition of Cracks or Pulses in equal spaces of time so quick that the interstices or intervals are not perceptible to sense . The more quick the Pulses are , the more acute the Tone is . Where the intervals are not equal , nor in musical proportion , the sound is not in tone but an irregular noise . The compass of Musick extends from such tones whose intervals are so great that the several Pulses are distinguishable by sense , to those whose interstices are so very small that they are not commensurate with any other . In which compass the several tones are infinite in number as all space may be divided in infinitum . But the tones useful in Musick are those within the scale , which are not very many , and they are placed in the scale as they have relation to one another . Of the Relation of TONES and the Vnion of mixt SOUNDS . WHen the Pulses of tones are coincident one with the other , there is an Union of the sounds . For when any Sound is made , solid bodies within the sphaere of it are moved , and if the body moved stands upon a spring ( as all instruments producing tones do ) it will vibrate by intervals according to the measure of the spring until the force be spent . Now if the moving force be repeated , as it must be where it proceeds from a tone , and the terms of the force are equal to the terms of vibration , every new stroke strengthens the former impression , and after some continuance the vibration of a Body affected by Sound , may become so great as to be sensible to the Eye and Ear. But where the terms of Vibration are not commensurate with the terms of concussion , the following pulses destroy the motion begun by the former , and the Vibration will never augment beyond what it was upon the first impression . Upon this Reason a string tuned in unison to another will manifestly shake when its fellow sounds , and another string that has a discording Tone , though of the same bigness , will not appear to be moved . And for this Reason , wheresoever the vibrations of two sounding strings are equal , the pulses will be coincident : for although one should set out after the other , yet by this affection they would by the second or third pulse become coincident . Where the terms are equal , and the coincidence is at every pulse , it may be said the same Sound though proceeding from several Instruments : for the mixed Sound has no alteration , but by being more loud and full by the addition . Where the Termes are 2 to 1 , or 4 to 1 , or 8 to 1 , or 16 to 1 , there will be coincidence to every pulse of the Base , and between those termes the treble is heard alone without any mixture : so that the Sound is not changed but augmented by the addition of stronger pulses at proportionable intervalls , which makes the pulses superinduced appear of the same nature , though more grave or acute ; this is the case of Octaves . Where the Termes are as 2 to 3 , every third pulse of the Treble , and every other pulse of the Base are coincident , but the intermediate pulses , sc. 2 of the Treble , and 1 of the Base are not so , but keep certain distances , which makes the mixture produce an alteration : but the coincidences being so frequent , and the distances of the intermediate pulses proportionable , the mixture is very pleasing , and is the principal Chord called the fifth . Where the Termes of coincidence are further off , as when they are but the fourth , fifth or sixth pulses of the Treble that are coincident with the third , fourth and fifth pulses of the Base , yet the mixture is pleasing , and produces Chords : which Chords are more or less perfect , according as they are more or less coincident . Coincidence upon every fourth pulse of the Treble is the fourth . Every fifth pulse is the third sharp . Every sixth pulse is the third flat . When the fifth pulse of the Treble goes with the third of the Base , it is a sixth sharp : the eighth pulse of the Treble going with the fifth of the Base makes a sixth flat . That these Chords have their pulses in such proportionable line is demonstrable by the division of the Monochord , which being stopt in ½ gives an Octave , in ⅓ gives a fifth , in ¼ gives a fourth , in ⅕ gives a third Sharp , in ⅙ gives a third Flat , ⅕ gives a sixth Sharp , ⅜ gives a sixth Flat : This is agreed by all that ever treated of Musick , therefore I shall speak no more of it . It may seem strange that a Coincidence in this manner should unite Sounds , and that the fifth and fourth pulses that are disagreeing should not hinder more , than the sixth coincident pulse could reconcile : and that a coincidence between the eighth pulse of the Treble with the fifth of the Base should make the Sounds agreeable , notwithstanding the variance of those which are intermediate . But this will be very clear , when it is observed that the intermediate pulses do not at all hinder , for they are all placed in such manner , in relation to one another , that where any of them distract the pulses of the concording string on the one hand , there are others that by being just as much on the other hand , set them right again : they are in balance one against another , so that it is as if there were no intermediate pulse at all , as to any effect of hindring the Coincidence . And the intermediate pulses being at such symmetrical distances a new proportion arises from the mixture of them , which makes the joined Sounds pleasing to the sense . Where the coincidences are more remote , and all the intermediate pulses disagreeing , as 7 to 6 , 8 to 7 , 9 to 8 , 10 to 9 , the by pulses are too many to be kept steddy , and the pulses on one hand prevail too far before those on the other hand come to set them right , so that the Sounds will not maintain their coincidences , but produce jarring and discord . When Sounds are in discord , the concussions caused by them are in opposition one to another ; and the Organ of Sense cannot be affected by both together , but they will appear ragged and jarring , and extream noisome . Nay some sounds will be so contrary to one another , & so hard a match , that they cannot sound both together , but each hindering the other will take turnes . Thus do they imitate the Drum in an Organ , by joyning two deep discording Notes , that rumble in that manner sounding by turns . And in tuning Organ-pipes it may be observed , that the Sounds of two Pipes whilst in discord will flutter , but when the discording Pipe is brought to the others Tone , the Sounds will as it were jump into Tune , as if they had attracted one another , and afterwards one clear and entire Sound will be produced . Upon this Relation of Tones depends the Scale of Musick , of which I shall shew the Degrees , and the reason why they are so placed , when I come to speak of Schismes . Before I leave this Head I must observe , that Octaves not altering the manner of Sound , but giving a fulness in duple proportions , which are comprehended in the same time , it follows , that all Octaves are easily brought in mind , and are as it were included in any Tone . This being considered , it will appear , that there can be no other variety of coincidence within the compass of seven pulses that is not allowed in Musick , and produces some Chord : For , ⅓ is as ⅔ 2 being the Octave to 1. ⅕ is as ⅘ 4 being in Octave to 1. ⅖ as ⅘ , 2 / 6 as ⅔ , ⅙ as 4 / 6 , as ⅔ . And the eighth coincident pulse in a sixth flat , comes in upon this contemplation , but as the reverse of a third sharp , ⅝ being the reverse of 5 / 4 , and the other sixth ⅗ is the reverse of 6 / 5. So that there can be no other coincidences under the distance of the seventh pulse , but what have the names of Chords , or the Octaves ; and we are not to wonder why there are no more concording Notes . How TONES are produced , and of assistances to the SOUND by Instruments . WHerever a Body stands upon a Spring that vibrates in equal Termes , such a Body put into motion will produce a Tone , which will be more grave or acute , according to the velocity of the returns . Therefore strings vibrating have a Tone according to the bigness or tension of them ; and Bells that vibrate by cross ovals , produce Notes according to the bigness of them , or the thickness of their sides : and so do all other bodies whose superficies being displaced by force , results by a spring which carries it beyond its first station . It is easie to comprehend how every pulse upon such vibrations causes Sound , for the gross Air is thrown off by the violence of the motion , which continues some moment of time after the return of the vibrating Body , whereupon some space must be left to that subtil matter , which upon the result of the Air starts as from a Centre ; which action being the same I supposed to be the cause of Sound , is repeated upon every vibration . It is more difficult to shew how Tones are made by a Pipe , where there are no visible vibrations . I will consider the frame of a Pipe , and the motion of the Air in it , and thereby attempt to find the cause of the Tone of a Pipe , and the pulse that gives the Sound . There is in any Pipe a Cavity of a certain gage or bigness which is exposed to the outward Air , but in some parts of it , and according to that Cavity is the Tone of the Pipe. The Air in any Cavity being capable of being compressed by outward force , if the Cavity be large , easily yields to a compression ; but if it be small , is more hardly compressed . When the compressing force ceases , the Body that was compressed with difficulty flies out with sudden violence ; that which is more easily compressed restores it self not so soon : whereby it happens , that every Cavity has a certain Tone according to the measure of the vibrations of the Air in it , which it will keep what way soever the force comes to it : As the water in a Shallow or Greek moved by the large waves of the Sea , retains not a motion in such huge waves , but in waves proportionable to its own bigness and depth . Hereupon I conclude , That any Pipe , whether made of Wood , Stone , Glass or Metal , has a certain and determinate Tone , according to its Gage and Cavity , which is the natural Tone which will be produced by blowing it . If the Cavity be small , the Sound will be acute , and may be made more acute by apertures , whereby the Cavity is diminished , and the inclosed Air exposed to the outward Air in greater measure . When I say , the Tone is according to the proportion of the Cavity , let the Pipe be made of what it well ; I do not deny but that if the materials of the Pipe be soft and yielding , it may give some small alteration to the Tone from what it would be if they were of a substance hard and firm , where the impelling Air would find a more brisk resistance : but the difference is inconsiderable , and the spring of the Air depending mainly upon the greatness of the Cavity , I take no notice of it . To shew how the pulses are caused , whereby the included Air is put into this motion , it is necessary to observe the frame of a Pipe , which chiefly consists in having a long slit through which the Air is blown in a thin film against or very near a solid edge that is at some distance opposite to it , in such manner that the intermediate space is covered by the stream of Air. This film of Air on the one side is exposed to the outward Air , and on the inside is defended from it by the sides of the Pipe , within which the Air inclosed in the Pipe stagnates , whilst the outward Air is by the blast put into a vortical motion . The vortical motion or Eddy on the outside is so strong , that there not being a balance to that force on the inside , the film of Air gives way , and the Eddy bears into the Pipe , but is immediately overcome by the blast , which prevails untill the Eddy overcomes it again ; and so there is a crossing of streams by turns and pulses , which causes the voice of the Pipe , the gross Air of one stream being thrown off by the interposition of the other . These vicissitudes or termes will answer the Tone of the Pipe according to the gage of its cavity : for the spring of the included Air helps toward the restitution of the blast and eddy in their turns , which causes those turns to comply with the Tone of the Pipe ; and therefore the same blast will cause several Tones , if the gage or measure of the included Air be changed by apertures in the side of the Pipe. But there must be some proportion between the mouth , ( so I call that part of the Pipe where the voice is ) and the gage of the Pipe : for though the pulses will be brought to comply with the Tone of the Pipe in any reasonable degree , yet when there is great disparity it will not do so ; as if the Pipe be too long for the proportion of the diameter , the pulses at the mouth cannot be brought to so slow termes as to answer the vibrations of the included Air , therefore the Pipe will not speak unless it can break into some higher Note . If the filmy stream of Air be too thick , the Pipe will not speak , because the eddy cannot break through ; if the opposite edge be too remote , the stream cannot entirely cover the aperture , for it mixes with the outward Air , and is more confused the farther it is from the vent or passage , whereby some outward Air may have communication to make an opposite eddy on the inside of the stream . For the same reason , if there be the least aperture in the region of the mouth of the Pipe , it will not speak at all . Hence is it , that the voice of Organ Pipes is so tender and nice : but shrill whistles depend not upon this ground ; for they are made in any small cavity where the blast is so applyed , that the erumpent Air must cross it , whether the stream be thick or thin . Therefore the bore of a Key , a piece of nutshell , or any other cavity will make a whistle , whose Tone will be according to the quantity of the included Air , for the less that is , the harder it is to be compressed , and the quicker and stronger it must break forth . Another kind of Whistle is , when a hollow body with a small cavity is perforated by opposite holes , a blast either way will cause a Tone , which seems to be made in this manner . The Air that is violently drawn or thrust through these holes is straitned at the passage by the swiftness of the motion , and within the cavity is somewhat enlarged , and consequently its force is directed , and it presses beyond the compass of the opposite aperture , whereupon it bears of all sides into the cavity ; hereby the Air within the cavity is compressed untill it breaks forth by crossing the stream , which being done by vicissitudes causes a Tone : this kind of action , as I imagine , is performed when men whistle with their lips . In some Pipes the pulses are caused by springs , as the Regoll stop of an Organ , which is commonly tuned by shortning the spring whereby it becomes stronger , but the Note will be changed by the alteration of the cavity ; and therefore to make them steddy , some that stand upon very weak springs have Pavelions set to them . A rustick instance may be given of the compliance of a Spring , in taking such vibrations as are proportionable to the Cavity ; It is a Jews-harp , or Jews-trump , the tongue whereof has natural vibrations according to strength and length of the Spring , and so is fitted to one particular Tone : But Countrey-men framing their breath and their mouth to several Notes make a shift to express a Tune by it . In a Shawm or Hautboys the Quill at the mouth is a kind of Spring , but so weak and indifferent that it complies with any measure , and therefore the Tone will be according to the apertures of the Pipe. The fluttering and jarring of discording Sounds , which I before did observe , is so regular , and the Sounds take their turns with equal interstices , which makes the joyning of them produce a harsher Sound than either had before : whereby Organ-makers imitate the Hautboys or Trumpet , without any Spring or Quill , by joyning discording Pipes . In a Sackbut the Lips of a Man do the same office as a Quill does in a Shaume or Hautboys ; when the included Air is lengthned , the Tone varies : nevertheless they can produce several Notes that are in Chord to the Tone of the Instrument , by strengthning the blast without lengthning the cavity : And in a Trumpet , which is the same kind of Instrument , ( only not capable of being lengthned ) they can sound a whole Tune , which is by the artificial ordering the blast at the mouth , whereby the Sound breaks into such Notes as are to be used . This depends upon the consideration of the varying and breaking of Tones into other Notes , whereof I am to speak particularly in my next Chapter , to which I hasten . Having shewed how Tones are produced by Instruments of Musick , I must take notice of other assistances Instruments give to the Sound . In Violins and Harpsechords the Tones are made wholly by the vibrating strings , but the frame of the Instrument adds much to the Sound : for such strings vibrating upon a flat rough board would yield but a faint and pitifull Sound . The help that Instruments give to the Sound , is by reason that their sides tremble and comply with any Sound , and strike the Air in the same measure that the vibrations of the Musick are , and so considerably increase the Sound . This trembling is chiefly occasioned by the continuity of the sides of the Instrument with the vibrating string : therefore if the bridge of a Violin be loaded with lead , the Sound will be damp ; and if there be not a stick called the Sound-post to promote the continuity between the back and belly of the Instrument , the Sound will not be brisk and sprightly . Such a continuity to the nerve of hearing will cause a sense of Sound to a man that hath stopped his ears , if he will hold a stick that touches the sounding Instrument between his teeth . The Sound of it self without such continuity would occasion some trembling , as may be seen by the moving the Vnison strings in the Instance before given ; but this is not considerable in respect of the other , though it be all the assistance that the structure of a Chamber can give to Musick , except what is by way of Eccho . This tremble of the Instrument changes with every new Sound ; the spring of the sides of the Instrument standing indifferent to take any measure , receives a new impression : but a vibrating string can take no measure but according to its tension . Therefore Instruments that have nothing to stop the sounding strings make an intolerable jangle to one that stands near , as Bells to one that is in the Steeple , and hears the continuing Sound of dissonant Tones ; such is the Dulcimer : but the Harpsechord that hath raggs upon the jacks by which the vibration of the string is staid , gives no disturbance by the sonorousness of the Instrument , for that continues not the Sound after the vibrations determined , and another Tone struck , but changes and complies with the new Sound . Of the varying and breaking of TONES . TOnes will by accident vary and break into other Tones , which are Chords to the natural Tone of the Instrument : which in Pipes is so regular , that the compass of the Musick depends upon it ; upon Strings it will happen , but not so gratefull to the ear , nor much in use . I will endeavour to explain how it is caused in Strings , and speak of Pipes afterwards . A perfect string produces a clear Sound by entire and equall vibrations , there being no inequality to hinder the motion from being uniform from one end to the other , according to the Laws of a Pendulum : but if the string hath any inequality towards one end , it will yield a jarring and distracted Sound ; for the resistances are not only at the ends of the string , but there are cross tugges that alter the course of the vibrations ; which is evident in the manner whereby Musicians try if their strings be true : for if the string be true the vibrations will appear as a clear filme ; but they will appear with cross threads if the string be false . If there be a long string Pendulum , the motion will be uniform and synchronous from the bottom to the top : but if there be a weight fastned to the string towards the top , it will hinder the regularity of the motion ; for the upper weight will be put into motion , and will have vibrations of its own , which will be mixed and confounded with the vibrations of the lower weight . In the same manner in a false string two or more sorts of vibrations are blended , which are not in proportion , but casual and discording , and therefore instead of a Tone produce an horrible jarr . Now as a string by such small accidents is brought to vibrations of several parts of the string that hold no proportion one to another , much more easily may it be imagined to have vibrations of uniform parts , that shall be synchronous , and produce one single Sound , as if the parts that vibrate severally are half parts , seconds or thirds of the string : and how this may be caused , I will enquire . If a string Pendulum be very long , and the weight at bottom be not sufficient to cause the whole string to divide the Air ; at first the Pendulum will be sustained by the resistance of the Air , and afterwards it will put the whole string into motion : but not that of a streight line , for the Pendulum will return before the direct motion performed at the top . This will occasion thwarting of motions , which being balanced between the force at the bottom and the check at the top , the crossing point will settle in such a division of the string , that they will continue uniform till the force be spent . I imagine , that if a musical string be so struck , that the whole string is not removed out of its place to cause the greatest vibration in the middle , there must be a crossing of vibrations : for before the motion communicated to the farther end , the part of the string that was struck may have restored it self to its first place . This crossing of vibrations , if the string be true , will be upon equall parts , and produce an Octave fifth , or some other Chord . It is common experience , that a great string struck near the Bridge with a Bow where the Rosin takes but small hold , will whistle and break into chords above ; which if it were struck by the thumb that removes it out of its place , would give the true Tone . The Trumpet marine that sounds wholly upon such breaks , is a large and long monochord play'd on by a Bow near the end , which causes the string to break into shrill Notes . The removing the thumb that stops upon the string gives measure to these breaks , and consequently directs the Tone to be produced . The jarr at the Bridge takes the same measure and makes the Sound loud , in imitation of a Trumpet , which otherwise would be like a Whistle or Pipe. The touch of the Thumb less hinders the Sound of the string when it is upon the point where the vibrations cross , than when it is in any other part : for we see when any great string has an entire vibration , such a touch would immediately extinguish the Sound . This makes the Trumpet Marine , with the Thumb placed upon it , take to such a Note , as that the division of vibrations shall lye just under the Thumb . Speaking of the counterfeit Trumpet , I must observe that the true one seems to give all its Notes by way of breaking , which causing the metal to jarr gives so loud a sound . I fancy the true gage of the Air included in a Trumpet , in comparison of its bore would fit an eight below the Note they call the Note of the Trumpet , because a fourth below it is so easily sounded , which is a fifth to the true Tone , in case it be placed eight Notes lower : As it easily divides into three to give a fifth , so it may well treble that division , and give a second to the Trumpet Note . And for the rest of the Notes which a Trumpet will easily produce , they are the third ♯ , fourth , fifth and sixth sharp , which arise upon the most easie divisions of the monochord , and therefore most readily produced by breaking , when the strength of the blast and the action of the lips direct it . The Trumpet not being able to answer a flat Key , the Sackbut as I observed before is made in such manner that it may be lengthned to supply this defect , whereby it will give any Note at the pleasure of him that plays : but when he is to Sound an eighth or fifth above , he never lengthens the Instrument , for without any remove of his hand , the Note easily breaks into those higher Chords . The Trumpet is of the nature of Pipes , and therefore properly leads me to speak of the varying Notes upon Pipes , which is so regular , and so much in use , that the compass of the Musick depends upon it . I have shewed that Sound does cause a motion not only of solid bodies , but of the grosser parts of Air within the sphere of it . Now if the Air that is moved by being inclosed stands upon such a degree of resistance to compression , that it has a spring vibrating in the same measure with the sound that puts it into motion , there will be the same effect as when two strings are tuned in unison , that is , the motion will be so augmented by succeeding regular pulses , that the enclosed Air may be brought to ring and produce a Tone . Vitruvius in his Architecture advises , that in making a Theatre there should be vases or hollow pots of several sizes to answer all the Notes of Musick placed upon the Stage in such manner , that the Voice of them which sang upon the Stage might be augmented by the ringing of them : And he mentions divers ancient Theatres where such were , in some of Brass , in some of Earth . An Organ-pipe of a very deep Base will not speak suddenly when it is alone ; but if an Octave be in play at the same time , it will answer the quickest touch : because the Tone of the lesser Pipe being in chord causes a motion of the Air included in the greater Pipe , and the vibrations of the included Air being coincident with those of the Tone of the Pipe , promote its speaking by putting the pulses at the mouth into a regular motion , or at lest assisting thereto . These instances shew the manifest effects of Sound : and certainly Sounds in discord are in contrariety , and offer violence one to another ; but Sounds in Musical Chords are consistent , and united together , and promote each other , as I have before shewn in what I said concerning the Relation of Tones . The synchronous motion of the pulses at the mouth of the Pipe with the vibrations of the included Air promote the Sound of the Pipe , and it is hard for a Pipe to speak where those motions are in opposition : but if by strengthning the blast the pulses at the mouth are so quickned that they bear a Musical proportion to the vibration of the Air enclosed , as 2 to 1 , 3 to 2 , 4 to 3 , 5 to 4 , &c. there will be no hindrance but some advantage ; so that it may be easily imagined that the pulses at the mouth in such case will receive no interruption by the included Air , but may maintain their stations , and produce a Tone varying in the same proportion from the Tone of the Pipe. It may be objected , that if it were so , there would be a mixture of Sounds ; and not only the Tone that is in chord to the Tone of the Pipe would be heard , but also the Tone of the Pipe with it . To which it may be answered , that the vibration of the included Air is not so considerable as to be heard distinctly , though it may give alteration to a Sound ; as we see , that when a Pipe gives the true Tone , it speaks more in the belly than when it breaks into an Octave . But to wave that answer , perhaps when the Note breaks , the column of included Air divides into proportionable parts , by reason that the vibrating force at the mouth , and the resistance at the aperture meet one another in the middle , or upon other divisions , which will make the vibrations of the included Air coincident with every pulse at the mouth of the Pipe : which is the more probable , because a very small aperture in the middle of a Pipe will make it break into an eighth above , which seems not to happen by any diminution of the included Air , but interrupting the intireness of the Column . Of the nature of Keys in MUSICK , and of a single TUNE . BEfore any Note struck the Ear is indifferent to all sounds , but when any Tone is heard , that indifferency is determined , and the mind taken up with the present sound . If the second Note be not of relation to the first , the imperssion made by the first will be wholly obliterated and forgotten , the sounds will be disjoynted and incoherent : But if the second Note be of relation to the first , it is confistent with the memory of the first : if the third Note be more in chord to the first , then is that remembrance continued and strengthned : if succeeding Notes are in discord ▪ or of less relation to the Key Note , the mind and fancy is drawn from the Key Note by the present Sound ; but by repeating the Key Note and its relatives with loudness and emphasis , the memory of the Key Note may be restored again . Thus in passing to and from the Key , by Notes that have relation to the preceding Notes may a Tune proceed to any length , and amuse the hearer : but when the fifth , which is the principal chord to the Key , and most strengthens the memory of it , comes in play , nothing can be more perfect and satisfie expectation but the Key Note it self , which gives a perfect acquiescence to the hearer , and a conclusion to the Tune . For this reason all Tunes end in the Key Note , and the next preceding Note is the fifth above . In the progress of a long Tune other Notes may gain so great impression in the mind by dwelling upon the relatives to them , that the first Key may be forgotten , and the same way new Notes may gain possession , so that the Key may change many times . Thus it is in long Fancies and Preludes , and it is no matter in such case what Key the Tune concludes in : but in short Airy Tunes there are but small digressions , leaning to the fifth or third , or other relative Notes , and sometimes suddenly closing upon them , which does not destroy the memory of the first Key Note , and therefore the Ear is not satisfied with such close , but expects another strain , which ending in the Key Note concludes the Song . Generally speaking , a Tune must begin and conclude in the Key Note , because that Note takes possession of the Ear ; but this is not such a Rule but that sometimes a Tune begins or ends upon Notes relative to the Key ; and the Key is shown by them , though it be not struck : as in the progress of a Tune the Key is to be traced by the relatives to it , as well as by the Note it self : Hereby it appears that any Note may be the Key Note , as to the pitch : As to the species or sorts of Keys they are two , viz. Flat and Sharp . When a Tune begins with a Flat third it must continue so ; for the third being a relative to the Key Note , is joyned with the memory of it , and become as it were part of it , and a third Sharp being discord to it would disjoynt the Tune , though it be a better chord to the Key Note ; it being necessary that the Tune should proceed with regard to the preceding Notes : for the same reason a third Sharp when once taken into play must be continued . When the third is Flat or Sharp the sixth must be so likewise , else the third to the Key which is of principal regard and relation to the Key , and sometimes hath closes upon it , will have neither a fourth above , nor a fifth below in the Scale , but a false fifth , which could not set it off in that lustre it ought to have . There is no natural difference betwixt the Musick in one Key Note or another ; accidental differences there are : for in some Keys the emphatical Notes lying high are more sprightly than in others . Upon some Instruments , by reason of holdings , or open strings the emphatical Notes are of a mellow and durable Sound , which gives advantage to the Key . Upon most Instruments the emphatical Notes are not in Tune , by reason of the Schismes of Musick , ( whereof I am presently to speak ) therefore such Keys are not in use , and when play'd upon yield but a harsh Tune . But these differences are but accidental , and relating to the advantages or imperfections of Instruments . I shall collect from what hath been said , That the Musick of a single Tune consists in the succeeding Notes having a due relation to the preceding , and carrying their proper emphasis by length , loudness and repetition , with variety that may be agreeable to the hearer . This is called the formality of a single part , wherein Musick is so copious , that it has afforded to every Age and Nation a several fashion , and to every Musician a particular stile . Graces in Musick depend upon the same reason with the formality of a single Tune , and skilfully applyed do much advance it , by strengthning the memory of preceding , and the expectation of succeeding Notes , the doing whereof is left to every Player . Of SCHISMES , and the Scale of MUSICK . THere are Schismes in Musick , because the Scale is naturally fitted to one Key ; and though it will indifferently serve to some others , yet it will not to all . The Scale of Musick is not set out by any determinate quantities of whole Notes or half Notes , though the degrees are commonly so called ; but the degrees in the Scale of Musick are fixed by the Ear in those places , where the pulses of the Tones are coincident , without any regard to the quantity . I shall endeavour to show how all the Notes come into the Scale by their relation and dignities ; and then it will be obvious why for easiness of instruction and convenience the Scale of degrees of Musick is made as the Musicians now exhibit it . The Key Note being given , the first Note in dignity is the fifth above , which must have its true place ; for whilst the Tune is in the Key , it has the greatest emphasis ; and upon any digression from the Key , this Note is nearest to usurp it : and therefore when the Chords to the Key Note are placed , the Chords to this Note are to begarded , for without them there cannot be any variety , this being the first step from the Key . The other Chords to the Key are the third ♭ and ♯ , the fourth and the sixth ♭ and ♯ . The Chords to the fifth above the Key are the 5 / 2 d , and 3 / 7 th ♭ and ♯ , which are the fifth and third ♭ and ♯ to that Note . When the fifth has usurped the Key , the fifth above that must have the same emphasis , and will bring in the sharp fourth , or false fifth , which is its third sharp . The half Note above the Key is farthest from the Keys relatives , and therefore the Sound of it removes the dominion of the Key Note farther off than any other ; the nearest way of bringing it in request is when the fifth below has usurped the Key , to which it is a sixth flat : The fifth below taking the Key makes an ingratefull remove , for it is not a Chord comprehended in the Key Note , but the Key Note is comprehended in that , and so it diminishes the regard to the Key Note more than any other , making the transition to the Key Note , not as a restitution , but as a digression to a secondary Key , which should not continue . These are all the Notes of the Scale within the compass of an Octave , and by this method should they be Tuned , viz. Third ♭ and third ♯ , fourth , fifth , sixth ♭ , and sixth ♯ , by the Key Note , second and seventh ♭ , and seventh ♯ by the fifth above the Key or its Octave ; false fifth or fourth ♯ must be third ♯ to the second , and the ½ Note above the Key must be a sixth ♭ to the fifth below the Key . An Instrument thus tuned will be exact to that one Key , and serve to play Tunes in that Key ; but when the Musick turns to other Keys that are not relative to it , the divisions and degrees that fitted the first Key will not sute with the others , but must be removed , and thereby the Schismes appear , without which the Notes which ought to be principal and most perfect Chords to the new Key , will be manifestly out of Tune . This will best appear upon view of the division of the Monochord , which I have set down in the plainest manner I could frame . A Monochord . 540 fourth below 360 second 270 180 fifth below 480 Key 320 fourth Octave . The Key Note is 360 , whose division gives all the Chords . The fourth below is 480 , whose division gives the 7 th and second . The 5 th below is 540 , whose flat 6 th is the half Note above the Key . The second is 320 , whose third sharp is the false fifth . The Divisions appear thus : 3 / 8 of 540 = 202 ½ half note above the Key Semitone is 22 1 / ● sc. 360 / 16th part of the string . 480 / 3 = 160 the second above the Key Semitone is 17 ½ sc. 3371 / 1922 / 7 tone is 40 sc. 360 / 9th p t , of the string . 360 / 6 = 60 the third flat Semitone 20 sc. 320 / 16th part of the string tone is 32 sc. 320 / 10th p t. 360 / 5 = 72 the 3 d sharp Semitone 12 sc. 360 / 25th part of the string 360 / 4 = 90 the fourth Semitone is 18 sc. 288 / 16th part of the string tone is 30 sc. 300 / 10th p t. 404 320 / 5 = 104 the false fifth Semitone is 14 sc. 2707 / 192ths of the string tone is 32 sc. 288 / 9th p t. 360 / 3 = 120 the fifth Semitone is 16 sc. 256 / 16th part of the string tone is 30 sc. 270 / 9th p t. 3 / 8 of 360 = 135 the 6 th flat Semitone is 15 sc. 240 / 16th p t of the string tone is 24 sc. 240 / 10 2 / 5 of 360 = 144 the 6 th sharp Semitone is 9 sc. 225 / 25th p t of the string 480 / 5 = 96 seventh sharp below semitone below the Key is 24 sc. 384 / 16 th part of the string tone is 40 sc. 400 / 10 480 / 6 = 80 seventh flat below Semitone is 16 sc. 400 / 25th part of the string tone is 24 216 / 9th Semitone betwixt sixth sharp above seventh flat is 16 sc. 216 / 13 ½ p t of the string Which is better represented to the view by the following Scheme , being an Octave divided into Semitones , the whole string being 360. places of the Semitones   22 1 / 2   40   60   72   90   104   120   135   144   160 168   180 quantity of the several semitones 22 1 / 2   17 1 / 2   20   12   18   14   16   15   9   16   8 12   what proportionable part of the string each semitone takes up 16   19 2 / 7   16   25   16   19 2 / 7   16   16   25   13 1 / 2   25 16   what part of the string each tone takes up   9 th   9 th   10 th   10 th   9 th   9 th       10 th   9 th   9 th   10 th     flat Key A la mi re B fa b mi   C sol fa ut       Da la sol         E la mi   F fa ut       G sol re ut     A la mi re The degrees of an Octave in a flat Key .   9   16     10       9       16     9       10     sharp Key C fa ut D sol re       E la mi   F fa ut         G sol re ut   A la mi re       B fa b mi     C sol fa ut           1●   1●       9       10     9       1●   By these divisions it appears , that the Tone above the Key , and that between the fourth and fifth , and that between the sixth and seventh , whether flat or sharp , are ninths of the string , which is called the Tone Major ; the other Tones are tenths of the String , and the natural Semitones are sixteenths . Other Semitones which are placed in the Scale , by the Rules before mentioned have other porportions , because neither Tone Major nor Tone Minor can he divided into sixteenths : therefore if one Semitone be a sixteenth in a Tone Major , the other will be 19 2 / 7 , and if one Semitone be a sixteenth in a Tone Minor , the other will be a 25 th , which is the Somitone that naturally lies between a third ♭ , and a third ♯ . If a Tone Minor be so divided , that one Semitone is 25 th of the string , the other will be 13 1 / 2. These unequall Tones and Semitones having their proper places in relation to the Key Note must needs produce Schismes upon displacing the Key Note . I shall give one instance : Suppose the Key Note a Tone lower , which is at 400 upon the Monochord in the first Scheme , then by the present Scale the fifth should fall upon the fourth to the former Key , which is 270 , but by the division of the Monochord 400 / 3 produces 133 ⅓ , whose complement is 266 ⅔ , so that the Schisme there is three and ⅓ , which makes a vast difference , and is occasioned , because , whereas there should be two Tones Major , one Tone Minor , and a Semitone to make a perfect fifth ; this consists of two Tones Minor , one Tone Major , and a Semitone . It will be easie , by turning the Octave Line divided into Semitones into a Circle , and supposing the Key Note upon other Semitones , to find the differences of the Tones and Semitones , that lye in order above it , from what they are in relation to the true Key Note , which will show more gross Disproportions or Schismes . Quarter Notes have been invented , which placed in those parts where these Schismes are the greatest , make the Instrument serve those Keys to which otherwise it would not be in tune . Organs and Harpsechords that have no quarter Notes are tuned with allowances , so that there is but one perfect fifth in the compass of an Octave , the rest bear on the one hand or the other , and so are indifferently well in tune to all Keys , but exactly in tune to none . Harpes , Lutes , and Lyra Viols , that are tuned to a particular Key , will be well in tune without any regard to this . Pipes may be helped by the strength of the blast , and fretted Instruments by a favourable stopping . The Violin has a great advantage by not being confined to frets : but above all , the Voice is most excellent , because it is not any way confined , but carried by the ear to those degrees which make exact Harmony . Of MUSICK consisting of several Parts in Consort . MVsick in Consort consists of Harmony , Formality and Conformity . Harmony is the gratefull sound produced by the joyning of several Tones in Chord one to another . I shewed before , that Tones in Chord one to another will joyn and give one entire sound , whereas discording Tones will jar ; and also that some Chords were more perfect than other , according as the coincidence of their pulses was more frequent : It will be proper here to say something concerning the several natures of the Chords in conjunction , and the qualities of conjunct sounds . In all conjunct sounds the Base is according to its name the foundation , and all the upper Chords are gratefull as they have relation to that , because it comprehends all the rest , and its pulses are according to Nature bigger and stronger than those of the other parts , and so of more effect to maintain the coincidence ; and for this reason , where a Tune begins with conjunct sounds , the Base is always the Key Note . Octaves as I have shewed before do not at all alter the sound , but only swell and fill it : for the sound has its quality from the terms of the interstices between the pulses ; which if they are larger makes the sound more grave , if they be less , the sound is more acute : Now as in Division , the mode of the time is never alter'd by doubling the number of Notes in the same space of time , but the mind or memory couples them and comprehends them in the same space as if they were whole Notes ; so is it by Octaves , being they increase by duplication of the pulses , in the same space of time it produces no alteration of the sound : And though there be Octaves above which are more acute , and Octaves below which are more grave , so that they differ from unisons ; yet as to appearance they are the same , in respect of such difference as there is between other sounds ; as if a man looks upon a Dye with the naked eye , and after should look upon it with a magnifying glass , though it appears bigger , yet by the figure and scituation he judges it the same . Therefore the Musick is not changed but filled by adding Octaves above the upper parts : but Octaves below the upper parts that should come below the Base , would change the Musick , by changing the foundation and basis of it , to which all the Chords would have other relations than they had to the former . A fifth is the principal Chord ( for the Octave cannot properly be called a Chord ) in which there is an acquiescence ; there being no other sound to which it can change to a more grateful one , and therefore is allowed in the close to fill the sound . A fourth by its coincidence of pulses should stand in the second place , but it is not allowed in Musick , according to the sweetness of its sound , because its Octave below the Base mends the Harmony so much , that it cannot be kept out of mind , but will be desired and expected : and therefore a fourth is a binding Note that strongly induces a close in the fifth below . So that a fourth is not for its sweetness allowed to be a Chord by most Musicians , because it is not stable but subservient to a change , which change is more induced , because only a sixth can be joyned with it , which will be a third to the fifth below , and so increases the expectation of a change . A third sharp is a Chord so gratefull that it is allowed in the close to fill the sound ; it being in Chord to the fifth bears it company , and its Octave to reverse would change the Musick into a sixth flat , which is the least pleasing of all Chords , and therefore is not at all regarded ; but the mind acquiesces in the third sharp . A third flat , nor the sixth flat nor sharp , claim not any place in the close , because they are in discord to the third sharp and fifth , so that both cannot be allowed , and the other are preferred : but they are in the body of a Tune very gratefull Chords that never offend the ear , nor do they invite any change by their Octaves below the Base , but afford a stable and pleasant Harmony . I shall not speak of discording Tones which are often conjoyned in Musick , because they are not allowed for their own sake , but for reasons which will appear in what I have further to say concerning Consort . Wherein the second requisite is Formality , which every part ought to have , though not to that degree of pleasantness that is expected from a single Tune , yet in a reasonable degree . The formality of a single Tune must be exact , because the Composer is not confined , but may follow his fancy ; but in Consort the Composer must consider the harmony of the Parts conjunct , and therefore is not at liberty . And there are allowances which the nature of the Parts require ; the formality of the Treble must be airy and brisk , that of the Base slow and robust , the inner parts are generally employed to fill the Musick with Chords , and have little curiosity of formality , except upon following a point : but these allowances considered , an expert Musician will give a competent share of formality and sweetness to every part , making the Treble move in a grave pace , and the Base rest , that the beauty of the inner parts may be discerned . The third requisite of Musick in Consort is Conformity of all the parts : as the Formality of a single part requires , that the succeeding Notes should be agreeable to the former ; so Conformity requires that each part should have the like tendency to the succeeding Notes . Which tendency is many times so regarded , that the present Harmony must yield to it : for if the succeeding Notes are of great relation to the Key , and the formal way to them in the several Parts is by discording Notes ; nevertheless that way which gives so good expectation must not be balked , but rather the discords will be allowed , whose harshness is taken off by the expectation of the succeeding Chords , and the Harmony of the following Notes is the more welcome for the badness of the passage . Discords are allowed in Musick upon this score , and they are also in other respects of excellent use ; as when the mind is to be carried from any particular Note , it may be affronted by a discord ; or if a Note in small esteem be to be favoured , some other Note may come in that agrees with that , and is discord to the rest , and so may draw the mind to the regard of that Note which it strengthens and supports . Infinite other instances may be made , but my business being only to illustrate the Reasons I go upon , and not to teach Rules , these shall suffice . From what I have said , it appears , that when each part has its kind and proportion of formality , and the parts are in Chord to the Base , and not in discord to one another , but carry all the Chords to fill the Harmony , when they have a like tendency to their respective succeeding Notes , when they imitate one anothers measure ; then is the Consort compleat : for the ear is pleased with the Harmony , and the mind is amused and entertained to observe the particular Parts how they dance to and from the Key , and from one Key to another , how they hunt one another , and in a manner imitate humane passions . To the end the hearer may the more indifferently observe the contexture of the Parts , it is necessary that they be fairly interwoven , one Part must not cling to another , by moving together in eighths or fifths which would draw the attention too much : for the same reason they may not jump into eighths , which I have heard called , hitting an eighth in the face ; but an equall hand should be held over all the Parts , and the sweetness distributed amongst them . I will not go about to describe Excellent Musick , which would require a Poet as well as a Musician ; I am only in the part of a Philosopher , to show what is allowable Musick , in order to make the Reasons upon which their Rules are founded understood . And that I have done , as it were by a glimpse , knowing the difficulty of being exact upon such a Subject ; He that desires to be more fully informed concerning it , may have recourse to other large Treatises that have been written of Musick by Authors of our own , as well as other Nations . There are tricks in Musick , as Fugues , Points , Descant upon plainsong Cannons , &c. the former , scil . Fugues and Points are extream delightfull , and embellish the Musick , carrying the attendance of the mind from one part to another , and restrain not the fancy of the Composer , but advance it . The other tricks that are more elaborate , are to teach or shew mastery in Composing , rather than to please ; for such fetter'd Musick is alwayes worse , and the hearer shall not observe the Art till he be told of it : it is like Acrostick Verse , or rhithm in Plays , which shew skill or labour , but serve not those ends for which the pieces were designed . Of TIME , or the measures of MUSICK . AS the Musick and Harmony of Tones depends upon the regular distance of the pulses , though the interstices are not perceived , nor can be measured by us : So when the interstices are so large that they can be measured by our sense , the observance of a regular proportion of Time affords great pleasure ; as in the beating a Drum , or striking a pair of Castanets . The due observance of time is gratefull for the same reason that I gave for the formality of a single Tune , because the subsequent strokes are measured by the memory of the former , and if they do comprehend them , or are comprehended by them , it is alike pleasant , the mind cannot chuse but compare one with the other , and observe when the strokes are coincident with the memory of the former . Therefore the less the intervals are , the more grateful is the measure , because it is easily and exactly represented by the memory , whereas a long space of time that cannot be comprehended in one thought , is not retained in the memory in its exact measure , nor can abide the comparison , the time past being alwayes shortned by so much as it is removed from the time present . The modes of Time are very few , being only in duple or triple proportion , and the diminishing is alwayes in Geometrical proportion , as two , four , eight , sixteen ; that it might serve not only to the Basis of the Time , but also to the other intermediate degrees of diminution , which are in memory , if not in play . The triple can give two spaces to one , the duple can give three spaces to one , and although the duple or plain Time seems to have spaces of even length , yet there is loudness and briskness given to every other pulse , which makes it eminent , and alwayes happens upon coincident strokes : this difference is between the fore-stroke and back-stroke in Musick , where the Notes are marked to be of an even length . These disparities of even and odd , and of two to one , and three to one are necessary , not only where Time alone is regarded , as in a Drum , or upon a Horn , to show the coincident strokes ; but in respect of Musick , for thereby length and loudness is given to the Key Notes , and such other Notes as should bear an emphasis : and the other Notes that have the short or odd foot , seem but steps and passages to them , and indeed are so little regarded , that whether Chord or Discord they must be taken if they lye in the way . In the same manner , in all shaking graces the hovering is unequal betwixt two Notes , the advantage is given to the true Note , and the other has but faint touches , to make preparation for that which is to succeed . It is now time to put bounds to this Discourse , which by reason of the Method I engaged my self in , is become much longer than I intended ; I will only add these Two Observations : 1. It appears plainly how Musick comes to be so copious : for considering the species of Keys , the number of them , the variety of Chords , the allowable mixing of Discords , the diversity of measure , it is not to be wondred at , that it should like Language afford to every Age , every Nation , nay , every ▪ Person , particular stiles and modes . 2. It appears that Tones or Modes of Musick in antient time could not be of other kinds than are now ; for there can be no other in Nature : therefore the great effects it then had , if truly related , must be imputed to the rarity of it , and the barbarity of the People , who are not transported with any thing after it becomes common to them . FINIS . MISTAKES . PAge 9. l. 18. for line read time : l. 25. for fifth and fourth read five and four . Pag. 24. l. penult . for 5 / 2 d and 3 / 7 th ♭ read 2 d and 7 th ♭ Pag. 30. l. 13. for Octave to reverse read Octave or reverse . Pag. 15. l. 12. so regular dele so . Pag. 26. It must be observed that the Monochords are not divided as they ought to be ; the Reader therefore is to regard only the Figures , and not the length of the Lines .