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EIGHTH EDITION – REVISED AND A UGMENTED
HARMONY SIMPLIFIED
A SIMPLE AND SYSTEM ATIC EXPOSITION
OF THE
PRINCIPLES OF HARMONY
DESIGNED NOT ONLY TO CULTIVATE
A THOROUGH KNOWLEDGE OF CHORD-
CONSTRUCTION
BTJT ALSO
TO PRACTICALLY APPLY THAT KNOWLEDGE
AND TO DEVELOP
THE PERCEPTIVE FACULTIES
*...* ,” BY
º * \s
F. H. SHEPARD
AUTHOR OF “How To MODULATE,” “PIANO-Touch
AND SCALEs,” AND “CHURCH-MUSIC AND
CHOIR-TRAINING.”
NEW YORK
G. S CHI RM E R
35 UNION SQUARE
I 904
i
i

Copyright, 1896, by G. SchIRMER.
s:S.*.*-,
s
PREFACE.
This little work offers no apology for its publication.
It aims at the following distinct objects: — I. To treat
the subjects of Scales, Keys, Signatures, and Intervals so
thoroughly that the pupil will be prepared to understand
with ease the principles of chord-construction.—II. To
present the subject of Chord-Construction in such a man-
ner that the pupil will be obliged to form all chords him-
self, thus deriving a practical knowledge of the subject.—
III. To discard all arbitrary rules. Instead of blindly
struggling with a mass of contradictory rules, the pupil
is made acquainted with the original principles from
which the rules are derived, and his judgment cultivated
to apply them with discretion.—TV. The principles of
the natural resolution of dissonances are shown, instead of
giving the rules for the resolution of chords of the seventh.
The pupil will apply these principles not only to chords
of the seventh, but to all fundamental dissonances. –
V. The chords of the Dominant Seventh, the Diminished
Seventh, the Major and Minor Ninth, and the Italian,
French and German Sixth, are shown to be but different
forms of the same chord, with a perfectly uniform reso-
lution, thus enormously reducing the difficulty of under-
standing these harmonies, and diminishing the complex-
ity of the whole Harmonic System.—VI. The system of .
“Attendant’’ Chords will be found very helpful in under-
standing those chords which, though outside the key,
evidently are closely related to some of its triads. It is
also of much assistance in reducing the art of Modulation
iv - AºA'Aº AºA CAE.
to a condition in which it can be studied step by step.–
VII. After the regular course in chord-connection is com-
pleted, a supplementary course of study is outlined, in
order to gain proficiency in practically using all the means
of giving variety to a composition or improvisation. This
proficiency is indispensable to young composers and
organists, but it is usually allowed to develop itself, as
nearly all manuals of Harmony stop at this point. To
expect a pupil to be able to introduce Suspensions, Pass-
ing-notes, Sequences, Anticipations, etc., into his improv-
isations, or even into his compositions, after reading the
explanation of them, is like explaining to a novice how the
Piano is played, and then expecting him to be able to per-
form.—VIII. A course in the Development of the Percep-
tive Faculties is given, training the pupil to listen intelli-
gently to music, to distinguish between the various chords,
etc., and to write, in musical notation, what he hears.--
IX. A chapter on Musical Form is added, together with
suggestions in regard to the Analysis of standard works.
Owing to the pressure of professional duties, as well
as to the consciousness of his inability to improve on them,
the author has taken the exercises with figured basses
chiefly from the “Manual of Harmony” by Jadassohn,
and the “Manual of Harmony” by Richter, indicating
the exercises of the former by the letter J., and those of
the latter by R. These exercises are supplemented by
Others, designed for special purposes.
TABLE OF CONTENTS.
PART I.
SCALES: KEYS : INTERVALS.
SC ANDES AND KIEYS.
CHAPTER I, pp. 3 – 26.
The major scale — Sharps and flats — Double sharps and
flats — Keys — Signatures — Circle of keys — To distinguish keys
having many sharps or flats — Relative sharpness of keys and
notes — Related keys—Specific names of scale-notes — Rela-
tive minor—Chromatic and Diatonic — Synopsis — Historical —
The perceptive faculties. -
INTERVALS.
CHAPTER II, pp. 26–42. -
General names — Specific names — Standard of measurement—
Major, minor, augmented and diminished— Extended and in-
verted —Consonant and dissonant — Application of terms—
Definitions — Enharmonic — Historical — Perceptive faculties —
Complementary Intervals.
PART II.
CHORDS.
TRIADS.
CHAPTER III, pp. 42 – 66.
Foundation of the harmonic system— Natural harmonics —
Triads — Marking — Specific names — Principal and secondary —
Doubling — Position — Four-part writing — Connection of triads
— Consecutive fifths and octaves — Open and close harmony—
Connection of triads in minor — Harmonizing the scale.
INVERSION OF TRT AIDS.
CHAPTER TV, pp. 66–81.
Figuring — Figured bass — Hidden octaves and fifths — Per.
ceptive faculties —Transposition.
CHOR1D OF THE SEVENTH.
CHAPTER V, pp. 81 — IOO.
Its construction — Resolution — Inversions — On the Prepara,
vi 7A A} ZAZ OA’ COAV7'Z2A77.S.
tion of dissonant intervals — Cadencing resolution — Leading of
the parts — Influences, combined and opposed —- Directions for
part-writing.
INVERSIONS OF THE CHORID OF THE SEVENTH.
CHAPTER VI, pp. IOI — IO 5.
Figuring and naming — To find the root — Resolution.
SECOND ARY CHORIOS OF THE SEVENTH.
CHAPTER VII, pp. IO 5 – 127.
Formation — Resolution — Preparation of dissonant intervals
— Succession of chords of the seventh — Secondary sevenths in
minor — Inversions – Cadences — Closing formula – Non-ca-
dencing resolutions – Analytical and comparative review — His-
torical.
CHORD OF THE DOMINANT SEVENTH AND NINTH.
CHAPTER VIII, pp. I27 – I 30.
Construction — Resolution — Inversions.
CHORID OF THE DIMINISHED SEVENTH.
CHAPTER IX, pp. 130 – 136.
Construction – Use in major — Similarity of sound — Resolu-
tion — Inversions — Figuring. -
CHORDS OF THE AUGMENTED SIXTH.
CHAPTER X, pp. I 36- 145.
Are altered chords – Construction — Resolution — Upon super-
tonic — Recapitulation.
ALTERED CHORDS: FUNDAMENTAL CHORDS.
CHAPTER XI, pp. I46 – I63.
Description — Change of root — To distinguish between altered
chords and foreign fundamental chords — The discovery of roots
— Ambiguous chords — Altered chords in general use — Neapol-
itan sixth.
FOREIGN CHORIDS.
CHAPTER XII, pp. 163 – I70.
Relation of dominant to tonic — The system of “attendant’”
chords — Their influence upon modern music — Various forms,
minor seventh, diminished seventh, etc.
7'4A / A. OA' COAMW 7 AEAVZ.S. vii
MODULATION.
CHAPTER XIII, pp. 170 – 183.
How effected—To connect any two triads—Use of “attendant’”
chords — To connect any two keys — Formula for modulation —
By means of dominant seventh — By means of closing formula—
By means of diminished seventh — To any chord of new key —
Change of mode.
PART III.
VARIETY OF STRUCTURE.
CHAPTER XIV, pp. 184 – 193.
Suspensions — Anticipations – Retardations — Syncopation.
|UNESSENTIAL IN OTES.
CHAPTER XV, pp. 193 – 203. -
Passing-notes — Auxiliary notes — Organ-point — Inverted
pedal – General recapitulation — Tabular view — Essential and
unessential dissonances.
MISCELLANEOUS SUBJECTS.
CHAPTER XVI, pp. 203–213.
Cross relation — The tritone — Treatment of chord of six-
four — Licenses — Sequences — Related keys – Naming the oc-
taves — The great staff— The C clefs — Chords of the eleventh
and thirteenth — Open harmony — Five-, six-, seven-, and eight-
part harmony.
HARMONIZING MELODIES.
CHAPTER XVII, pp. I24 – 223.
The campus firmus — The chant — Speed in writing — Practi.
cal application,
AN ALYSIS AND FORM.
CHAPTER XVIII, pp. 224 – 235.
Method of procedure — Sonata-form — How to trace the
theme — Harmonic analysis — Rondo-Form — Primary form —
Phrase — Period — Motive — Thesis and antithesis.
IMPORTANT.
Not E I. The student is urged to make frequent
and persistent use of the keyboard for all appropriate
exercises here given, for by this the practical efficiency
of the study is greatly increased. Exercises in Scale,
Interval, and Chord construction, in Chord connection,
and Chord resolution, are suitable, and also the exercises
in Part Writing, under proper conditions.
Not E II. For use in Class Drill the “Keyboard
Diagram,” published separately, is of value, for by its
use a large class may receive the same practical and
thorough keyboard drill as the single individual at the
piano.
Not E III. Teachers (and those studying without
a teacher) are invited to address the author for a (free)
set of questions for use in the class room and for other
hints in regard to the use of this work. See page 24.
HARMONIZING MELODIES.
Not E IV. For special work in harmonizing melo-
dies see Chap. XVII. This work may be commenced
after Chap. V., or even earlier, if simple exercises are
chosen.
PART I.
CHAPTER I.
SCALES : SIGNATURES : KEYS : CIRCUPE OF KIEYS :
- HISTORICAL : THE PERCEPTIVE FACULTIES,
- \
Construction of the Major Scale.
1. A Major Sca/e is a succession of eight tones,
placed at a distance of either a Who/e or a Half-step
apart.
A Half-step or Semitone, is the smallest interval
formed upon the Piano-keyboard; that is, from any key
to the next one, white or black; e.g., C to D2: E to F : .
Aſ to B, etc. -
A Whole Sfez is a step as large as two Half-steps;
e.g., C to D : E to F#: G: to Af: B5 to C.
2. The eight notes of a scale are called ZDegrees of the
scale, and are numbered from the lowest, or Keynote, up.
ward to the octave of the keynote.
3
4. AAAEA/OAVY S/MAZZZZZZZ).
3. Notice, when playing the scale of C on the Piano,
that from the 3rd to the 4th degree, and from the 7th to
the 8th, are /a/f-steps, while between all the other degrees
are w/o/e steps. This forms ozer raz/e for Z/2e construc-
fºoze of any Major sca/e, (also called Diatonic * Major
scale,) wit/Łozzá regard Žo #/ºe starážng-?/ace. There-
fore, we will write the succession of figures, indicating
the position of the half-steps by the sign S-1, thus making
a ZFormezz/a, or general pattern, by which we can con-
struct a scale starting from azzy note; thus:–
I 2 3 4 5 6 7 8. Briefly expressed for memo-
S-' S-->''
rizing, this formula is as follows:—
The Aſa/f-steps are from 3 to 4 and from 7 to 8.
All other steps are Whole steps.
4. To illustrate this formula, let us begin on the note G,
and, following the above rule, form a scale :-
G. A B C D E F G.
I 2 3 4 5 6 7 8.
`-- \-
by step, comparing the notes with the formula :—
Let us examine this step
I to 2 should be a whole step, i. e., G to A — is right.
2 to 3 should be a whole step, i. e., A to B — is right.
3 to 4 should be a half-step, i. e., B to C — is right.
4 to 5 should be a whole step, i. e., C to D — is right.
5 to 6 should be a whole step, i. e., D to E — is right.
6 to 7 should be a whole step, i. e., E to F — is wrong,
since E to F is only a / adf-step, where a whoſe step is
required. To correct this, F: is used instead of F, giving
the proper distance from 6. 7 to 8 should be a half-step,
*– “--→
* The word ZXiatomic means literally “through all the tones.” Its
applied meaning is, that one (and only one ) note is to be written upon
each degree of the staff. It will be seen later that the word is also
used to refer to scale-modes, to distinguish them from notes altered by
accidentals. (See § 44.)
A/4/8//OAVY S/M/A2Z/A/A2/). 5
*-*
i. e., F# to G — is right. (The Fit really corrects two
faults, as without it the step 7 to 8 would have been too
great.) Expressed in notes with the formula, the corrected
scale reads as follows:–

() *~, *2
is Ezº. 2–2–23–ºf–H
Fig. 1 - H(AS z-a
LSPE.
l 2 3. 4. 5 6 7 8
In this way the pupil should test each note in the following
exercises.
5. In constructing scales, observe the following points:
1. Do not write two notes upon the same degree of
the staff; e. g., A and Aff.

II. Do not skip any letter; e. g., E
(The letter B is skipped.)
ſ)
LZ
Lºſ Ll. *2 =
GBEZE"
Tº JT
NOTE. The word Scale is derived from Scala, meaning “ladder.”
The lines and spaces are used consecutively to form a regular series of
steps, ascending or descending. If two notes should be written upon
one degree of the staff (e.g., I), it would be necessary to omit the
note on the next degree (e.g., II) to make up for it. Such a method
would make a very irregular looking scale or ladder; e.g.,

→=z---tº-2-
- t e2– - -
Fig. 2. H&H Lºz. e2 f:
U l 2
*S 4. d 6 7. 8
2, 2 =#2
III. To avoid the errors mentioned in I and II the
beginner should always first make a skeletozz, or outline,
of the desired scale, i. e., the notes only, without sharps
or flats, writing the formula of figures underneath. After-
wards he may bring it to the required standard of steps
and half-steps by using sharps or flats. For example:–

–0. zºº
| 2% - eº ex eº tº
Eig. 3 || ſty. T. Aº Ø €2 H
LSPI 2 Yºr T.
* J 2 3. 4. 5 6 7 8
N-' See*
6 AZAA’A/OAVY S///ZºZAF/A2/D.
The next step is to “write in ’’ the sharps necessary
to make the notes correspond with the formula; thus:
I to 2 should-be a whole step; a whole step from F: is
G#: therefore, write a sharp before G.
2 to 3 should be a whole step; a whole step from G# is
Aſ : write a sharp before A.
3 to 4 should be a Żalf-step; a half-step from Aff is B–
is right.
Proceed in this manner till the scale is completed, result-
ing as shown in Fig. 4.

H2A - †2–#2–44–ºf–ſ.
Fig. 4. Tſº tle +tep *zz e) TT T
LºvE7 IF2 H- *r |
U L 2 3. 4. 5 6 7 8
`--~~ ~~~
Exercises.
6. (a.) Construct the Skeleton and Formula, and
write Major scales starting from the following notes: C;
G; D : A ; E ; B; Fit; C#.
(ó.) Construct the same scales at the keyboard.
Double Sharps.
7. Write the scale of G: as above. N. B. It will be
observed that the step 6 to 7, from Eff a whole step up-
ward, is not properly expressed by simply writing F#, as
that is only a half-step from Eff. It is here necessary to
raise the Fif another half-step, to make the required dis-
tance from Eſt, which is done by using a dozó!e sharp,

º . . . E-jº-jº-T^*TH
written x, giving Hº- H
LTVSLM I.
J 6 7
Exercises,
Write the scales of Dit, Air, Eß, and Bł, using
double sharps where necessary. Repeat at keyboard.
AAA’ MOAVV SZA/A2Z////2Z).
7
The Use of Flats.
8. Flats are introduced where without them notes
would be a half-step too high. For example, in the scale
starting upon F, (write it,) the interval from 3 to 4 is
a whole step, while the formula requires a half-step.
This is rectified by the use of a flat before B.
Exercises.
Write the scales of F, Bb, Eb, Ab, D5, Gb, and Ch.
Repeat at keyboard.
Double Flats.
9. In the following scales, double flats, written bb, will
ſ
be required. From the foregoing, the pupil should be
able to find the reasons without further explanation.
Exercises.
Write the scales of Fo, Bbb, Ebb, Abb, and Dob.
Repeat at keyboard. -
Advanced Cozz"se. -
1c. From a consideration of the above it will be seen, that in one .
sense there is but onze Major scale. The so-called various scales, F,
D, C#, Bb, etc., are but exact reproductions of each other, varying only in
pitch. The name of the scale, therefore, merely indicates the name of
the starting note or Keynote. There is a popular idea among Piano-
pupils that the scale of C Major, having no black keys, is the one per-
fect scale. But it will be at once seen that the Major scales are all alike
in the manner of construction, the black keys upon the Piano simply
serving to bring all the notes of the scale into proper relationship with
each other, i. e., at the proper distance from each other. For exam-
ple, it should not be said that there is a wide difference between the
scale of C and the scale of Dº, because one has no flats and the other
so many. Rather should it be said, that these five flats serve to make
the two scales alike, by keeping the series of steps and half-steps
absolutely the same.
Keys.
Pegular Cozerse.
II. After writing a few scales as above indicated, the
8 AAA’A/OAVY SAA/A/, /AP/AE 7).
pupil will understand that the notes of the scale bear a
certain relationship to each other. The starting-point of
each scale is termed the Keynote; the group of tones
composing the scale, considered collectively, is called a
Rey. •,
Signatures.
I 2. Zwercises. (a.) Returning to the exercises in §§ 6
and 8, the pupil will gather the sharps or flats used in con-
structing each scale, and place them in a group immedi-
ately after the clef, thus forming the Signature of the key.
Signatures are a zeszz/Z of this uniform construction of the
scale, and not the cause or origin of the various keys. -
(6.) Recite the order of sharps in signatures.
(c.) Recite the order of flats in signatures.
Circle of Keys with Sharps.
13. In forming the key-signatures as above, notice:—
(a. ) That each successive scale has one more sharp
than the one before it; e. g., C has no sharps, G has one
sharp, D two, A three, etc. -
14. (6.) That the note on the 5th degree of one scale is
used as the first note of the next scale; e. g.,
No Sharp.
l 2 3 4. 5 6 7 8
H2A Ez=#|
Fig. 5. | agº. &2 €2
-- • J -2- 2 tº
One Sharp.
ſº 8
() I. 2 3 4. 5 ° 44; 2. --
| L7 Aº. 22 jº- |
| 24ſ zºº C/ cº-
| | If TN *> C2 fºLºr | . .
LSP == | |

15. (c.) This succession continues till the note Bit is
reached. This note being the same as C natural, we may
be said to have completed the Circle of Keys, starting from
A/AA’A/OAVY SAA)/A2Z.Z.A./A2/). 9
C and continuing till the same note (though called B::)
is reached. This is called the Circle with Sharps.
16. ( d.) The sharps or flats of a signature are always
written in the order in which they successively appear in
the Circle of Keys; e. g., Fit being the first to appear, is
always written first,--at the left, no matter how many
sharps there may be in the signature. C#, being second,
always comes next to F# in any signature. Written in
Order, and numbered, they appear as in Fig. 6.

Notice, also, that if a certain signature has one sharp,
that sharp will be the one at the left in Fig. 6. If a
signature has two sharps, they will be the two at the left
in Fig. 6. And no matter how many there are, those at
the left will always be included. To learn the order in
which the flats appear, observe the order of their entrance
in the illustrations and exercises in §§ 19–22.
17. (e.) It may be especially noticed, not only that
the note upon the 5th degree is used as a starting-point
for the succeeding new scale, but that the Zasz Żalf of
one scale (four notes) is used as the first half of the
next new one; e. g., Fig. 5. (See also $$ 32 and 45.)
18. (f.) But one note ( or letter) is altered in passing
from one scale to the next in succession. ZZZ's altered
zzote is always ozz #/.e 7#/. degree, and is shown by the
added sharp appearing in the Signature.**
* This order will be observed by reference to the entrance of each successive
new sharp in the Exercises, § 6. g
* This fact may be used to find the Key indicated by any signature: The last
new sharp being always at the right in the signature, we may say that the
right-hand sharf is always on the 7th degree of the scale. And, knowing the
7th degree, we may easily find the 8th degree or Keynote. (N. B. The octave
of the keynote is the same as the keynote itself.)
IO AAA’A/OAVY S/M/A/L/AF/A2Z).
Circle of Keys with FIats; Circle of Fourths.
I9. A Circle of Keys using a gradually increasing
number of Żafs, can also be formed, by using the 4th
degree of each scale as the starting-note (keynote) of the
next One ; e. g.,
No Flat.
F-
Fig. 7. Ezę Aº Z2 2–2–H
Ll e) 2 tºº I
-e- &º |
One nº T
() H 2 3. 4. Aº
L LZº \ º ºn C’ tº
|Tººlſ } lºn_ C’ Gº” |
ECB) I zºº &” Izcz
NSL' Cº & Fº i
J | *
_*T
Exercises.

2O. Write out the Circle of Keys with flats, using
double flats where necessary.
21. It will be noticed that whereas in the Circle with
sharps the last half of each scale forms the first half of the
next, in flats this is reversed, the first half of one
becoming the last half of the next. (To understand this,
write it out in notes.) The pupil will further notice,
that the added or new flat will appear each time upon the
4th degree.*
22. In the Circle of Keys with sharps, the 5th note
of the 'scale is used as the Keynote of the following scale.
In the Circle with flats, the 4th note is so used. Now,
counting four notes of the scale upward reaches the same
note as counting five notes downward.** Therefore, these
circles are called the Circle of Fifths, the sharps counting
* Therefore, to recognize any key with flat signature, notice that the rights
hand flat is on the fourth degree of the scale; and to find the 1st degree or key-
note, count downward from 4 to 1.
* In finding the fifth below, do not count 1, 2, 3, 4, 5; but, instead, count 5,
4, 3, 2, I, remembering to keep the half-step between 4 and 3, in order to preserve
the correct form in the new scale.
A/AA’A/OAVY S/M/AOA-7A/A2Z). T I
upward, i. e., by ascending Fifths, and the flats down-
ward, i. e., by descending Fifths.
23. These circles may be represented as follows, the
figures opposite each key indicating the number of sharps
or flats in the scale :-
Fig. 8. Fig. 9.
Read around to the right. - Read around to the left.
F B- Diº-e?
N. B. In finding the above number of sharps or flats
in a scale, remember that a Double sharp counts the
same as two single sharps.
24. As the keys having more than six sharps or six
flats are unnecessarily complicated in notation, it is cus-
tomary to use the sharp keys for the first half of the circle,
from C to F#, and the flat keys to complete the round;
e.g., Fig. I O.
Fig. 1 O.
Read to right or left.
In this way the change is
usually made from F: to Gb,
or vice versa; though it may
be made at azzy Żołmż żn the
circle, e. g., from G3 to A2,
from F9 to E, etc., and is
called an AEzz/harmozzzc change
of key. See $78.


I 2 AAAA*//OAVY SAA/A2ZZZZZZZ).
Advazz.ced Cozzz'se.
25. There is an interesting way of learning the number of sharps in
a scale where there are more than six: It will be seen at a
glance that the key of C has no sharps, and the key of C# has seven
sharps. In other words, each of the seven notes has been raised by
a sharp. Similarly, if the key of G has one sharp, the key of G# will
have I + 7= 8, since each one of the notes in its scale must be raised
to change the key from G to G#. Similarly, the key of D having two
sharps, the key of Dſ will have 2 +7 = 9. Similarly, the key of A
having three sharps, the key of Aff will have 3 +7 = Io. Therefore, to
find how many sharps there are in a key when the Keynote is written
with a sharp, simply add 7 to the number of sharps in the signature of
the key of the same /etter without the sharp.
26. The same principle applies to flat keys having more than six
flats; e. g., Bb has two flats; therefore Bbb will have 2 + 7 = 9 flats.
27. Another interesting point in this connection may here be devel-
oped : — #
In the Circles of Fifths in §§ 13–24, the circle began each time
with the key of C. This is not at all necessary, it being quite as easy
to begin upon any other note and complete the circle back to that note
again, proceeding in either direction.
Let the pupil begin upon Gb and form the circle by ascending
fifths. This will decrease the number of flats by one each time till C
is reached, after which sharps will appear and increase successively.
Vice versa, a circle can be constructed beginning upon F# and pro-
gressing by descending fifths. Notice that in both cases the succession
passes through the key of C and changes from flats to sharps, or vice
versa, without altering the conditions in the least.
28. From this it will be seen that Flats and Sharps, in their rela-
tion to each other, are like degrees above and below Zero on the ther-
mometer, sharps being above and flats below the zero-mark. Or they
might be compared to Positive and Negative quantities in Algebra.
Keyboard and Written Exercises.
Form examples of the above-mentioned circles, starting in turn
from C#, D, D#, E, F, F#, G, G#, A, Aff, and B, progressing first by
ascending fifths, and afterward by descending fifths.
29. Resulting from the relationship of sharps and flats, keys are
frequently compared with respect to their relative “sharpness,” the
key having the fewest flats or the most sharps being called the sharpest
key. Or they may be placed in order, thus:—
Cb Gb Db Ab Eb Bb F C G D A E B F# C#
7 6 5 4 3 2 I o I 2 3 4 5 6 7,
and compared by saying
A/A ACA/OAVY SAA/A2ZZAP/A2/). I 3
that one key is so many “removes" to the right (i. e., sharper) or left
(i. e., flatter) from another key, counting through the key of C regard-
less of differences; e. g., G is two removes to the right from F, or Bb is
four removes to the left from D. (See Weitzmann’s “Musical Theory,”
page 90.) In a similar way the notes themselves may be compared,
saying that D is a sharper note than G, since its key is represented by
one more sharp, etc. This point is further noticed in § 250.
Exercises.
Compare the sharpness of the following keys, i. e., tell how
many degrees or “removes" from the first to the second in each
pair, and state which is the sharper of the two :-
Keys of A and B ; A and D ; B and F#; Ab and D ; Bb and At: ;
C and B; ; Gb and Ab ; D8 and Eb ; G: and Ab ; F and G; G and A ;
A and B ; B and C. -
Exercises.
A'egzz/ar Cozerse.
3O. By means of the statements in foot-notes to §§ 18
and 2 I, the pupil should be able to recognize at sight any
key from its signature :-
What keys are represented by the following sig-
natures P−

L 9: b b-B-H : : #—- b-L5 5-H
Eg-Hº-5-Hº-H
—3–5– -#–E–F–b-rá-E-F-I-b=1#-F#-r-r
Fá; ºft##############|

31. It is also desirable to know the number of sharps
or flats in the signature of a given key, without reference
to a table.
Exercises.
Give the number of sharps or flats in the signatures
of the following keys: A, D9, G, B5, Ab, D, B, F#,
Gb, Ep, E. &
N. B. If necessary to do so, write out each scale to
find the number of sharps or flats.
I4 AZAA’A/OAVY S///A/LAA"/ZZ).
Related Keys.
32. Keys having most notes in common are said to be
ze/afted to each other. In the Circle of Fifths, each key is
related particularly to the one before it, since one half of
it is found in that scale ; and also to the one following,
since the other half will be found in that one (see $45),
e. g., the key of C is related to the key of G ; also
to the key of F. This subject will be developed further.
(See §§ 17 and 334.) *
Exercises.
Name the two keys related to the key of B: of F#:
of D : of A; ; of Ep: of A: of Gb : E : Dž.
Facility in Distinguishing the Various
Degrees of a Key by Nunn ber and by Name.
33. To thoroughly prepare himself for the subsequent
chapters, the pupil should learn to recognize at a glance
the various degrees of any scale, and indicate them by
number or by name.
t Keyboard and Mental Exercises.
Placing any desired scale before the pupils (for
example, the scale of B7), the teacher should ask various
questions like the following:—
Which degree of the scale is Ep P Azes. 4th degree.
Which degree of the scale is G F Azes. 6th degree.
Which degree of the scale is D F Azes. 3d degree.
This exercise should be carried through various keys,
and continued till some proficiency has been gained. The
exercise may be varied by such questions as the follow-
ing :-
What is the 2nd degree in the scale of A major P
Ams. B. ** ;
What is the 3rd degree in E major P Ams. G.
A/A ACA/OAVY S////2ZZZZZZZ D. I Š
Specific Names.
( Zo &e Zeaz-zzed.)
34. Each Degree of the scale has also a Specific name,
which is often used instead of the number, as follows:–
Ist degree, Tonic. -
2d degree, Supertonic.
3d degree, Mediant. (Meaning midway between Tonic and
Dominant.)
4th degree, Subdominant.
5th degree, Dominant.
6th degree, Submediant. (Midway between Tonic and Sub-
dominant, when the latter is
written be/ozy the former.)
7th degree, Subtonic or Leading-Tone.
8th degree, Octave or Tonic.
Mental Exercises.
Apply test-questions, as shown in § 33.
Notice that the prefix ‘‘ Sub '' means “below,’
“Super,” “above:” e. g., Supertonic means the degree
above the Tonic, and Subtonic the degree below the
Tonic.
The Tonic, Dominant, Subdominant, and Leading-
note are especially important to know, and the pupil
should be ab/e to ſized them withozef Żesitation in azzy'
Áey.
3.
and
The Min Or Scale.
35. It was noticed that in the Major Scale the half-
steps occur from 3 to 4, and from 7 to 8. The Minor
Scale is formed by placing the half-steps between 2 and 3,
5 and 6, 7 and 8.

Fig. 1 1. Fé
U
b2–2—2—
* :
Cºr
5 6 N.B. "s—”
`-- `--
R
Dr
*
º
C2
-tº-
l 2
I 6 AARMOAVY S/MPZZZZZZ).
This is called the AZaz-mozzzc Minor Scale, to dis-
tinguish it from the AZe/odºc Minor Scale, which has a
different and irregular arrangement of the half-steps, as
shown in Figure I2. (See also $46.)

() -
Fº 2-52 H
Fig. 1 2. º =-z-e? -bz-z. * .
LVSU' pez 2–1 P. 2 B2
UTLET&2 4- 5 6 7 8 7 6 5 4. 2–2–
l 2 3. N-" S-' 3 2 L
S- N-º
36. The Harmonic Minor Scale is the basis of the
chords in the Minor Mode, * while the Melodic Minor
Scale is generally used in melodies. It may be consid-
ered as a ‘‘ free '’ form of the Harmonic scale, made
necessary by the fact that the interval of 1, steps from 6 to
7 in the Harmonic Minor Scale (see Fig. I I) is rather
un melodious, though not unmusical.
37. From the foregoing comparison of the Major and
Minor scales, the pupil will realize that f/e character of
a sca/e defezza's zºozz #/ºe Złoszážoze of the half-steſs.
EXerCises.
38. Form Harmonic Minor scales, and write the
figures under each note as shown in Fig. I I, starting from
the following notes: A, E, B, Fit, C#, G#, D#, D, G, C,
F, Bb, Eb, Ab, D5.
Relative Minor.
39. Every Major scale has what is called its “Relative
Minor,” which is the Minor scale having most notes in
common with it, and having the same szgzzazzare. This
Relative Minor is always founded (has its keynote, or
Tonic ) on the sixáſ degree of Że Major scale. Thus,
* The words “Major Mode” and “Minor Mode” are terms used when we
do not refer to any particular key, but wish to speak of the character of Major
or Minor in a general way.
AAA’A/OAWTV S///A2/.../A./A2/D. 17
, the sixth degree in the scale of C is A ; therefore, the .
Relative Minor of C Major is the scale ( or key) of A
Minor. (In finding a relative minor, it may be easier
for the pupil to look for the keynote I steps below rather
than the sixth above, the result being the same.)
Exercises.
Find the Relative Minor (and write the proper sig-
nature) of C Major; of G, D, A, E, and B Major; of F,
Bb, Eb, Ab, D9 Major.
40. Correlatively, each Minor has its Relative Major,
which is found on the third degree of the Minor scale.
For example, the relative major of A Minor is C Major.
In other words, A Minor is the relative Minor of C
Major ; and C Major is the relative Major of A Minor.
Mental Exercises and Drill.
Find the Relative Majors of the following Minor
scales: A, E, B, F#, C#, G#, D#, D, G, C, F, Bb, Eb,
Ab, D5.
Signatures in Minor.
41. The pupil will notice that the Relative Minor of
any Major scale has the same notes as the latter, except-
ing the seventh degree, which is raised by an accidental.
For example, A Minor has the same notes as C Major,
excepting the G#. This accidental raising of the seventh
degree is caused by the fact that the seventh degree, or
“Leading-tone,” should be only a half-step distant from
the Tonic. (See § 46.)
In collecting the sharps or flats to form the signature
of a minor key, this fact should be considered :- 7%.e
accidenzga/foºzzed before &/ºe sevezz/. degree does zeoé &e-
Zozºg to the Szgzzazz/re. -
2
I 8 A/AA’A/OAVY SAA/A2/.../A./A. ZD.
Exercises.
Write the signatures of the following Minor keys,
proceeding as directed in § 12 : A, E, B, F#, C#, G#.
D#, D, G, C, F, Bb, Eb.
The Circle of Keys in Minor.
42. The Circle of Fifths can be made with Minor keys
as well as with Major.
Exercises.
( a.) Form the Circle with sharps, beginning with
the key of A Minor.
(6.) Form the Circle with flats, beginning with the
key of A Minor.
(c.) Form the Circle beginning upon various other
notes.
The Chronnatic Scale.
43. When the half-steps lying between the notes of the
Diatonic scales are included, thus producing a scale of
half-steps exclusively, it is called a Chromatic scale. It
is customary to use sharps in writing the intermediate
half-steps in an ascending chromatic scale, and flats in
the descending scale ; e. g.,

ſº) —r
| W
- Hº H-2-#2–2–2
J-a-ha-z-z---"
TTV *— ||
HG===Pºpºbziz Eºs H
el) 62 zºº z - pa


-eº-
Chromatic Alteration.
44. When a note is raised or lowered a half-step by
Aſ AA’A/OAVY S////2/2/AC//2 ZO. I9
an accidental, consequently wit/Łozzé c/azagºzag ſº fosz-
£zozz zañoz the staff, it is said to be chromatically altered;

().
€. g . ; H&EzHz=
J
A Chromatic Half-Step is one expressed upon ozze
degree of the staff; e. g., A – Aff.
A ZOZałoſzęc Half-Step is one expressed upon Zwo
degrees of the staff; e. g., A — BP.
In general, a Diatonic progression is one where the
Žežter is changed in the succession of notes; and a Chro-
matic progression is one where the Zetter is zeof chazzged,
but altered by the use of an accidental.
At the close of each chapter the pupil should make
al synopsis of the principal facts contained therein, class-
ifying and arranging them in order. The following
table is intended to assist the pupil in this.
Synopsis of Chapter I.
ſ - Formula :- Half-steps 3–4 and 7–8.
Keys.
Signatures.
! -- & . . Ascending.
circle of Fifths: };}.
Fifth above, or Dominant.
Relative Keys: } Fifth below, or Subdominant.
Relative Minor.
Major :
Specific Names.
Major scales all alike.
Scales : « pe Harmonic; Half-steps, 2–3, 5–6,
Formula | 7–8.
Melodic; Half-steps, up, 2–3,
l 7–8: down, 6–5, 3–2.
Minor : { Relative Major.
Signatures : Same as Relative Major.
'8"**** i Omit sign of raised Leading-note.
Leading-note raised by an accidental.
Position of half-steps.
Notation,
Chromatic: {
S.
2O * AAA’A/OAVY S//l/A2ZZAP/A2/D.
&
Historica.I.
45. The Modern Scale is a gradual development from
the ancient Greek Modes, in which the semitones occu-
pied varying places in the scale, according to the mode.
See Grove’s “Dictionary of Music;” Vol. II, p. 341, and
Baker’s “New Dictionary of Musical Terms;” p. 88 ef
seg. The Major Scale may be considered as composed
of two Tetrachords,” placed one above another; e. g.,
C D E F G A. B C
\— >-1, \ S-1,
Tetrachord. - Tetrachord.
Until the 13th century, the use and influence of the
semitones in Music were not fully realized; therefore,
in the music previous to that time, we find (according
to modern standards) a lack of Tonal feeling, or sense of
being in some particular key. In the time of Palestrina
it became customary to szzag the seventh degree as if it
were only a half-step from the eighth, although this was
contrary to the notation, showing the need of something
beyond the scales then in use.
In the seventeenth century the modern scale began
to displace the Gregorian Modes; the sharps and flats,
instead of being dispersed through the composition or
left to the discretion of the performer, were gathered to-
gether to form the signature; the dividing lines between
the keys were thus more distinctly marked ; and Modern
Music, as opposed to the Ancient Modes, soon made a
distinct place for itself.
46. The oldest form of the Minor scale was as shown
in Fig. I4.
# A Tetrachord is a scale of four notes, having one half-step. Tetrachords
belonged to the musical System of the ancient Greeks. -
AAA’ MOAVY S/MPZ/A/AE/O. 2. I
—ſ) 2-, 2 2 gº
| V. r.ºr
[[I2.
Fig. 14. Eſº-2–2–2 2-ep
Eg,
&
1 2 3 4 5 s 7 8 7 e_5 4 3 2 1
As the feeling of Tonality developed, a “Leading-
note ’’ was demanded which should point more decidedly
toward the Keynote, and thus impart a greater feeling of
satisfaction when the final chord was reached.* Thus
the 7th degree of the scale was raised by an accidental,
giving the form as in Fig. I5, which is seen to be our
present Harmonic Minor scale.
O 2, t_2 -6°-tº-2
Fig. 15. Eſº-2-2 £2–2--
IVU' T.
J 1 2 3 4 5, 6 7, 8 7 6 5 4 3 2 1
S- N- S-> S- ? S-' S->
This form leaves an interval of 11 steps between the
6th and 7th degrees; and for the sake of a smoother
effect it became customary to raise the 6th degree also a
half-step, where the harmony would allow it, giving the
form shown at (a), Fig. 16, which is our present
Melodic Minor scale.
( a.) (6.)
–0– *~, tz ºtiz n-, -
EPA > z zł2–zº::=H
Fig. 16. E-fºis-22-62 (2–2–-
| NU T.
U T. 2 3 4 5 6 ºf 8 7 6 5 4 3 2 HL
A “Leading-note ’’ being unnecessary in a descend-
ing scale, the two notes raised by accidentals in the
* The need of a “Leading-note ’’ to give the feeling of satisfaction when the
final chord is reached, is shown by comparing (a) and ( & ) in Fig. 17.
(a.) ( ò.)
Fig. 17.

2, 2 AAA’ // OA/Y SAA/Z’/_/A//? /).
ascending scale are usually restored in descending
[(6), Fig. 16], giving the complete Melodic minor
scale now used.
Exercises in Musical Dictation, for the Develop-
ment Of the Perceptive Faculties.
47. If we would rightly understand Music, it is indispensable that
we become able to recognize what we hear, just as we recognize
printed words upon first sight.
The reason so few have the faculty of listening intelligently, is
not that it is difficult, but because little or no attention has been paid
to this most important subject. Briefly summed up, the steps of the
process of development consist in gaining the power : —
. To distinguish Half-steps from Whole-steps.
. To distinguish the various notes of the scale.
. To distinguish Intervals.
To distinguish the Major from the Minor Mode.
. To distinguish Chords and their inversions, and to realize their
position in the key.
6. To trace simple Modulations.
7. To distinguish the Divisions of Time, Rhythm, etc.
8. To note the various features of Form, learning to recognize
Motives, Themes, succession of keys, Periods, and the general plan
of construction. -
9. To be able to express all of the above in Musical Notation. *
.
By taking this study step by step, and in connection with the
study of Harmony, there will be added interest in the latter by reason
of the ability to apply each point as soon as learned. There will also
be a deeper and more practical comprehension of Harmony, and a
more intelligent knowledge of Music as an Art and a Science.
To Distinguish Notes of the Scale.
48. (a.) First teach the pupils, by experiment and careful concen-
tration in listening, to distinguish between Half and Whole steps in
both upward and downward progression. This may occupy parts
of six or eight lessons. -
(%). The best and only really successful manner of teaching the
notes of the scale and how to distinguish them, is through the medium
of the voice. The foundation of the musical perceptions lies in the
possession of a “working ” knowledge of the Major scale. The first
* The above represents the complete process, facility in all of which is
attained only by gifted minds. But a moderate degree of proficiency is within
the reach of any one possessed of ordinary perserverance.
AAAA’A/OAVY S/M/A2ZZAZZZZ). 23
step is therefore to thoroughly practise singing the major scale, using
the syllables Doh, Ray, Me, Fah, Soh, Lah, Te, Doh!.” This should
be continued till the pupils can skip from any degree to any other, and
can also recognize the same when sung or played by the teacher.
(c.) In connection with the above, the teacher should sing, or play
the ascending and descending scale, while the class, provided with a
book of score-paper, write each note as it is sung. IDuring this
exercise (of writing, or musical dictation ) the teacher should frequently
ask, “What was the last note sung P” requiring as an answer the name
of the syllable, Doh, Ray, etc. *
49. (d.) The scale may now be broken up; for example, going up a
few notes and coming down part way; then going up a little further,
etc., taking care to have all the progressions diatonic, - i. e., no skips,
and no notes altered by accidentals. (The pupils should write these
notes as sung or played.) p
(e.) Afterward, simple skips (3ds, 4ths, and 5ths) may be inter-
spersed, always keeping enough of the diatonic progression to retain
the feeling of tonality, and taking care to increase the difficulty very
gradually.
These exercises must be practised thoroughly, in order to lay the
foundation for the more difficult subsequent studies. The keys in
which these dictation-exercises are written, should be frequently
changed during a lesson, that all keys may become familiar. It is
not necessary that the teacher should play in a different key when
the change is made. He may simply say, striking any note on the
Piano : “This note is Doh : write in the key of ——,” After a time
he may say : “Now write in the key of ’ mentioning any key he
may desire. Thus the pupils will become able to express themselves
in one key as easily as in another, and will realize that the great point
is the relationship of the sounds rather than the actual notes.
50. Although the ability to sing any succession of tones may not
appear very requisite for the first exercises, it will be found in the sub-
sequent studies in recognizing chords, modulations, etc., that the
highest possible development of this power is of great advantage.
Therefore, the practice of singing the scale and skipping about in it
should be continued for some time. A diagram like Fig. 18, written
on a wall-chart, is best for the first practice.
* The use of syllables is helpful in establishing the relationship of the
various notes to each other.
24 A/AA’ MOAVY S/MAZZZZZZZX.
Fig. 18.
Fah! 5.I. Besides practice in singing different tones, the pupil
Me! should be exercised in thin/-ing how a succession of notes
Ray! would sound. For example, taking a short succession
DOH! like -
TE O- or ; , Or: *——--
tº reº. Hé BBHEEE::=||
SOH Etzit-z-lif-2-Ea. ==F2=== T I
FAPH > -e)— —C-
ME the pupil should, by remembering the syllabic names of

RAY the notes and the sounds connected with those names, try
DOH to think how the passage would sound, afterward compar-
Tel ing with the effect when sung or played.
Lah,
Sohl 52. While exercising the pupil on Pitch, studies in Rhythm
should be given, by means of notes of various lengths, suc-
cessions of notes with rhythmic flow, etc. Rests should also be intro-
duced. The inexperienced will find material for such exercises in any
book on Sight-singing or Musical Dictation.
Specimen Test Ouestions.
Illustrating the Drill which should be given at the end of each
chapter.
Additional questions may be obtained (free) from the author, at
Orange, N. J.
I. Where are Half steps in the Major Scale P State
two or three foundation principles covering its con-
struction.
2. For what are Sharps and Flats used P” Also
Double Sharps, and Double Flats P
3. How many Azza's of Major scales are there, and
why P
4. What is a Signature ?” Give its origin. *
5. Describe Tetrachords and their office in the Order
of Keys. *
6. Give the Order of Scales with Sharps. Also
with Flats.
* But few reach the underlying thought in these questions.
Aſ A A'A/OA/V SZA/A2/...//º/A2/D. 25
7. What is the difference between a Scale and a
Key P* |
8. What is the difference between the Harmonic and
Melodic Minor P
9. Name the Keys related to G Major and give
reasons therefor.
Io. How would you discover a key from the Signa-
ture in Sharps or Flats
I 1. What is the Signature of any Minor Key P
12. What is the office of the Half-step in scale con-
struction Pº
13. Why is there an accidental in every Harmonic
Minor scale P
14. Was it there originally
15. How would you change a Major to a Minor key,
or vice versa P + -
16. What do you understand by the term “Tonality” P
How is it developed, and how does it differ from
“Key" P + º
NoTE. The more obvious questions are here omitted, but
should be included by the teacher, and possibly used to “lead up to ”
these questions.
NOTE. The author has recently introduced into his own work
a system of Daily Drill upon each subject as it is completed in the
course of study. The suggestion, it is hoped, will prove of as great
value to others as it has proved in his own experience. A specimen
drill may be obtained as above.
CHAPTER II.
INTERVALS.
SPECIAL NOTE. – On taking up this subject, it is well to observe
that it is divided into four general sections, which at first are studied
rather independently of one another, viz.: The Names of Intervals;
the Specific Names; Inversions; and Consonant and Dissonant,
Try to keep these four lines of study distinct in the mind.
* These questions are designed to stimulate original thought.
26 AAA’AZOAVY S/M/ZZZZZZZZ).
*
53. An Interval in Music is like an interval anywhere
else, – it is an expression of dºzsáazz.ce between two
things. Consequently, it may be defined as the distance,
or d/2/erezzce Žzz Żºłch, between two given tones. *
54. An Interval may be formed by two notes, either
sounded together, or in succession.—
(a.) is called an Harmonic
I-–f). (a.) – ( ò.) Interval.
Fig. 2 O. EG-4–Ez-e- (6.) is called a Melodic
J iſ Interval.

Ceneral Nannes Of Intervals.
55. An Interval is named according to the number of
degrees of the scale included in its extent.
Thus, the Interval from C to D “ ” is called a 2nd,
because two Degrees of the scale are concerned in its
production. Similarly, from C to E is a 3rd, from C to
F a 4th, from E to B a 5th, etc.
56. To determine the name of an interval, count the
degrees, including those upon which the notes of the
interval stand (i. e., including extremes). For example,
in determining the name of LazL, count the degrees
upon which C and A stand, as well as those lying
between, giving the total of six ; therefore, the interval
in question must be a 6th. N. B. Unless otherwise
indicated, intervals are usually counted from the lower
note upward.
Advazzeed Cozerse.
* The word Interval may also mean the relationship of two notes in respect
to pitch; or the effect produced by the two notes sounding together or in suc-
cession.
** The lower note of an interval or chord is always mentioned first.
A/4 RA/OAVY S/M/A2/./A'/AE ZO. 27
Table Of Intervals.

... 2, EA 2––a–2–H
Pig. 21. Hº Aerº) Z2 €2 T.
[ISU' *ſº zy-cz T
U T2- -3-
Union ºf . ſ. ſ. ſ. ſ. ſ. ſ. 3ſ.
Or Prime.*
Keyboard and Writtern Exercises. * * -
57. (a.) Form tables similar to the above, starting
from the notes D, F, E, G, B, and A (all in the key
of C). º
(6.) Form similar tables in the keys of G, F, D,
Bb, etc.
(c.) Write all the Seconds in the key of G ; e.g.,

• D
(d.) Write all the Thirds in the key of F.
(e.) Write all the Fourths, Fifths, Sixths,
Sevenths and Octaves in the key of E ; in the key of Bb ;
A ; D5; F#.
(f.) Repeat all of the above at the keyboard.
Specific Names of Intervals.
º § t - º
58. Intervals are of various kinds, the names of which
fairly express their meaning, as follows: —
Perfect : //zezzá. The difference between the two
will be explained in § $ 60, 73 and 76.
Major : {. ... The norma/ or standard of measure-
* When two voices sound the same note, there is no difference in pitch,
and therefore no interval between them. Consequently, the Unison cannot
strictly be called an interval.
** Pupils are liable to make mistakes when counting an interval upon
the keyboard ; but when written, by counting the lines or spaces upon which
the notes stand and all the intervening lines and spaces, mistakes become
impossible. Or better still, count the number of letters involved, including
eXtremeS.
* * * For the present the pupil need only know that Unisons, Fourths,
Fifths and Octaves may be Perfect, but not Major. (Some theorists call the
Perfect intervals Perfect Major, to distinguish them from those which are
simply Major.)
28 AARMONY S/MPZ/F/ED.
Minor: meaning “less * by a semitone than Major.
Diminished: meaning still less, or less by a semitone
than Minor or Perfect.
Augmented: meaning increased, or greater by a semi-
tone than Major or Perfect.
. The difference between the various kinds of intervals is illus-
trated by the following, from Eugene Thayer : — ‘Let us take a pair
of hand-bellows, and allowing them to take their natural position,
find them to be nearly wide open — the handles well apart. Let this
position represent the Major interval. If the upper handle be pressed
down a little, the distance between the two handles (or the interval)
is lessened : — this corresponds to the Minor interval. If we now
raise the lower handle, pressing them still nearer together, the dis-
tance (interval) is again decreased, representing a Diminished interval.
Again, letting the handles spring back to their original (normal) posi-
tion, representing the Major interval, if we raise the upper handle, or
depress the lower one, we increase the distance between them, thus
representing an Augmented interval.’
The Standard of Measurement.
59. Consider the scale of C upon the keyboard.
From C to any other degree of the scale of C, or from C to any
white key upon the Piano, is a Major or Perfect, i.e., a Normal,
interval.
(For example, see Fig. 21. All the intervals there
given are Major or Perfect.) This gives us a practical
standard of measurement by which we can measure any
zzzzez-va/; for, as we have seen in the above definitions,
a Minor interval is a semitone smaller than a Major, an
Augmented a semitone larger than a Major, etc.
60. Of the Normal Intervals (as shown in Fig. 21) the Unison,
Fourth, Fifth, and Octave are called Perfect; while the others, namely,
the Second, Third, Sixth and Seventh, are called Major. The
same statement in more general terms would be, ‘‘Normal Unisons,
Fourths, Fifths and Octaves are called Perfect ; while Normal
Seconds, Thirds, Sixths and Sevenths are called Major.” Still
another form of the statement is, “The Normal intervals are divided
A/A ACA/OAVY S///A2/C//7ZZZZ). 29
Into two classes, half of them being called Perfect and half Major.”
Memorize the first statement above, and do not seek to understand
the reason for the above divisions until you study the Inversions.
The reasons will become more apparent as you go into the subject.
61. It is not the mere elevation or depression of the
notes that changes an interval, but the fact that the tones
are either separated further from each other, or are
brought nearer together; i. e., the dºstazzce is changed.
62. Let us make a practical application of the above.
We found in § 56, that from C to A (counting up-
ward) is a Sixth ; and, according to $ 59 and foot-note,

it is a Major Sixth : {=
—eº-
Let us apply some of the changes mentioned in § 58
to this. Lowering the upper note a semitone, we have
*-ºs---º-º-º-º-º:
#EE which, being a semitone less than the Major
-e)—
Sixth, is called a Minor Sixth.
Again, taking this Minor Sixth, by again decreasing
the distance between the notes, this time raising the
lower note by prefixing a sharp, we obtain a Diminished

Sixth : * Fifty-pz-.
THzT
Again, returning to the Major Sixth as a starting-
place, if the upper note be raised a half-step, the
distance between the two notes will be increased,

forming an Augmented Sixth : E Liſz .
U —eº-
Exercises.
Name each of the following intervals.
ſy
E 2% | | | | . . C2 |b B Tº
z-Ez-H===|P2|Pºll
Hº-H2-H2=E= =|bºx=Ez-EEEZE|P2. ITI
Tiz TzTº #2. Tai TzT-zz z22 -z-T-2.Éz.
*The interval of the Diminished 6th is not commonly used (see Table,
$64), but it is useful here for illustration.

3O A/A Ae/l/OAVY S//l/A2/.../AP/A2/).
Exact Measurern ent Of Intervals.
63. An interval can be exactly measured, and its Spe-
cific name placed beyond doubt, by counting the num-
ber of Z/a/f-Sáez’s contained in it (just as we counted the
number of degrees to obtain the General name). For
example, from C to A is a 6th. Counting the number
of half-steps, we find it has nine. Therefore, as our
Standard Sixth contains nine half-steps, any other A/ajor
s?xáž, without regard to its position, ſ/zzasz Zave the
sazze 7zzzzzzóer of /a/f-szeźs. According to $ 58, an
Augmented Sixth must have one half-step more, or ten
half-steps: and a Minor Sixth one half-step less, or eight
half-steps. In this way we may compare any interval
with the Standard of Measurement, and learn whether it
is Major, Minor, Diminished, or Augmented.
64. As no interval is commonly used in more than
three of these forms, a table is subjoined, showing them
in order as generally used. -
Table Of Intervals.
Showing the number of /a/f-steps in any interval.
[For reference; — not to be memorized.*]
Diminished. Minor. Perfect. Major. Augmented.
Primes: - - O -
Seconds: - I - 2 3
Thirds : 2 3 --> 4 -
Fourths: 4 -* 5 - 6
Fifths: 6 - 7 -*. 8
Sixths : - 8 -* 9 I O
Sevenths : 9 IO - I I -
Octaves: II - I 2 - -
Ninths : - I3 -*. I4. I 5
* It is unnecessary to memorize this table, as the pupil can easily find the
number of half-steps in a given interval by the use of the principles shown in
§ 63.
AARMONY SIMPZ/F/AEA). 3 I
65. In working out the following exercises, the pupil
should first find the note for the General name of the
interval as shown in § 56, afterward adding any sharps or
flats necessary to bring it into correspondence with the
requirements of the Specific name. For example,
“What is the Major Sixth from E. P.” Process : —
Beginning to count with the note E, the sixth count will
bring us to C; therefore, a Sixth from E must be C; C is
thus the Gezzera/ name for the desired interval. Next,
a Major Sixth must have (refer to the standard of
measurement) nine half-steps: as there are but eight
half-steps from E to C, it is evident that the latter must
be raised by a sharp, giving, for the Major Sixth, C#.
Advazzced. Cozz7-se.
66. The standard of measurement, § 59, showed the intervals from
the note C to every other note in the scale of C to be “Normal” inter-
vals. In a similar way, from the A’eymože of any other key Zo away 7zoze
of that scale would be also a “Normal ‘’interval, e.g., from Ab to any
note in the scale of Ab would be just as “normal” as from C to any
note in the scale of C. Therefore, instead of counting the half-steps
in naming or forming a specific interval, the practised musician would
think, “What is the ‘Normal' interval 2° counting from any given
note (by transferring his thought for the instant to the key of that
given note), and would raise or lower that normal note to obtain the
required interval. For example: What is the Augmented Sixth from
F# 2 Process : — If we were in the key of F#, the Normal Sixth
would be found by counting up to the 6th degree of the scale, giving
the note Diſ. (Having found the desired interval, do not think
further in the key of F#.) As the required Augmented Sixth is a
half-step greater than the Normal, the D# must be raised another
half-step, giving the note DX (double sharp).
A'eg-zz/ar Cozzrse.
67. Remember that the General name is obtained by
counting the degrees of the scale, while the Specific
name is found by counting the /a/f-steps. Therefore,
32 AAAA’A/OAVY SAA1/A2/_/AF/A2/D.
the use of sharz's or ſlaſs cazz Zeever c/azzge &/ºe General
zzazze of an interval ; – a Sixth remains a Sixth even if
there are several sharps or flats prefixed. The 42nd of
Sixth it would be is quite a different question, coming
under the head of Sãecážc name.
Exercises.
68. (a.) Form a Major Sixth from each of the follow-
ing notes, counting upward : —D, E, F#, B, A, Bb, Ab,
Db, Af, G, Eb, Gp, Cp, G#, C#, Fb, Bit, etc.
(6.) From the same notes, form Major Thirds,
Minor Thirds, and Minor Sevenths.
(c.) Form Diminished 7ths from D, E, F:, B, A,
Bb, Ab, Ajº, C, Eb, Cb, G#, C#, Fb, Bº, etc.
(d.) Form Augmented 4ths from D, E, F#, B, A,
Bb, Ab, D9, Af, Git, Eb, Gb, Cp, G#, C#, Fb, etc.
NOTE. In accidentally raising or lowering a note, it is not custom-
ary to raise or lower it beyond the pitch of the natural next above or
below ; e. g., B would not be double-sharped, since that would bring
it beyozza! C, the next natural ; nor would F have a double flat, since
that would take it beyond the next natural.
(e.) Repeat all of the above at the keyboard.
Extended Intervals.
69. As an octave above any note is considered a repe-
tition of that note and bears the same name, so intervals
(with the exception of the Ninth), if they extend over
more than an octave, are considered as repetitions of the
smaller intervals formed by the same notes an octave
—62
nearer together. Thus: Fé – which is an interval
-62–
of an Eleventh, is considered as an extension of # 9
-2. T
A/4/8//OAVY S////º/, /Ai/A2/D. 33
which is a Fourth. Therefore, in finding intervals, the
notes should be brought within the compass of an Octave.
Exercises.
Name the following intervals, lowering the upper
note, or raising the lower, one or two octaves:
—eº-
-º- -—
—eº- e2 2 –2- – -ez- -2– *-mº –62– #2


|-
L
|
- - - ^2 --- ----------…-a - Jº 22 --------- 2–H––
e2 -2- -2 = €2 - º –62–
The interval of a Ninth is usually not contracted in
this way, as the chord of the Ninth requires that interval
to be nine degrees from the root. See Chapter VIII.
6
Inversion Of Intervals.
70. By Inversion of Intervals is meant that the notes
change their relative positions;– the upper one, by being
lowered an octave (retaining its original name), becom-
ing lower than the other; or, the lower one, by being
raised an octave, becoming higher than its fellow. Thus,
the interval at (a) in the accompanying figure becomes
like (6) by lowering the upper note, and like (c) by
raising the lower one, which is the same thing as (6),
but an octave higher.
a “” (*) (2)
EZ-2–E–F–2–H
ECBE2–E–2–1–H
J Teº/

Keyboard and Writtern Exercises.
Invert the following (a) by lowering the upper note
one octave; (3) by raising the lower note.
ſ).

zºº
{_*
L W Aº.) Cº Aeº Aer", aeºl I
Hº-2–º † ––2–2 3–2– H
LNE 2–2–2–2—2—3—22 3. T.
71. Subjoined is a Table showing a few intervals in-
verted. The lower staff shows the result of inverting the
intervals contained in the upper staff. Notice that in the
34 AAA MOAVY S/MAZZZZZZ).
tables the inversions are produced by raising the lower
note one octave. It would have been quite as easy to
lower the upper notes one octave, writing the inversions
in the Bass clef. The quarter-notes in the lower staff
show the notes which have been raised an octave.
-ee- -62–
is Prime Second Fourth
Fig. 23. becomes becomes becomes becomes
-tº-
Octave. Seventh. Sixth. Fifth.
()
LZ .T.
ſº E--|-2–H2– |-52–-Fi
N.J. e) . I–tz– H
QL, —eº- —eº- -º- -62– - *---------- #2-
Fifth Sixth Seventh Octave Augmented I)1minished
become becomes becºme becomes becomes becomes
O | i
Tº/ → T] } —, } J T
Zſ O |TºTT|TºzzTº *H
GP=2–|-2–H–1–1–2–1–1 =E
J Fourth. Third. Second. Prime. Diminished. Augmented.
72. From the above let us notice the following : —
(a.) To learn what will be the inversion of an interval
(that is, the interval which will result by inverting), sub-
tract the number of the interval from 9, and the result
will be the interval produced by the inversion. For ex-
ample, what would the interval of a Sixth become by
inversion ? Process : 9 — 6 = 3; therefore, a Sixth,
when inverted, becomes a Third. (See p. 42, Ad-
dendum.) *
The following table shows the fact still more
clearly : —
From 9 9
Substract I 2.
Result 8 7
:
f
i
i
t

A/AA’//OAVY SAA/AZ /AP/AE Z). 35
From the first table (Fig. 23) we notice also :—
73. (Ó.) By inversion | Major intervals become Minor.
By inversion Minor intervals become Major.
l Augmented intervals become
By inversion Diminished.
|By inversion º d intervals become
Augmented.
By 1 * | Perfect intervals remain Per-
y 1nversion
fect (and therefore Normal).
This peculiarity of the Perfect intervals renders it
necessary to class them differently from the Major, though
in practical Harmony this distinction does not affect
their use. A further difference between Major and Per-
fect intervals appears in $ 76.
Keyboard and Written Exercises.
74. (a.) Find the Perfect intervals in Fig. 21. (There
are four.) -
(ó.) From the note D form a series similar to Fig.
21, and invert each interval as shown in Fig. 23.
(c.) Write examples of Diminished and Augmented
intervals, and invert them. To learn what Diminished
and Augmented intervals are in use, the pupil may refer
to the Table in § 64.
Consonant and Dissonant Intervals.
75. In the preceding paragraphs, intervals were classed
according to the number of half-steps contained. They
are also classed, according to their musical effect, as : —
(a.) Cozzsozzazzá, meaning those intervals upon
which it is agreeable to pause, and which do not need
to be followed by another interval to produce a pleasant
effect ; and
36 AAA’A/O AVY SAAZAZ ZAZZZZZO.
(6.) Z2&ssozzazzá, or those which are not satisfactory to
dwell upon, or to use in the final chord of any composition.
Consonances are further divided into Perfect and
Zmperfect Consozzazz.ces, with reference to the degree of
concord, as follows : —
r All Perfect intervals, viz.,
Perfect Prime (or Unison),
Perfect : * J Perfect Octave,
| Perfect Fourth,
| Perfect Fifth.
Consonances. 3
Major Thirds and Sixths.
Imperfect: | Minor Thirds and Sixths.
Seconds and Sevenths, together with all
augmented and diminished intervals; i.e.,
all intervals other than the Perfect inter-
vals and Major and Minor Thirds and
Sixths.
Dissonances.
º
Exercises.
(a.) The pupil will refer to all the previous exercises
and illustrations in this chapter, particularly to the Table
in § 64, and mark each interval as Perfect or Imperfect
Consonance or Dissonance. -
(6.) Both at the keyboard and in writing, form first
all the consonant intervals and then the Dissonant inter-
vals from the note D.
(c.) Proceed similarly from the other notes.
76. A furthur difference between Major and Perfect
intervals appears at this place. When a Major interval
* The distinction between perfect and imperfect consonances is of no
importance to the general student, who will recognize an interval or chord .
either as a consonance or a dissonance. There need be no further distinction
at present.
Aſ4 AEA/OA/V S///A2/_/A2/ZZO. 37
is decreased by a semitone (see § 62), it becomes a
Minor Interval, but its classification as Consonant or
Dissonant is 72 ever chazzged by £7,2's red/zzcážozz. For ex-
ample, a major 6th being consonant, the majozor 6th will
be consonant; or, the 7zajor 2nd being dissonant, the
7/27/207 2nd will also be dissonant, as shown in the above
table; whereas, if a Perfect interval be decreased by a
semitone, it at once loses its characteristic of being
“Consonant ’’ and becomes a ‘‘Dissonant ’’ interval.
amºmºmºmº-º-º-º-º-º:
For example, # = is a Perfect Fifth. If we lower
—eº-
the upper note a semitone, the result is £º which
—eº-
is a Diminished Fifth and a Dissonance. Thus we see
that a Major interval can be made less (Minor) wizāozzº
changing Žts classification of “Consonant’’; while a
Perfect interval cazzzzoá preserve its original classification
when thus altered. *
Confusion Of Terrns.
77. There is much confusion in the terms used in
connection with the Theory of Music. Carefully notice
to what each term refers. A few examples are given
below of the various meanings of certain words : —
ZJegree may refer to the various steps of the Scale.
ZJegree may also refer to the lines and spaces of the
staff.
Stez's may refer to the various degrees of the Scale.
* The word “Perfect” conveys but little meaning, as these intervals are
perfect only in respect to their quality of remaining “Normal” when inverted,
while Major intervals do not. A more descriptive name might be “Sezzsätive ’’
interval, as such an interval cannot be changed in any manner without produc-
ing a dissonance.
38 AAA'AZOAVY SAMAZZAZZZ).
Szeźs and A/a/f-Stef's also to the distance between
tone S. *
Tozzes and Semezzozzes may refer to the distance be-
tween tones.
7 ozzes may also refer to sounds, regardless of dis-
tance from other sounds. *
Azzáez-va/ refers to distance between tones.
Azzáez-va/ sometimes refers to the steps of the scale.
The names of the ZJegrees of £/ºe Scale (as Fifth
degree, Third degree, etc.), are liable to be confused with
the Z72.Éerva/s of the same name : therefore be careful to
say whether you mean Degree or Interval.
Definitions. Ye
78. Z27 atomic Zºzłerva/s. The word Diatonic refers to
the scale; a Diatonic interval would be, therefore, an in-
terval formed by two notes of the scale without sharps or
flats other than those indicated by the signature.
Chromažác /zzáez-va/s. The word Chromatic in
Music refers to the half-steps lying between the notes of
the scale, and which are produced by the use of acciden-
tal sharps, flats, or naturals, to change the diatonic
tones. A Chromatic interval, then, would nean one
where at least one of the notes has an accidental sharp,
flat, or natural before it.
N. B. A. Half-step can be either Chromatic or
Diatonic ; e. g., from C to C# is a Chromatic half-step,
because only one note (C) is concerned in the interval.
(See § 44.) But if C# is called Db, the half-step be-
comes Diatonic, because two notes ( or two degrees on
the staff) are concerned. -
* The words AVote and Tozze are often used interchangeably, though a tone
is properly a sound, and a note is a character to represent a sound to the eye.
AAA’ MOAVY S/M/A/L/A/Z/). 39
Afzz/ a7-7/20722c. This word refers to the notation
only ; * when the same tone is expressed in two different
ways, there is said to be an Enharmonic Change; e. g.,
Ab when changed to G# is said to be enharmonically
written, because the name has been changed while the
tone remains the same. (See foot-note, and $ 24.)
This chapter should always be studied twice (repeated very care-
fully) before proceeding, as it is impossible to understand the full
ſmeazzing of the first part before the last part has been studied.
SynOpsis.
79. Before proceeding, the pupil s/ozz/d zeof faz'ſ to
write a syzoſºsz's of the chapter as suggested at the close
of Chapter I, and endeavor to gain an orderly view of the
subject. Failure to do this is often the cause of very con-
fused ideas in regard to Harmony.
Historical.
8o. The beginning of Music was Melody, everything
being in unison and without accompaniment. In some
MSS. of the IOth century, examples of church-music are
found, progressing at the regular interval of a Fourth.
The meaning of this has been disputed; some claiming
that it was intended to be sung in unison and then re-
peated a Fourth higher, while others think the two parts
were to be sung together, the effect of which would be
disagreeable to modern ears.
At about this time a ‘‘Drone Bass '' was sometimes
used —i.e., a Bass continuing upon one note regardless of
the melody. In this way various intervals, such as Fourths,
Fifths, and Sixths, were necessarily, though quite acci-
dentally, formed. Soon afterward (IIth century) it was
* Advanced students of theory may know that Enharmonic intervals have
a very slight difference in pitch ; e. g., G# has a few vibrations more per second
than Ab, though the Piano does not show it.
4O A/AA’A/OAVY SAA/A2///7/A2 ZO.
discovered that two complete and independent melodies
might be sung together and produce a pleasant effect.
From this discovery came Counterpoint, and before the
close of the 14th century music was written in four parts,
though little was known of the effects of harmony. At
this period the controlling principle was to invent several
melodies which would not conflict when sung together,
rather than to study the effect of the combination of three
or four tones forming a chord. Consequently, at this
time, till the close of the 14th century, the harmonic
effects were accºdezz/a/ rather than studied.
The Perceptive Faculties.
(Continued from page 24.)
Intervals.
81. The perception of intervals, though more difficult than of single
tones, need not cause any especial trouble if properly presented, and
if the first steps have been thorough. It is probable that the student
will advance more rapidly in Theory than in the development of the
perceptions. Do not try to make the two keep exact pace, though
in explaining each chapter, the ear as well as the eye and the under-
standing should be actively interested.
Process.
82. Isà Step. This chapter should be taught as a direct continua-
tion of the lessons on the degrees of the scale, not as a new subject.
For example, taking up the subject at (c), § 49, after singing or
playing —T-L and the succession has been named Doh, Ray,
==Hz-
by the class and written in notes, call attention to the fact that the pro-
gression has been explained in Chapter II as an interval of a Second.
(This forms a Melodic interval; see § 54.) In a similar way, the
teacher may proceed up the scale, the next time taking the notes D
and E, the third time E and F, etc., being careful that the pupils do
not lose sight of the syllabic names. As often as they forget or miss
them, return to Doh, and let them sing (or recognize) up to the desired
notes.
A/AA’A/OAVY S/M/A/, /AP/A2/). 41
N. B. Being a dissonance, the two notes of the interval of the
Second should not be sung together, unless once or twice merely to
show their dissonant character.

83. 2nd Step. Sing or play the notes == requiring the
syllabic names as before, and allow them to be written. Explain that
this progression forms a Third, and proceed up the scale, taking the
notes D and F, E and G, as shown above, requiring first the syllabic
names, after which they should be written.
Next, returning to C and E, allow part of the class to sing the
lower note, calling it /Joh, while the remainder sing E, calling it Me.
This illustrates the Harmonic interval, as singing in succession repre-
sented the Melodic. -
Continue up the scale as before, but now allowing both notes to
be sung together and properly written to express the harmonic
interval. *
84. 3rd Steff. Treat Fourths, Fifths, Sixths, Sevenths, and Octaves
(not exceeding the limit of the voices) in a similar manner, first Melod-
ically, and then Harmonically.
Carefully call attention to the m2/sical effect of the different inter-
vals as well as to the various distances apart.
85. 4th Step. Sing or play successions of two single notes, requiring
first the syllabic names and then the interval.
86. 5th Step. Play various intervals (harmonic), first striking
the notes in succession (“spreading ”) if necessary, requiring both
the syllabic names and name of the interval. Zet everything be
written as soon as the pupil recognizes it, to gain the habit of
expressing his impressions. (Begin this step [$ 861 with Octaves
and Fifths.)
87. 6th Step. Striking a Major Third, change it to Minor by low-
ering the upper note, calling attention to the different musical effect
and the means of producing it; explaining at the same time that some
of the Thirds in the scale are Minor without any change, for example,
from Ray to Fah, Me to Soh, etc.
88. 7//, step. Display Major and Minor Sixths in a similar manner.
Introduce Diminished and Augmented intervals very cautiously, on
account of their difficulty.
42 AAA A2A/OAVY SAAZZZZZZZZZZ).
89. In general. Arrange the exercises carefully in point of pro-
gressive difficulty. Do not let the pupil get confused in regard to
the syllabic names. He must have a firm hold of the Tonality. Be
patient.
The pupil may now take two-part songs ( or the soprano and alto
of hymns and choruses ), and try to think how they would sound,
afterward comparing with the effect when played or sung.
Exercises in Rhythm should be continued.
(Addendum to § 72.)
Complementary Intervals.
Any two intervals which,when added together, form an octave, are
called Complementary intervals, since each completes, or complements
the other in the formation of the octave. This is simply another state-
ment of Inversion, for any interval and its inversion form Comple-
mentary intervals. Z//ustration — A Sixth and a Third are Comple-
mentary, or the Sixth is said to be Complementary to the Third, and
zºice zersa. Similarly, Fourths and Fifths, or Seconds and Sevenths,
are Complementary.
AAA’ MOAVY SAMAZZZZZZZ). 43
PART II.
CHAPTER III.
TRIADS.
The Foundation of the Harmonic System.
NOTE. § 90 is not to be studied. It is designed more especially
for the teacher and for those inquiring minds who would know some-
thing of the Scientific basis of chord-formation, and observe the won-
derful symmetry and simplicity of Nature’s laws. -
Advanced Cozz?"se.
Harrn Onics.
90. Science has demonstrated that a musical tone is not one simple
sound, but is made up of the combined sounds of many different tones,
softly sounding with the principal or Primary tone. It has also been
proved that these secondary tones bear a certain relation to the prin-
cipal or Primary tone, and though they sound but faintly (being
inaudible to untrained ears), can be distinctly recognized by those.
who are trained in this direction. These secondary or accompanying
tones are called Ozez-Zozzes or //a2-772 ozzzcs.
When a long string, tightly drawn, is put into vibration, it vibrates
in its full length alone only an instant; after a short time it vibrates
also in sections (without interfering with the full-length vibrations)
producing higher tones simultaneously with the principal or funda-
mental tone. For illustration, if a string producing the tone B:
is put into vibration, this tone will be very distinct, but the presence
of the following tones, sounding very faintly, can be proved.

–0. # *
te |THT2TV. | ſ,
rºl -- & j-T- iº TIT | [−1 i i -
Fig. 24.59 ±ffºrtiñºz-ºff H
• I | $2––2–1–1----|--|-- -T-
– 2 3 O -4-5 6 7 8 9 LO LL 12 13 14, 15 16
—eº-
1.
Primary tone.
* These harmonics are not exactly true to pitch.
44 - A/AA’A/OAVY S.A.ſl/AZ ZAZYZZ).
This series is called the Harmonic Chord, or Nature’s Chord
Those who are already familiar with chords will observe, that the
first six notes sounded together are simply an ordinary chord. If the
next note, Bb, is added, a Chord of the 7th is formed. If to the last
chord the ninth note of the series is added (the eighth note, C, is
merely a duplicate of the lower octaves), a chord of the Ninth is
formed. In these three chords, or rather in this one Harmonic Chord,
is the basis of 4/ke AZarmozzic system, from which the various chord-
formations can be logically developed. The above is designed to show
four points, viz.:-
(a.) That a musical tone is made up of many tones sounding
together as above stated.*
( ò.) That a chord, as commonly understood, is an imitation, at
the hands of Man, of the great chord of Nature, or at least it has been
made to correspond very closely with it.
NOTE. Young students are liable to be troubled by the fact that
some of the remoter harmonics are strongly dissonant with the funda-
mental tone and triad. But this need not disturb them, as the
harmonics are more indistinct as they are more remote from the
Fundamental tone, and the finest ear cannot detect more than six or
seven. Therefore, the upper ones are too weak to have much effect
upon a tone, though Science conclusively proves their presence.
(c.) That chords are produced by a process of adding ſo, or
&zzi/a'izzg. zºom, a 7zote ca//ed' Z/ e Azazzdazzezzła/, or Æoof. The Chord of
the 7th was produced by addizzg ozze 7zoſe to the chord already forwaed ;
and the Chord of the 9th, by adding sºl/ ozze more.
(a.) Conversely, that the chord built upon a Root is considered
as derized from that Æooz.
&
Adeg 24/ar Cozerse.
Triads.
91. When any note is taken, together with the intervals
of a Third and a Fifth above it, a Triad is formed. A
Triad, then, is a chord of three notes: a Fundamental
Z
* There is a strong analogy between a single tone and a ray of light. When
thrown through a prism, light is seen to be a compound of various colors, the
prism serving to separate the ray into its constituent parts. Similarly, a tone
can be shown by the laws of sympathetic vibration to consist of the Primary
tone and Overtones, as shown in § 90. -
A/AA’A/OAVY SAA1/A2/.../A/A2/D. 45
—tº
or Root, together with its Tºp
and Fifth, counting upward; e.g., –2–
As shown above, the whole Harmonic System may
be said to rest upon this simple Triad. A distinguished
musician has declared, “There is but one chord in the
world, the Common Triad. All others are merely addi-
tions to this.”
Exercises.
(a.) Write the scale of C, and upon each note, used
as a Fundamental, construct a triad, without considering
whether the intervals are Major or Minor (see Fig. 25).

O.
[TTWT *2 –
Fig.25. Hº- -a-2-ETC, > z → |
L VU * C >. 22 *L* |
U- Iz – 22 ſtºr
(6.) Write similarly the scale of G, F, D, B, etc.,
not regarding sharps or flats except to place them in the
signature, and construct a triad upon each note, as above.
(c.) Repeat the above exercises at the keyboard,
and, in addition, take each of the remaining major keys.
Marking the Triads.
92. In § 2 it was shown how each degree of the scale
is numbered from the lowest to the highest. The Triads
are described in a similar manner, by indicating upon
which degree of the scale they are founded ; for exam-
ple, “Triad on the 3d degree, ” “Triad on the 6th
degree,” etc. For this purpose Roman Numerals are em-
ployed, being written under the staff as shown in Fig. 26.

- ts º
L–{} zº º 62 22T.
- | L2T º (2 23 *2 2. 2 - ||
Fig. 26. Efts. 2 22 25 £2 2% 2 f_* |
-$7–%. Z2 62 £2 III
I II III IV V VI VII I
Exercises.
|Mark the Triads formed in the exercises in § 91.
46 AARMovy SZMPZzzzzz).
Specific Names of Triads.
93. Triads are divided into four kinds, Major, Minor,
Diminished, and Augmented. These varieties corre-
spond closely with the intervals of the same names, for
they are named, accord'Zazgº to ZZe 272.Éerva/s of w/.2c/.
#/.ey are com/josed, as follows: —
A Major triad has a Major 3rd and Perſect 5th.
A Minor triad has a Minor 3rd and Perfect 5th.
A Diminished triad has a Minor 3rd and Dimin. 5th.
An Augmented triad has a Major 3rd and Aug-
mented 5th. - -
These four kinds of triads are indicated, in marking
the triads, as follows:—
Major, by a large Roman numeral, for example : I.
Minor, by a small Roman numeral, for example: II.
Diminished, by a small Roman numeral with the
sign 9 affixed : v1.19. -
Augmented, by a large Roman numeral with the
sign affixed : III’. -
Exercises.
(a.) Write the Harmonic Minor scale of A, and form
triads upon the various steps, as in § 91. Next, describe
each triad (Major, Minor, Diminished, or Augmented),
and mark as above indicated.
(3.) Repeat the process in E, D and B minor.
(c.) Repeat the above at the keyboard, adding
other Minor keys.
Principal and Secondary Triads.
94. The triads upon the Tonic, Dominant and Sub-
dominant (see § 34) are called the Principal or Primary
Triads, for the following reasons : —
(a.) They are most frequently used.
(3.) They embrace every note of the scale.
AyAA’A/OAVY SAAZZZZZZZZZZZ). - 47
(c.) They are sufficient to determine, beyond doubt,
the key. w
The Triads upon the remaining degrees are called
Secondary Triads.
Exercises.
Returning to the exercises in §§ 91, 92, 93, the pupil
will describe each Triad, indicating the Secondary
Triads by the proper Roman numeral, and the others by
the first letter of their names; thus, T, (Tonic); D,
(Dominant); and S. D, (Subdominant).
DOubling.
95. In a Triad there are but three different notes.
Therefore, if we write music in four parts, one of the
three notes must be doubled, i. e., must appear in two
parts. 7%e Zºundamental is the best note for dozó-
/ºng, azzd #/ºe 7% ird the Žoorcsá. (See § 162.) The
four-part chord resulting from the doubling of one note
of the triad is called a Common Chord; e. g.,
ſ\
| W t
| Lºſ *2 OT =
H(GB)—2––
J -3-
Position.
96. The three notes composing the Triad do not need
to be always in the same order, with the Fundamental
lowest and the Fifth at the top. The Fundamental or
the Third may also occupy the highest place, and the term
Position is used to denote which note is highest, as
follows:—
(a.) When the Fundamental or its octave is highest
(in the Soprano ) the chord is said to be in the Position
of Ż/ºe Octave.

48 AſAA’/l/OAVY S////2/2/A'ZZ /O.
( 5.) When the Third is highest, the Chord is in the
Aosition of f/c Z%ird. &
(c.) When the Fifth is highest, the chord is in the
Aoszężon of Z/e Zºft/.
Fig. 27.
Position of the Octave. Position of the 3d. Position of the 5th.
Keyboard and Written Exercises.
(a.) Form the triad upon each of the remaining
degrees of the key of C, showing each triad in its three
positions, as illustrated in Fig. 27, which gives the triad
upon the first degree. Use two staves in writing.
(6.) Form Major triads of A, E, F, Ab and B5 in
the three positions, using the proper (key-) signatures
in each case.
Four-part writing ; Connection of Triads.
97. Each chord of four notes is considered as written
for a quartet of voices, Bass, Tenor, Alto and Soprano.
The Soprano and Bass are called the Outer or Æxtreme
parts: the Alto and Tenor are called the Zizzer parts.
In four-part writing the effect should be considered from
two points of view : —
(a.) The Melodic effect of each part (as it would
sound if sung alone).
(6.) The Harmonic effect of the four parts sounding
together, and the connection between the successive
chords.
Before proceeding to practical exercises in connect-
ing chords and leading the parts, the pupil should learn
something of the difficulties in the way of making a good
effect, as follows:–

Aſ A A2//O AVY SAA/A2/L/A2/A2/D. 49
Consecutive Fifths.
98. If we play a series of Thirds, for example,
ſ)
E Z-HE+a- etc., the effect is not unpleasant. If
@#####4.
2-2-2–
we add a Fifth, changing each Third to a triad, thus:
etc., we find the effect harsh and un-
pleasant. This disagreeable effect was evidently not
produced by the Thirds sounding in succession, for the
following: etc., is, if possible,
still-worse. Therefore, we may conclude that the bad
effect is produced by the succession of Fifths.”
Consequently, Cozzseczzłżve Aºſths are not allowed.
COnsecutive OCtaVeS.
99. Again, if in a four-part chorus two voices sing the
same notes, either in unison or an Octave apart, there
would be in reality but three different parts, which would
weaken the harmony. Therefore, Cozzseczzężve Octaves
(and Omaisons) are not allowed.
IOO. In order to learn how to avoid Consecutive Fifths
and Octaves, the pupil should realize that in the progres-
sion of the parts, three different movements are possible :-
(a.) Parallel Motion, in which two parts move in the
same direction; see (a ), Fig. 28.
(6.) Oblique Motion, in which one part remains
stationary, while the other moves; see ( & ), Fig. 28.
(c.) Contrary Motion, in which the parts move in .
opposite directions: see ( c.), Fig. 28.
* The harshness of consecutive 5ths is caused by the suggestion of two dif-
ferent keys in succession without proper (modulatory) connection.
f


5O A/ARMOAVY S/M/A2/_/AP/AE O.
(a.) (6.) (c.)
Fig. 28.
In four-part writing, two or even three different
kinds of motion can occur simultaneously between the
different parts. Parallel motion between three parts is
permitted, if no Consecutive Fifths or Octaves result from
it. Parallel motion between all four parts is not good,
and it is difficult to avoid the forbidden consecutives if the
parts all move in the same direction.
TO AVoid Consecutive Fifths and Octaves.
Let one or two parts progress in contrary motion to the others.
This rule will cover all cases.
Open and Close Harmony.
IoI. When the Soprano, Alto and Tenor all lie
within the compass of an octave, the parts are said to be
written in CZose Harmony. If they exceed the compass
of an octave, they are in Oñeza Harmonv
Close Harmony. Open Harmony.
l
Fig. 29
Close Harmony should be used in the following
chapters unless otherwise indicated.
TO COInnect TWO Triads.
NOTE. The following is of especial importance, and should be
thoroughly mastered before proceeding.
Io2. Under this head two cases are to be considered :-


AAA’A/OAW V S///ZºZAZAZ Z). 5 I
( a.) Weeze &/ºe Zwo gºverz chord's have one or more
zzołes 272 comzzzzoz.
(6.) Where 4/kere is 720 commong tozze to serve as a
connecting-link. -
When the Chords have a Note in Common.
Let us take C – E – G and A – C – E, for example,
to connect. Having two notes in common, it is evident
that there is a close connection between them, and it is
only necessary to make this connection apparent to the
ear. If we play the two chords thus:

O). OR :
–––––2 H
=z-P-4–|===|
à—e-–1–3—s 2–-f
------- —eº- sº-62
there is to the ear no connection whatever. But when

[ LZ
played thus: Hº-> 2= the connection is very ap-
N &_º
- - —eº —
—eº->~-tº-
parent. This is because the zoſſes com/2022 to 60%
chords are retained in the same parts. That is, the
Tenor and Alto, which have the notes C and E in the
first chord, retain them in the second. Therefore, zzozes
com/zozz £o 60% chord's are to Óe retazzed Zzz ž/he samze
farás.
It will be seen, that to follow this all-important
principle, the “position ” of the chords must be adapted
to the necessities of the situation, sometimes one note
being highest and sometimes another.
The Process.
Iog. The following is given to illustrate the mental
process by which the beginner should solve every prob-
lem. Having written the first chord in notes:—
Zsá step. What are the notes of the second chord P”
* This question, though unnecessary here, is of importance when the pupil
begins to work exercises from a given Bass, as in § III.
52 AZAARAZOAVY SAA/A/LA'ZAZ ZD.
(N. B. If the pupil has trouble in keeping the notes of the sec-
ond chord in mind during the following steps, he may write them
on a separate slip of paper.)
272d Szeź. Is any note common to both chords?
What note is it P -
3rd Szeź. In which part (Soprano, Alto, etc.) of
the first chord is this “ common ’’ note found P Azzs.
In the - (Here mention whether it is Soprano, Alto,
Tenor, or Bass), therefore it must appear in the same
part in the second chord.
Záž szeź. Write it, and connect with the same
note in the first chord by a tie. (Do not write any
other notes yet.) . .
5:/, step. Name the remaining notes of the second
chord.
6th step. Which “position ” of the second chord
will enable the remaining notes of the first chord to pro-
gress in the smoothest manner to the remaining notes of
the second chord P
Illustration.
IO4. To connect the triads C–E–G, written thus:
# = nº G–B–D.— It is apparent that G is the
—eº—
—eº-
3.
“ common ’’ note or connecting-link. Therefore, as G
is in the Soprano in the first chord, it must be in the
Soprano in the second ; according to § 103, 4th step, we

have : Tzºf:L". It is now apparent that the remain-
ing notes of the second chord, B and D, must lie àc-
Zow G (as the Soprano is always the highest part ),
—0.

As this makes a smooth leading
thus : E 24 2->
HºpF#–
-º- -a-
A/AA’A/OAVY S/M/A/_/AW/A2/D. 53
of the Alto and Tenor (no wide skips”) the effect is
good.

º 2->
3.
Cº.
If the first chord is in this position : EGE
the connecting note, being G, is in the Altö in the first
chord, and must appear in that part in the second
chord. Now it is plain that we must so arrazzge #/.e
7-emaining 720tes of the second chord, B and D, that
the Soprano and Tenor of the first chord will each have
a noće ſo w/ºzcſ. Žá may frogress; therefore, we cannot
place &otſ, B and D below G, as was the case before, but
One should be a 6 ove and One àe/ow, and the choice of
position must depend upon the possibility of making a
smooth progression. Let us try with D above and B

–2
cº’
—ſ)
below, giving : H&Ez== and compare it with the
——eº—
U -
effect when we place the B above and D below, thus:

ſ).
f ‘LZE=E. It will be seen that although the former
(#3–3–
will answer, the latter gives the better effect, because
there are no skips. Again, taking the first chord in this

ſ)
& & D LZ /2 & tº
position : HG=#EZE we find the connecting note in
J ~ e ©
the lowest part; therefore, both the remaining notes of
the second chord must be written above the connecting

_ſ).
note, giving : Ezº—? 62
- —º e
# giving; E65–3–2–
U ~%
Keyboard and Written Exercises.
ros. ( a.) Connect the triad of C with that of F Major,
* In the early exercises the parts should not make very wide skips from
note to note, but should progress by the smaller intervals (2nds and 3rds) wher-
ever possible. In composition, where the parts progress by the smaller inter-
vals, the effect is restful and tranquil. Where they progress by the larger
intervals, such as 4ths, 5th, 6ths, and 8ves, the effect is bolder and more
aggressive.
54. Aſ AA’A/OAVY SAA/A2/, /AC/A2 ZD.
taking successively the various positions of the first
chord, as illustrated above. Use one staff in writing.
(6.) Connect (in three positions) the triad of C
maj. with that of E min. ; with A min.
Connect (in three positions) the triad of D min.
with that of F maj. ; with A min. ; and with G maj.
Connect (in three positions) the triad of E min.
with that of C maj. ; with G maj. - -
Connect (in three positions) the triad of E min.
with that of A min.
Connect (in three positions) the triad of F with
triads upon C, A, and D (all in the key of C).
Connect (in three positions) the triad of G with
triads upon C, E, and D
Connect (in three positions) the triad of A with
triads upon C, D, F, and E.
Connect (in three positions) the triad of B with
triads upon E, D, and F.
Note that all the above are in the key of C Major.
(c) Transpose ( & ) into other keys, and repeat.
(This transposition will not be difficult, if we remember
that to transpose a note or a chord it is given the same
relative place in the new key that it occupied before being
transposed. E. g., if a triad is on the second degree in the
key of C, when transposed it must be placed upon the
same degree of the new key: if on the fifth degree in the
original key, it must be placed upon the same degree in
the new key. Likewise the “position ” and inversion
of a chord must correspond when transposed. If we
substitute the Roman Numerals (as shown in § 92) for
the letters C, D, E, etc., in exercise ( & ), it will be easy
to find the notes corresponding to these numerals in any
desired key. g
( d.) Write ( & ) in four parts, as illustrated in Fig.
AAAA*A/OAVY SAA/AZZAZZZZ). 55
30; the root of each chord being written in the Bass,
which will remain the same for all positions.
ſ)
Z . Ø gº
{G}=2 2–|L2-L3—H2–3–
g —eº- -z-
Fig. 3O
--- eº £2 e2
-) E. | .
Af 2 &2 C/
º º
To connect two Triads when there is no
Connnn On N Ote. r
IO6. Although two given chords belonging to the same
key may not have a visible connection by means of a
common note, there is a certain relationship through their
being members of the same key, ( see the Author’s “How
to Modulate,” $ 3,) and with a careful leading of the
parts they may be used in succession.
Especial attention must be given to avoid consecu-
tive Fifths and Octaves, remembering that Contrary
Motion is the means of so doing. It should be noticed
that some Positions are much better than others for a given
connection, and that some Positions cannot be used at all.
The smoothest connection is usually where the three
upper parts move in a direction contrary to the Bass.
The Process.
Ioſ. The mental process of finding the correct leading
of the parts is somewhat as follows: -
Aºxamp/e for 2//us/razzoz. Connect the triad of
C, in the position of the 3rd, with the triad of D. Ex-
pressed in notes, thus:

56 AZAA’MOAVY S/M/A/AAP/A2/).
(zsá step.) What are the notes of the Second
chord P Ans., D F A.
(2nd step.) In which direction does the Bass move
in the example P Ans., Upward; therefore it would be
well to have the three upper parts (or as many of them as
possible) move downward ( to move contrary to the Bass).
(3rd step.) Which position of the second chord
allows the proper progression of the parts, without Con-
secutive Fifths and Octaves P.
(Or, 3rd step.) Write the notes of the second chord,
so that each part shall progress in the desired direction,
avoiding Consecutive Fifths and Octaves.
(záž szeź.) Would any other position give a better
leading of the parts, by avoiding large skips or otherwise
producing a better general effect?”
N. B. All of the upper parts are not obliged to
move contrary to the Bass. Sometimes it is better to
have only one part progressing contrary to the Bass.
Fig. 31 illustrates the connection of the triad of C
(in its three positions ) with that of D. N
( a.) (6.) (c.)
Fig. 31
*>
* There are other influences affecting the leading of the parts, which are,
however, as yet too advanced for the pupil. After having studied as far as $170,
the pupil should review this section.


AAAA’ MOAVY S/MAZ/AP/AE ZO. 57
Io8. At (a) it is necessary to double the Third to
avoid Consecutive Fifths with the Bass, which would
arise if the Alto should progress to A. Notice also that
the Tenor should not progress downward to D at this
place, as bad hidden Fifths with the Soprano would
result. (See § 134.)
Exercises. -
Io9. Copy the following, and fill up the vacant parts,
applying the “mental Process * to each of the ten sepa-
rate examples.
Eff-2-2 =Fáº-Ez==E=E=l
Kºz-Ez=E2 =z-Ez–E4E=|
º . z-z--~~~-
Fig. 32.
*2
& . º º
©: Aſºº e2 = 2 62 I-2
|-2′- º
|
C :
Key of II III III IV IV V TV v I VI VII
VII.O I II III II. II I IV V II IV
At N. B., Fig. 32, the Third was doubled, as the
Leading-note should only under exceptional circumstan-
ces be doubled (see $162 ). The above examples do not
sound well unless used in connection with other progres-
sions, when they lose much of their harshness. The
teacher should give examples in other keys, and as soon
as the class can “figure * inversions (see §§ 125 – 132),
this section should be again taken up, using chords in
their inversions.
Exercises.
(a.) In the key of G, connect the triad upon each

58 AAAA’ MOAVY SAMA'/.../A.Z.A./).
degree with the one upon the degree next above, trying
the different positions to make the best effect possible.
( 3.) Repeat in the keys of Bb, A, and F.
(c.) Repeat the above at the keyboard, adding all
other Major keys.
Review of the Connection of Triads.
I Io. ( a.) Avoid Consecutive Fifths and Octaves.
(6.) Contrary motion is the means of avoiding them.
(c.) If there is a connecting note, keep it in the
same part in both chords.
( d.) If there is no note in common, adopt contrary
motion and avoid wide skips, especially guarding against
consecutive Fifths and Octaves.
(e.) In doubling notes, the Fundamental is the best
note, the Third the poorest. The Leading-note should
be doubled only under exceptional circumstances: though
doubling any part is better than open consecutives.
(f.) Avoid wide skips. Ilet each part be melo-
dious.
(g.) Avoid progressions of Augmented intervals,
as they are not melodious.
Part-writing.
I I I. Having learned to connect two given triads, the
pupil should proceed to put his knowledge into practical
use by writing exercises on given Basses. In these exer-
cises is nothing new ; each exercise may be considered
as a little series of examples illustrated in § $ IO2 to 1 Io.
N. B. A figure over the first Bass note of an exer-
cise, indicates whether the Third, Fifth or Octave of the
Bass note is to appear in the Soprano.
Should the pupil need further guidance, the follow-
illustrating Fig. 33, will help.
2
ing “mental process,’
A/AA’ MOAVY S/M/A2///7/A2/). 59
&2
|
22–
U
|
|
l
L
Fig. 33. B: & 2 T.
E
2
|
|
II 2. Process: The Figure 8 over the first note indi-
cates, that we are to begin with the octave (or double
Octave) of the Root as the highest note, giving the
chord in this position : ===||
—eº—º-
The first problem then is, to connect this chord with
the chord founded on F, as indicated by the second Bass
note in Fig. 33. Now let the pupil go through the
process shown in § IO3, giving as a result:
The next problem is to connect the chord last found
with the chord founded on C, as indicated by the third
note in the given bass. Following the same process
brings one more chord. Continuing in the same way
gives the completed example:
Fig. 34.
I IV I V I
II.3. In the first exercises the Soprano part is given as
well as the Bass, leaving the pupil to find the names of
the remaining notes in each chord and to place them
so that they will progress as smoothly as possible.


6O A/AA’A/OAVY S/MA’/ ZAZZZZY.
The parts should not cross; for example, the Alto
should not go higher than the Soprano or lower than
the Tenor. Write the exercises in close harmony.
I 14. The various parts should not exceed the compass
of a good voice of corresponding pitch, as shown in
Fig 35.
Soprano. Alto. Tenor. A Bass.
ſ) —eº- --- 2. -
. . . F-27 -2–H–2–|<\;=2–E–2–H
Fig. 35. [Tſºts Z 2T L^T2 Z "
- LVS2. A 27 I’ I
U —62– Tz. Z2
2- -
The pupil should always mark the Roman numerals
in the exercises, as shown in Fig. 34. A/ways wrºte
Ž/ezzz àefore àegzzzzzzzzg: £o forma z/Ae chords.
II 5. Exercises. & ~
1. 2.

AARMONY SIMPL/F/Ep. 61
5. 6.
116. In the following exercises the pupil will write
the Soprano as well as the other parts. Where the
figure 3 is found over the first Bass note in an exercise, it
indicates that the first chord should appear in the posi-
tion of the 3rd. The figure 5 shows that the position of
the 5th is desired. Where no figure is given, the posi-
tion of the octave is to be written. This applies to the *
first chord only of each exercise.
Jadassohn. Richter.
$): 7 —-T— | | [TøTI | `-- [º 2 || |
e ZT ºr P. E. Tº | | T. | | CE* L T.I.
_^T\DT22TDTTT22TTT2 T.IFT2, I | 2 | | | 2 ||
— —- e; L – L l L | L I.
- I IV. I V I I V I - IV V I
R R.
3 —eº-
9:7; | 2 || > || Tz : . [ _ ſº || || – | *
• Tº […] Tº | | | | || Lºtz I | |TC’ II. T. L.T.
L^T\Lyº & TI ºt | 2 | | 2 || || | | | ex I T2 I.
I L–L Lºl | “Tº | | | | ITT I.

62
AAA’A/OAVY SAAZZZZZZZZZZ).

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Exercises.
117. The pupil is recommended to repeat the exer-
I-
HG)
[TC^T\D


UIL’
dif-
111 a.
ferent position, in order to realize the different treatment
C1SeS 111
this chapter, starting with the Soprano
umstances. It will be found
that some of the exercises cannot be worked out so
11 C
require
d by the changed C
ther; consequently, by
ion as in ano
t
in one posi
smoothly
Aſ4 A*//OAVY S/A/A/C/AP/A2/D. 63
this practice, the judgment will be sharpened to discern
the choice in progressions.
I 18. In cases where this book is used as a preparation
for the study of Analysis, or for Piano-students who are
unwilling to study Harmony (part-writing ) but who
desire to thoroughly understand the construction of the
chords, the above exercises may be omitted. In their
place the pupil may take Sonatinas, Sonatas, etc.,
mark the key, indicate upon which degree of the scale
each triad is found, and its classification (Major, Minor,
etc.). He should be taught, that in considering the
harmonic structure of a composition, a broken chord is
marked the same as one which is not broken. For ex-
ample, (a ), (6), and (c) of Fig. 36 are all considered
to be the chord on C, and are marked accordingly.
(c.) _---~
( a.) (6.)
Fig. 36.
—Cº- —
—T
C. : I I e º tº tº g © I © ge © e
This practice is also recommended to those who
take the regular course, as most essential.
Connection of Triads in Minor Keys.
119. In taking up the Triads of the Minor Scale, the
principal point for the beginner is to avoid the step of an
Augmented Second between the 6th and 7th degrees,
where a good connection can be made otherwise. Being
a difficult interval to sing, the Augmented Second is not
much used in strict writing. For the same reason, all
Augmented intervals (in the progression of a single part)
are undesirable for the beginner.
Exercises.
120. (a) Write the harmonic Minor scale of A;





64 - AAA MOAVY S/MPZ/A/zz).
|
place the Roman Numerals under the notes; form the
triads upon each degree as in § 91.
(6.) In the following exercises the Roman Nu-
merals will be used to indicate the triads. Instead of
saying “Connect the triad on A ( or on the Ist degree)
with the triad on D (or the 4th degree ), we shall say,
“Connect I with Iv,” the chord mentioned first being
written first and connected with the other one.
( I.) Connect I with Iv; with V; with VI; with 119.
( 2. Connect 11° with Iv; with VI; with V; with
VIIQ. -
Connect III with 1; V; VI; vi.1°.
Connect IV with I; 119 ; V ; VI.
Connect V with 1; III : viro.
Connect VI with 1; 11°; III : Iv.
Connect v1.1° with 1; III ; V.
i
.
12.I. (c.) Repeat in the key of C minor: in the key
of G minor: in the key of F minor.
(d.) Repeat the above at the keyboard, adding
other Minor keys. -
1 22. In § 4 I we learned that the 7th degree of the
Minor scale must be raised by an accidental to make a
Leading-note to the tonic. This Chromatic Alteration
must be indicated in the Bass of the exercises in Minor,
and is written as follows:
I 23. When a sharp, natural, or flat appears over a
given Bass note, it is intended that the note standing a 3rd
above that Bass note is to be made sharp, natural, or flat
as indicated by the accidental; e. g., Fig. 37, (a ), (6, )
(c.) If the 5th above the Bass is to be altered, or
any other interval, the figure representing the interval is
written with the accidental; e. g., Fig. 37, (d), (e), (f).
A/AA’//OAVY SAA1/A2///7/A2/D.
№
Çſ)
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A diagonal line through a figure shows that the inter-
va! represented by that figure is to be made sharp;
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Exercises.
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Synopsis.



I 24. Form a synopsis of the chapter as usual.
CHAPTER IV.
Inversions Of Triads.
125. It is not necessary that the Fundamental note (or
root) of a Triad should always occupy the lowest place.*
The Third or the Fifth can also occupy that place, and
when this occurs, the chord is said to be inverted.
When the Fundamental is lowest, the chord is in its
Direct form. . . . . . . . . . . .
When the Third is lowest, the chord is in its I st
Inversion.
When the Fifth is lowest, the chord is in its 2nd
Inversion. (See Fig. 38.)
Notice that “Position ” relates to the Soprano or -
highest part, while “ Inversion * relates to the Bass or
lowest part.
* By inversion the Root is not changed, but transferred to a higher part.
The root of a chord is the Bass note only when the chord is not inverted.
A/AA’//OAVY S////?/L//º/A2/). 67
Keyboard and Written Exercises.
(a.) Form various Triads, and show their Inver-
sions, as illustrated in Fig. 38. Avoid doubling the
Third.
( a.)
Fig. 38.
I I I
Direct *. ISt 2nd
Form. Inversion. Inversion.
126. (6.) Write various Triads in their several In-
versions and Poszázozzs, using two staves. The pupil
should not forget that Fig. 38 represents not three differ-
ent chords, Özzá three forms of ozze azed #4e same chord.
We could not say (because E is in the Bass) that the
form marked “ Ist inversion” in Fig. 38 is the triad on E.
It is the triad on C in an inverted form. The note C is
the fundamental or root from which the chord is
derived, which note may be placed lowest or highest.
Therefore, in marking the triads, the inversions are to be
marked like the direct form (the same Roman numerals),
as shown in Fig. 38. The pupil should carefully dºstºne-
guish between the actua/ /3ass note, and £4e roof of
the chord. The Bass note changes with each inversion,
while the real roof of the chord remaizes the same for
a/Z Zzzwersiones azed. Zoszłżozzs. - /*
Figuring Triads.
127. In § 56 the pupil learned to recognize intervals
according to their distance from a lower note, and to
indicate the same by figures. In a sinnilar manner,
whole chords can be figured, by indicating the interval

68 A/AA’A/OAVY SAA1/A2/_/AC/A2/D.
which each note forms with the Bass or lowest note.
For example, if we have a note with the figures 5 and 3
Over it:
5
BEE
we understand that the interval of a Third from the
note C is required, and also the interval of a Fifth, from
the same note. Thus: -
If we have the same note with the figures 6 and 4
over it, we should form the intervals of a Fourth and a
Sixth from that note:
128. These intervals are not necessarily in the same
octave as the Bass note, nor in the exact order indicated by
the figures, as their arrangement depends upon the pro-
gression of the parts in preceding chords.
Exercises.
(a.) Figure the chords in Fig. 38.
(6.) Write the scale of C major, and form a triad
upon each degree. Write each triad in its direct form
and both inversions, using two staves, and writing in
four parts. Figure each chord thus produced.
(c.) Write on an upper staff (treble) the chords
indicated by the figures over the following Bass notes.


AAA’A/OAVY S/MAE/L/A’ſ A ZO. 69
remembering the caution above given in regard to the notes
being neither in the same octave as the Bass note, nor
in the order expressed by the figures:–
6 6 6 6 6 6 6 6 6
3 4 3. 4. 3. 4. 4. 3 4.
|- i-º--~, º : –2 .
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(d.) Repeat the above at the keyboard.
To find the Root of an Inverted Triad.
129. A Triad is formed by taking a note and adding
its 3rd and 5th (see § 91 ); and a triad so taken would
be figured #, being in its Direct form. If an inverted
triad is taken, the root of which is not known, we can
find the root by continuing to invert till the chord can be
figured #, i.e., is in Direct form. When in the Direct
form, the root is always the lowest note.
Exercises.
Find the roots of the following chords, and mark
each with the proper Roman Numeral :—

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2.
130. Notice that the First Inversion of all the triads is
figured 3, and the Second Inversion 3. From this fact a
chord in its first inversion is often called a “Chord of
the Six-Three,” or simply a “Chord of the Sixth’’; and
its second inversion is called a “Chord of the Six-Four.”
Conversely, when a chord is marked 3, we know
the Bass note is the Third from the root (in other words,
the chord is in its first inversion ); when marked š, the
Bass is the Fifth from the root, the chord being in the
second inversion.
From this (the last preceding statement) the root
of the chord may also be found.
7O AARMOA-P S/MPZZAZED.
Exercises.
(a.) Name the roots of the chords expressed here:
6 6 6 6 6
4- 6 4- 6 4- 6 4- 6 6 4.
9: 22T. a 2 2–1 | | | H
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(6.) A lay the chords indicated by the above Bass
notes.
I31. There are a few conventional rules for Figuring
chords, which the pupil must know :-
(a.) When no figures are given, the Common
Triad is intended.
(6.) 6 means the same as 3; a “chord of the Sixth.”
is the same, therefore, as a “chord of the Six-three.”
(c.) A sharp, flat, or natural, placed after a
figure, is the same as if placed before a note, meaning
that the note indicated by the figure is to be made sharp,
flat, or natural, as the case may be. If a sharp, flat or
natural is given without any figure, the Third from the
Bass is intended. A line through a figure, e. g., 3, is the
same as a sharp after it.
( d.) The doubling of the parts, positions, leading
of the parts, etc., are not indicated by the figuring.
( e.) Oftentimes the figures of a chord are not all
given, only the characteristic or most important being
written, the others being understood, as at ( ò).
(f.) In writing a note indicated by a figure, do
not consider the key or signature : simply count the
degrees of the staff (beginning with the line or space
occupied by the Bass note ) just as in § 56.
(g.) If there are two sets of figures over a given
Bass note, it means that the chord represented by the
first set of figures is to be followed by the chord repre-
sented by the second set while the Bass is held, the time-
AAA’A/OAVY S/M/A/./A./A2/). 71
value of the Bass note being divided between the two
chords; e. g.,
Exercises.
132. (a.) Applying the above rules, fill out four-part
chords from the following figured Basses, also marking
each chord with the proper Roman Numeral. (There
is no connection between the successive chords.)
6 6 e g 6 g 5
6 4- 4- 6 2–3–2 * * : ##
EC) Tº | 2-, P’ a TTC’T I
|Tºº T2:... Tº T. 2-, Tº
| Lº Tº T. tº | 2 || . | “TT22 .
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(6.) Play the chords indicated above.
Exercises in Part-writing, introducing Inversions
and Figured Bass.
133. The mental processes described in §§ 103 and
Io'7, should be carefully applied in the following exercises.
One question might be added to the process when con-
sidering inversions, viz.: “What is the root of the
chord, and upon which degree of the scale is it (the
root) P” In every case the chord should be marked with
the proper Roman Numeral (which must appear as the
answer to the above questions ) before proceeding with
the connection of chords.
N. B. When a chord appears successively in two
different positions or inversions, it is obvious that the
rule in § IO2 (to keep the common notes in the same
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the parts.
In general, it will be found that the different
rules must yield One to another as circumstances demand.
(See §§ 161 et seq.)
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Hidden Octaves and Fifths.
I34. Hidden Octaves and Fifths occur when two
parts, moving in parallel motion, strike an octave or
fifth. If the notes over which they pass should be
written out, consecutives would appear. Although not
so disagreeable as open consecutives, and not positively
forbidden, Hidden Consecutives are better avoided,
unless by their use a better progression can be obtained.
The effect of Hidden Octaves or Fifths between the
two outer parts is much worse than between the inner
parts, or between one inner and one outer part.
Where both parts skip to the Octave or Fifth, the
effect is worse than if one moves diatonically to its
place. Hidden Octaves and Fifths arising as shown in
Fig. 39 are freely permitted.
Hidden Octaves. Hidden Fifths.

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and 8ves altogether, but should discriminate in regard
to the effect, rejecting those that are harsh. Contrary
74.
AAA ACA/OAVY SAA/A2Z/ZºZAZ Z).
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but the pupil should know that an awkward pro
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of a part is worse than the hidden consecutives, and
choose the lesser of two evils.
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Harm Onizing the Scales.
135. An excellent exercise, at every stage of advance-
ment, is the practice of harmonizing the scales in every
AAA'MOAVY S/AZAZZZZZZ). 75
key, and using as many different chords and as much
variety as the pupil may have studied at the time. It
will be noticed that every note of the scale may belong
to three different chords, and either one of these three
chords may be used to harmonize that note if a smooth
connection with the preceding and following chords
can be made. w ;
The scale to be harmonized should be written
sometimes in the Bašs and sometimes in the Soprano,
(see examples below ). [For advanced pupils it may
also be written in the Alto and Tenor.] When written
in the Bass, it should be observed that there can be no
common notes to connect two successive chords, unless
chords of the 7th are used, for which see later chapters.
Exercises.
(a.) Fill out the four parts in the following:—
I. 2.
6 6 — -ę2– 6
—eº- 4.
5. 6
6 6 6
TN 3 6 2–2–3 *r 6 6 2–2–2 *r.
apº
tº 4 ºn 62 | 2- 2 - |T
LL’ zy-rz Taº Tº |
L | T.

76 Aſ AA’A/OAVY S///Z2/C/AXAZZX.
7. - 8.
2- ? -2- :
- *2 -
B: C’ & ºt,
{- tº
(6.) Harmonize the ascending scale of C in as
many ways as possible, using only the triads with their
6
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22
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inversions.
(c.) Harmonize the descending scale similarly.
(d.) Harmonize similarly the ascending and de
scending scales in all other keys.
(e.) Advazzced Cozerse. Harmonize similarly the
Minor scales. -
(f.) Repeat all of the above at the keyboard.
Synopsis.
I36. Write a synopsis of the chapter as at the end of
Chapter III. -
The Perceptive Faculties.
Continued from page 4o.
Triads.
I37. After teaching the pupils to recognize two tones sounding
together, it is but a step further to recognize three tones. This
section is merely a continuation of the foregoing, and may be treated
Somewhat as follows:– -
Isé Szeź. (a.) Teacher sounds the note C, and says: “This tone
is Doh. Write it in the key of — —” (mentioning any key, not
necessarily the key of C).
(6.) Teacher sounds E and asks, “What is this tone?”— Axas.
A/e. —“Write it.”— Two pupils sing Doh and Me.
t (c.) Teacher sounds G and asks, “What is this tone *— Axas.
Sož. —“Write it.”— Third pupil sings Soh. Three pupils sing the
three notes together.
(d.) While the chord is being sounded, the teacher says, “Re-
mainder of the class sing Me ; (sing Soh ; sing Doh). Which note
is highest ? – Which is lowest P – Which between P”
Arizowy S/MPL/F/ED. 77
In this way the pupils learn to hear and distinguish the individ-
ual notes from the mass of sound, for as soon as they have sung them
a few times while the chord is sounding, they will be able to hear
the individual tones, and thus recognize the component parts of a
chord.
The teacher should not confine himself to the triad on C, but
may take any Major triad in the middle of the keyboard or of the
voices. The note which is represented by Doh should always be
announced, to give a starting-point. *.
I38. 272d Steft. Having trained the pupils to recognize the notes
of the triad by the above and other exercises which his ingenuity or
the necessities of the case may suggest, the teacher should proceed
to train the pupils to recognize the different positions of the 7%riad.
Process:– (a.) Teacher sounds triad C – E – G, and asks, “What
are the syllabic names of these tones — Which is highest P – Which
lowest ?” f
(6.) Teacher sounds same triad, but in position of the Octave,
repeating the change to make it forcible, as follows:

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- *------- --- — -ę2—e 2— -
–2–3–E–3–2–1:
—e 2-
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and asks, “Which note is highest in the last chord P – Which is low-
est –Which between P’’ Require the pupils to sing the notes one by
one, using the syllabic names, while the chord is sounding. Also
ask them to fix their attention strongly on one individual note in the
chord, while the teacher plays the chord, and try to hear it, i. e.,
to individualize the note from the chord, and thus cultivate the
perceptions.
In the same manner the remaining positions should be taught.
139. 3rd Step. Chords of four zones.
(a.) Let three pupils sing the triad C – E – G. Teacher sounds
C (3rd space, treble) and asks, “What is this note P’’— A72s. Doh.—
“Which Doh P”— Azas. Octave above the first Doh.— Fourth pupil
sings upper Doh. Four pupils sing, forming the chord, while re-
mainder of class sing single tones as before. Teacher asks, “Which
note is highest ? – Which is lowest — Which is intermediate 2–
Which note is doubled P” -
NOTE. The piano may be used to produce the chord, but it is
far preferable to have it sung.
Proceed as above with other two positions.
78 AAAACA/OAVY S/M/A2Z/AP/A2/).
rAO. 4% Steft. Zºzzersions.
Play the following, asking questions as before, concerning the
highest and lowest notes, etc.:
Then play the passage next given, calling attention to the move-
ment of the bass, and to the different musical effects of the different
inversions, wrong doubling at X, etc. Repeat with other Major
chords, asking questions as above.
X
I4I. 5% Stee. Al/zzzo” Z%-zaaſs.
Play:
calling attention to the different effect of the Minor, showing how it
differs from the Major, asking questions as above, etc. Take in
succession the Minor triads of the key of C (also other keys), and
question in regard to highest and lowest notes, etc.
142. 6th Steff. A'rogression of a Żarz. -
Play little progressions where a single part moves, requiring the
class to recognize which part moves and what the progression is.
(The answers should be in syllabic names, and the notes written as
recognized.) To illustrate, play :



A/AA’A/OAVY SAA/A2Z MAW/A2/O. 79
Process : — First name the notes in the first chord; ascertain, the
position and inversion, and write the notes. Then study the pro-
gression. -
Next take up examples where two parts move without change of
chord ; e. g.,
Lack of space prohibits the multiplication of these simple ex-
amples, which can be taken from many sources or invented by the
teacher. Many examples should be studied before proceeding.
I43. 7th Step. A rogressione of Żarts with change of chords.
(a.) Without Znversions. Give some examples, if necessary
selecting from the first exercises in part-writing (§ 1 13, etc.), calling
especial attention to the progression of the Bass; for if that can be
ascertained, the fundamental of each chord is clear, and with it the
chord itself, though the position may remain in doubt. (The posi-
tion will be discovered by requiring the pupils to sing the notes of
the chord, using the syllabic names.)
Notice also the progression of the Soprano, whether up or down.
The first exercises should consist of but two chords— one pro-
gression, — and should illustrate the progression from the Tonic to
the Dominant or Sub-dominant, after which the progression from the
Tonic to the remaining degrees of the scale may be studied, and later
exercises may be extended to take in several progressions. It is of
especial importance that the exercises be carefully written.
I44. (6.) A^rogressions with Zºzzersions.
This is more difficult than the preceding, and requires patience
on the part of both teacher and pupil. At first give chords, the nat-


8O A/A ACA/OAVY S///A2/_/AP/A2/D.
ural progression of which can be easily traced, as for example those
given here. Those progressions are best which have some tied notes.
as the attention can be concentrated on one or two moving parts.
Simple, well-known harmonies only should be used, leaving the more
difficult ones till a later period. The teacher should constantly lead
and direct the perceptions by questions as illustrated above. Each
step should be expressed in notes.
145. It will be advantageous at this point for the pupil to refer to
the exercises he has already written, and try to think, from looking
at the progressions, how they would sound. Indeed, he should never
look at a chord without trying to realize its effect.
NotE. The treatment of the Perceptive faculties is here given,
not as a complete exposition of the subject, but merely as a suggestive
outline, to be expanded and adapted by the teacher to the needs of
individual cases.
Transposition.
146. The pupil will gain a practical idea of Trans-
position through the exercises used in developing the
perceptive faculties, if the teacher will vary the keys in
which the pupil writes what he hears. For example, the
teacher may say when beginning an exercise, “ This
tone is Doh '' (striking some note); “write in the key
of G.” After a few moments he may say, withozºz
chazzgring the Žitch of /20%, “Write in the key of Zºº”;
and the pupils will soon find that they can as well express
the relations of the notes to each other in one key as
in another. - -

A/A/0/1/OAVY S/A/A/C/A/A2/D. 81
IMPORTANT NOTE.
In this book the chords of the Dominant 7th, Diminished 7th,
Major and Minor 9th, and the Augmented #, § and 3, are treated as
different forms of the same chord, having the same root, same disso-
nant intervals, and same resolution. In learning the natural reso-
lution of dissonant intervals in general, the proper resolution of
all these chords is learned, thus simplifying and systematizing the
subject to a remarkable degree. Therefore, study Chapter V
thoroughly, repeating again and again, if necessary, till the subject is
really clear.
CHAPTER V.
CHORDS OF FOUR NOTES: THE CHORD OF THE SEVENTH.
Its CO nstruction.
147. As stated in § 90, the whole system of chords is
a process of building, or adding upper notes to some
note considered as a Root (Foundation, or Fundamental).
The various triads were formed by adding a 3rd and a 5th
to such a Root-note. If we add not only the 3rd and the
5th, but also the interval of a 7th to the Root-note or
Fundamental, we shall have a Czord of Že Sevezz/.
To illustrate, =#E represents the root G with
its 3rd and 5th forming a triad. If the interval of a 7th
—£2—
(from G) is also added, we have Fáž, called a
Chord of the Seventh. (It may be noticed in reference
to this building-process, that each note is at the interval
of a 3rd — either Major or Minor — from the note next
below. In the following chapters it will be seen that this
82 A/AA’A/OA/ V SZA/A2ZZZZZZZZO.
same rule of placing the successive notes a 3rd apart is
followed in forming chords of the Ninth ; also in what are
called, by some theorists, the chords of the Eleventh and
the Thirteenth.) -
As the character of Triads differs according to the
character of the component intervals, (Major, Minor,
etc., see § 93, ) so the character of the Chords of the
Seventh must differ.
Exercises.
148. (a.) Write chords of the 7th upon every note
of the Major scales of C, G, F, and D, describing the
character of the triad as in § 93, and indicating, on a sep-
arate line, the character of the 7th. For example, form-
ing the chord of the 7th on the third degree of the scale
of C, it would be described as in Fig. 40.

()
| LZ gº I
Fig. 40. E&E||
sº-2-2–2
III with
Minor Seventh.
The Roman Numeral, being small, indicates that the
triad is Minor. The character of the 7th is plainly
expressed. - -
(6.) Write chords of the 7th upon every note of
the Minor scales of A, E, D, and B, indicating the char-
acter of the triad and the 7th as above.
(c.) Repeat all of the above at the keyboard.
149. The pupil, while writing the above, should
notice the following :-
( 1.) That some of the chords, particularly in the
Minor keys, sound so badly that they cováu not be used.
(2.) That the chord of the 7th formed upon the 5th:
degree, the Dominant, is a/Čáe Zzz AZajor azed A3%zzor
A/AA’A/OAVY S////P/L/AP/A2/D. 83
and is not only the most agreeable one, but is the only
one having a Major 3rd and Minor 7th.
(3.) That none of the chords of the 7th are satis-
factory to rest upon, but, like the Augmented and Di-
minished intervals and triads, seem to require something to
come after them to create a feeling of repose.
(a.) ( ò.)
Fig. 4, 1.
For example, the chord (a ), in Fig. 41, although it
sounds well, is evidently not satisfactory to dwell upon,
or to use as the final chord of a composition, as it seems
to suggest something which should follow to make it
complete. Notice that the chord marked (6) gives this
sense of completeness and repose. •
150. This leads us to consider that all chords may be
divided, with respect to this quality (repose or the lack
of it), into two kinds: Zmedefezzdezzá chords, or those
which are satisfactory to pause upon ; and Z06%ezzdezzá
c/ ord's, or those which demand that some chord should
follow to establish repose. This classification corre-
sponds with the division of intervals into Consonant and
Dissonant (see $ 75), for those chords containing conso-
zzazz àzzáerva/s exc/zzszve/y are /indepezdezzá, while
those containing evez ozze dissozzazzú Zìzáerva/ are /De-
Žezzdezzá chords.
151. This demand on the part of a Dependent chord
to be followed by something reposeful, is satisfied if a
consonant chord succeeds it. The process of passing

84 AZAA’A/OAVY S////2ZZAZAZ ZX.
from a Dependent chord to one that is consonant (Inde-
pendent) is called “reso/ving ” it, and the chord to
which it progresses is called the “chord of reso/ºzáčozº.”
It is necessary to resolve dissonances, not only
because they are unsatisfactory to rest upon, but also be-
cause there are tendencies on the part of certaine &nder-
va/s cozzzazzed Zzz them, azed of certazzz zotes of £4e
sca/e, to Ž7-ogress £72 deſizzăţe direczáozes.”
The Principle of Tendencies: Melodic
Tenden Cies.
152. ( a.) This tendency of certain notes of the scale
to progress in definite directions may be illustrated by sing-
ing the Major scale up to and including the 7th degree, then
suddenly pausing without singing the remaining (8th)
degree. By thus pausing, a sense of incompleteness will
be felt, a desire for the delayed note. Thus it is clear
that the 7th degree has a strong tendency to progress to
the 8th degree, which is the Tonic, or most perfect
reszzzzg-?/ace 772 &/ºe w/o/e scale. On account of this
marked tendency toward the tonic (or its octave), the 7th
degree of the scale is called the Zeadžzzg-zzołe.
(6.) Similar experiments will show that the 3rd
degree of the scale has a distinct tendency to ascend,
though the tendency is not so strong as in the case of the
7th degree; and that the 4th degree tends downward.
(c.) An accidental sharp tends to continue upward,
and an accidental flat downward. (N. B. When a nat-
ural is used to raise a note already flatted by signature
or otherwise, it is like a sharp in its effect, and has the
same tendency to ascend. Likewise, when a natural is
* In fact, the reason that some chords are unsatisfactory to pause upon is
simply because certain intervals and notes have the above-mentioned tenden-
cies; for while perfectly agreeable to listen to, they point unmistakably toward
Something which is to follow.
A/AA’A/OAVY SAA/A2/_/A'ZAZ /O. 85
used to depress a note already sharped, it is like a flat in
its effect, and has the same tendency to descend.) Notes
having a tendency to progress in a particular direction,
are called Zezzdezzcy-zzołes.
Tendency of Continuity.
153. A tendency to progress in any desired direction
may be given to a note, or a natural tendency counteracted,
ây aft/roach Zzag #/a/ Zaote from a cozzłrary direczzoz.
Thus, if it is desired to have the 7th degree progress
downward, it can be done by approaching it from above:

Fá. H. This might be called the Zendezzcy
e J. "
of Cozzzzzzzzzzy, i. e., to continue in a given direction
after having started.
Harnnonic Tendencies.
154. An A/armozzic Zezdezzcy is the tendency of a
dissonant interval, or of the notes forming it, to progress
in certain definite directions. . It is apparent that the nat-
ural (Melodic ) tendencies of the above named Tendency-
notes are not so strong but that they may be overcome
by the tendency of Continuity. But, when this natural
tendency is Žežg://ezzed by the fºresence of dissozzazz àzz-
Žerva/s, the demand for progression is quite unmistakable.
Let us examine the effect of dissonant intervals upon the
tendency to progress.
( I ) Play the following and pause:

—º-
#
the ear will then demand that Gif shall progress to A
This is caused, first, by the fact that in touching Gif we
have started on the road from G to A, and having com-
;
86 AFAA’Al/OAVY SAA/A2ZZA'ZZZO.
pleted half the distance (theoretically a little more than
half), it is only natural to desire to continue to the desti-
nation. It would be useless to go half-way, and then turn
back. (See § 152, c.) Secondly, it is caused by the
fact that we have at x a perfect 5th, followed by an aug-
mented 5th. The perfect 5th has been made larger by a
sharp, and it would be expected to develop into something
else instead of retreating. Thus it is apparent that the
cozzzózzzed influences at work must create a demand for a
chord to follow any dependent chord.
(2.) Again, striking the interval at (a), Fig. 42,
we find a strong tendency to progress to the interval at (6.)
This is caused by the same Zendezzcy of azz azgmezzłed
Žzzéez-va/ (here an augmented 4th ) toward a further di-
gression of the Žarás. -
ſ) (a.) (ó.)

I –– ----------- m.
Fig. 42. E ===H
–2-2– -
(3.) On the other hand, if we take a Normal inter-
val and diminish it, there is a strong tendency to sáz// fur-
Žer cozzáracá, as in Fig. 43, where (a ) is the Normal
interval, (6) the diminished and (c) the result of the
tendency toward further contraction.
(a.) (6.) (c.)

E={}=2–2 = 2= -
Fig. 4s. Hº-Hº-à-2–H
LSP. *I
These are illustrations of Harmonic Zendencies.
To formulate the illustrations in Figs. 42 and 43,
the following is given :-
AZZ Azgmented Žzzęervals Zezed toward, further
ex/5azeszozz. -
AZZ ZDāmāmzshed intervals tend toward further
cozzzz-acázozz.
NOTE. This law is a direct resuit of the principles stated in
$$ i 52 (c) and I 53.
A.Y.4A2A/OAVY S/M/A2ZZZZZZZ). 8 7
Advazzced. Cozzrse.
From the above it will be seen that there is an e...ceedingly close
connection between Melodic and Harmonic Tendencies. In fact, an
Harmonic Tendency might be defined as the result or effect produced
by the presence of a Melodic Tendency-note in a dissozzazzf interval.
The dissonance serves to heighten and emphasize the tendencies of the
single tones.*
A’egzz/ar Cozzrse.
I55. In $ 75 it was stated, that Dissonant intervals
were so named on account of their unrestful effect, requir-
ing or pointing to some other interval to follow. It may
also be stated, that f/e matzara/ tendency of a dissonant
272.Éerva/ 2's ſo frogress to #/.e nearest cozzsozzazzá 272.Éerva/
ôe/ongºng to the Áey, the tones moving according to the
principles shown in §§ 152 – I 54.
As chords are made up of intervals, it follows, that
dissonant (i. e., Dependent) chords are those which contain
dissonant intervals, and the natural resolution of a chord depends
upon the tendencies of the dissonant intervals contained in it.
Now, let us apply our knowledge of Tendencies to
the Chord of the Dominant Seventh.
Chord of the Dorminant Seventh : Resolution of
Dissonances: Application of the Principles
Of Tendencies: Cadencing Resolution.
I56. The chord of the 7th which is founded on the
5th degree of the Major and Minor scales, has already
been mentioned as being the most agreeable of all chords
of the Seventh, and is peculiar in being the only one
having a Major 3rd and a Minor 7th. Having a very
close relationship with the chord on the Tonic (see $$ 158
* A consonant interval, being restful in its nature (see $75), would serve
to hide rather than to emphasize the melodic tendencies of the single tones.
88 AAAA/OA/V SZMPZZZZzZ).
and 266), this chord plays an important part in forming
a key, and is called the chord of the Dominant (“ruling”)
Seventh. The pupil is, of course, already familiar with
this chord, as it is used very frequently.
I57. According to the principles stated in § 155, it be-
Comes necessary to examine the structure of the chord of
the Dominant 7th, and find its dissonant intervals, if we
would understand its resolution. Taking the chord in the
Order in which it is constructed, let us examine it in detail.
—eº — 2.
H =#E From G to B is a Major 3rd, which is a
consonance; from G to D is a Perfect 5th, which is also
a consonance; from G to F is a Minor 7th, and here we
find the first dissonant element, for we have learned that
sevenths are dissonances (see $75). Again, starting from
the second note of the chord, B, we find that from B to D
is a Minor 3rd, a consonance: from B to F is a dimin-
ished 5th, forming a dissonance. Here, then, is the
second dissonant element. Further, starting from the
third note of the chord, from D to F is a Minor 3rd, a
COIlSOIla Il C62.
We have learned that the character of a chord (con-
sonant or dissonant) depends upon the character of the
intervals contained in it. Therefore, we see that the reason
this chord is dissonant is, that it contains the dissonant inter-
vals of a Minor 7th from G to F, and of a Diminished
5th from B to F. ( Notice that if the note F were absent,
there would be no dissonant intervals; i. e., the addition
of a 7th to the triad changes an /zzdefezzalez: Triad to a
APežezdent Seventh-Chord.)
The tendencies of these dissonant intervals, in regard
to resolution, are as follows:—The tones of the Dimin-
—eº—
ished 5th : Fº tend to approach (§ 154 ), F
A/A ACA/OAVY SAA/A/L/A"/ZZO. 89
progressing downward to the next step, and B upward
—º-ºs-2— & –2—
Ez-ZTE. The minor 7th : Fá.€2— tends also
SU -**-* -º-º-º:
JT & gº gº
to converge, F passing downward, while G remains
O 2-, *
* | LZ º 2
stationary, or may progress upward; Ez. e
EGB-2–-2–
UT *
In addition to these Harmonic tendencies, we must
also consider the Melodic tendencies mentioned in § 152.
Here we have the Leading-note, B, tending strongly up-
ward, and the fourth degree of the scale, F, tending
slightly downward. As these Melodic tendencies agree per-
fectly with the Harmonic tendencies, the natural resolution
Of the chord becomes clear. Let it be noticed, that the
tones without any special tendency may progress either
upward or downward, or may remain, as may be neces-
# sary either to avoid consecutive 5ths or 8ves, or ſo ſi/Z zeź
Že chord of reso/zzzzozz to advazzage. In accordance
with the natural resolution of the dissonant intervals, the
resolution of the chord is as follows:—
V7 I
In the different positions of the chord, although the
notes may change their mutual intervallic relationship (e.g.,
by inverting the intervals), the tendencies and progres-
sions of the individual tones remain quite the same as
above described. Fig. 44 shows the different positions of
the chord of the Dominant 7th, with their natural resolu-

90 A/A ACA/OAVY S////2Z, ZAZZZZ).
tions. Notice that in every position the Leading-note, B,
progresses upward, while F, the 4th degree of the scale,
moves downward. Notice, also, that the interval of a
Diminished 5th, B – F, at (a ) and (6), Fig. 44, ap-
pears inverted, i. e., an Augmented 4th, F – B, at (c)
and (d), the augmented interval expanding for its
resolution, and the Diminished contracting ; w/22/e 4/26
progression of the 7zzdzvādza! £ozzes remains the same
(i. e., B moves to C, and F to E, in both cases).
(a.) . (ó.) (c.) (d.)
Fig. 4.4.
N. B. The 7zazzazzaz resolution of these intervals is
a/ways the same, therefore, wherever we find them,
whether in chords of the Dominant 7th, Diminished 7th,
Minor 9th, or Augmented 6th, we may expect them to re-
so/ve just Zhe same. When they do not follow this natu-
ral resolution, there is a reason for it, explained in §§ 161
to 169, and 192 to 198; but the Žºržzzcáž/e remzazzas 2.72-
c/azzged.
The Natural Or Cadencing Resolution.
158. In § 156 we noticed the close relationship of the
Çhord of the Donninant Seventh to the Tonic triad. It
will now be observed, that the tendencies of the tones F
and B in Fig. 44 are toward E and C respectively,
which are parts of the Zozz/c friad, while G may re-
main, thus completing the triad. When the chord of ,


A/A/R//OAVY SAA/A/L/A/A2/). 9I
the Dominant seventh is resolved thus to the Tonic Triad,
the resolution is called the Cadencing Resolution.*
If the above-mentioned tendencies are respected, and
the remaining parts are led as smoothly as possible,”
avoiding unnecessary skips and consecutive 5ths and 8ves,
the pupil will not need detailed rules, other than those al-
ready given, for the following exercises. One or two
hints may, however, be of service. -
Remember that it is better to double the Fundamen-
tal or 5th of a chord than the 3rd. Sometimes the 5th of
the final chord must be omitted to secure a good leading
of the parts, another note being doubled in its stead; or
the 5th of the chord of the Dominant Seventh may not ap-
pear, for the same reason. (This also applies occasionally
to the triads.)
Exercises. * *
(a.) Fill out the chords marked I in Fig. 45, lead-
ing the parts upward or downward as indicated by the
diagonal lines;*** and explain the tendencies as above.
V7 I V7 I V7 I V7 I
(6.) Form Cadencing resolutions of the chord of
Fig. 45.
* It should be observed, that the triad on C is the resolution of the Chord
of the Seventh upon G, and that C is a 4th higher than G. Therefore, when
away Chord of the Seventh resolves to the Triad a 4th higher ( or a 5th lower),
this is said to be a Natural or Cadencing resolution. (See § 190.).
* The pupil should carefully note the difference between progression and
resolution. A resolution is a progression, but is influenced by the presence
of dissonant intervals, and is therefore not free. A resolution implies the pres-
ence of a dissonance in the previous chord.
* In the natural resolution, the dissonant tones (and, in fact, all the
tones) must move diatonically. (See § 3, foot-note, and $ 44).

92 Aſ A A MOAVY S/MP/L/AP/A2/).
the Dominant Seventh in four positions, in the key of F:
in the key of G ; of BP; of A; of D; of F#. Designate
the tendency-notes by heavy lines indicating the direction
in which they resolve, as shown in Fig. 45.
(c.) Repeat the above at the keyboard, continuing
till facility is gained in every Major and Minor key.
I59. In the first foot-note of § 158, it is shown that
a chord of the Dominant 7th resolves to the triad a 4th
higher. Conversely, if we would find that Chord of the
Dominant 7th which shall resolve to any desired triad, we
need merely to look for the note a 4th lower than the Root
of the triad; and, having the root, we can build the
chord as shown in § I47. *
Exercises.
Name the Root of the chord of the Dominant 7th
which shall resolve to the triad of D; write the whole
Chord of the 7th and resolve it.
Name the Root and write the Chord of the 7th which
shall resolve to the triad of A; of G ; of BP; of F#; of
Aft; of B; of F; etc.
Exercises.
16o. In the following exercises, the Chord of the 7th
will be indicated by the figure 7 over the bass.
3 6
R. 32- agº 7 j ~ * 6 4. 7
EAE-(BEEE?–E2EEEEEEEE-2–H–Ha-H
| H | [TL- E U T. E LT 2– –H
3 6
R 6 j 6 6 7 R.-3- 2. e Z
Hº:7; L- | | | | || [2 º' | | | | LP-L)
Q:-7ts LE” A TIBTI 2TIPTICT__ | ſlº ----
| -2TVLy CT_ a–E–F–2–Ea–f4–E H2=HIGHH-H
| LTTU tº | | TUT L *T || |
T- I-r-
6
-a- 6 6 7 6 4. 7 J. 6, 6
• | 2-, a [ ] | 2 [- T. Tº T. T.
B+Hz–Hºf Hºff=EEEE||#zīz-
L E-El ' [. |-El 2–1– Zººl D -



AyAA’//OAVY S////7Z/A/Zºº /). 93
6 J
7 !—ern 4- 8 7 __-) 3 7
E9Ez=E: C’ €2 [T2 | | ſ: :* -2 —£4—
- E - E - T - L. F. Tº | - ---
E É–2–E=E2–E–F–F– Ez=-Hº-j-i-Lę–i-
| | | T ſ [… 2- L "T". g L. ——
T Lºſ I
6 6 3 Z
9, 2 9. 6 4, 6,
Egº)†-É–E–F–F2 }_{T_ ºſ || | | || | | ||
w • * : |- | T- ^2 IT | |[[ ] T 2–3 | I
i` F- [T] ØTTP, | _º|| 2–3 & C. E. | | | |
L– |--|--|-- Lº -2T2 Cº. [-2,--I-I


The Principles of Part-leading: “Influences,”
Combined and Opposed.
I61. It has been said that the rules of Harmony Were
made only to be broken, and that every rule has more ex-
ceptions than applications. It would seem better, there-
fore, to review the principles from which the rules are
derived, and thus gain a sound judgment in regard to the
leading of the parts, which must ultimately replace any
rules that could be given.
The sources of the rules which are commonly given,
are found in the 22ecessity of cozzsäderāzºg Že followzzagº
Żołmżs 272 order to Zºrodzące good effecá Zºe Zará-wrážng.
1.) The Harmonic effect of the four )
parts together. £X
(2.) The Melodic effect of the indi- (see $97.)
vidual parts. J
(3.) The Tendencies of certain notes of the scale,
and of various dissonant intervals; i. e., the Melodic and
Harmonic Tendencies. (See §§ 152 to 155.)
(4.) The bad effect of Consecutive 5ths and 8ves.
(5.) The bad effect of doubled 3rds.”
(6.) The Prominence of Outside Parts. **
(7.) The desirability of Connection between suc-
cessive chords.
(8.) The arrangement of the notes in a chord; i.e.,
their distance apart.***
* : *k: ###: See the following paragraphs.
94 AAA’ MOAVY S/M/2///º/AEA).
The above-mentioned points may be called, for con-
venience, “Influences '' which affect or control the lead-
ing of the parts. Sometimes these various Influences
agree, or combine to demand the same progression; some-
times they oppose one another.
N Otes upon the Preceding.
I62. *By doubling the 3rd a certain dissonant overtone (See § 90 :
and Note, p. 44) is brought into prominence, making the chord some-
what rough in effect. Therefore it is not well to double the 3rd with-
Out some definite reason.
Furthermore, in the Tonic triad, and also in the Dominant triad
or Chord of the 7th, chords which appear very frequently, the 3rd is a
tendency-note. (See § 152.) Now, it will be seen that tendency-notes
should never be doubled, if possible to avoid it, as the result must be
either consecutive 8ves or the contradiction of the tendency by one of
the notes. Therefore, where the 3rd is a tendency-note, it should not
be doubled. Where it is not a tendency-note, it may be freely doubled
if thereby a better leading of the parts is obtained. (The chief Ten-
dency-notes (Melodic ) of a scale are the 3rd and 7th. When the 3rd
of a chord happens to be one of these notes, it is better not doubled.)
163. *It will be observed, that the Soprano and Bass parts are
more conspicuous than the inner parts. Therefore, that which might
be allowed in the inner parts may be found very disagreeable — and
consequently be forbidden, – when occurring in the outer parts. In-
cluded in the above are found, most frequently the two points of
(a.) Disregarded tendencies: e. g.,
(a.) Bad. (ó.) Good.
Fig. 4-6.
At (a), Fig. 46, the upward tendency of the Leading-note, B, is
disregarded, it being led down to G, with very bad effect. At ( & ) the
same thing is done, but in an inner part. The effect here is very good,
as the Alto, an inner part, is less prominent than the Soprano, and as
the note to which the Leading-note would have progressed is still

A/A A MOAVY S////2/, /AP/AE/O. 95
found in the last chord. Again, by the progression of the Alto Lead-
ing-note down to G, the last chord has the 5th which would other-
wise be lacking. * -
(b.) Hidden Consecutives: e.g.,
(a.) (0.)
Fig. 47.
The progression at (a ), Fig. 47, is too harsh to be effective, the
hidden consecutives appearing in the outer parts; but the progression
at ( & ) is much more agreeable, as the hidden consecutives are be-
tween one inner and one outer part. Also, where the natural ten-
dency of a note is disregarded, the effect of a Hidden Consecutive is
less likely to be agreeable than where the tendency has not been dis-
turbed. When considering the introduction of a Hidden Consecutive,
this point should be considered. In the example, the downward
tendency of F (the 4th degree of the scale) is disregarded, with bad
effect where the neglect is made prominent by being in the Soprano.
In the Alto it is less disagreeable, though it is easily seen that the effect
of such progressions might be made still better by observance of the
Tendencies.
Distribution of the Parts.
164. *To produce the best effect, the notes of a chord should be
at about an equal distance from each other. If necessary to distribute
them unequally, the larger intervals should be in the lower parts,
Excepting between the Bass and Tenor, there should not be more
than an octave between two neighboring parts. Play the following:
Bad. Good.


96 Aſ4 AC//O/VV S////2Z/A"/A2 ZO.
Opposition Of Influences.
I65. An illustration of this opposition is given in Fig. 48. In this
example there is a tendency on the part of the Leading-note, B, to as-
cend. If this tendency is followed, the next chord will have no 5th.
——ººl——-º- -
–2–F––––H-
Q- —————eº—"—
Fig. 4-8. -
-tº-
tº:-2–E–H
ja” |
-- E "I
As in some cases (for example in a full chorus) this would weaken
the effect of the four voices singing together — see “Influences I and
8 * — it is sometimes better to sacrifice the upward tendency of the
Leading-note in order to gain a full effect in the following chord,
giving the progression :
In disregarding an Influence as was just shown, the pupil should
guard against violating some other Influence; for example, if the
Leading-note were in the Soprano or Bass, it could not progress
downward on account of Influence 6. The effect would be very bad,
as shown in Fig. 46, (a).
Again, if the Bass note G, in Fig. 48, should progress dozezzzwara.'
to C, instead of upward, the leading-note could not pass downward, on
account of the bad Hidden 5ths (both parts moving by a skip, see
§ 134); e.g.,
I66. Another illustration of the manner in which these influences
may oppose each other is shown in Fig. 49.


A/AAC/l/OAVY SAZAZ /Ai/A2 ZD. 97
Fig. 49.
At x the 3rd of the chord, E, is doubled, in opposition to Influ-
ence 5. The reason for this is shown in Influence 2, namely, the
advantage of a smooth progression of the parts: also in Influence 4,
for if the Tenor note, E, in the chord marked x, be changed to C in
order to avoid doubling the 3rd, the result would be Consecutive 5ths
with the Alto, which are much worse than a doubled 3rd. Contrary
motion and the Z endency of Continuity combine to prevent any bad
effect which might be expected from doubling this Tendency-note.*
167. One more illustration may be given : — Influence 7 recom-
mends the retention of a common note in the same part (see also
§ Io2). But it occasionally happens, that other considerations, par-
ticularly Influences 2 and 8, are more important, and demand that this
Influence be sacrificed for them. This is shown in Fig. 50. Here
the note C, which in the first chord is taken by the Tenor, is in the
second chord taken by the Alto.”
Fig. 5 O.
# A Melodic Tendency may be disregarded far more freely than an har-
monic tendency, since the former can be removed by Continuity. (See § 153.)
* If circumstances should allow the rearrangement of the first chord, it
would still be possible to retain the common note ; e. g.,
This would illustrate the fact that in writing exercises, if the pupil finds it diffi-
cult to make a certain connection, by going back a few chords and working in a
different position, a way may be opened.



98 A/A At’A/OAVY S//l/A/, //ſ/A2/).
Many other illustrations might be given, showing how circum-
stances alter cases, and that what is good in one place may not be
best in another. The pupil should understand that part-writing is not
a question of following rules, but is a matter of judgment, controlled
by the considerations above mentioned.
In general the pupil will find that the more prominent of the
above Influences are Nos. 3, 4, 6, and 7.
Ceneral Directions for Part-writing.
I68. In summing up the above, and formulating di-
rections for Part-leading which shall be simple and yet
adapted to all cases, the following may be given :-
( I.) Avoid Consecutive 5ths” and 8ves.
( 2.) Avoid Hidden 5ths and 8ves only when they
make a bad effect.
(3.) A note common to two chords is to be retained
in the same part, unless some other Influence requires
another progression.
(4.) Smooth progressions are better than wide
skips in the parts.
(5.) Study the Influences. If they agree, there
will be no question in regard to the progression. If they
disagree, let the stronger rule unless consecutives are pro-
duced.
(6.) Listen to the effect. If it is bad probably some
Influence has been disregarded.
I69. From this time forward, the teacher, when cor.
recting exercises, should designate which Influence has
* A single exception may be given. A Perfect 5th may be followed by a
te 2---2—--2— -
Diminished 5th, thus, ====Fº: but not reversed, thus,

—H-E--
Hé-É -*-2-* -
z-ZZT |
al)
Good.
ſ
Bad.
AyAA’//O AV V SZA/A/./A./A./O. 99
been disregarded in each case; or he may simply draw a
line through the wrong note and mark the number of the
Influence which, if followed, will rectify the error, leaving
the pupil to change it. This will awaken the critical
powers, and cultivate the judgment. Also allow the
pupils to correct one another’s work according to the same
plan, in each case giving the reason for the correction.
NotE. The pupil should distinguish carefully between the chord
of the Dominant seventh ozz G and the chord of the T) ominant seventh
in the Aey of G. The former has the note G for its root; while the
latter is built upon the 5th degree (the dominant) of the scale of G,
i. e., D.
Exercises.
I7O. Mark the Roman Numerals under the Basses
before proceeding.
J 6 6
• 3 6 7. –––. | 6 4 6 8.7
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Exercises in Harnnonizing the Scale.
Harmonize the Major and Minor scales, using
chords of the 7th where possible, and the triads with
I7I.
rking both at keyboard and in writing.
1nvers1ons, WO
Synopsis.
Write the usual Synopsis of the chapter.
Aſ AA’A/OAVY S///A/.../A./A2/D. iOI
CHAPTER VI.
INVERSIONS OF THE CHORD OF THE SEVENTH.
r 172. We have repeatedly seen the different Positions
of the Chord of the Seventh. We will now consider the
Inversions, which are very similar to the Inversions of
Triads, though a little more complicated, owing to the
presence of four notes in the chord. Compare the fol-
lowing with $ I 25. .*
(a.) When the Root is in the Bass, the chord is in
its Z2%rect form.
(6.) When the Third is in the Bass, the chord is in
its Isà Zzzvez'szozz.
(c.) When the Fifth is in the Bass, the chord is in
its 2d. Zzzverszozz.
(d.) When the Seventh is in the Bass, the chord is
in its 3rd /zz verszozz.
The Inversions are figured and named as follows:—
Direct. Ist Inversion. 2nd Inversion. 3rd Inversion.
7 6 6 6 4 6
5 Or 7 5 or 5 4. Or 3 4. Or 2
3 3 3 2.
Six-Five-Three, Six-Four-Three, Six-Four-Two,
OI’ O1" - OT
Six-Five. Four-Three. Second.
Example:

I O2 A/AA’A/O AVY SAA/A/LAA"/A2 ZD.
- Exercises.
(a.) Taking each of the 12 keys in turn, write
Chord of Dominant Seventh in its several inversions, and
figure them. Vary the positions in the different exercises.
(6.) Repeat the above at the keyboard, in all keys.
To find the Root Of a Civen Chord of the Seventh,
Proceed as shown in § 129. When the chord is in
its “ Direct form,”
2
it is said to be placed in 3rds, since
each note is a 3rd above the one next below. It should
be noticed that when placed in its Direct form, a chord is
always figured § or such part of these figures as may be
necessary. If either of the figures 2, 4, or 6 appears, a1;
'inversion, and not the direct form, is present.
Exercises.
(a.) Write the chords indicated by the following fig-
ured Basses, and mark the appropriate Roman numeral:
6 6 6
5 6 4- 4. 4- 6 4. 6 6 4.
3 5 3. 3 2 2 5 3 5 2 2 5 3
7
9: H––––––. E2FE:
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H2=E=E2-E2-E-E2-E2ji===EEEZE *f;

(6.) Play the chords indicated by the above figured
Basses.
Resolutions of Inversions Of the Chord Of the
Dorminant Seventh.
173. If the simple tendencies shown in § 157 are fol-
lowed, the pupil will have no difficulty in resolving the
inversions of the Chord of the Seventh. Remember, that
the Leading-note tends upward, the 7th from the root
downward, Augmented intervals tend to increase, while
Diminished intervals contract. (See §§ 152 to 155.)
Exercises.
(a.) Following the above principles, resolve the
inversions shown in Fig. 51, and place the proper Roman
Numeral under each chord.
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175. Exercises in Harmonizing the Scale.
Harmonize the scales, using the chords of the 7th
with their inversions, and the triads with their inversions.
CHAPTER VII.
SECOND ARY CHORIDS OF THE SEVENTIFI.
176. The chord of the Dominant Seventh, because it
plays such an important part in the key, is also called the
Principal chord of the seventh.* The chords formed
upon the remaining degrees (for they are nearly all found
in Harmony) are called Secozzdary or Co//aſſera/
Sevenths.
Formation of Secondary Chords of the Seventh.
As seen in §§ 147 and 148, they are formed by the
addition of a 7th to the triads upon the various degrees
of the scale. As the triads are of various kinds, viz.,
Major, Minor, Diminished or Augmented, the Secondary
seventh-chords will have the same variety of formation,
* It is also called the Fundamental Seventh, since its intervals are formed
like those of Nature’s (Harmonic) chord, with Major triad and Minor 7th
from a Root-tone. (See § 90.)
roö AFAA’A/OA/V S/M/A2ZZAP/A2/D.
thus contrasting with the Dominant Seventh with its
Major 3rd and Minor 7th.
This irregularity of construction should not be considered a fault,
for the chord of the Dominant 7th points so strongly to the Tonic,
that if a/Z the Chords of the Seventh were like it the sense of Tonality
would be disturbed. (See § 266.) As it is, the characteristics of the
key are much better preserved than would otherwise be the case.
Again, as we need Major, Minor, Diminished, and Augmented triads
to make up the complete list of triads in a key, so do we need the
same variety in the structure of the Chords of the Seventh.
Resolution of Secondary Chords of the Seventh.
177. As the Secondary Chords of the 7th are formed
in a manner similar to the chord of the Dominant Seventh,
so their resolution follows in a general way the same pat-
tern ; viz., the Chord as a whole tends to resolve to the
Triad situated a 4th higher than the root of the Chord of
the Seventh. This is the same as from the Dominant
to the Tonic. (See § 158, foot-note.) More accurately
expressed, the chord D–F–A–C would tend to resolve to
the triad on G, for G is a 4th higher than D. So also
E–G–B–D would resolve to the triad on A, since A is a
4th higher than E. -
The individual notes in a Secondary Seventh-chord
have a tendency, though not so pronounced, to progress as
in the Dominant Seventh-chord; viz., the 7th from the
root may descend, and the 3rd from the root may ascend.
Fig. 52.
For example, in Fig. 52 the general tendency is to the
triad on G (the Cadencing Resolution ). The 7th, C,
being a minor 7th and therefore a dissonance with the

Aſ AS/CA/OAVY S////2Z, ZAZYZZ). 1 o'7
root, tends downward; F tends upward, not so much on
account of any dissonance or “Influence,” as for the rea-
son that it is the shortest way to a place in the next chord,
and that we are accustomed, in the chord of the Domi-
nant 7th, to hear the corresponding tone pass upward.
According to Influence 8, it could also pass downward to D,
making the second chord fuller. For many cases this would
be better than the upward progression, provided that it made
no bad hidden 5ths with the Bass. If the Bass should move
upward to G, this would be quite satisfactory; e. g.,
Fig. 53.
Exercises.
178. (a.) Form Chords of the 7th upon all degrees
of the scale of C Major, and resolve them as shown in Fig.
52, Or 53. -
NOTE. The resolution of the seventh-chord upon the 4th degree
of the scale to the triad upon the 7th degree, is not commonly used, for
the following reason :- A Dependent chord demands a resolution
to an /ndependent chord. Now, as the triad on the 7th degree is a ZX-
minis/led triad, it is not Independent, and is therefore not suited to be
a chord of resolution. But it is possible to use this progression if
the triad upon the 7th degree should in its turn be followed by an in-
dependent triad; e.g.,
Or -
()
—?—ee—2——2—ea— -- （- ºr-
Fig. 54. HºHº E2 =4=} (sees iss)
U -
–3–2–3–1–3–2–a–
Another restriction in the use of the chord of the 7th on the fourth
degree of the scale is shown in the foot-note to § 187.
(6.) Write the Secondary Seventh-chords, with
resolutions, in the keys of F, G, D, Bb, A, Ep and F#.
(c.) Repeat the above at the keyboard.

IO8 Aſ A A2A/OAVY SAA/AZZAZZZZZO.
Chord of the Seventh upon the 7th Degree in
Major.
179. As a Secondary chord of the 7th, the natural res-
olution of this chord is :
O
Fig. 55. E24– 22 | |
Hºp-º-Hº-E
|
VII.O 7 IIT
This is quite correct. But a more common resolu-
tion is found in a consideration of the following:—
We have seen how the Leading-note (7th degree of
the scale) has a strong tendency to progress to the Tonic.
(See § 152.) The triad formed upon this note has also
a strong tendency to progress to the Tonic triad (see
Fig. 56), resulting from this tendency, while the chord
of Z/2e 7//, upon the same note is even more strongly in-
clined to progress in the same direction. E.g., (play
it ) :
a.) ( ò.)
Fig. 56.
Triad. Seventh.
There are two reasons for this tendency; viz.,
(a.) The tendency of the Leading-note, mentioned
above. -
(ó.) The similarity of construction to the chord of
the Dominant Seventh, which progresses naturally to the
Tonic. For example, G–B–D–F (play it) is the chord of
the Dominant 7th, resolving to the Tonic triad C–E–G
(play it). If now the Root, G, is omitted, we have the
triad B–D–F remaining, which resolves just as if the Root

Aſ AA’ MOAVY S/A/A2/, /Ai/ZZ). IO9
were present. This chord without the root (B-D-F), is
seen to be the same as the triad formed upon the 7th de-
gree of the scale. Now, as the triad upon the 7th degree
has such a distinct tendency toward the Tonic triad, it
will be readily understood that the chord of the seventh
upon the same degree has a similar tendency, which is in-
creased, rather than diminished, by the addition of the
7th. This similarity to Dominant harmony will be further
explained in Chapter IX.
18O. From a consideration of the above, it will be
seen that the Chord of the Seventh upon the 7th degree
may be looked upon in two ways: (a) As an incom-
plete form of Dominant harmony, (in which case it
would resolve most naturally to the Tonic triad, as in
Fig. 56, 6); or ( & ) As an ordinary Secondary Sev-
enth-chord upon the 7th degree, resolving most naturally
to the triad a 4th higher, as in Fig. 55.
Preparation Of Dissonant Intervals.
181. A dissonance may be either agreeable or disa-
gº eeable. This anomaly is explained by the fact, that
alfhough a chord may sound well, it is technica/Zy
called a dissonance if it d'ezzazza's Z/a/ azzoáže?" c/hord
should follow to give a feeling of completion or repose.
..(See §§ 150 and 151.) It was formerly the rule, that
all dissonances should be “prepared.” At the present
day it is the custom to “prepare * only harsh disso-
nances. The chord of the Dominant seventh was the
first to be freed from the restriction, and the chord of the
Diminished seventh is also free,” while the Secondary
Chords of the Seventh, and the Chord of the Ninth (par-
* Though not requiring preparation, it is well to approach the milder disso-
nances by a Diałozzic séeſ rather than by a skip. -
I IO AAAA/OAVY SIMPZZZZZZ).
ticularly the Minor Ninth, because it is a marsh disso-
nance), are usually prepared. “Preparing ”-a dissonance
means, that the note which causes the dissonance shall have
been present as a consozzazz.ce in the chord immediately
preceding ; e. g. ſ)
22-2—-
Hºa–H
* J eº 22
5 * >
The note C, having appeared in the first chord as a con-
sonant note, is thus “prepared '' in the second chord where
it is a dissonant note.
182. Instead of being “prepared,” all dissonant notes
may enter diatonically; i. e., from the next step above
or below. E. g.,
(The dissonant note C enters from the next step above.)
In general, therefore, we should not skip to a dissonant
interval, but either “prepare * it or lead stepwise into it.
183. A dissonant note, i. e., a note which forms a
dissonance with another, should not be doubled. Being
a tendency-note, as all dissonances are, if it were to be
doubled either consecutive 8ves would result, or a contra-
diction of its natural tendency by one of the notes. (See
§ 162.)
I84. Exercises.
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Succession of Chords Of the Seventh ; Resolu-
tion of One Seventh-Chord to an Other Seventh-
Chord.
185. Instead of resolving to a triad, as shown in the
preceding chapters, a Chord of the Seventh may progress
to another Seventh-Chord; e. g.,

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directly from one Seventh-Chord to another, considering
that the Tonic Triad, or regular resolution, is implied in
its enlarged form.
Aa'vazzced. Cozz7°se.
See ‘‘How to Modulate,” page 42.
A'egaa/ar Cozzrse.
I86. Exercises.
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Secondary Sevenths in Minor.
Advazzced. Cozzrse.
Exercises.
187. (a.) As in § 148, the pupil will form Seventh-
Chords upon each degree of the scale of C Minor, and
describe them.
He will notice that some of these Seventh-Chords,
like the triads of the Minor scale, are too harsh for practi.
cal use, owing to the various extremely dissonant intervals
contained. It will be noticed that, beside the Dominant
Seventh (which is a/Zée Zoe Major and Minor), the
most agreeable of the Secondary Chords of the Seventh in
Minor are those upon the 2nd and 7th degrees. The
others, either on account of their harshness or the forced
leading of the parts in their resolution, are but seldors
used.
(6.) The pupil should try to resolve the Seventh-
Chord upon each degree of the minor scale — i. e., the
Cadencing resolution to the triad a 4th higher — and he
will see the difficulty of resolving some of them without
bad leading of the parts.”
*-*
* The pupil will find, in resolving the seventh-chord upon the 4th degree,
that the Bass, if moving upward to its note of resolution, passes over the inter-
val of three whole steps, an awkward skip called the Tritone, which is forbidden.
lt may progress downward to the octave of the same note without hindrance.
Being comparatively ill adapted for singing, like the step of the Augmented 2nd,
the Tritone is not to be used for the present. (See § 329.)
II.4. AFAA’//O AVY SAA)/A2/.../A'ZAZ /).
188. It will be observed that the chord upon the 7th
degree, though a very agreeable chord, does not resolve
well to the Augmented triad a 4th higher, but rather in-
clines to the triad upon the Ist degree. In this it is seen
to correspond with the same chord in Major, i. e., the
Chord of the Seventh upon the 7th degree (see § 179),
and is explained in the same manner, viz., by the strong
tendency of the 7th degree of the scale, or Leading-note,
toward the Tonic. Fig. 59 illustrates the chord of the
seventh upon the 7th degree in minor, with the resolution
to the tonic as described above. The interval B–AP is
a Diminished 7th, and from this interval the chord is
named the chord of the ZOzzzzzzzz's/ed. Sevezzé/. It will
be further explained in Chapter IX.
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Inversions of Secondary Chords of the Seventh.
A'egzz/ar Cozzrse.
189. In $172 the pupil learned to form Chords of the
Seventh upon every degree of the scale, also to invert
and figure them,
Aſ4 AEA/OAVY S////2/2/A'ZZZZO.
I I5
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Cadences: Closing Formula.
I90. It has been remarked that the succession of the
Chord of the Dominant 7th and the Tonic triad, which
gives such a feeling of a close, is called a Cadence, or
Cadencing Resolution, also called the Authentic Cadence.
There are various forms of ending a musical thought,
more or less elaborate and of varying character as
regards the decisiveness of the close. In ordinary ca-
dences the Tonic chord occurs upon an accented part of
the measure (4/ºesis ), and the Dominant Seventh on an
unaccented part (arsis. ) w
These various Cadences are named and defined as
follows:–
Perfect Cadence. The most absolute close : both the
Soprano and Bass of the last (Tonic ) triad sound the
Root of the chord. (Ex. a, Fig. 60.)
Imperfect Cadence. Not so decisive as the first : either
the Soprano or Bass does not sound the root of the Tonic
(closing) triad. (Ex. 3, Fig. 60.)
Plagal Cadence. Where the final chord is preceded by
the triad on the Subdominant instead of the Dominant:
an old church-form. (Ex... c, Fig. 60.)
Half-Close. Where the Dominant follows the Tonic
instead of preceding it. (Ex. d, Fig. 60.)
Deceptive Cadence. Where the Dominant Seventh-
chord, instead of resolving to the Tonic triad, progresses
to the triad on some other degree of the scale, thus disap-
pointing and deceiving the natural expectation that it will
resolve to the Tonic. (Ex. e, Fig. 60. See § 192.)
Modulatory False (Deceptive ) Cadence. Where the
Dominant Seventh-chord, instead of resolving to the
Tonic triad, progresses to a chord in a foreign key, thus
producing a modulation. This will be further explained
in § 195. (Ex. J , Fig. 60.)
AAA’A/OAVY SAA)/A2/./A.ZAZ /O. I 17
(a.) ( ò.) (c.) (d.) (e.) (f.)
Fig. 6 O.
Exercises.
(a.) Return to the exercises in §§ 170, 173 and
174, and describe the cadences.
(6.) At the keyboard, form examples of each of
the different Cadences, using many different keys.
Closing Formula.
191. A more extended form of close, which includes
the Cadencing resolution shown above, is called the
Closing Formula. It will be seen that not only does the
chord of the Dominant 7th point directly to the close,
but that there is a distinct impression in the preceding
chords. Many changes can be made in the succession of
chords constituting the Closing Formula, there being no
rule as to their order. A few of the more common forms
are — (a.) IV, V7 I. (4.) IV, I'í V7, I. (c.) 11, V7,
I. (d.) IV, II, V7, I. Play them.
The Closing Formula is useful in giving a sense of
close at the end of a phrase, or in establishing a key after
a modulation. (See § 289.)
Keyboard Exercises.
IMPORTANT NOTE. The Closing Formula should be made the
basis of an extended course of Åeyboard AExercises, in connection with
the following chapters, including all the Major and Minor keys.
Non-Cadencing Resolutions of the Chord of the
Seventh.
192. The resolution of the Ł)ominant seventh-chord to
the Tonic triad has been shown as the most natural pro-
gression. There are many other resolutions possible,

II 8 A/A At’A/OAVY SAA1/A2/.../AP/AE ZO.
which are called zoza-cadezzczng resolutions, for the rea-
son that the Chord of the Seventh does not move in the
manner of a Cadencing Resolution to the triad a 4th
higher (i. e., the Tonic triad ), but progresses to the
triad upon some other degree of the scale, or even to a
chord in another key. Non-cadencing resolutions are
useful in composition when it is desired to employ the
chord of the Dominant 7th and still avoid a close which
is so plainly indicated by the use of the Dominant 7th
followed by the Tonic triad.
Among these Non-cadencing resolutions are the
ZDece???ve Cadezzce and the Modze/azory Zſa Zse Cadezzce,
both of which are classed among the cadences (§ 190 ) by
name only, not being #7-zze Cadences.
In Non-cadencing resolutions the Tendencies and
Influences are in a somewhat greater degree disregarded,
the progressions consequently being usually rather un-
natural, and in some cases quite forced. But if we were
to use only the simplest and most natural progressions,
the variety of effects would be very limited. It will be
observed that in the Non-cadencing resolutions the disso-
nant intervals do not always resolve to the nearest conso-
Ila Il CéS. -
I93. As the pupil, after studying the use of the common note in con-
necting two triads (Ioz ), at once learned how to connect two triads
withozzi that common note, thus enlarging his powers, so here, after
learning the natural resolution of the chord of the 7th, the pupil finds
enlarged possibilities in the management of these chords by the use
of the Non-cadencing resolutions. They should be understood not as
contradictions, but as enlarged liberties in the treatment of the Chord
of the Seventh, for instead of forcing the Chord of the Seventh
always to resolve to the Tonic, it is allowed, so to speak, to
mingle with a larger circle, or to progress to triads upon other
degrees of the scale, or in other keys. This gives it a freedom
similar to that of the triads, which are at liberty to progress not only to
other triads having a common note, but also to nearly all others which
Aſ AA’A/OAVY SAA/A2/.../AP/A2/). I IQ
can be reached without bad leading of the parts. Many of these pro-
gressions should not be called resolutions, since the Tendencies and
Influences are disregarded, but should rather be called com/nections,
being connected with the following chord in the same manner as the
triads. Indeed, it should not be forgotten that Chords of the 7th are
merely Triads with one or more notes added, and therefore they may
easily be expected to retain the properties and privileges of triads.
Exercises.
194. Pelow are given examples of Non-cadencing res-
olutions and connections. Analyze them, pointing out
the unnatural progressions of the dissonant intervals, and,
if possible, giving the reason. It will be noticed that the
7th is frequently stationary, or even progresses upward,
thus giving the effect of a connection or progression from
chord to chord, rather than the resolution of a dissonance.
When the Tendencies and Influences are disregarded,
especial care must be taken not to violate the rules of
correct part-leading.
N. B. N. B.
Fig. 6 1 .
C V7 VI V7 III V7 a V7 C V7 Aº V7
C V7 aſ V7 C V7 IV V7 II V7 G. V7 C V7 e V7
The possible combinations with the Non-cadencing
resolutions of the Chords of the Seventh are almost lim-


I 2G) A/AA’MOAVY S/MAZZAP/A2Z).
itless, as will be shown in the next exercises. The above
examples marked N. B. show the connection of the Dom-
inant seventh-chord with the Dominant seventh-chords of
various foreign keys: such connections will be further
explained in the chapter on Modulation.
Keyboard Exercises.
Advazz.ced. Cozzz'se.
I95. Non-cadencing Connections with Triads
in the Key.
(a.) Starting upon the Chord of the Dominant 7th in the key of
C, try to resolve it to ( or connect with ) the triad upon each degree of
the key of C. If the effect is not good, try a change of position in the
first chord; if the different leading of the parts does not produce an
agreeable effect, reject the triad and try the next one.
( ò.) Repeat in various keys. r
Non-Cadencing Connections with Triads Foreign
to the Key.
(c.) Starting upon the Chord of the Dominant 7th in the key of
C, try to connect it with the Major triad upon each degree of the
Chromatic scale. Reject the unsatisfactory progressions.
(d.) Try to connect the Chord of the Dominant 7th in C with
the Mžzzor triad upon each degree of the Chromatic scale, as above.
(e.) Starting upon the Dominant Seventh-Chord in other keys,
try to connect with the Major and Minor triads as before, rejecting all
progressions that cannot be made effective.
Non-Cadencing COnnections with Dominant
Seventh-Chords in Foreign Keys.
(f) Starting upon the chord of the Dominant 7th in C, try to
connect it with the chord of the Dominant 7th in all other keys (pro-
ceeding Chromatically as before).
(g) Starting upon the chord of the Dominant 7th in other keys,
try to connect with all other chords of the Dominant 7th as above.
In the above exercises it will be found that those connections are
best which have a note common to both chords, and that few con-
nections can be made without it. -
The exercises at (f) and (g) will be treated further in Chapter
YIII.
A/AA’A/OAVY SAA/A/AAP/A2/D.
I 21
Exercises.
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Non-Cadencing Connections of Secondary
Chords Of the Seventh,
197. We have seen how the Chords of the Domi.
nant Seventh are frequently connected with chords
other than those forming the Cadencing resolution.
The Secondary Chords of the Seventh are capable
of being treated in a similar manner. Many of them,
especially in Minor, which cannot be used in the Ca-
dencing resolution, may be connected with other chords
with very good effect. As in the free resolution of the
Dominant Seventh-chord, the 7th from the root may pro-
gress downward, remain stationary, or progress upward,
as desired. -
Keyboard Exercises.
198. ( a.) Try in succession the Secondary Seventh-
Chords in the key of C major, and find as many agreea-
ble connections with other chords as possible (even con-
necting with chords in other keys), proceeding in detail
as shown in § I 95.
(4.) Proceed similarly with the Secondary Seventh-
Chords in C minor; also in other keys.
Rules for Figured Bass.
199. Short horizontal lines following figures denote
the retention in the following chord, or continuation, of
the notes indicated by the figures. E. g., the notes in-
dicated by 6 and by 3 are continued into the following
chord. In notes, thus : —

AAA’A/OAVY SAA/A2ZZAP//º/).
I 23
Even when the Bass note changes, the horizontal
lines denote the continuance of the notes already sound-
ing, whether indicated by figures in the preceding chord
or not ; e. g.,
Exercises.
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Analytical and Comparative Review.
201. The pupil should strive to keep his knowledge
collected and classified. To this end it is desirable to
tabulate some of the facts already learned, the student
being expected to find the definitions and commit them
to memory if he is not already familiar with them.
( I.) //ow Że terms Major, Minor, Augmented,
and Diminished are zºsed. … *
I. Intervals : — \
there are — Major, Minor, Augmented,
II. Triads:– idiminished.
there are —
III. Chords of the --
Seventh :— Major, Minor, Dimin-
the 7th may be— ished.
AAA ACA/OAVY S/M/A2ZZAP/A2/). #25
(2.) How Że zerm Principal 7s 2/sed:—
I. Triads: — Tonic, subdominant, and Dominant
II. Chords of the Seventh : — Dominant. *
(3.) A/ow &/ºe Zerme Secondary Żs zºsed:—
I. Triads: — Upon all degrees not occupied by
Principal triads. w
II. Chords of the Seventh :— Upon all degrees not
occupied by Principal Seventh.
(4.) Of Zezedezczes —
( I. Of Leading-note — to the Tonic.
II. Of the Third — upward.
- III. Of the Fourth — downward.
Melodic :— { IV. Of Continuity — to continue in
either direction.
V. Of an accidental Sharp —to ascend.
Q VI. Of an accidental Flat — to descend.
ſ I. Of a Diminished Interval;- to be-
come still less.
II. Of an Augmented Interval;- to be-
come still greater.
Harmonic :—
\-
(5.) AWałura/ Aesolutions:–
I. Of Dominant Seventh ;- to triad a 4th higher,
i. e., the Tonic.
II. Of Secondary Sevenths;–to triad a 4th higher.
III. Of Seventh-Chord on 7th degree;— to Tonic
or to triad a 4th higher.
(6.) Non-Cadencing Æeso/utions:–
I. Of Dominant Seventh ; – to secondary triads
in the key. -
II. Of Dominant Seventh ;- to foreign chords.
III. Of Secondary Sevenths;– to various triads
in the key.
IV. Of Secondary Sevenths;– to foreign chords.
x 26 A/AA’A/OAVY S/A/A2ZZZZZZZ).
(7.) Fºgºzzzzzz.g. Zºzvez'szozzs :—
I. Of Triads; — According to distance from actual
Bass. -
II. Of Chords of the Seventh ; – Same as triads.
Synopsis.
Write the usual Synopsis of the chapter.
Historical.
Concluded from page 39.
Triads and Chords Of the Seventh.
2O2. With Palestrina (early in the 16th century) the
Harmonic effects began, though unconsciously, to appear
upon the horizon of musical development. First the
Common chord was used in its direct form, then with its
inversions. Next we find the alternation of consonances
and dissonances, and after a time Suspensions and Reso-
lutions. The use of the Chord of the Seventh (Domi-
nant seventh ) met with much opposition at first. For
many years its dissonant notes were “prepared,” but in
recent times gradually increasing freedom has been al-
lowed, until now the chord can be used without especial
caution. Following in the path of the Chord of the
Seventh came the Chords of the Ninth, the Chord of the
Diminished Seventh, and the chords of the Augmented
Sixth (to be described in subsequent chapters), all of
which have been shown to be various forms of Dominant
(or Dependent ) harmony. Afterward came the various
forms of ornaments, and devices for imparting variety,
shown in Part III.
The development of the Harmonic System, and of
the modern scale as opposed to the Gregorian Modes,
were to a great extent coincident and mutually dependent;
for, whereas the Gregorian Modes were formed in refer.
Aſ4 ACA/OAVY S////º/, /AP/A2/D. 127
ence to the Melody, the modern scale was designed with
direct reference to the requirements of chord-construction.
(See § 46.)
This brings the history to the close of the 16th cen-
tury, when it was substantially as it is to-day. The
boundaries of the keys had been well defined, and the use
of the more ordinary chords had become common.
Since then more freedom in the use of the Dependent
chords has been gained, and a knowledge of those closely
related chords which lie just beyond the limits of a key,
but are used as if they belonged to it. (See Chap. XII.)
During the last two centuries progress has been more in
the line of development than of discovery.
(End of Historical Remarks.)
The Perceptive Faculties.
203. The teacher will not need further detailed instructions, as
the same manner of hearing the tones individually, of singing them
by syllable, of writing them, and hearing them collectively, is here
followed. The teacher should be careful to grade his instruction.
in this department well within the abilities of the pupil, and to pro-
ceed very slowly. Exercises in Rhythm, and in Altered intervals
(Aug. and Dim.), may properly be introduced or continued at
this period.
CHAPTER VIII.
THE CHORD OF THE DOMINANT SEVENTH AND NIN THI.
2O4. The formation of chords has been repeatedly
shown to be a process of building, or adding to a Root or
Fundamental note. (See §§ 90 and 147.) It has also
I 28 A/A ACA/O/VY SAA/A/C/A/A2/D.
been noticed that each note added is at the interval of a
3rd from the next lower note. !
If, according to this plan, a note be added to the
Chord of the Seventh, there will be produced a chord of
the Seventh and Ninth, called also the chord of the Ninth.
As the one most commonly used is derived from the
Dominant, we will consider only that one at present.
In Fig. 62 is shown, at (a ), the chord of the Seventh,
and at ( & ) the same with the 9th added.
- (a.) ( ò.)

e 13:
* –3–L-3—I:
Fig. 62. –3—H-3—E
In a Major key the 9th will be Major; and in a
Minor key the 9th will be Minor, as shown in Fig. 63;
the 9th, A, being made flat by the signature.

The pupil should not look upon this as a new and
strange chord, but as a Chord of the Donninant Seventh
with an interval added. The Chord of the Seventh was
produced by adding a note to the triad, and the Chord of
the Ninth is formed by a further addition of a note to the
chord of the Seventh.
2O5. The characteristics of the chord (the dissonant
intervals and the Tendencies) are zeof chazzged by add-
zzag #/ºe 7zew Zzzáerva/, as may be seen by tracing the
dissonant intervals in the same manner as shown in
§ 157. It is apparent that the added note merely creates
two new dissonant intervals, the 9th from the root, and
the 7th from B. * As both these intervals would be re-
* In the chord of the Minor Ninth there is also the dissonant interval of a
Diminished 5th, D-Ab, in Fig. 63.
AAA’Al/OAVY SAA1/A2/_/AF/A2/D. I 29
solved by allowing the 9th, A, to descend in the resolu-
tion of the chord, it is apparent that the addition of the
new interval does not alter the matural resolution of £/ke
zzzzder/yzzz g chord of Že 7áž, or in any way change its
nature. We merely need to be careful to avoid consecu-
tive 5ths, which may occur in adding the new note. The
Tendencies of the various notes and intervals are not
changed. Therefore, the chord of the Dominant Seventh
and Ninth is seen to be ozz/y are enlarged form of Dom-
Žzzazzā Āſarmozzy. -
2O6. Fig. 64 illustrates the resolution of the chord of
the Dominant seventh and ninth according to the above,
the first chord being used to prepare the dissonance (see
§ 181 ), which is particularly harsh when entering
abruptly. As there are five notes in this chord, ozze must
be omitted in four-part writing. The 5th, being the
least essential and characteristic, and also the tone with
which the ninth might create consecutive 5ths, is usually
the one left out.
Maior. Minor.
Fig. 64.
Keyboard and Written Exercises.
207. From the chord of the Dominant Seventh in
every key, both Major and Minor, form the chord of the
Seventh and Ninth ; find and describe their dissonances
and Tendencies as shown in § 157; prepare and resolve
them as shown in Fig. 64.
The consideration of the above is of great importance and
should be thoroughly understood, as the following chapters are de-
rived directly from this section.

I3O AARMONY SIMPZ/F/AEA).
Inversions and Figuring.
2O8. The inversions of this chord are used, excepting
those in which the root and the 9th come too close to-
gether. The figuring is similar to that of the Chords of
the Seventh, the added note simply adding a figure.
Exercises.
Form examples of inversions of the Chord of the
seventh and ninth.
Secondary Chords of the Seventh and Ninth.
209. Secondary chords of the Seventh and Ninth are
occasionally used, though not often. Not belonging to
Dominant harmony, the 9th and the 7th (the dissonant
intervals) must both be prepared. In the Dominant
Seventh and Ninth-Chord the preparation is not obliga-
tory, though customary.
SynOpsis.
Write the usual synopsis of the chapter.
CHAPTER IX.
THE CHORD OF THE DIMINISHED SEVENTH.
21o. The Chord of the Seventh upon the 7th degree
in Major has already been mentioned as partaking of the
qualities of Dominant harmony ($179). The Chord of
the Seventh upon the 7th degree in Minor partakes of
these qualities in a still more marked degree. (See
§ 188.) They are both considered as incomplete forms
of Dominant harmony. The one formed upon the 7th
AAA’//O AVY SAAZAZ, ZAZZZZO. I31
l
degree in Minor is especially important, as it occurs very
frequently, gives a smooth effect without being prepared,
and is of great value in modulations. (See § 3OO.)
Construction of the Chord of the Diminished
Seventh.
2 I I. This chord is derived from the Chord of the
Dominant Seventh and Ninth in the Minor mode, by
simply omitážng &/he roof.
(a.) ( ò.)
Fig. 65.
In Fig. 65 at (a ) is given the Chord of the Domi-
nant 7th and 9th as shown in Fig. 63. If the root is
omitted, we have the chord shown at (6), Fig 65, which
is a chord of the Diminished Seventh, but it is cozzszań-
ered as derived from #/.e roof G (indicated in Fig. 65
by W. ), and therefore having the same reso/zation as if
Že roof were acázza/Zy, Zºresenzá. Therefore we say that
the chord of the Ozmázzi's/Aed. Seventſ, as azz àzz.com/Zeze
form of Domžzzazzá harmony.
In the chord of the Dominant 7th and 9th the disso-
nant intervals are the Minor 7th from the root and the
Minor 9th. In the chord of the Diminished Seventh,
the same 7zołes, F and Ab, form f/he dissozzazz.ces,
appearing as a Diminished 5th and a Diminished 7th
from the Bass of the chord. These dissonances are re-
solved in the same manner as if the root were also
sounding, e. g.,
E-9 b – #S3--
3-2–
Fig. 66. E Fu-Hiſ O 1 :
* U


I 32 A/AA’/l/O AVY S////2/_/AWAZ /O,
Keyboard and written Exercises.
212. (1) Form Chords of the Minor 7th and 9th
upon all notes from C to C, i. e., upon C, C#, D, Dſt,
etc.; also using flats instead of sharps, as D2 for C#, Ep
for Dit, etc.
(2) From each chord of the Minor 9th just
written, form a chord of the Diminished 7th by onlitting
the root and writing the sign W” in its place.
(3) Resolve each chord of the Diminished 7th
according to the tendencies in § 157. N. B. It will be
found that the resolution is the same as if the root were
still sounding; see Fig. 64.
Use Of the Chord Of the Dinninished Seventh in
Major Keys.
213. In § 204 it was apparent that the Chord of the 9th
is Major in Major keys, and Minor in Minor keys. The
Chord of the Minor 9th and its derivative, the Chord of
the Diminished 7th, are, however, often used in Major
keys, the 9th from the root being lowered by an acci-
dental; e. g.,
bº, 2
* gº ——e)—Cº.— º
Fig. 67 | §2. OI 2
As the Chord of the Dominant Sevezzáž is alike in
Major and Minor, we may say that it resolves equally
well to Major or Minor triads; and the same holds good
of a/Z forms of Dominant harmony, whether Chords of
the 7th, of the 7th and 9th, or of the Diminished 7th.
Keyboard and Written Exercises.
214. (I ) From the Chord of the Dominant 7th, in
all major keys, form Chords of the Major 9th as shown

AZAA’//OAVY SAA/A/L/AP/A2/D. I33
in Fig. 62. From these chords of the Major 9th form
chords of the Minor 9th by lowering the Ninth by an
accidental. Omit the root of the Minor ninth-chords,
producing Chords of the Diminished 7th in Major.
(2) Resolve these chords of the Diminished 7th
as in Fig. 66 or 67. N. B. The chord of the Dimin-
ished 7th resolves to either a Major or a Minor triad, as
mentioned in § 2 I 3.
Sinnilarity of Sound Of the Dinninished Seventh-
Chords.
215. Write the chords of the Diminished Seventh as
in Fig. 68.* Now play them upon the piano, and it
will be seen that there are apparently but three differ-
ent chords, if we consider that inverting and changing
the notation do not alter the sound. This is shown in
Fig. 68, where the chords are divided into four groups,
w, x, y, 2 ; and, by trying at the Piano, it will be seen
that No. 1 of group w is the same as No. I of group X,
or y, or 2, in that the same notes are struck on the key-
board. The difference consists in the fact that the chord
is inverted and differently written. Therefore, any chord
of the Diminished Seventh can, by changing its nota-
, tion, belong to four different keys. This subject will be

explained further in § 3OO.
(zy ) ( x ) (y) (2)
D. 1–2–3–1–2–3–1–2–3—1–2–3–II
Fig. 68. HGºzºzºáž à ||
**@####. :#2 tº pro. -
Roots : ; G y G# / A #}#};}}#}}}#};}} F:
Keys: § {:}; }#: E i Fi Fi G | Gº | A Bb B
I 2 3 I 2 3 I 2 3 I 2 3
* The pupil should write a series (Chromatic) to represent the roots of the
chords, as shown in the ſine marked “Roots” in Fig. 68 and try to build the
required chords from these roots (as shown in § 212) without referring to Fig.
68 unless necessary.
I34. AZAA’A/OAVY S////2ZZZZZZZZ).
The chord of the Diminished 7th, being Dominant
harmony, does not require preparation.
Inversions and Figuring.
216. The chord of the Diminished 7th is used in all
inversions, which are figured by counting from the actual
Bass note, as for other chords. The sign 9 is used to
indicate Diminished.
- Exercises. .#
( a.) |Form a series of Diminished seventh-chords
similar to that shown in Fig. 68, but with the sharps
changed to flats; e. g., instead of using F# for the Root
of a chord, write it G5, which will cause the whole
chord to appear without sharps. Divide the series into
groups as shown in Fig. 68, and number them. Write
also the Roots and Keys under the chords as there shown.
217. It will now be observed, that by changing the
notation of the Root (i. e., from a sharp to a flat, or vice
versa), the notation of the whole chord is changed, al-
though the notes on the keyboard remain the same.
218. It will also be seen, - the first chord of each
group (see Fig. 68) being the same, that, by a change
of Root (and therefore of notation), the same chord (i. e.,
upon the keyboard) may become Dominant harmony in
four different keys, as shown by the series of keys in
Fig. 68. As Dominant harmony resolves naturally to
its Tonic, it is clear that by proper notation these chords
of the Diminished seventh can resolve to any one of four
different keys.
Exercises.
219. (6.) Completing Fig. 68 as required in the
foot-note, § 2 I 5, take the first chord of each group in
Fig. 68, and resolve it to its proper Tonic triad as indi-
cated by the notation.
AFAA’A/OAVY S/MAZZAP/AEA). I35
(c.) Take the second chord of each group, and pro-
ceed as before.
( d.) Take the third chord of each group, and pro-
ceed as before.
(e.) Name the Root of the Diminished seventh-
chord which shall resolve to the triad of D major.
(N. B. The Atooſ of the chord is desired, not the Bass
note. Remember that the Root of the chord of the di-
minished seventh is the same as the Root of the Dominant
harmony from which it is derived; therefore, to find the
Root of a chord of the Diminished seventh, the pupil may
proceed as in § I 59, and, having the Root, the chord
may be developed as shown in § 2 I 2.) Write the chord,
and indicate the root by the proper sign.
(f.) Name the Root, and write the chord which shall
resolve to the triad of D minor; of Ap major; of Ap
minor ; of F#; of Gſt; of Aſt; Bit; B5 ; D9; Eb.
(g.) Repeat (e) and (f) at the keyboard.

22 O. Exercises.
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Exercises in Harnnonizing the Scale.
221. Harmonize the scales, using chords of the Di-
minished seventh where possible, together with the chords
previously learned. Try this exercise also at the key-
board.
Synopsis.
Write the usual synopsis of the chapter.
CHAPTER X.
CHORIDS OF THE AUGMIENTED SIXTHI.
222. Most decided differences of opinion still exist with
regard to these chords. They will here be shown to
be forms of Dominant harmony, or derived directly from
it. This exposition will be found by far the simplest
AZAA’A/OAVY SAA/A2Z/A/A2/). , 137
and most practical, giving a more intelligible clerivation,
and a wider application, than is possible in any other
way.”
223. The chords of the Augmented Sixth are Chro-
matically Altered chords, i. e., chords in which some
note has been changed without radically modifying the
chord or its progression. (See § 246.)
As the Chords of the Dominant Seventh, the Domi-
nant 7th and 9th, and the Diminished 7th, belong to
Dominant harmony, though each appears in a different
form (one note more or less; with the Root or without
it; etc.), so the chords of the Augmented Sixth are no
exception, but may be developed from Dominant har-
mony, as will be shown.
COnstruction and Resolution.
224. These harmonies appear in three forms, viz.,
Augmented Six-Three, Augmented Six-Four-Three, and
Augmented Six-Five-Three chords, e. g.,
–0.
| LZ. —º-
Fi .69. E —62—— ==Hz=||
g {##E –Rºz-i-Ézº—l.
22 pæ b%
g" 3' 6'
3. §
To Construct the Augmented six-Three Chord.
225. Let us take a Dominant seventh-chord, for ex-
ample:
* Although the full application of the theories here advanced is original
with the author, there is abundant authority to support his views. The investi-
gations of the last half-century seem to converge, but the results of research
had not yet been systematized and the practical application shown. While not
claiming the discovery of new principles, it is here attempted to arrange and
apply the truths brought out by Day, Ouseley, MacFarren, Parry, Piutti and
other theorists. --

138 AAAEMOAVY S/MPZZAZAEA).
onnit the Root, ===, and Chromatically lower the
- –23– –
5th from the Original Root, giving the chord : E –.
§2–53–
This is called the Chord of the Augmented Six-Three.
The Root being G, and the original chord an ordi-
nary Dominant 7th, the natural resolution is to the triad

on C: E ====just as it wozz/d Öe £f the moſſe D
wez-e Zzož aſſez-ed.
Notice that the Leading-note progresses upward, the
Minor 7th downward (as in the ordinary progression of
a Dominant 7th chord), and that the interval of an Aug-
mented 4th is resolved naturally by further expansion, as in
choirds of the Dominant 7th, Diminished 7th, and Minor
9th ; while the 5th lowered by an accidental follows the
natural tendency downward. The characteristic interval
of the Augmented 6th, D5–B, from which the chord is
named, resolves by further expansion.
Exercises.
Taking in turn the chord of the Dominant 7th in
every key, place it in its second inversion, omit the Root,
lower the 5th (from the Root) by an accidental, thus form-
ing a chord of the Augmented Six-Three, and resolve it as
shown above.
TO COnstruct the Augnmented Six-Four—Three
Chord.
226. If the same Dominant seventh-chord is taken in
its second inversion as before, but this time without omit-
ting the Root, and the 5th lowered as above, we shall
have the same Augmented Sixth-chord as before, with
the addition of the Root, G : # = This is called
- —p:/2–
Aſ AA’A/OAVY SAA/A2/.../AP/A2/D. I39
the Chord of the Augmented Six-Four-Three. For pre-
cisely the same reasons as the Augmented Six-Three
chord, the natural resolution is to the triad on C:

O
| *C2
—e 2cº-C*-
E —I-e-2-ceº-
ºn-ex-
Exercises,
(a.) Taking in turn the chord of the Dominant 7th
in every key, place it in its second inversion, not omitting
the Root, lower the 5th (from the Root), thus forming
a chord of the Augmented Six-Four-Three, and resolve
it as shown above. .
(ó.) Repeat the above at the keyboard.
TO COnStru Ct the Augmented 6–5–3 Chord.
227. If we take the same Dominant harmony as be.
fore, this time with the AZZzzor 98% from the Zºo of added,

tº- t
º- 2— & º g gº g &
=%–, place it in its second inversion, omit the
—2—
Root, and lower the 5th (from the Root) by an acci-
–2—
Augmented Six-Five, which has the characteristic of sound-
ing like a Dominant seventh-chord. This chord, being
derived from the same harmony as before, though in a
fuller form, has the same natural resolution to the triad
dental, we shall have the chord : ſº called the

ſ)
on C. §ºsa–
But here are consecutive 5ths, which may be avoided
in various ways. Among them may be mentioned: (a)
Resolving first to an Augmented º or 3, which, being pre-
cisely the same harmony, does not affect the character of
the final resolution: or (6) delaying the resolution of
14O AZAA’//OAVY SAAZZZZZA'ZA, Z2. '
some of the parts, thus forming a chord of the 3 on the
Tonic before the common chord enters. Both ways are
exemplified in Fig. 70.

ſ ) i ] —l
| jº', | __
m EZE====l-nza-Tº-LEi
Fig. 7 O. J. JC’Tººl zºº T12/22 C2 C I
lºº ºf 23 Lºſº, J C
J Va -3- V. r §
| 6 * 5
6 * 4- 3. 6
# 3 4.
V V I V IV I
Exercises.
(a.) Taking in turn the chord of the Dominant 7th
in every key, add the Minor 9th, place it in its second in-
version, omit the Root, lower the 5th (from the Root) by
an accidental, thus forming a chord of the Augmented
Six-Five-Three, and resolve it as above.
(3.) Repeat the above at the keyboard.
228. The chord of the Augmented Six-Three is
called the Italian Sixth ; the chord of the Augmented
Six-Four-Three is called the French Sixth ; and the chord
of the Augmented Six-Five-Three is called the German
Sixth.
In the Italian Sixth, there being but three notes, it
is necessary to double one of them. The best one to
double is the 7th from the frzee Root. (N. B. It is quite
proper in this case to double the 7th, since by the omis-
sion of the Root the downward tendency of the 7th is less
marked than if it were present.)
Another reason is, that the lowering of another note by
an accidental disturbs the feeling of Tonality, so that the
7th does not seem to have the full tendency downward.
(See “How to Modulate,” $$ 44 and 45.) The ten-
dencies thus having been removed or modified, can hardly
be said to have been violated.
N. B. The pupil should now review chapters V to
AyAA’A/OAVY SAA/A/L/AP/A2/D. I41
X, especially comparing $$ I57, 173, 177, 179, 18O, 205,
2 I I, and 224 – 228. He must not fail to understand
practically that, as asserted, the Chords of the Dominant 7th,
Diminished 7th, Major and Minor 9th, and the three forms of the
Chord of the Augmented 6th, are nothing more than different forms
of the same Fundamental harmony, derived from the same Root,
having the same dissonant intervals, and the same resolution.
NOTE. All chords of the Augmented sixth are properly classed
among the Altered chords. (See Chapter XI.)
Chord Of the Augmented Sixth derived from the
Supertonic.
229. There is another chord of the Augmented Sixth,
which, although it is not strictly in the key, is in such
common use that it will be mentioned here.
The chord in question is the one which resolves to
the Chord on the Dominant. Therefore, its Root should
be found a 4th lower than the Dominant, i. e., on the
Supertonic. In order to have exactly the form of a Dom-
inant seventh and ninth-chord (which must be exact in
all its intervals if it is to serve as the basis of an Aug-
mented Sixth-Chord), the 3rd from the Root must be
Major. Therefore, in Fig. 71, F must be made sharp,
though the signature does not require it. The Minor 9th
from D, which is necessary for the Six-Five form, is EP,
which also is not indicated by the signature. Thus this
chord Héâ is not so strictly in the key as are the
-$2–73– *
above examples.
Taking this chord as the basis, by placing it in its
second inversion and lowering the 5th from the original
Root, which Root is to be omitted (remember that the
Root is D), we shall have a Chord of the Augmented
Sixth, which resolves to the Dominant.
I42 Aſ AA’A/OAVY S///A/.../A.ZAZ ZX.
\
(a.) ( ò.) (c.) ( º |
~
—ſº-#2 *=[-æº-Ébzº-3-Hbº-p
Fig. 7 1. Héº p-a-2– 2–?-?= *::::==#|
• D -
b. V sº V 64' V bº-
3. 4. 5 5 4.
3 3. 3 —
II II - II II

In Fig. 71 are shown the various forms of 3, #7, and ; ,
at (a ), (6) and (c). The consecutive 5ths at (c) may
be avoided as shown in (d), and as mentioned in § 227.
23O. This chord was discovered and used before the
one derived from the Dominant (Fig. 69 ), and was long
considered the only one in the key. But, as just seen, it
is not so strictly in the key as the one derived from the
Dominant, as there are no less than three altered notes
in the Six-Five form, and two altered notes in the other
forms. (For further explanation of Augmented Sixth-
Chords see “How to Modulate, " Chapter V.)
Exercises.
23 1. (a) Form chords of the Augmented Sixth (in
three forms) upon the Supertonic of all keys, and resolve
them to their Dominant triads as shown in Fig. 71.
The pupil must not fail to follow the process given
in § 229, of starting from a given Root, building the
chord of the 7th (or 7th and 9th, as may be required),
not forgetting that the 3rd from the root is to be raised
by an accidental, placing it in its second inversion, omit-
ting the root or not as required, and lowering the 5th
from Original root.
(ó.) Repeat the above at the keyboard.
232. Exercises.
7
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i44. AZAA’A/OAVY S/M/A/E/A/E/D.
233. Sometimes the Augmented Sixth-Chord upon
the Supertonic, instead of resolving directly to the Dom-
inant, progresses to the Tonic Six-Four Chord, which
is thus interposed between the Augmented Sixth and its
natural resolution, the Dominant. This is the case at
the points marked N. B. in the second and third exer-
cises in § 232.
Exercises in Harmonizing the Scale.
(a.) Harmonize the scales, using chords of the
Augmented 6th where possible, together with all the
chords previously learned.
(ó.) Try these exercises also at the keyboard.
Exercises.
234. Compare the formation of the different chords
with each other as shown in § 228, and, taking any note
for a Root, try to develop the different chords from that
Root. Repeat this exercise at the keyboard.
SynOpsis.
Write the usual synopsis of the chapter.
Recapitulation.
235. It cannot be too strongly impressed, that the
whole harmonic system is a process of building from a
Fundamental, or Root. From the Prime tone is devel-
oped the triad, by adding a 3rd and 5th. The Chord of
the Seventh is formed by the addition of another note;
and the Chord of the Ninth by still another. The chord of
the Diminished Seventh is formed from the Chord of the
Minor Ninth by the omission of the Root. The Chord of
the Augmented Sixth is formed by inverting the Chord of
the Minor Ninth and Chromatically Altering the 5th from
the Root. 7%e triad is the foundation of all chords,
A/AA’A/OAVY S////2/C/A/A2/). I45
The following Synopsis of Chords shows this in
detail.
n Diminished 7th.
ſ Minor r Aug.”
9th. 3
( Domi- Aug- 6
FUNDA- ) nant 7th. U mented Aug •4.
MENTAL, The 6th. 3
PRIME | Triad.
TONE, | Major 9th. Aug.6
O1" 5
ROOT. J | Secondary 7ths. - 3
236. It will be further observed that
(a.) The natural resolution of all Dependent chords is gov-
erned by the same Tendencies and Influences.
(b.) The same laws of Part-leading control the connection
of all chords, Independent or Dependent. -
(c.) Dependent chords may sometimes progress without ca-
dencing resolution, in which case they are governed, not by the
laws of natural resolution, but by the laws of part—leading in
chord-connections as in Independent chords.
237. From a consideration of the above it will be
seen, that the different chords are but different forms or
manifestations of the same Primary chord. It is, there-
fore, but logical that, as above shown, the same laws
should govern all the forms. The Harmonic System is
wonderfully simple, yet complete.
I46 Aſ AAC/I/O AVY SAA/A/L/AF/A2Z).
CHAPTER XI.
ALTERED CHORDS : FUND AMENTAL CHORIDS.
How to Distinguish thern ; Their Roots and Keys.
238. Any note of a chord may be Chromatically
raised or lowered ; e. g.,

().
| LZ
—Tº-º-º-º-e?— —
EGHzºz–Hºz=z-H
2- zº—bæ2–1-
—tº
—eº-
When this occurs, certain changes take place which
render it necessary to consider the chord from a new
point of view. To enable the pupil to understand the
changes which take place, it is necessary to study the
following.
()
Preliminary Premises. .
239. ( I.) Fundamental chords (i. e., chords like
Dominant chords, also like Nature’s chord), can be
built upon any and every note. (See § 91.) Funda-
mental chords may appear as triads, Chords of the 7th, of
the Diminished 7th, of the Major 9th, or the Minor 9th.
They must have, counting from the Root, a Major 3rd,
a Perfect 5th, a Minor 7th (if a chord of the 7th ), and
a Major or a Minor 9th (if a chord of the 9th). Or, for
convenience in comparing, the chord may be described
by describing the successive 3rds when the chord is in its
Direct form, as follows:—
From 1 to 3 is a Major 3rd, from 3 to 5 is a Minor
3rd, from 5 to 7 is a Minor 3rd, and from 7 to 9 is either
a Major or a Minor 3rd according to the key. Placed
AAA’A/OAVY S//l/A/LAYAF/O. I47
one above the other as in the chord, it may be expressed
as follows:—*
9
}Major or Minor.
7 j . .
}Minor.
Minor.
º
| Major.
I -
This might be called the Formula for constructing
Fundamental chords, since they must correspond exactly
with it in order to be Fundamental.
Exercises.
240. Form Fundamental chords in the four forms mentioned, up-
on all notes of the Chromatic scale, and compare them with the
formula.
241. (2.) Fundamental Dependent chords, like Dom-
inant chords, whether appearing as Chords of the 7th,
Diminished 7th, or of the 9th, resolve naturally to the triad
a 4th higher. (See foot-note, § 158.)
242. (3.) All Fundamental chords are considered
as built, each upon a particular Root. The chord of
resolution is a 4th higher than this Root, in every case.
243. (4.) Change of Æoof. This can best be ex-
plained by illustration. By reference to § 241, it becomes
apparent that the natural resolution of any dependent
chord is to the triad a 4th higher.
Reference to Fig. 68 and the accompanying text
shows that the same notes (on the keyboard) may be
* If the Root is omitted, as in the chord of the Diminished seventh, the
Major 3rd from I to 3 will not be present in the formula. ---
148 Aſ A A' /l/O AVY S///A2ZZAP/A2/D.
derived from different Root-notes, the only difference be-
ing in the manner of writing the chords, i. e., the nota-
tion. .
It may be said, conversely, that the different moſa-
£zoza shows //, at #/.e chord's s??-??ºg from different
Zºoofs. To illustrate, (a ) and ( & ) of Fig. 72 are
alike in sound. But, if a chord of the Diminished 7th
A(a.) ( ò.)
s [ITVT
*7*EGFR+===H

-3. X s ez-
is built upon the Root G, it will be like (a ), while a
similar chord erected upon the Root Aff will be like (6)
when inverted. The two chords, which sound alike,
have different notation àecazese #/hey are erected zºozz
different /Poofs. Reference to § 2 I I will show that
their resolutions differ radically. This is on account of
the law of Tendencies shown in § 152, viz., the Leading-
note tends toward the Tonic, the fourth degree of the
scale tends downward, and the chief dissonance, the Di-
minished 7th between the Leading-note and the 9th from
the original Root, tends to contract. Therefore we may
say that, by the change of notation, the Root is changed,
and, consequently, the resolution is also changed.
Therefore, if we would have a proper resolution,
the chord must be so wrzážezz as £o S/?ow w/??c/, 7zoáe 2s
Že Zeadžzeg-zzołe, w/ºcſ% &/ºe 9//, from Že origºzza/
Zºoof, etc., 272 order £o Azzow Żow to a/7/y the Zaw of
7 ezza!ezzczes.
244. In $ 243 is shown how a change of notation,
or Enharmonic change, as it is called, implies a change
of Root, even where the notes on the keyboard remain
the same. In cases where one or more notes are really
Aſ4 /ø//O AVY S////º/, /AP/A2/D. I49
altered by accidentals, the change of Root is even more
—H-—eº–
clearly apparent. For example, –2 T is the chord
—£2—
of the Dominant 7th on the Root G, resolving to the triad
of C. If the note G in this chord is chromatically
—-º–
e —62–– • * *
raised, thus: H HåT. the chord is like the chord of the
Diminished 7th built upon the Root E (which is of course
omitted ), resolving to the triad on A. Therefore, the
Root of the chord, as well as the resolution, may be said
to have been changed by the alteration of the single note.
Consequently :
245. (5.) By a change of Root a change in the res-
olution is necessarily caused.
Now we will proceed to consider the Altered
chords.
246. By reference to the foot-note, § 158, it becomes
clear that the 7za/zzra/ resolution of any dependent chord
is to the triad a 4th higher than the Root of that Depen-
dent chord; and we have just seen that when through a
change of notation, or other causes, the Æoof is changed,
the natural resolution of the chord is completely changed
in consequence. This fact is illustrated in Fig. 68 and
the accompanying text.
A change in a chord, whether of a note or simply
in the notation, which produces a change of Root (and
therefore of resolution ), is called an A/armon?c change.
Where the change simply affects ozze Zará frazsáezz//y,
72 of Żroducing a change of Æoož and reso/ºzážom, the
change is called a Melodic change.
Where a chromatic change in a note is made as sug-
gested in § 238, the result must be one of two things:
15O AAAA’A/OAVY S/A/A2ZZZZZZZZ).
either the Harmonic change just mentioned, or the Me-
lodic change. *
By an A/armozz?c change a completely new chord is
formed, which is outside the key, speaking strictly, since
it contains a note foreign to the scale of the key. Such
changes will be considered under the head of Foreign
Chords, Chapter XII.
By a Meſodic change the alteration has more to do
with a single part, rather than effecting any change in
the character of the chord. Such changes produce Al-
tered chords, if they have sufficient duration to be consid-
ered as chords; or Passing-notes, if of insufficient duration.
Such alterations may occur in Chords of the 7th as well
as in triads. -
But the pupil will desire to distinguish between Al-
tered chords and Foreign chords, and to discover the
Roots and resolutions of the Foreign chords. The fol-
lowing is the method :—
TO Distinguish between Altered Chords and
Foreign Fundannerital Chords.
247. ( I.) For convenient survey, place all the notes
within the compass of one octave, striking out all dupli-
cates. -
(2.) Place the chord in 3rds. (See § 172.)
(3.) Construct a descriptive formula of the 3rds as
shown in § 239, and compare it with the formula of a
Fundamental chord there shown. If they correspond,
the chord in question is a Fundamental chord. If not, it
is clear that either it was not originally a fundamental
chord, or that some interval has been altered. (If the
Root of such a chord is unknown to the pupil, he must
discover the altered note or notes by comparison with the
formula before proceeding to find the root by the method
A/AA’ MOAVY SAMAZZAP/AEA). 151
outlined in the following paragraph.) But, before pro-
ceeding, let us illustrate the above.
248. For example, to find whether
is a Fundamental” or an Altered chord : —
Placing all the notes within the compass of one octave,
gives: E IgE. Inverting, to obtain the required
Tºp 5:22–
() *
| Tº
Béz- C2 s I
#532–l:52–H52=Ha-LH
6 —eº- –63– –62–
4- 6 —eº- Eeº-
2 4. 6 #3-
l 3. 5 7
I. 3 5
I. 3.
I
the last being the required form.
Describing the 3rds as required in § 239, we have
the formula 7 | minor
| minor.
3 j . .
1I] 11] O.T.
I
* It should be noticed that the Dominant is the only Fundamental chord
of the Seventh which is to be found in any key. The Secondary Sevenths do
not correspond perfectly in their intervals with the intervals of the Fundamental.
(This accounts, in part, for the prominence given to the various forms of Dom-
inant harmony.)
Chords which are not Fundamental chords 272ay be Secondary chords.
Therefore, if the formula does not correspond with the formula for a Funda-
mental chord, we should compare it with the Secondary chord having the same
Root (provided that the given Root represents a Secondary chord) before
deciding that it is an Altered chord,

I 52 AAAAA/OAVY S/MPZ/A/AEA).
Comparing with the standard formula:
Standard Formula of the
Formula : Given Chord :
9 ſº & g 7
} major Or minor . . . . . . minor |
7 . 5
} minor • . . . . . . . . In 11101. |
5 e º 3
} minor • - - - - - - - - In 111C1' |
I
3
} major
I
we find it agrees with it in every particular, as far as it
goes. It is therefore a Fundamental chord without its
root, i. e., a chord of the diminished 7th.
- —eº-
Again, to learn whether the chord f b%– is a
Fundamental chord or not :— Proceeding as before gives
the formula : | major.
5 §
| II].11101",
3 *
| maj Of".
I
Comparing this with the standard formula, we find
that the intervals of the given chord cannot be made to
correspond with three szccessive intervals in the standard
formula. Thus
Standard Formula of
Formula : Given Chord :
9 © * * * > 7
| major or minor . . . major : corresponds.
} minor e & G tº gº tº minor) : corresponds.
5 * g 3
! 111111OT • * * * ... • major : does not cor-
3 I respond.
j major
I
AyAA’A/OA/V S/M/A/LAA"/A2/D. I53
Therefore, even if the Root of the given chord were
found, whatever note it might be, it could never form a
Fundamental chord in connection with the notes as
given. Comparison with the chords of the 7th upon the
various degrees of the scale, by comparing the formulae,
shows that this chord might be the Chord of the 7th
upon the 1st degree of the scale of Bp major, resolving
naturally to the triad upon the 4th degree; e. g.,

F-2-b=--—
|-ºp
E9–%-35–
—2-ee-
~22- -2.2"
Exercises.
State whether the following chords are Altered
chords, or Fundamental chords, or whether they might
be secondary chords in some key : —

C2
O -
& Lºs |Tº T
Zºz- **H:3– Eºlia –––––––.--—l-2 ll
ºzººlººliº Flºz–H2=H2=H.
Eğa. ===Baz-i-º-º-H2+2====t
To Discover the Root of any Fundannental Chord.
249. ( I.) Write all the notes in the compass of one
octave, striking out duplicates. *
- (2.) Place the notes in 3rds, as shown in § 247.
(3.) If it is a triad (three notes), the Root will
be the lowest tone. (This is merely the result of the defi-
nition of the Direct form of a chord. See § 125.) It
will now be apparent whether the chord is (I ) an ordi-
nary Major or Minor triad; (2) an Altered triad; or (3)
an incomplete form of a Fundamental Dependent chord.
* Sometimes a note is omitted in a Chord of the 7th, or 7th and 9th. The
pupil should refer to § 248, and observe how the intervals in the Fundamental
chord would occur if the Root were omitted; for without the Root a different
order of intervals would result, which might lead the pupil to think a chord to
be an Altered chord when in reality it is an incomplete form of a Fundamental
chord.
I 54. AyAA’A/OAVV SZA/A2/./A./A2/).
N. B. Remember that a Diminished triad may be
considered as an incomplete form of a Chord of the 7th,
and resolve accordingly. (See § 179.)
25O. If it is a Chord of the Seventh (four notes), we
must first be sure that it is a Fundamental and not an
Altered chord. How to accomplish this is shown in
§ 247. If shown to be a Fundamental chord, either with
or without the Root, we may proceed as follows:– Com-
pare the notes as shown in § 29, to discover which note
is relatively the “sharpest " and which the “flattest.”
In comparing the notes, Ž/ e s/ a7%est ozze wa// &e
łże Zeadºng-note. (The flattest note will be the 9th,
if it is a Chord of the 9th, otherwise it will be the 7th.)
The Leading-note being a Major 3rd above the Root of a
Fundamental Dependent chord, to find the Root when the
Leading-note is known simply count a Major 3rd down-
ward from that Leading-note. (N. B. The Root may
not be present in the chord. It never is in chords of the
Diminished 7th.) When the Root is found, it can be
proven by the ‘‘ flattest” notes, which should be the 9th
or the 7th from the Root as above shown. (For further
explanation of this point, see ‘‘How to Modulate,”
p. 18.)
251. ZZZzzsárazio” of Żreceding Section. To find the
ROOt off Bz- Comparing the notes to find the
“sharpest” note, we see that B is represented by five
sharps; D by two sharps; F by one flat; and Ab by four
flats; consequently B is the “sharpest” note, and there-
~fore the Leading-note. As the Root of the chord should
be a Major 3rd below the Leading-note, by counting
downward a Major 3rd from B we find that G is the Root
AAA’A/OAVY S////2/./A/AE /). I55
of the chord. Building a Fundamental chord upon the
Root G, we have G–B–D–F–Ap, which is a chord of the
Minor 9th, and corresponds to the notes of the given
chord. Therefore, the chord in question is a Chord of
the Diminished 7th upon the Root G, resolving to the
minor or major triad on C. (See $213.) -
Again, to find the Root of the chord E Ez=
e & Bºža
Comparing as before, we find that CB is represented by
seven flats; D by two sharps; F by one flat; and Ap by
four fiats; consequently, D is the “sharpest” note. A
Major 3rd below D is BP, which is consequently the
Root of the chord. Placing the chord in 3rds, and
writing the Root in its place, the full chord is seen to be
a Chord of the Minor 9th upon the Root Bb.
252. Zo discover £ze w/ºaz Āey szecſ, a foreigzz chord
Žs writáezz, simply remember that the “sharpest " note
is the Leading-note, or 7th degree of the scale. There-
fore, the chord E –52– may be said to be written in the
–2–
22

key of C minor, and the chord E =52– in the key of Ep
-> ºf 52. T
minor. (See also “How to Modulate ’’ $ 20.)
Exercises.
253. Name the Roots and Keys of the following
chords:—

EžHaji=E,
+%–Egºz-Hºz–E
Ambiguous Chords.
_ſ)
EZ-Ha-EBHzz–Exz2–
E £ºlº #
254. Sometimes a chord may occur' which might be
either an Altered chord or a Foreign chord. E. g.,
I56 A/AA’A/OAVY SAA/AZAZZZZZO.
F#–C–D: might be either a chord derived from the Sec-
ondary 7th on the 2nd degree of C Major (by raising F
and D by accidentals;– notice that the chord appears
without the 5th ; –write it), or it might be considered as
derived from a new Root, B, being an incomplete form of
the Chord of the Diminished 7th (write it). -
To learn which of two Roots is intended, examzzze
#/.e 7-eso/zzłżozz : for if the resolution is the same as it
would have been without the alteration, it proves that
the chord is Altered ; whereas, if the resolution is differ-
ent, it shows that the chord is a Foreign chord. For
example, in the above, if the Altered chord derived
from the Root D is intended, the progression would
be to the chord G–C–E, which is considered as inter-
polated” between the chord on D and its natural reso-
Jution which follows. (See a, Fig. 73.) If the Root
B is intended, the resolution would be to the minor triad
on E (a 4th higher than B). (See 3, Fig. 73.)
( a.) ( ò.
Fig. 73.
* By an interpolated chord is meant a chord placed between two chords
which naturally belong together. For example, the natural resolution of the
seventh-chord upon D is to the triad on G. But the chromatic alteration of the
note D, thus: E —#2 I, inclines it away from its place in the chord of
T1:22T
}
G, and would cause an awkward effect should it return after Starting else-
where. Consequently, the triad on C is interpolated for smoother effect; but
the £7-zze resolzation is only delayed, for it enters immediately after. (See
Fig. 73, a.)

A/AA’A/OAVY S////?/, /A/AE /). I 57
Treatment Of Altered Chords.
255. As mentioned, any note of a chord may be al-
tered by an accidental; and when the resulting change
does not cause a change of Root, it is called simply an
Altered chord; e. g., # = is the common triad on
–2-
C ; if the note G is raised chromatically, thus: Hé 2. TI
we say that the note G has been altered from its oſſina
condition, and the whole triad might be called an altered
triad. The triad has not been essentially changed (we still
look upon C as the root), but the note G, having been
raised, is strongly inclined to progress to the next note
above, A. Such alterations may occur in seventh-chords
as well as in triads.
—,
256. The pupil needs little guidance in the treatment
of Altered chords, other than to remember that the ten-
dency of a chromatically raised note is to ascend, and the
tendency of a chromatically lowered note is to descend.
The general rule that accidental sharps tend upward, and
accidental flats downward, is good to remember, but it does
not convey the whole idea, for a zeazz/ra/ may have the
effect of ražszzag a note previously flatted by signature or

accidental; e. g., Hºt +, The natural here raises
• D

- —ſº- O—
the Ep chromatically, and is similar to: E =EE.
In the same way, a natural may chromatically lower a
: ------
note : e. g., fºr-º- Thus it is clear that flats,
$2=E=E=
naturals and sharps are re/azzve rather than specific
terms. -

158 AſAA’A/OAVY S/M/A/, /Ai//º/).
A chromatically altered note, being a tendency-note,
S/202, Zd 7zoá á e d'ozzó/ed.
Altered Chords in General Use.
257. Of the many altered chords, those most in use
2.1 e :
.) The Triad with raised 5th :
) The Chord of the 7th with raised 5th ;
) The Chords of the Augmented 6th;
) The Neapolitan 6th. (See § 259.)
The progression of these chord's is usually the same
( a
( ò.
( c.
(d.
as if the unaltered intervals were present; while the pro-
gression of the altered notes depends upon the tenden-
cy of the accidental alteration. The changes are simply
melodic changes of a single part, for the purpose of
variety or of softening a harsh effect. *
Exercises.
(a.) Write examples of all the above-mentioned
Altered chords in various keys.
258. (6.) Exercises.
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Neapolitan Sixth.
259. ( Osual ex//azzation. For azed/or’s exposition of the chord, see
§ 261.)
Among the altered chords is one in such common use as to receive
a distinctive name. When the triad on the 2nd degree of the Minor
scale : # = with its Root lowered by an accidental 56.2–
—2– 2–
-2" 5%–
is used in its first inversion, Hée E a very soft effect is pro-
—2—— -
duced. The chord is considered effective only in this inversion, and is
called the Neapolitan Sixth ; e.g., -
Fig. 74.
This alteration of the note on the 2nd degree is purely arbitrary,
like the lowering of the 5th in the Chord of the Augmented 6th; and it
is frequently used, probably on account of the fact that the natural (un-
altered ) triad on the 2nd degree in Minor is a Diminished triad, and

Aſ A A'A/OAVY S////2/C/AP/A2/D. I61
therefore has tendencies of too pronounced character for effective use
in ordinary chord-connections (not resolutions). It was found, how-
ever, that by lowering this note the apparent tendency was hidden,
making the chord more manageable.
Keyboard and Written Exercises.
260. Form chords of the Neapolitan 6th from the triad on the 2nd
degree of every Minor key, and resolve them.
Derivation of the Neapolitan Sixth-Chord.
261. (7%e fol/owing is submitted entirely upon the author's respon-
sibility.)
The Neapolitan Sixth is believed to be a form of the Augmezzzed
sixth-chord, with sºftcient Zicense in its treatmezzt to admit of the
smoothest effect in Minor.
The following examples will illustrate the assertion and the grounds
for the belief. --
BANISTER.
X
Fig. 75.
EMERY.
Fig. 76.
BEETHOVEN.
Fig. 77.



162 AAA’ MOAVY S/MA’/.../F/A.D.
The license mentioned above is this — That the notes Comprising
the full chord of the Augmented 6th are ofteza dºz/idea! beſweeze two
chords. The chords marked X in the illustrations are the chords in
question.
If the chord marked x in Fig. 75 is a chord of the Augmented 6th,
it is the 5th from the Root which is altered by an accidental. The al-
tered note being Eb, the root should be A. Let us assume that the
Root is A, and develop the chord from it. The chord of the Minor
9th upon A, (from which the Chord of the Augmented 6th is devel-

oped,) is = =52–. Omitting the Root and lowering the 5th,
#3:
we have –22––
Now, this chord is the same as the chord marked * in Fig. 75, ex-
cepting that the Leading-note, C#, which appears 27, the 7text chord, is
absent, leading us to think that the notes have been divided between
the two chords.
262. Again, in § 224, the chord of the Augmented 6th is shown in
Major, with the dominant of the key as the Root. Notice that, when
the Dominant is the Root, it is the 2nd degree of f/le sca/e w/ic/, is Zhe
chromažica/Ay altered 7zote. If the above assertion is wrong, is it not
rather strange that the note which is altered by an accidental to pro-
duce the chord of the Augmented 6th in Major should happen to be
the same note that is so altered in the Minor key P And is it not still
more strange that the resolution of the two chords should be the
same P And is it not strange that the process of building a Funda-
mental chord upon the chosen Root should result in the desired
Chord of the Neapolitan Sixth
In further proof, the example in Fig. 76 is offered. Here the Nea-
politan 6th, marked X, which is built upon the Root E (since the chro-
matically altered 5th above the root is B?), resolves directly to the triad
on A (a 4th higher than E ) without the help of any other chord. No-
tice, however, that the next chord comes in to supply the Leading-
note, for the cadence has not been quite strong enough without it.
The next example, Fig. 77, from Beethoven, refutes the idea that
the chord is good in Only one inversion. Here the chords marked X
have the chord of the Augmented 6th divided between them, and the
notes, though identical with those of the other examples, are in a
different inversion, giving an excellent effect.
AſAA’A/OAVY SAA)/A2/, //7/A2/D. 163
It is submitted that the example from Beethoven is as effective
as the examples in Fig. 75 and 76.
The pupil is recommended to read $$ 42–50 in “How to Modul
late.”
Exercises.
263. Form chords of the Neapolitan 6th, from the Dominant as a
Root, in every Minor key, and resolve them.
264. Attention is again called to the wonderful simplicity of the
system of developing the chords shown in this volume. By bringing
the chords of the Dominant 7th, Minor and Major 9th, Diminished
7th, Augmented 3, Augmented $, and Augmented 3, and the Neapol-
itan 6th all under one head, derived from the same Root, having the
same dissonant intervals, and the same natural resolution, one is inclined
to accept the statement that “There is but one chord in the Universe,
the Common Chord. All others are merely additions to this chord.”
SynOpsis.
Write the usual synopsis of the chapter.
\
CHAPTER XII.
FOREIGN CHORIDS.
265. The object of this chapter is to enable the stu-
dent to recognize some of those chords which, though
technically foreign to the key, so constantly intermingle
with chords which belong wholly to the key. These
foreign chords have such a peculiarly close relationship
to the chords of the key, that we cannot well say that we
are in a foreign key when they occur, but that a foreign
key is suggested or touched. (See Grove’s Dictionary of
Music, Vol. II, p. 35I.)
I64 A/A A2A/OAVY SAA1/A2/_/A2/A2/D.
The following chapter will be developed from a prin-
ciple which is already familiar to the pupil, viz.,
The Natural Resolution Of Donninant Harmony to
the TOnic. -
266. By Dominant harmony is not meant the chord
of the Dominant 7th alone, but also the chord of the Dom-
inant 9th (both Major and Minor), the Chord of the
Diminished 7th, and the various forms of the Augmented
Sixth-chord, which are all forms of Dominant harmony,
and resolve to the Tonic.
Keyboard and Written Exercises.
Preliminary to the following, and to enable the
pupil easily to grasp the subject, he should form chords
Złęe #/.e Domažzzazzá złż, 207,one every (c/aromažác) degree
of £7, e sca/e, and reso/ve #/.em, ZZAe #/.e Domezzazzá 72%,
to #/.e #z-Żad a z//, / ºgher. Do not write any signatures,
and do not call them Dominant and Tonic chords. Sim-
ply notice that the Chord of the 7th upon any note re-
solves to the triad a 4th higher, and observe that the ten-
dency of the seventh-chord toward the triad a 4th higher
is so strong that there is clearly a close relationship be-
tween the two chords. This relationship is the same as
the relationship of Dominant to Tonic, but they shozz/d
mož öe ca/Zed. Dominant and Tonic unless they are con-
sidered as belonging to some key, and that is not now
desired. The object here is to show the re/afzons/ iſ of
the two chords, whether they are in a key or are consid-
ered by themselves.
The intervals of a chord of the Dominant 7th are a
Major 3rd, a Perfect 5th, and a Minor 7th. Therefore,
in forming these chords, the pupil will see that these
intervals are present, and will use accidental sharps and
AWA A2A/OAVY S////?/L/A2/A2/D. 165
flats to secure them. (These chords are the same as
the Fundamental chords described in the last chapter.)
267. The next step is to learn the reverse of the above,
viz., To find that chord of the 7th which shall resolve
to any given triad, Major or Minor.
Process.
As a chord of the 7th resolves naturally to the triad
a 4th higher, to find the triad which shall resolve to a given
triad, we simply need to look a 4th lower than the Root
of the triad. -
Z//ustration. To find the chord of the 7th which
shall resolve to the triad (Major or Minor ) upon A :
Looking a Perfect 4th below A, we find E to be the Root
of the desired chord of the 7th. Completing the chord
of the 7th upon E, by the addition of a Major 3rd, Per-
fect 5th and Minor 7th, we find the full chord to be :

--------------- –0
— º— ... * & —--— ---gº----->
f =#E’ resolving to : Hé–4 = =#2=.
& e)— —e”—"— º–
OI 2
N. B. Remember that the chord of the 7th resolves
to either Major or Minor, since the chord of the Domi-
nant 7th of A Major is the same as in A Minor.
Keyboard and Written Exercises.
268. Taking each ( chromatic ) degree of the scale,
in turn, find the Chord of the 7th which will resolve to
the triad upon that degree. Complete the chord of the
7th, and resolve it to the proper triad, as above shown.
269. The pupil has now learned, that there is a Chord
of the 7th closely re/afted fo every AZajor azed. MŽzzor triad.
Therefore it would not be strange to find, that these re-
lated chords are sometimes used, although they are not,
strictly speaking, in the key.
I66 A/AA’A/OAVY SAA/A/C/AP/A2/D.
Fig. 78.
I. I V7 I
Notice that the chord marked x is not strictly in the
key of C, but is apparently like the Dominant 7th in the
key Of A. It does lead to the chordſ of A, and is in
So far like the chord of the Dominant 7th in the key of A.
But the chord on A is in the key of C (on the 6th degree).
Now let it be noticed that the chord marked x is ZZAe the
chord of the Dominant 7th : but as Z/Zere cazz àe Özef ozze
c/Zord of £7.6 ZXoyzzzzazzá 7//, 772 a Key, we must adopt some
other way of describing the relation of this chord to the triad
on A, and will call it the “Azzezzdazzz' chord of A. (The
reason for thus naming such chords is more clearly de-
scribed in the author’s “How to Modulate.”)
27O. From a consideration of the above, §§ 265 to
269, it is clear that each major and minor triad in any key has
its attendant chord.* As shown in the following example,
these attendant chords can be used with good effect.
They are indicated by [A].
Fig. 79.
I [A] II [A] V A] *
* The triads upon the 7th degree in Major, and the 2nd and 7th in Minor,
are prohibited from having [A | chords, The reason for this prohibition is,
that being Diminished triads, and therefore not consonant, they could not be the
resolution of a dissonance (see S 151), and therefore could not stand in the
relation of Tonic, which would be required if they were to have [A] chords.
(It has been shown that although not Tonic and Dominant, a triad and its [A]
chord stand āzz the relationship of Tonic and Dominant.) For the same reason,
the Augmented triads in Minor are prohibited from having [A] chords.



AAA’A/OAVY S////7ZZZZZZZZ). 167
VI [A] III [A] IV [A] V V7 I
N. B. In practical composition, [A] chords would
not be so frequently used as in the above example, which
is giver to show how the [A] chord of every Major and
Minor triad in the key can be used.
Keyboard and Written Exercises.
271. ( a.) Taking the key of G, find in succession
the [A] chords which shall resolve to the triads on II,
III, IV, V, and VI, proceeding as in § 267.
(6.) In a similar way, take all the Major and Minor
keys in turn.
Much repetition and persevering practice are neces-
sary to give the required proficiency. Before proceeding,
the pupil must be able to give instantly the [A] chord
of any Major or Minor triad.
272. It is remarkable what frequent use of the [A]
chords has been made by composers, beginning with
Beethoven. In the following example, from Mendels-
sohn’s Spring Song, are five [A] chords in seven meas-
ures. The explanation is found in the marking under the
staff. For example, [A] of II means the [A] chord re-
solving to the triad on the second degree of the scale.
Therefore, after the [A] of II we may expect to hear the
chord on II. In the second measure we do hear it, but as
it has a major 3rd Dit, it becomes also the [A] of V,
For further explanation of this example see “How to
Modulate,” p. 7.

I68 A/AAA/OAVY SAMAZZZZZZ).
Fig. 8 O. a V ---
I [A] of II [A] of V
3 4 2-5
S-
N-
V [A] of v1 v1 v? I [A] of II
II [A] of IV IV




AAAA*//O AVY S////2Z/ZºZAZ /). 169
II? V7
grazioSO.
V7 V7
273. The pupil should examine some of Beethoven’s
Sonatas, and also examples from Mendelssohn, finding
the [A] chords and indicating by proper marking to which
degree of the scale they are attendant. He should also be
on the alert to find examples of [A] chords in the music
in daily use.
Exercises.
274. (a). Write little successions of chords, intro-
ducing one or two [A] chords. Be careful not to
wander away from the key, but see that each [A]
chord resolves to some triad in the key. There need be
but three or four chords, after which a close may be
reached by a Closing cadence.
(ó.) Repeat the above at the keyboard. (Continue
this keyboard drill indefinitely, becoming familiar with
a/Z keys.)





170 A/AAEM/OAVY SAAZZZZZZZZZZ).
275. A remarkable feature of [A] chords is that
they give great variety by enlarging the boundaries of the
key, so to speak, instead of confining everything to the
chords upon the seven degrees of the scale, and their in-
Vel’S1 On S.
Another highly practical use of the [A] chords is
their wonderful power in modulating. This will be ex-
plained in the following chapter.
Synopsis.
Form as usual.
CHAPTER XIII.
MODULATION.
276. Modulazzo” is the passing from one key to
another; and is effected by the use of one or more chords
characteristic of (belonging to ) the key Zo which it is
desired to modulate.
There are innumerable ways of modulating, but the
very multiplicity of the means employed has always made
it most difficult for the beginner to grasp them, and the
usual result is utter confusion of ideas, and little practical
skill in passing from key to key. The method here
presented is held to be simple, systematic, and compre-
hensive.
277. Modulation is effected by connecting some chord
of the “old key * with some chord in the “new key.”
(N. B. “Old key ’’ and “new key ’’ refer, respectively, to
the key from which, and the key to which, it is desired to
modulate.) Therefore, if we can find a method of connect-
ing any two triads, the difficulty is easily solved.
A/A/8A/OAVY S////2Z/A/AE Z). 171
Notice, we do not say that Modulation is effected by
connecting the “old” Tonic triad with the “new” Tonic
triad; but by connecting any (Major or Minor) triad of
the “old” key with any of the “new” key. Our range
of possibilities in variety and delicacy, and means of hid-
ing the modulation, is therefore very large if we can mas-
ter this one point, viz., to cozzzzect azzy Żwo frzad’s.
To Connect any TWO Triads.
278. It has been shown at the beginning of study how
chords are connected by means of a common note. (See
§ 102.) We have also studied in the last chapter the sys-
tem of Attendant chords, and learned that any Major or
Minor triad may have its appropriate [A] chord.
Upon trial it will be found that if there is no direct
cozzzzection àetweeza Zwo gºvezz chord’s Öy meazes of a comi-
mozz 7zołe, the cozzzzeczzoze cazz àe 772ade 6 y &/ºe zºse of ozze
or 3oz/, of their Aztezzdazz/ Chords. Thus it becomes
possible to connect away two chords without considering
whether they belong to the same key or to different keys.
For example, let us connect the chord of C with the
chord of Fit. As there is no common note to connect
the two triads, we will write them with their Attendant
chords, which we will indicate by [A].
The second chord in Fig. 81 is the [A] chord of C,
the third chord that of F#.
-z-
Fig. 8 1. _-s \–
[A] of C. [A] of F#.

172 AAAA/OA/V SZMPZZZZZZ).
279. Usually only one [A] chord is necessary, as for
example in connecting the triads of C and D Major, shown
in Fig. 82.
Fig. 82.
[A] of Z).
Thus it will be seen that although two chords may
not have a common note to connect them, when we con-
sider their Attendant chords a connecting-link will become
apparent.
28O. In the following exercises the pupil will connect
two given Major or Minor triads.” The mental process,
given below, will be of much assistance. The example
given to illustrate the process is:—To connect the triad of
C major with the triad of Bb major.—
Process.
NOTE. Follow this process with the hand upon the keyboard,
playing each chord as mentioned. -
Given, to cozzzzect &/ºe triad of C with 4/ºat of Æb :
zsz Sáez. What are the [A | chords of the triad
from which and the triad to which we would pass?”
3. Azas. The [A] of the triad on C is G–B–D–F.
The [A] of the triad on B9 is F-A-C-Eb.
(Write the notes for reference).
* Should any two triads have a common note, the connection may be made
without the help of the [A] chords. But in many cases it will be observed that
the use of the [A] chords gives a smoother connection and more repose when
the final chord is reached.
* For the present we will use the [A] chords in the form of a chord of the
7th.

AZAA’A/OAVY S////2/2//7/A2/D. I 73
272d Steff. Is there any note common to the triad of
C and the [A] of Bb.
Azzs. Yes, C is common to the two chords, and will
enable us to make the connection.
3rd Stez). Of the four chords before us, viz., the
triad on C and its [A]; and the triad on Bb and its [A | ;
how many do we need to make a good connection ?
Azas. Three, the triad on C, the [A] of B5 and
the triad on B9.
Záſ, Steft. Write them, trying to secure a good lead-
ing of the parts.
Fig. 83.
C [A] of Bb. Bb C [A] of B5 Bb
Could this connection be made in any other way P
Azas. Yes, both [A] chords could be used instead
of one, as there is a note common to both [A] chords.
F is that common note.
The connection using both [A] chords is shown in
Fig. 84. -
Or :
Fig. 84.
C [A] of C [A] of Bb Bb C [A] of C [A] of Bb. Bb
Keyboard and Written Exercises.
N. B. While working out these exercises, the pupil should
constantly refer to the notes in §§ 282-284.


1 74 AAAA’A/OAVY SAMAZ //, //º/).
281. ( a.) Connect the major triad on C with the major
triad on C#. |
Connect the major triad on C with the major triad
On D.
Connect the major triad on C with the major triad on Dſ.
Connect the major triad on C with the major triad
on E.
And so on, till the triad on C has been connected
with every other triad. Then—
(6.) Connect the triad on C# with the major triad
on C.
Connect the triad on C# with the major triad on D.
Connect the triad on C# with the major triad on D:.
And continue through the chromatic scale as before.
(c.) Starting from the triad upon each remaining
note of the scale, connect with every other triad.
(d.) Connect as above each Minor triad with all
other Minor triads; and with all Major triads.
282. In doing the above exercises, it may be possible
to make many connections in two or more ways, viz.,
(a.) Without any [A] chord.
(6.) Using the [A] chord of the triad to which
we pass.
(c.) Using the [A] chord of the triad from which
we pass. -
(d.) Using both [A] chords.
N. B. The Enharmonic change is often employed,
changing sharps to flats, and vice versa.
283. If only one [A] chord is used, that of the triad
£o which we progress will usually be the better one, for
the following reason :
The natural tendency of an [A] chord is strongly
AſAA’A/OAVY S//l/A/L/AP/A2/D. I75
toward its triad, like the tendency of a Dominant seventh-
chord towards its Tonic triad. Therefore, in connecting
two triads, if the [A] of the one from which we go is
used, the natural tendency would be to 7-e/zzzzzz to that triad ;
whereas, if the [A] of the triad to which we go is used,
there is a natural tendency to continue to that desired
triad. This explains why some of the connections made
by the pupil will be harsh and forced. (The next para-
graph will show how the above-mentioned tendency to
return may be hidden, and the harshness avoided.) The
difference in effect between the [A] from which, and
the [A] to which we go, is illustrated in Fig. 85.
(a.) (6.)
Fig. 85. T2-
#-2-
[A] of C. [A] of B.
(a) is not positively bad in effect; but the superior-
ity of (6), using the [A] of the triad to which we pass,
is manifest in its smoothness and repose.
284. Zo remove Že Zezdezzcy to re/aerºz shown ºn
the [A | of the triad from w/ic/, we frogress.--It will
be found that by 27, werážng this [A j chord, the natural
tendency toward its triad is to a great extent hidden. In
composition, chords are inverted not only to give variety,
but also to induce a smoother leading of the individual
parts. 7%zes the meſodžc Zezdencies of Żndºvādaza/
Żarts become more fromânezzá, and the Žarmonic Zeze-
dezzcºes Zess So.
From this we learn that :—
(a.) Inverting an [A] chord reduces the force of
its characteristic tendency toward its triad.



176 A/A ACA/OAVY SAA1/A2/./A/A) /O.
(6.) Melodic tendencies of the individual parts also
serve to cover the same tendency.
This is illustrated in Fig. 86, where the same con-
nection as in (a ), 'Fig. 85, is given, using the [A] of
the triad from which we pass, and producing a very sat-
isfactory effect.
-z- 3.T.2.
^----> #2.
Fig. 86.
[A | of C.
Therefore :—In using the [A] of the triad from
which you progress, always invert it, and consider the
melodic tendencies, making the individual parts progress
with as little skipping as possible.
TO Connect any TWO Keys.
285. Having learned to connect any two triads, we
proceed to connect any two keys; for it is evident, that
the connection ( or modulation ) is effected by selecting
a triad from the old key and one from the new key, and
finding the connection Öezweezz &/ºese #wo £z-Żad's, as shown
above. And when the two triads are connected, the keys
are thereby connected, and the modulation is effected.
Therefore, the connections shown in Figures S1 to 86,
might be taken as a method of passing from one Aey to
another, instead of from one c/º ord to another.
/
Keyboard and Written Exercises.
286. ( a.) From every Major key modulate to every
other Major and every Minor key.
(6.) From every Minor key modulate to every other
Minor key and every Major key.








A/A/0/1/OAVY S//l/A2Z/AW/A2/D. 177
287. Note I. It should be observed that the [A | chords resolve
equally well to Major and Minor triads. Therefore, the Major and
Minor triad of any degree (for example, the Major triad of G and the
Minor triad of G ) would both have the same [A | chord.
288. Note II. Notice that the [A] of the Tonic chord (or key)
to which we modulate is nothing more or less than the chord of the
Dominant Seventh resolving to its Tonic.
289. Note III. To thoroughly establish the new tonality (or con-
sciousness of the new key), the Closing Formula should follow the
connection of the two triads, particularly if the triad to which we pro-
gress appears in an inversion. The sense of incompleteness without
the Closing Formula is illustrated in the following:
Tº
H
-º-º:2- --- - -
- Cº. I2 .22 completed .2 ºz. #2- ~~~~
Fig. 87. *_2 #z. by : :* †-- ---
–2–#2-#4–E–H
#3–H
- g-:2
IV. I4 V7 I
290. In the preceding pages, we have learned to con-
nect any two triads, and, in a similar way, any two keys.
The process, being founded upon a principle whicſ. Žs
followed imp/citly in al/ cases, might be represented by
a formula which shall give a visible plan of procedure, and
show between which chords the [A] chords are to be in-
troduced, if at all. The chord-connections shown in §§
278 to 288, would be represented by the formula :-
Old Chord, [A], New Chord.
The method of connecting two keys by connecting the
tonic triad of the old key with the tonic triad of the new
key would be :—
–– [A |, I
Old Key New Key
291. The terms Old key, and New key, are used to
indicate briefly that the chords designated by the Roman




I 78 AAA'MOAVY SAMAZZZZZZZ).
Numerals belong to the key from which, or the key fo
which, we modulate.
The Roman Numerals indicate upon which degree.
of the scale the chord ( a common triad when not other-
wise indicated ) is to be taken.
[A] indicates that an Attendant chord is to be in-
serted if necessary. Sometimes two [A | chords may be
employed to advantage.
292. Observe that the [A] of I is simply the
----------——ºr
- New Key
chord of the Dominant Seventh in the new key. As the
progression of an [A] to its triad is precisely the same
as that of a Chord of the Dominant Seventh to its Tonic
triad, we may draw the logical conclusion that if we
cazz Żass to #/.e Zozzęc of a Forez gzz Áey, throzºgſ, its
ZDomažzzazz.f chord, we cazz Żass to any of Aer AZajor or
AZZzzor triad of a foreigzz Áey &y zeszzºg Attendazet
chords.
As these Attendant chords are so easily found, and
have a most intimate relation with their Primary chords,
they will prove a simple, practical and correct means of
connecting the original key with any desºred chord of the
new key.
293. With the assistance of the Attendant chords it
becomes possible to formulate the principal methods of
Modulation, giving a most thorough and comprehensive
view of the whole subject.
If we modulate by means of the Dominant Seventh-
chord of the new key, we must connect the Original key
and the New /90m2272azzá, if we modulate through some
other chord of the new key, we mezzsá connect with
z/az chord. Upon this plan the Formulae are con-
structed.
A/A /ø/l/O AVY S//l/A2/_/AP/A2/D. I79
Modulation by Means of the Dominant Seventh-
Chord of the New Key.
2.94. According to the heading of this section, we
7
must pass through V ; therefore, the first prob-
New key
º * I w V7 - -
lem is to connect and _. Should there
Old key New key
be a note common to both chords, we can proceed at once
to the desired chord. If not, the Prinzcáž/e of Ažáezzalazzº
Chord's will supply the connection. Thus, the formula
becomes I [A] V’,” I Observe that [A ||
–––? -
Old key New key
may indicate the [A] chord of either the Old Tonic or
the New Dominant, or of Öož/, if necessary.
To illustrate, let us modulate from C to Ft.
I
Now the formula becomes more specific :
Old key
represents that on F:,
I
represents the triad on C :
New key
V7 e
the Dominant Seventh-chord on C#. As
New key
and
there is no connecting-note between the chord on C and
that on C#, we resort to the Attendant Chords, and dis-
cover that we can use eſt/ser the Attendant chord of C
or that of C#.
Writing the chords and the formula together shows
plainly the connection, using first the [A] chord of
I and then the [A] chord of V
——?
Old key New key
resented in Figs. 88 and 89.
as rep-
*An [A] chord can resolve to a Seventh-chord instead of to a simple triad, on
the ground that one Dominant Seventh-chord can resolve to another (See § 185.)
18O A/A ACA/OAVY S/A/A2Z ZAZAZZO.
Fig. 88.
I, [A] of I V7, I
Old key New key
Fig. 89.
I [A] of V, V7, I.
2
Old key New key
295. In every case of Modulation through the Dom-
inant Seventh of the new key, there will be a feeling of
incompleteness. This will disappear if, after the new
Tonic has been reached, the “Closing Formula " is
added. This is illustrated in Fig. 9o, where the same
Modulation as in Fig. 89 is given, with a slightly differ-
ent leading of the parts on account of the Closing For-
mula following.
Fig. 9 O.
I,[Alof V.V.", I, II Iſi, V7 I
2 •
Old key New key Closing Formula
Keyboard and Written Exercises.
296. For the first exercises, start from the Tonic triad
of C and pass to all other keys &/ºrozºg/, the new Zomż-



A/AA’//OAVY S///AZ /AP/A2/O. 181
name: Sevent/-chord, using the [A] chords if necessary
to make the connection. Next, proceed from C# to every
other key; then from D ; and so on, till every Aey has Óeeze
zzsed as a starážzeg-Złoż72% from which to modulate to every
other Áey. To gain the fullest benefit, the pupil should
practise modulating 60//, at #/.e. £eyôoard and Žzz wrićzzg.
297. Attention must be paid to the correct Zeadžzzg.
of the parts. A Modulation which is harsh in one posi-
tion and with a certain leading of the parts, may often be
much improved and softened by a change of position and
different movement of the parts.
It will be found that while many of these Modula-
tions are harsh in spite of a good leading of the parts,
when made direct/y through the new Dominant Seventh,
they may 6e made very //easazzá áy the zase of ozze or
ãož/ | A Johords. The student must not fear to take the
chords in their different inversions to induce a smooth
leading of the parts.
A good effect depends also upon a proper arrange-
ment of the accents, as shown in § 190. (See also “How
to Modulate,” $ 15.)
298. When we use the [A] chord of the new Dominant, we touch
the Key of the Dominant of the new key, as we make use of the
Seventh-chord on its (the Dominant’s ) Fifth degree. Thus, in Fig. 89,
the new key is F# and the key of its Dominant is C#. Now it will be
seen that the [A] chord, having B::, is like the Dominant Seventh-
chord in the Key of C#. Tr. Stainer says, in his “Composition,” that
a new key should be entered through related chord's or re/ated £eys.
Here it is plain that we have entered through a related key, that of
the Dominant. Thus it appears how the System of Attendant Chord's
fills the requirements of related chords or related keys in Modulation.
Change Of M Ode.
299. The change from a Major key to the Minor key
of like name (e. g., C Major to C Minor) cannot be
182 Aſ A A' /l/O AVY S////2ZZAZZZZ).
called a modulation, since the key-note is not changed, but
merely the mode. Notice that the chord of the Dominant
7th is the same in both Major and Minor, and that the
two triads may follow each other without the interposi-
tion of any modulating chord (Fig. 91, a ); or the com-
mon Dominant 7th may be interposed (Fig. 91, 3).
Many examples of this interchange between Major and
Minor may be found in the works of the masters.
(a.) (b.)

rºot. Hå | H
ig- g =G= - *" | “... " ºr - Yºº -- ~~3mº ----------, -----
§2–3–53 |=2–2=52–H
3oo. In the preceding paragraphs we have entered the
new key at the Tonic triad or the Chord of the Dom-
inant. It is equally convenient to enter at any other
(Major or Minor) triad of the scale. To construct the
formula for such a case, we should merely substitute the
V
desired degree for the term " .
New key
It is also possible to leave the “old” key at points
Other than the Tonic triad.
The [A | chords can be used, not only in the form
of seventh-chords, but also in the form of Diminished
7ths, Augmented 6ths, or Chords of the 9th. These
different methods, together with the possible diffel ent
points of leaving the old and entering the new key, offer
great variety in the means of modulation. The chord of
the Diminished seventh is especially useful in Modulation,
since it has a direct and natural resolution to fozer d'ážer-
ezzá chords. (See § 2 I 5.) Having just seen that it is pos-
sible to enter the new key at various points, each one of
the above-mentioned chords of resolution might be con-
sidered either the Tonic, Dominant or Supertonic of a
AAAA’A/OAVY S/M/A2ZZZZZZZZO. 183
key.” In this way, each one of the four chords might repre-
sent not ozze, but #/ºree different keys. The four different
chords would then together represent twelve different
keys; i. e., a/Z the different keys. It is therefore possible
to modulate from any chord of the Diminished seventh
direct/y into any one of f/e Zwelve Major and twelve
AZZzzor Áeys.
By means of the above-mentioned methods, it is pos-
sible to pass directly from any key to any other. This is
a most desirable accomplishment for Organists, concert-
players and accompanists, who are frequently called upon
to bring two wholly unrelated keys into immediate prox-
imity in successive selections. But it must be understood
that such promiscuous intermingling of keys is never
allowed in constructing any single piece of music. In
Composition the range of selection is usually limited to
the “Related keys;” viz., the keys of the Dominant,
Subdominant, and their Relative Minors, and the Rela-
tive Minor of the key itself. (See §§ 39 and 334.)
Modulation by Means of a Conn m On Triad.
In connecting two related keys, it will be found that
instead of a single common note serving as a connecting-
link, there is a complete chord which is common to both
keys, offering the closest possible connection. E. g., in
connecting the keys of C and G, the following triads will
be found the same in both keys: —C: I and G : IV; C :
III and G : VI; C : VI and G : II. Any one of these
chords may be used as the connecting-link, the chord be-
ing approached as belonging to the key of C and left
* Fach of these chords could just as well be taken as a Mediant, Subdomi.
nant or Submediant, as for Supertonic or Dominant. The three selected are
merely more prominent, and suffice to enable one to modulate to all keys.
184 A/AA’ MOAVY SAA/A2ZAP/A2Z).
as belonging to the key of G, as shown in the marking
under the illustration.
( a.) ( ò.) (c.)
C. : I C: I - III C. : T VI
G. : IV 13 V7 I G: vſ 11g v V7 I G : II V7 I
* Keyboard and Writtern Exercises.
Starting from various keys in turn, modulate, by
means of a common triad, to each Of the related keys, as
mentioned above.
There are also many other ways of modulating, which
are not so comprehensive in their application as those
already described, but are useful where circumstances
happen to favor their introduction. Being of good
effect and in common use, a few of them are men-
tioned:—(a) Compound modulation, passing through
a series of keys to the one desired : (6) Single Note Con-
nection; (c) By means of the False Cadence; (d) By
means of Enharmonic Change.
All the above-named means of modulation, together
with the principles of artistic modulation, are described
in detail in the author’s “How to Modulate.”
Synopsis.
Write as usual.

A/AA’A/OAVP S/M/A/.../A.ZAZZO. 185
PART III.
CHAPTER XIV.
VARIETY OF STRUCTURE : SUSPENSIONS : ANTICIPATIONS :
RETARD ATIONS.
3OI. For the purpose of giving variety to the harmonic
structure of a composition, many devices are employed.
Among them may be mentioned Suspensions, Anticiza-
Žions, A’etardazzozas, Passing-AWoźes, Passing-Chords,
Changing-Wotes, AAAoggiaturas, Organ-Points, Sus.
Zaized AVoćes, azzd Syſzco/a/2072s.
These devices should not be looked upon as altering
the principles of chord-construction already learned, but
as means of giving greater variety to a composition.
They are to Musical Composition what interior decora-
tion is to Architecture, merely a means of Ornamenting
and enriching a substantial structure.
Suspensions.
3O2. In a succession of chords, when one tone is de-
layed, or held over till after the next chord has entered, a
dissonance is formed, called a Suspension. This delayed
and therefore dissonant tone moves but one step down or
up, usually down, to its tone of resolution in the next
chord.
186 AZAA’A/OAVY SAA1/A2/ZZZZZZZO.
The essential features of a suspension are:—the Pre?.
a razzozz, the ZOZSSozzazz.ce, and the Areso/zzzzoz. The
Preparation consists in the suspended tone being pre-
viously heard as an essential part of a chord. The Disso-
nance, technically called the Percussion, is caused by the
progression of a single part being delayed while the remain-
ing parts proceed. The Resolution is effected by allow-
ing the delayed tone to proceed to its place in the following
chord. In Fig. 92, the Suspension is in the Alto ; the
first note is the preparation; the second, connected with the
first by a tie, is the Dissonance, or Percussion; and the
third note the note of Resolution.
`--~~
Fig. 92.
2.
303. Let the pupil notice the following conditions im-
plied by the definition and illustrated in Fig. 92 –
(a.) One note is held over and prevented from pro-
gressing with the others. This is accomplished by the
use of the tie.
( 3.) By being heard in the first chord, the sus-
pended tone is prepared. The Preparation should be as
long as the Dissonance, else the Preparation would not be
sufficiently marked.
(c.) The Preparation, Dissonance, and Resolution
should be in the same part. Otherwise we could not have
(particularly in vocal music) any effect of Preparation or
of Resolution. -
( d.) The Suspension, or rather the Dissonance,

AyAA’A/OAVY S//V/A2///7/A2/). 187
should be heard on an accented part of the measure. A
Dissonance on an unaccented part of a measure is not SO
prominent, and might be considered as a passing effect,
i. e., a passing-note. But as the peculiar effect of sus-
pense is desired, it is necessary to bring it into the fore-
ground by placing it upon a prominent (accented ) beat.
(e.) The tone that is delayed should not be heard
meanwhile in another part, else there could not be the
effect of suspense or delay. An exception to this is when
the Bass takes the note of resolution at a distance of not
less than an octave from the suspended tone, when it will
not be disturbing. , -
(f) The purity of the part-writing must not be
forgotten. Suspensions do not excuse consecutive 5ths or
8ves, though one part may be delayed.*
(g.) A Dissonance is presupposed in a Suspension.
Therefore, in passages where the delayed tone does not
create a dissonance, there is not technically a Suspension,
though it is treated precisely as if it were.
(/.) The suspended tone should move but one
step to its tone of resolution. Where the delayed tone
progresses by a skip, it is classed among Retardations.
(See § 312.)
Figuring Suspensions.
3O4. Like other chords, Suspensions are figured by
counting from the Bass note. To completely express a
suspension by figures, requires that both the dissonance and
the resolution be figured.
Exercises.
305. (a.) Turning back to the exercises in the early
* It is held by some writers that a Suspension does cover bad progressions
or consecutives, which are therefore allowed where the effect is good.
188
AAAEA/OAVY SAMAZZZZZZ).
It will be found
ying the various posi-
into all the different parts.
ions
f
tions and deciding which are practical.
that all are not equally effective.
Exercises.
(6.) Write examples of simple chord-connections,
ry to introduce Suspens
(c.) Repeat (ó.) at the keyboard.
7fs
Uy
—T-
e
* .
306.
pages of the book, the pupil may try to introduce Suspen-
sions into the chord-connections, tr
Write in various keys,
and t

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AAA’ MOAVY SAMAZZZZZZZ). 189
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307. Suspensions may occur in two or more parts at
once, in which case they are subject to the same rules as
when occurring in only one part. (Fig. 93, a.)
Suspensions may also occur with a progressing Bass,
i. e., while the tone of resolution is sounding, the Bass
progresses to another tone, thus producing a new chord-
formation (Fig. 93, 6), or another inversion of the same
chord.
(a.) (ó.) (c.)
Fig. 93.
Suspensions may also be resolved ornamentally, i.e.,
by the use of interpolated notes between the suspended
note and its resolution. The note of resolution must be
the same as if no ornaments were introduced ( Fig. 93, c).
3O8. Exercises.
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6 7 4: . 62
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I92 AAA’A/OAVY S/A/A/, /Ai/A2/D.
3 Io. Notice the following in reference to the above
example:
(a.) Ozámportazaf Zositions: Suspensions occur
upon the accented parts of a measure; Azzężcz/jačzozzs,
upon unaccented parts. Anticipated notes are also usually
short, never taking more than half the value of the pre-
ceding note, and usually less. Anticipations, therefore,
are seen to Occupy unimportant positions, in respect to
both rhythm and duration.
(6.) Anticipations are usually restruck, i. e., not
tied to the note which they anticipate.
(c.) Anticipations do not need to be prepared and
resolved like Suspensions. They may enter freely by
skips, and proceed by skips if desired.
Keyboard and Written Exercises.
31 I. Form examples of Anticipations in various keys.
N
Retardations.
31 2. Retardations are the opposite of Anticipations.
A tone of the chord is held over while the remaining
tones progress to the next chord. Retardations differ
from Suspensions in being treated freely like Anticipa-
tions; i. e., they require no preparation, but may enter
by skips; and (6) they are allowed to progress by skips,
not being forced, like Suspensions, to progress to the note
only one degree higher or lower.
Fig. 95.

A/A/8//OAVY S/MAZ ZAZZZZO. I93
Keyboard and Written Exercises.
313. ( a.) Form examples of Retardations, in va-
rious keys.
(6.) Form examples, mingling Anticipations and
Retardations.
Syncopation.
314. Syncopation is a kind of irregular Rhythm,
where the more important notes are placed upon unimpor-
tant beats Or parts of beats; or where the notes fall between
the beats. It may be produced by Anticipation or by Re-
tardation; i. e., by pushing forward one part ahead of the
others, or by holding it back till the others have moved.
Fig. 95 is an example, the note marked X serving to form
a Syncopation, which is continued by the retarded notes
marked o. $
Synopsis.
Write as usual. *
CHAPTER XV.
TJNESSENTIAL NOTES : PASSING-NOTES.
315. Those notes which, coming after a chord, are
not essential to it, but lie between the essential notes, are
called Passing-notes.
(a.)
Fig. 96.

I94 AAA’ MOAVY S/MPL/A/A. D.
(*)
2.
Notice the following:— -
( 1.) In Fig. 96 the notes marked x do not beiong
to the chords.
(2.) These marked notes serve to connect the
chord-notes melodically with each other. In Fig. 96,
( & ), the chords are like those at (a ), but in (a ) the
notes marked X serve to lead very smoothly from one
chord to the next.
(3.) These Passing-notes may occur in any part.
They are usually found upon the unaccented portions of
the measure, when they are called Regular Passing-
notes; but are occasionally found upon the accented parts,
when they are called Irregular Passing-notes.
(4.) The harmonic structure of a composition is of
the first importance, forming the basis or skeleton. The
passing-notes and other ornaments are to be added after-
ward.
316. Passing-notes may be chromatic as well as dia-
tonic. In Fig. 97 the notes marked o are chromatic;
those marked X are diatonic.
Fig. 97.


AAA’A/OAVY S/MA2ZZZZZZ). I95
The pupil should find and write the chords forming
the harmonic structure of Fig. 97, as at (), Fig. 96.
Care must be exercised in securing a correct leading
of the parts in the structure of the harmonies, i. e., in the
chords before the passing-notes are added, since concealed
5ths and 8ves may, by the use of Passing-notes, become
Open Consecutives. -
Keyboard and Written Exercises.
317. (a.) Return to the first exercises, Chapters I
and II, and insert passing-notes where possible, either in
the given Bass or in the upper parts.
(ó.) Try this exercise at the keyboard.
Exercises in Harrnonizing the Scale.
Harmonize the scale, using Passing-notes where pos-
sible, together with the chords previously learned.
3.18. Two or more Passing-notes may be used simul-
taneously, or even all the notes in a chord, thus forming
a Passing-chord. Occurring upon unaccented parts of a
measure, Passing-chords are not expected to always har-
monize perfectly, but may be looked upon rather as a
number of Passing-notes leading melodically to the next
chord upon an accented part of the measure; for upon
the principal beats the harmony should be quite correct,
though liberties are allowed on the weak beats.
Fig. 98.

196 AFAA’A/OAVY SAA/A/CAP/A2/D.
319. The pupil may not clearly distinguish between
altered chords and chords with chromatic passing-notes.
The following constitutes the difference :-
( I.) To be an Altered chord, the tempo should be
slow enough, and the accents such as to allow the al-
tered note to be heard as part of a chord. A chromatic
or diatonic scale-passage, accompanied by a single chord,
would be said to consist principally of passing-notes;
C. g. 3
Fig. 99. ſ
(2.) Only chromatic alterations can be considered
in connection with altered chords. If another note of the
Scale is substituted for a note of a chord (making a dia-
tonic instead of a chromatic change ), it is, of course, a
passing-note. A note may be said to belong to a chord
even if it has two flats or sharps before it, but as soon as
it changes its name, it loses its membership in that par-
*---------,
ticular chord; e. g., FX belongs to the triad: —T-2–
- #º-
but if we call it G, it could not belong to the triad of D;
Auxiliary N Otes.
32O. An Auxiliary note is one used for ornament or
embellishment, and is found one degree above or below
its principal note, which belongs to the chord. It pre-
cedes the principal note, and is heard either with or be-
fore the remaining notes of the chord; e. g.,

A/AA’A/OAVY SAA1/A2///º/A2/D. 197
Fig. 1 OO.
|
The peculiarity of the Auxiliary note is, that while
it may enter by a skip (i. e., need not be prepared ),
it must progress by a single step to its note of resolution.
(See Fig. IOO.) These notes are also called Changing-
notes, Appoggiaturas, and Free Suspensions.
32 I. Trills, Shakes, Turns and all similar ornaments
are classed with Auxiliary notes. This principle is well
expressed in “Musical Composition,” Goetschius (N. Y.,
G. Schirmer), as follows: “Every harmonic interval is
attended by four Neighboring tones, consisting in the next
higher and lower Letters, in their notation as whole step
and half-step. Thus:
“”— (6.)
O. 2- S 2-> -
Fig. 101. Ezº-2-e-Be ==Bºº-Hº-Hº-be-H
| \S . |
S. ~
rº-
*--------
The Neighboring tone cannot be chromatic (as at Fig.
IOI, 6), because the Letters must differ.
“The Neighboring tones may occur in almost any
connection with their own harmonic interval (Principal
tone) as Unessential or Embellishing notes.
“All the common forms of Embellishments or Grace-
notes (the Turn, Trill, Appoggiaturas, Mordent, etc.), are
based upon the association or alternation of a Principal
tone with one or another of its Neighboring tones, thus:

198 Aſ AA’/l/OAVY SAA/A/LAXAZ ZD.
Fig. 1 O2.
2 3
“o signifies • Neighboring note.’
Keyboard and Written Exercises.
Construct illustrations of the above.
Organ–Point.
322. An Organ-Point, or Pedal-Point, occurs when a
note in the Bass is sustained through a succession of chords
in the higher parts, part of which chords only are in
harmony with the Bass note.
Fig. 1 O3.
Notice that the chords marked X do not harmonize
with the Bass, but, alternating as they do with chords of
which the Bass note is a part, the effect is still good.
Essentials of Correct Organ–Point.
(a.) The first and last of the series of chords should harmonize
with the sustained note.
(ó.) The first chord should be heard upon an accented beat.
(c.) Chords harmonizing with the sustained note should pre-
dominate, though they may occupy either accented or unaccented
beats.
(d.) As a rule, the Organ-Point is on either the Tonic or the
Dominant.
The lowest part above the Organ-Point may be looked upon as
forming an independent Bass for the upper parts, although the figur-
ing is reckoned from the Organ-Point if that is the lowest note
present.


AAA’ MOAVY S////27/AP/A2/). f 99
Keyboard and Written Exercises.
Construct illustrations of the above, and also of the
Inverted Pedal. (Next paragraph.)
Inverted Pedal, or Sustained Note.
323. When a sustained note, similar to the above, is
found in one of the upper parts, it is called a Sustained
Note (or Inverted Pedal). Its treatment is quite similar
to that of the Organ-Point.
Fig. 1 O4.
3.24. Exercises.
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23 L-II
Ceneral Recapitulation.
In looking back over the last two chapte
twill
be seen that the various ornamental devices employed pro-
rs, i
325.
duce dissonances, though of a passing or transitory na-
The notes which produce these dissonances do not
ture.
belong to the chord, i e., they are 7zoż Zssezzzza/ notes.
these notes with the notes which produce
1ng
Compar
the dissonances in the Chords of the Seventh and other
AZAA’A/OAVY SAA/A2Z/Zº/A2/D. 2OT
similar chords, we find that in the latter the dissonant
notes belong to the chord, i. e., they are essezzężał notes.
Essential notes are those àe/ozºgrózz.g. áo a chord; i. e.,
not transitory or ornamental. -
Unessential notes are those notes used with a chord,
but 220% 6e/ozag Zºg áo Zł. Changing-notes, Appoggia-
turas, Turns, Trills, and other ornaments are formed by
employing Unessential notes.
This leads us to divide Dissonances into two classes : —
those produced by Essential notes; and those produced by
Unessential notes.
Dissonances formed by Essential notes are called Es-
sential Dissonances. -
Dissonances formed by Unessential notes are called
Unessential Dissonances. -
Essential Dissonances may be further divided into
Fundamental dissonances, or those formed like Nature’s
Chord; and Non-Fundamental Dissonances, or those not
formed like Nature’s chord; e.g., Secondary Sevenths, etc.
Essential Dissonances, especially the Fundamental
Dissonances, resolve naturally according to the Cadencing
resolution. -
Unessential Dissonances are free in their resolution,
or are controlled by the Melodic Tendencies of the indi-
vidual tones.
The pupil is now prepared to understand the following.
Division of Chords into Three Classes.
326. Chords are divided into Consonances, or Inde-
pendent Chords, and Dissonances, or Dependent Chords.
Dissonances are divided into Essential Dissonances,
and Unessential Dissonances, as explained above.
Essential Dissonances are divided again into Funda-
mental, and Non-Fundamental Dissonances.
2O2 A/A ACA/OAVY S/M/A/L/AE/A2/).
The above might be shown by a tabulated synopsis.
ſ Con- Major Triads. -
SO112.1]-
ces. | Minor Triads.
r Riminished Triads.
Dominant seventh-chords.
Diminished seventh-
| chords.
Minor ninth-chords.
ſ Fun- || Major ninth-chords.
da- J Attendant chords.
ITO e1)- (The natural resolution of
327. < tal these chords is to the triad a
Chords. & 4th higher. Occasionally they
progress by a False Cadence to
ſ Es- Other chords, but the unnatural
Se]] - « effect of most of these false ca-
e dences only serves to prove the
tial. principle.)
Non-
º {iº seventh- and
ninth-chords. *
IYD e11–
Disso- U tal.
nan-
| CeS. r Altered chords.
Suspensions. **
Passing-notes.
Un- Anticipations.
eS- J Retardations.
Sen- || Appoggiaturas.
Stial. | Trills, Turns, etc.
(The resolution of these chords de-
pends upon the Melodic Tendencies of
S the individual tones.)
- # It is scarcely necessary to class these Secondary chords separately from
the Fundamental dissonances, since they usually resolve in the same way to
the triad a 4th higher. *
* Although the resolution of Suspensions may not seem, at first sight, to
be dependent upon the Melodic tendencies of the single tones, yet when we con-
sider that the natural tendency of one tone toward its place in the next chord
has been checked, and brought into the foreground, it is clear that the melodic
tendency is even stronger than in other cases.
AEWAA’//O/WV S////?/, //º/A2/). 2O3
From the above it is clear that all the chords used in
Music may be divided into three classes: Consonances,
Essential Dissonances, and Unessential Dissonances.
The Consonances are governed by the simple princi-
ples of chord-connection and part-leading; the Essential
Dissonances are governed by the simple principles of the
Natural Resolution of Dissonant Intervals; and the Unes-
sential Dissonances are governed by the simple principles.
of Melodic tendencies, or surrounding circumstances.
Synopsis.
Write as usual.
CHAPTER XVI.
MISCELLANIEOl]S OBSERVATIONS : CROSS REI, ATION : THE
TRITONE : THE GREAT STAFF : NAMING THE OCTAVES :
LICENSES: SEQUENCE. *
Cross Relation.
328. Any tone in a chord may be succeeded in the
next chord by the same tone altered by an accidental.
But, unless the same part takes both tones (the natural
and the altered ), there is said to be a Cross relation,
often producing an unpleasant effect. The unpleasant
effect in cross relation is caused by the fact that these two
tones (the natural and the altered ) suggest two different
keys at nearly the same instant, thus producing a contra-
diction. The bad effect can be avoided by producing
both tones in the same part, giving the effect of Żrogres-
store rather than contradiction.
2
O
4.
AAAA*//OAVY SAA/A/.../A/A; /2.
Bad. Good.
Fig, 1 O5.
The above-mentioned rule, of keeping both tones tº
the same part, might well be counted among the Influen-
ces, since, like all other definite rules in Harmony, it is
occasionally broken. For instance, in a modulation,
there are two keys in close succession, and thus there is
no contradiction.
Even where there is no modulation, the rule is some-
times disregarded, if thereby a better leading of the parts
can be secured. Other exceptions allowed are Chro-
matic passing-notes (since the structural purity is not af-
fected ); Appoggiaturas (for the same reason); and
notes which are variable, as the 6th and 7th degree in the
Minor scale. (See Grove’s Dictionary, Vol. I, p. 5or.).
These (apparent) exceptions are allowed, since the con-
tradictory effect is less marked than in other cases, or is
entirely absent.
NoTE. When the note to be chromatically altered is doubled in
the first chord, it is obvious that only one of these two notes should be
altered, since consecutive 8ves would occur if the rule were applied to
both notes; e.g.,


A/AA’A/OAVY SAA/A2///º/A2/D. 2O5
The Tritor, e.
3.29. When a part ascends by an interval of three
whole steps, it makes an unmelodic progression called
the Tritone (literally, “three-tone’’). This can occur
only in passing from the 4th to the 7th degree of the scale
(unless an accidental is used). It forms an interval of
an augmented 4th. The upward progression of any aug-
mented interval is rather awkward, and this is particularly
bad because the Leading-tone ( or Sensitive note, as the
French call it ) is implicated. Although not absolutely
prohibited, the Tritone should not be used without some
very good reason.
The Chord of the Six-Four.
33O. The chord of the 3, although it is an inversion of
the independent triad, does not give a feeling of repose,
especially when succeeding a dependent chord; e. g.,

—eº— ---
2 * e
Fá áº. but seems to point decidedly toward the
end of a musical thought. For this reason, while well
adapted to introduce a Cadencing Close, it should be used
with care in the middle of a phrase. Under the condi-
tions mentioned below it does not point so clearly to a
close, and therefore may be used at any time :-
(a.) In connection with chords on the same Bass
note; e. g., Fig. IO6, (a).
(6.) In connection with chords on the same root;
e.g., Fig. IO6, (6).
(c.) In connection with chords on neighboring
Bass notes; e. g., Fig. IOG, (c).
(d.) When it is a Passing-chord; e. g., Fig. IO6,
(d).
to6 AAAA*//OAVY SAA/A/L/A/AF/O.
(a.) ( ò.) (c.) (d.)
Fig. 1 O6.
Licenses.
Advazz ced. Cozz7-se.
331. Liberties are sometimes taken with the interval of the 7th in
chords of the seventh, which, though considered as exceptions, are
rather confirmations than contradictions of the law of resolutions.
There are—
(a.) Delayed resolutions of the 7th : Where one or more chords
are interpolated between the chord of the seventh and its resolution,
in which interpolated chords the dissonant 7th appears as a conso-
nance. The resolution of the 7th must, however, ultimately occur.
E. g., Fig. IO7, (*):
(?.
) ( ò.)
Fig. 1 O7.
( 5.) Transference : Where the dissonant 7th is transferred to
another part and there resolved. It will be observed that the resolu-
tion still takes place, though in another part. E. g., Fig. IO7, ( & ).
APegzz/ar Cozzz'se.
Secluences.
332. A Sequence is a repetition of a progression.
The progression (i. e., a succession of two or more
chords) is repeated in gradually ascending or descending
Success10n ; e. g.,


AAAA*//O AVY SAA1/A2Z, ZAZAZ /). 2O7
(a.j (6.) (a.) (b.) (a.) (6.) (a.) (6.)
Fig. iO3.
In this example, the Bass alternately descends a 4th
and ascends a 2nd.
To harmonize a Sequence, the parts should move
so that the Sequence may be preserved in the chords and
in the movement of all the parts. Thus, if in the first
or “pattern ''-progression the Soprano of the first chord
is (for example) a I oth from the Bass (see a, Fig IC3),
the interval of a I oth should be found in the 1st chord ot
each following progression. (See a. a, a, a, Fig. Io8.)
Furthermore, if in the pattern-progression the Soprano
should progress one degree downward to its place in the
second chord, the same movement should be found at
the corresponding place in the following progressions.
(See 5, 6, 6, Fig. IOS.)
To carry out a Sequence exactly, it is frequently ne-
cessary to take liberties with the rules of part-leading, ten-
dencies, doubling, and especially the rule regarding the
common connecting-note for two successive chords re-
maining in the same part.
Sequences may occur in progressions of triads, of chords
of the seventh, or of suspensions. They may also consist
of the repetition of a series of two, three, or more chords.
R. Exercises.
EC): l i 2- | 2 | a | e” |
e ZT-T} {- || 2–3 |_2 | |-2 { |
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T I |-- L- | | | | |
&

208 AFAA’A/OAVY S/A/A/C/AP/A2/D.

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N. B. The Tritone is here allowed, for otherwise
the sequence, would be broken.
Advazzced. Cozerse. [Quoted from Banister’s “Music.”]
333. “A Sequence is termed Real when all the chords, or intervals,
are major, minor, etc., at each recurrence of the pattern-progression as
at the original occurrence of it.
“A Sequence is termed Tonal when the chord or intervals, at each
recurrence, are according to the key in which the passage occurs, and
therefore do not strictly resemble the Original pattern. This is the
more frequent kind of sequence. Fig. Io9 is a Tonal sequence; two
of the ascending 2nds are major, one (from D to Eb) minor; more-
over, some of the chords are major, others minor.
“The preservation of a sequential progression, will often lead to
and justify exceptional intervals, doublings, etc.; the symmetry of the
sequence outweighing the objections which might otherwise lie against
such exceptional arrangements. Design, using the word in its artistic
sense of intelligent aim at a defined and desirable effect, especially
with regard to form, reconcies and more than reconclues the mind to
i
A/AA’A/OAVY S////2/2/AP/A2Z). 2O9
details which, taken by themselves, would be questionable or even
positively objectionable.
“In Fig. I Io, for example, the Tritone 4th in the Bass, from C to
F#, and the non-resolution of the Diminished 5th in the Tenor, at #,
till the next chord but one, are both justified by the sequential form
of the passage.
“Such exceptional progressions, however, though permissible
BANISTER.
Fig. 1 O9. 2 2.
|
2. |
2.
|-
| 2-
–– –
in the course of the sequence, must not occur in the original pattern,
in which the writing must be perfectly pure.”
BANISTER.
Fig. 1 1 O.
Related Keys.
334. In § 32 the keys related to a given key were
stated to be the key having one more sharp (its Domi-
nant), and the key having one less (the Subdominant).
To these may be added the Relative Minors of the key
itself, of its Dominant, and of its Subdominant. Thus
the relative keys of the key of C are: the key of G (the
Dominant), the key of F (the Subdominant); the key
of A minor (Relative Minor of C), the key of E minor





















2 IO AAA’A/OAVY S///PZ/ZºZAZZ).
(Relative Minor of G), and D minor (Relative Minor
of F). To this may be added, as it is so frequently
used —though not allowed by all theorists —the Zozzc
Minor, or Minor key of the same name, in this case C
minor.
The related keys of a Minor key are the Minor keys
of its Dominant and Subdominant, and the relative
Majors of all three, i. e., of the key itself, of its Domi-
nant, and of its Subdominant, to which we may also add,
as above, the Zozzic Major. Thus, the related keys of
C minor are G minor and F minor, Eb major, B major,
Ab major and C major.
Narning the Octaves.
3.35. Musicians speak of Three-lined A, Great-octave
B, Small-octave F, etc. The system of naming the vari-
ous octaves is as follows:–
This note and the
six notes below are
called the Sub- Contra- Great Small
Octave. Octave. Octave. Octave.
-*. [- | ---
HG * f E | =======
i → | | 2:, lizº T
| L exe-Z L.
– – 22- -2- C b
–– --- C —B -
Eff CC—BB
Marked | or B C -B
Three- Four-lined
Twice-ac- lined Octave.
Once-accented cented, or Octave. —º- *~~2:…
or One-lined Two-lined __*: **T
Octave. Octave. 2 -º T -2 ° -
ſ) sº-sº- a- --—- -----, ----------- -
[… [. T]
E VZ ====E2=- | e | I
--------- * | | |
--- TI- | t |
el) z-
Marked & E c B C b C. 5
Cl b1 C2 b3 C3 b3 C4 _b4
or: tſ bº cº’ º,” C” bºzzcze” beeee


Aſ AA’A/OAVY S/A/A/C/A/A2/3). 2 II
The Great Staff; the C Clefs.
336. In very old music, instead of two staves of five
lines each and an added line above the Bass or below the
Treble for middle C, a great staff of eleven lines was
used ; and the various parts, Bass, Tenor, Alto, and So-
prano, were placed high or low upon this staff, accord-
ing to the pitch of the voice:
Fig. 1 1 1.
V/
J O Zºº
g- TſN
7 NSU
C—-g J. - - - - - - -
4. 9:


The notes in the great staff were written just as in
the present system, G being the lowest note in the Bass,
and leading up step by step to the 5th treble line, which
is F. Notice that the 6th line is C, corresponding to our
middle C. In fact, our staff is the same as the old one,
except that to help the eye the middle line is omitted un-
less actually in use, when it is written as an added line,
and the two sections are separated a little.
The sign # is called the C clef, and always de-
notes middle C, or the 6th line of the great staff. In
forming a Tenor staff, for example, it is considered in
which part of the great staff the chief notes of the Tenor
lie (all staves consisting of five lines and four spaces).
Now, the Tenor sings most easily from the 3rd line of
the great staff to the seventh line, or from small D to
one-lined E. It not being necessary to employ all of
the Great staff for the limited compass of the Tenor, it
became customary to take out the proper section of the
great staff, leaving the clef to denote which part had been
taken. Reference to Fig. I 12, (a ), and II 2, (6), will
2 I 2 AAAA’A/OAVY SAA/AZ ZAZZZZZO.
make it clear how the Tenor, Alto and Soprano staves
were formed.
The C clef, then, instead of moving about for the
different staves, in reality remains stationary, different
parts of the great staff being used with it to suit the com-
pass of the different voices.
Fig. 1 12, a. Treble
Or
Tenor Alto Sop. Violin
Tenor. Alto. Sop. Clef. Clef. Clef. Clef.
Middle - F - #
#H#H#HC ----
*m-º.
Middl
C.
Fig. 1 12, ( ò.). -
Tenor. Alto. Sop. Treble.
is: —£).
& --|--|-- {-} Li-
Middle C. i-T-C-i- ſº
F-T-C-fºr- \SL/
FETC. J.I.
Exercises.
These clefs should be brought into use, either by
writing future exercises in them, or by copying past exer-
cises, hymn-tunes, etc., employing a separate staff for
each part, thus forming what is called Vocal Score.
Chords of the Eleventh and of the Thirteenth.
337. According to the principle of forming chords by
tae addition of a note a 3rd above the last note, we may
form chords of the I Ith by the addition of a note to the
Chord of the 9th ; e. g., ; and if to this Chord of
the 11th we add still another 3rd, we shall have a Chord
—eº-
of the I3th ; e. g., ##
—3–



AFAA’A/OAVY S//l/A/_/AP/A2/D. 2 I 3
These chords have no practical application in Har-
mony, since so many notes must be omitted in four-part
writing, and the dissonant intervals prepared, that they
become practically nothing more than suspensions.
Exercises in Open Position, Or Dispersed
Harnnony. -
338. The pupil is now sufficiently experienced to
write in Open position, placing the Tenor part upon the
Bass staff. It is not required that every chord shall be in
open position; when more convenient, close position may
be used.
In distributing the parts, try to keep the larger inter-
vals between the lower parts. Avoid, if possible, hav-
ing more than an octave between the Tenor and Alto, or
between the Alto and Soprano.
Exercises.
Refer to the exercises in the preceding chapters, and,
ignoring the figure over the first Bass note (i. e., trying
various positions), write them in Open position. The
results will not always be satisfactory, but the comparison
of the effect in the various positions will be helpful.
Five, Six, Seven, and Eight-Part Harmony.
339. Having studied the principles of Harmony rather
than a series of set rules, the pupil will be able to write in
more than four parts, without special directions. The Ten-
dencies and Influences will need to be interpreted with
rather more freedom, on account of the increased compli-
cation resulting from the larger number of parts.
Exercises. *
The pupil will attempt to compose phrases of eight
measures, introducing five, six, seven or eight parts.
2, 14 AAA’ MOAVY S/M/A/.../A/ZZ).
CHAPTER XVII.
HARMONIZING MET, ODIES.
34o. The pupil has learned to build chords upon a given
Bass, and to connect them. It is now necessary to find
appropriate harmonies for a given melody, or to supply
the remaining parts for a given Tenor or Alto. Hitherto
the chords have been chosen for the pupil; now he must
choose them for himself. Especial care is required in
this, one of the practical applications of the previous study.
The pupil has used chords in their various inver-
sions. He has also learned that any particular note may
belong to several chords, a fact which renders the first
attempts somewhat confusing. For example, the note C
may belong to any one of the following chords:–C–E–G,
F–A–C, A–C–E, D –F–A–C, or F-A-C-E, all of which
are strictly in the key of C, besides the list of altered,
diminished, and [A] chords. The best harmony for a
given note will depend principally upon the chords pre-
ceding and following. In the exercises below, the appro-
priate harmony will be indicated.
Exercises.
C G C gºmº, F d7 G.7 C
a J. 2-ſ S_2~
ſ" [Al---- | 2 || 2 || L tº Lºt- Lºtz [Teº =
Eºs (E-2–H–––– E–2–H | |- | -]
J
[TVSU L L- | | | | | -]
el)
a. d7 G7 C d7 G C
[TL/ L 25 ul- LT2 … sizıs | | |
[T 2. a 2 E-G- Lºcº | 2 | a_2 | a_2 | 2-D LIT & I
[T ºf TY | E. | T –– Lºtz |
TVSLM L– | L | l L -


el)
AFAA’A/O AVY SAA/A2/.../A'ſ/2/D.
2 I 5
C7
Bb
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Bb

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tº’
zºº
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B. A 2–H–2–H
ſ
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a.º.
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2
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L
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Cz
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F7
C7
Bb
F7
Bb

Bb
F7 Bb C7
IBb

b
Ež
E{G}
E=E=}
L
–3–E–2–
[T
_*~
P-
|
z=z-E
-z-E-
E
–3–E–2–E
H------
-z—
B

D7
_---~~
a'7
D7
—T-
| VºI.
D7
ar/
D7

n!.
|- |-
_--> _s=-s,
–2–E–2–H
|-
E-z-
-— ~
2—Ha—
[T lºº
EGB-
§ || ?
| | /| |_
s|\!
|-|-|-|-
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bb eb Db D, Gb
eb
Db

L
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Gb
eb
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b
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35-5
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216 AAAA’ MOAVY S/M/A2ZZA, ZAZ.Z).

–943 H | Ti_ ſº 2-5 2—E-2 I
***{#=========E=E.
{G} 44 L- L | | | –
U
#
º E7 f.; by E7 A by A. E7 A
* #TEº-F-2–E2-EF2=E=E E 2–H E H
- T N_ --~ | -> - | E–2–E. -- —62— -
9 | | L L L L | |

341. In the following exercises, the melody to be har-
monized (also called the , Cantus Firmus) is placed in
the Alto, the parts to be supplied being the Soprano,
Tenor and Bass. Write the exercises in Open position.
J. C d7 G7 2. d G7 C G7
(T) -
LTTWT. | | | [ L L | T
Lºſ ZT- | | I | L L | T]
ICTYALT 2-hl L 2 [ | L | | T]
VSU tºr | | Taº ||2-) | L L___Lºº |
J– cº C/ 2 Car
`--
C F bO C d C G7 C
O
LZ | L | | | [. L |
Aſ | L__ººl cººl | | L L I -
I ºf TY Li Zºº L. F. TI | 2 || > || L |
SPZ-2–L L L | LIFTU-2–LI2–Li
J. F C F gir C. F., B} e? F g F C F
ſ)
–LA- [TTTTLITUTILITITſ | [" | [T |
-ſºpéH2-H2-H2-H2=E=E=E=E=HEEEE||
WH-2–E–H–E2–H2-H2-H2–E–E2-E2–H2=E==E=||
J ** N-T ſº tº
d A7 d g e? A7 d g A7 Bb g A7 d
/Y_
LZ , i. [TL TI [−[−L [T] | || [TT
Aſ Pºſº | | | | | Ti T 25 | | | | |
ſº L^\Dy LT! | 2 || || || || Pº I | | L | | | ||
\SL7 || 2 L_- U_ LP U2-, L.P. Tº | L-> I L in L |
Y-' #




In the next exercise, the Cantus Firmus is in the
Tenor. Supply the other parts, writing in Open position.
Eb dO Eb Ab B} Eb Ab
*--!> 1— L | | | | (2 | –63– T
| L l T

A/AA’A/O AWY SAAMAZ ZA'/A2/D. 217
7
- 2-
eº- E–2–E–2 2. E–2—t 2T2
EJ2E EEEEEEE||
5-5 L |- L– | | L -- --
g f{O £ C g a? D7
J 62– -e)— –62 -2- 2-s
* * Aº
EGH p 7fs [ | ſ L L–Gr [Tcz T]
* , , | T | | | | |
LZ Tºº VLZ | | | L | | |
L pr——r— U | L L |-- | T]
8. a? 8. D Eb 2% D7 8
eº —eº- £2 zºº — —62– 2
|-GH-p--E-LEE-Hºº--E-2–EEEEE|
Lººp | | | | | | L I
L UZ L L L L L L |
d A7 d A d g A7 d cio d e? A d
–3- -a- _----> * -2. LT2. -2.
J -2- -2. 2. #2- 2 -2 #2- 2 = * * * -2-
Tº e | | [T. | | ſti L [ [TI II | [ "
• , YT). LT [. LTTE TIL |T. DTI | |
EP-5\P | Ti T IET [TI | | | |
Dy Tm UTLIT L L-L LTI | TI ſ t
g D7 Eb ag g aº g aº Eb ao g D g
J —cº- -62– *2 zºº —eº- –2– -e)— 2 agº fº Agº º
g Ł fºr [ _[-cz-L---L---T |
EGHBZE=E=E=E-E–F–H H
|-2=h^{}_LEEEEEE=E=====EEEH
L–17– i Ll | | | | LTL L | L. L.





342. In the following exercises, in which no assis-
tance is given, the pupil should endeavor to find chords
which progress smoothly from one to another, constantly
looking ahead to see if the following chord will easily
succeed the one under consideration. The following
hints will be found helpful:—
(I.) Use simple harmonies. Do not attempt to
be original at first, but be content with commonplace
effects. -
(2.) The Principal triads are used more than the
others, but the Secondary triads should not be neglected.
(3.) Inversions are conducive to smooth progres-
sions.
2 I 8 - AAA’ MOAVY S/MAZZZZZZZ).
(4.) Contrary motion is like oil, - it helps the
smooth running of the parts.
(5.) Do not let too many parts skip at one time.
(6.) Avoid consecutives:–not only 5ths and 8ves,
but also 4ths, 2nds and 7ths.
(7.) Keep the parts at about an equal distance
from each other.
(8.) Do not let any part exceed the limits of a good
voice of corresponding pitch.
(9.) Use the # chord in the middle of an exercise
with caution. This chord usually indicates a close too
keenly for use except in a cadence, or under special con-
ditions. -
(IO.) Secondary chords of the seventh resolve,
like the chord of the dominant, most naturally to the triad
a 4th higher.
( II.) Apply the principles of Influences and Ten-
dencies.
( 12.) When the Soprano is low, the chords should
be in close position. . With a high Soprano, the chords
should be in Open position.
Exercises.
Dr. CROFT.
(). l ar, n /*N
|--2,4-75 –H H Ez Ez-Ha H–––E–H
- —- — –2–H2—2–H2—#!---|--|-2————2-j——
EGº-2E=EH = Hº =#2.Éziºzizi
- /*
==E=Hz | HFFFE-Fa-H
Fºº-ziążzHz=zFZEEHz=złż-H
L- | T |- U | [. JJTC’ | L | | L I


[\SL/
e J
I-
*

I |
| LT 2-5 L |
Fº: FF-FFFF-FF-F2 TFE -
Egºzłłażze = H£2EE 2–2.Ézi

# EEEEEEE E-FFFFFFFF |
Hºff====#2-#ziążH
LSP--- Lºr CTL L. Ll LC- 2–23 Laz III
ſ
AAA A2/1/OAVY S////2///7/AC/D. 219
Other chorals and slow hymn-tunes should be se-
lected and used as melodies for harmonization. They
may be used in the Alto or Tenor as a Cantus Firmus,
when transposed to a key suited to the voice taking them.
Observe the Soprano Clef below. See p. 212.
[ * * | | _ ! E–2–~–E | |
| .**7ts tº TøTiz, Ti Hº-H-22–H–H------|-2-H2–
| Ll tº tº Tº TUDIE’ ſ [Tº TLeº ITCZ L | Lºcº Lº I | |
Hºt —I- [T] LTL L [ | | TI I |
|ſ||
Ll ºf *2 Aº _->
| T. ſ C [ _---~ [… | + | a_2 || 2 || 25 Tl
| LT'º 2-, | L 2. X-5 ſ | -I- Lºc---->|--
Tºti ºf Tcz. T L–2–E–Cz-E--> | | | | T
Liº." L tº TL L. | | L– L | |
| •º
º
L1- 2->
E–F#–2–E–2–E–2–H–2–E–2–E–F–F–F–F–2–EEEEE|
t - º aº
ºil, ºr ſº F-2––2–H–2–E i Lº
Hziº |- E |- | L L– | { E H
l
|ſ||
J 2.2
º arl-- Lls €2 2_-tº- - -2- -e- eº Aº Lia º ^2 u. zºº
E575±E: H-EEE-HHHºF #H
-- MDZ–|| |-|--|- || || || || | Lºſ | | | || *
EPH-V-f E-H----|--|--|---EEEEEEEEE|
H
{ }
J. ^2__2~
ſ ºn 25 | | | | | || 2 | X_2_L || || || 2–3 | | | ſ T
| *... ſºlº ſº. 2 || 2 || | | | | | < || 2 ||25 || 2 || || || 2 || 25. Tº TT25T T
| | | | | |p\L |—|-11–––––––––1|–1–– |- LIZO. Tº TT
L-Tºilº –––––––––––L––––––––––– LTTT T.





343. An interesting form of exercise in harmonizing
melodies is the Chant. Being one of the shorter forms, it
will be easy for the pupil to compose little melodies in
the form of a chant, and then add the other parts as in
the previous exercises.
The chant in its simplest form consists of four parts:
(1) The first Reciting-note; (2) A short Cadence of
two measures; ( 3 ) The second Reciting-note; (4) A
fuller Cadence of three measures.
22O AAA’A/OAVY SAA1/A2///7/A2/).
The Reciting-notes, or Recitatives, are so named be-
cause they have no definite duration, but must be held till
a certain number of syllables, sometimes few and some-
times many, have been sung.
The first cadence is called the Mediation. The sec-
ond cadence is called the Cadence.
There should be no mark of rhythm in a chant,
owing to the variations in the length of the recitative.
Both the Mediation and the Cadence should be in strict
time, however.

E-## [−-i-L-I [==Hiſ
!—l-l-------|--|--
Fi LIT ICTY H2–2-E2–|-2 Eji=||
is is. Hºp e2 | ITI E*-2+2-2+2-II
Q_
Reciting-note. Mediation. Reciting-note. Cadence.
A Double chant is, in form, like two single chants in
Succession, with suitable harmonic connection.
Exercises.
Form the melodies of single chants, and harmonize
them.
NOTE I. It is still better to think both the melody and its ap-
propriate harmony together, as all musicians do, on account of the har.
monic connections, or the relations of the chords to each other.
Not E II. (From Banister’s “Music.”)
344. “In commencing an exercise in which the melody is not given,
observe the early progression of the Bass. If it ascends, be care-
ful not to begin with the parts so near to it as to force too much
similar motion. If, on the other hand, the Bass descends, begin suf-
ficiently near it to prevent the parts becoming too much separated
from it.
“In all cases, throughout the exercises, look forward, endeavor-
ing to trace the consequences of each position and progression, as
much as possible.”
The above, with slight modification of the terms to make it gen-
erally applicable, forms excellent advice for this period, when the pupil
makes his first attempts in independent writing.
Aſ AA’//OAVY S//l/A/, /AP//EZ). 22 I
345. If the pupil can now compose little melodies of
four or eight measures, hymn-tunes, or chants, it will be
of great assistance. As he will need help in regard to
the formation of phrases, periods, sections, whole and
half-cadences, etc., it is well to take some standard hymn-
tune or short melody, and carefully analyze it, to find the
number of measures in each phrase, and trace the caden-
ces and modulations; then try to form a new melody after
the pattern of the model.
To Acquire Speed in Writing.
346. In order to gain facility and ease of expression,
it is well to apply speed-tests in writing exercises. To do
this, review the exercises in the earlier chapters, allowing
the shortest possible time for each exercise.
Practical Application of Studies in Harnnony.
347. The true student will not fail to make practical
application of all the subjects developed in the pages of
this book. The exercises are designed to cultivate not
merely a theoretical but a practical working knowledge
of the chords. But in regard to proficiency in Modulat-
ing, in the use of Sequences, Passing and Changing-notes,
Suspensions, Anticipations, Retardations and Attendant
chords, while instruction must lead, it cannot do the work.
Every one must strive for himself, not only to understand
these things, but to introduce them into his productions.
He should be able to modulate correctly and without hesi-
tation, and to introduce suspensions, passing-notes, sequen-
ces, etc., into his improvisations in a natural and finished
manner. This proficiency is indispensable for composers
and organists, and is necessary for all who would have
a broad and thorough knowledge of Music. -
For this reason, the course in Harmony should not
222 A/AA2A/OAVY S/M/A/.../AP/AF/O.
be considered completed until several months have been
devoted to the study of the subjects here mentioned, and
the power of easy manipulation gained. It is not suffi-
cient to Azzow about these things; we must do them.
To gain this proficiency, the pupil must work for
himself, under the eye of the teacher. Exercises cannot
be given, as everything must be evolved from the brain
of the pupil if he would gain complete independence.
But the following is given to secure systematic application.
Order of Study.
348. A practical order of study in undertaking the
above will be : — • -
Freedom in the use of the following : (I ) Second-
ary Triads in Major : (2) Secondary Triads in Minor :
(3) Secondary Chords of the 7th, including the Prepa-
ration of the dissonant notes: (4) Chords of the 9th,
with Preparation : (5) Chords of the Diminished 7th :
(6) Chords of the Augmented 6th in the three forms,
on the Dominant Root, also on the Supertonic Root:
(7) Altered Chords: (8) Attendant Chords: (9) Mod-
ulation : (IO) Passing-Notes: (1 I ) Changing-Notes:
(12) Suspensions: (13) Retardations: (14) Antici-
pations: (15) Sequences: (16) Trills with various
endings: (17) Turns: (18) Mordents: (19) Appog-
giaturas: (2O ) Use of the Old clefs.
How to Study the Above.
( a.) Zºrst Séeſ, Zake ovae szóject at a time, and,
practising systematically through all the keys, form ex-
amples in connection with a suitable preceding chord
(a proper introduction ) and a suitable chord to follow
(a proper continuation). Do not try at this period to pro-
duce a com plete musical thought (pupils frequently make
AſAA’/l/OAVY S//l/AAC/A/A2/). 223
the mistake of attempting so much that the immediate
object is lost to view ), but simply learn the use of the
particular subject under consideration. -
(6.) These studies should be made both at the key-
board and in writing.
(c.) Analyze examples from standard writers.
Examine all music with which you come in contact, look-
ing for instances of the points which you desire to learn,
and noticing their treatment.
(d.) Persist in practising each subject till its use
becomes thoroughly familiar.
( e.) 272d Szeź Compose complete phrases con-
taining illustrations of the point under consideration.
(f) Improvise short phrases, containing the de-
sired points.
(g.) 3rd Steft Take two subjects and try to intro-
duce them alternately, or as they suggest themselves.
(A.) The pupil is warned against allowing too
much outside matter to enter into these improvisations,
for if he wanders in search of effect of any kind, he at
once forgets the object of the study, viz., to gain such
control as will enable him to introduce at will the various
subjects studied.
349. It will be found that after thorough study of this
branch of Harmony, the command of the chords and their
connections, and of the means of giving variety, will be
greatly increased. And at the same time the musical
thoughts will flow more freely, because the power of
expression has been developed.
After composing phrases as above, the pupil will
naturally attempt to construct little pieces, by uniting
several phrases. For this he will need special guidance,
which is supplied in the chapter on Form. (See § 359,
et seg.)
224. AſAA’A/OAVY S////2/.../A./A2/).
CHAPTER XVIII.
ANALYSIS AND FORM.
350. In a work like the present it will be impossible to
give more than a mere introduction and general outline
of the subject, leaving matters of detail to books which
are devoted exclusively to this department of musical
study.
Analysis means taking apart or dissecting, and is the
opposite of Synthesis, which means putting together or
constructing.
In considering the structure of a composition, or ana-
lyzing it, it is natural that it should first be divided into
its two or three main portions, these portions being after-
ward taken up, one at a time, and subdivided and exam-
ined till all the details of construction are clear.
Each of the different Movements of a composition
(for example, a Sonata), is considered as a complete
structure; but all are related to each other by the succes-
sion of keys and by the relationship of the musical thoughts
in each. The work of the Analyst is, then, to take a com-
plete movement and show its component parts and details
of construction.
35 I. The basis of consideration in tracing the larger
divisions of a movement is, primarily, the Theme and the
different ways of repeating it. The first thing is, then,
to understand something of the Theme.
The Theme, or Subject, is like the text of a sermon;
we do not expect to hear it (the text) constantly repeated,
but it is given out or announced at the beginning; is
often explained, bit by bit; is considered from different
points of view ; and at the close there is a sort of recapit-
AAA’A/OAVY S////2///º/A2/D. 225
ulation or review. So with the Theme. After it is
announced other matter is introduced, enlarging upon it,
as it were. Next, it may appear in little pieces, called
Motives, which are worked out, giving unity as well as
ſariety. Of course, a number of keys are introduced, but
they are usually related to one another very closely. How
to find the Theme will be shown in § 354, where further
particulars and an illustration will be found.
F Orrn.
352. Form relates to the manner or order of introduc-
ing the various keys, the number of subjects, the manner
of their repetition, etc., - in other words, the desigzz in
constructing. There are various forms, such as the So-
nata-Form, the Rondo-Form, the Dance-Form, the Pri-
mary Form, or Song-Form, etc. These forms vary in
their design as above mentioned.
The SO nata–F Orrn.
The Sonata-Form being a standard, and affording
proper material for analysis, will be considered first.
The Sonata-Form does not relate to the Sonata as a whole,
but merely to the first movement. The other movements
are usually written in the Rondo-, Song-, or Primary
Form. The first movement of a Sonata will therefore be
considered.
Two Subjects:–In the Sonata-Form two subjects, or
themes, are found. One is in the key of the Tonic (the
original key of the piece), and the other in the key of
the Dominant.
Three Divisions:– There are usually three divisions
in the movement. They are distinguished by the group-
ing of the keys and themes. The treatment of the two
themes, the order of the keys, and the three divisions, are
shown in the subjoined synopsis.
226 AARMONY SIMPZZAZAD.
$ 353. Synopsis of Sonata-Form.
d I. Key of Tonic : 1st Theme.
II. Connecting-Passage, mod- wº
ulating to - First Part. Is u-
III. 2nd Theme, in key of Dom- sually followed
inant. by double bar.
IV. Supplementary matter and
Codetta. J
V. Development, or Free Fan-
tasia, using short motives
Second Part.
Not followed
without much restriction, by a double
leading back to key of | *
Tonic. - J
VI. Repetition of 1st Theme in
Original key.
from either theme, and pass-
ing through various keys
VII. Connecting-Passage, not
modulating. p
VIII. 2nd Theme, not in the Dom- Third Part.
inant key, as before, but
in the Tonic.
IX. Supplementary matter.
X. Closing Passage, or Coda. J
N. B. There are many modifications of the above,
which cannot be described in this sketch, but the pupil
should attempt to note and describe them.
Application.
354. The pupil should now take some examples, and
try to locate the various points mentioned above. It will
be easy to find the Development if the double bar is
present, likewise the modulatory passage and the key of
the Dominant; also where the third part begins with the
A/AA’/l/O/WY S//l/A/.../AP/A2/D. 227
return to the key of the Tonic. (The pupil may now
try to find these points in various examples.)
A/ow to ſized the 7% enze :-In Sonatas of simple con-
struction, the Thenne usually begins with the first mea-
sure of the composition, unless a short introduction is given,
which introduction 1s easily discovered by its character.
It is more difficult to find the exact close of the Theme
without special investigation, as shown below.
The Theme should be more or less complete in
itself. This does not imply that a full close should mark
the end : on the contrary, the last note of the theme can
be, and often is, the first note of a supplementary section
or of the modulating passage. \
(a.) If the original key is not soon restored after a
modulation, but goes on into the key proper for the 2nd
theme, we rhay know that the Ist theme has ceased, and
that the modulatory passage has begun. *
(6.) There is no definite standard for the length of
the Theme. It may be of four measures, and it may be
of fifty; it may have repetitions and modulations (short
ones only); or half-closes and other irregular features,
which are at first confusing. Therefore, the best way
to get the first impression is to watch the modulations,
and note whether they return to the tonic key or lead on
to the key of the 2nd theme.
(c.) Compare that which is thought to be the
theme with the recapitulation, i. e., VI of the synopsis.
If the two coincide, the pupil may be sure that he has
found the theme. Not E. By comparison of the theme
* A change of key often occurs without any indication in the signature.
Therefore, the pupil must carefully observe the chords themselves, watching
the accidentals and all Chords of the Seventh.
In studying the chords, be careful to exclude all Passing and Auxiliary
notes from consideration.
228 AARMONY SZMPZ/A/AEA).
with its repetition, the exact ending of the theme may be
found ; for only so much as is a part of the theme prope:
is repeated in the recapitulation. Where the repetition
digresses from the exact notation of the first presentation.
usually marks approximately the end of the theme proper.
(There may be exceptions to this rule, as there are to
most rules, but it will prove a valuable guide in the
majority of cases.)
7 o żrace #/2e 272d, 7% enze : — It usually begins soon
after the modulation to the Dominant key is established.
But, to be sure of its exact beginning and ending, com-
pare with the recapitulation. That which was in the key
of the Dominant should be, at the repetition, in the key
of the Tonic. -
When the pupil can distinguish the boundaries of the
first and second subjects, the development, the modula-
tory passages connecting the different parts, and the re-
petitions of the themes, as outlined above, it will not be
difficult to recognize the supplementary matter and clos-
ing passages or coda, for they would be contained in the
matter not already classified.
As mentioned before, there will be many modifica-
tions of these features, some of them occasionally being
omitted entirely, and the order of keys and the arrange-
ment of the matter being sometimes very different from
the order here indicated. But in this chapter it is possi-
ble to treat only of the standard form, leaving all excep-
tions to works devoted entirely to this subject.
355. It will be well to begin by analyzing a Sonatina
(a little sonata), as the construction is more simple and
the various parts more definitely indicated than in the
Sonata. .*
Owing to the limited space between the staves, it is
AARMONY S/M/PZ/F/AEA). 229
necessary to use abbreviations to mark the themes, con-
necting-passages, etc. The following are suggested and
used in referring to the different parts : —
Ist Theme, I. T.; Connecting-Passage, C. P.; 2nd
Theme, II. T.; Supplementary Matter, S. M.; Coda, C. :
Development, D.; Half-Close, 96 Cl. ; etc.
Before beginning the analysis, the measures should
be numbered for reference. The beginning of the 1st
and 2nd themes should be marked first, leaving the close
of the themes to be decided when the C. P., S. M., and C.
are found.
Exercises."
Taking in turn the sonatinas indicated below, the
pupil will find and mark the various points outlined in
the synopsis, in the following order: — I: III: V: II:
IV : VI: VII: IX: X. (See synopsis, s 353.)
2–~ 2–––––. Z--—º-—s -
Or I: VI: III: VIII: II: VII: V : IX: X,
tracing them in pairs as indicated by the brackets. For
example, taking the Sonatina, Op. 49, No. 2, by Beet-
hoven. -
I begins at measure I (ends at meas. 8).
| VI begins at measure 67 (ends at meas. 74).
III begins at measure 20 (ends at meas. 36).
| VIII begins at measure 87 (ends at meas. IO5).
II begins at measure 8.
| VII begins at measure 74.
V begins at measure 53.
IX begins at measure IOS.
X begins at measure I I6.
The sonatinas to be analyzed are:—
Clementi, Op. 36, No 1. (N. B. The C. P. is
short; modulation effect-
ed by a Half-Close.)
23O Aſ AA’A/OAVY SAA/A/C/A/A2/D.
Clementi, Op. 36, No 2.
Clementi, Op. 36, No 3.
Clementi, Op. 36, No 4.
Clementi, Op. 36, No 5.
Clementi, Op. 36, No 6.
Kuhlau, Op. 20, No. 1. (C. P. omitted.) -
Ruhlau, Op. 20, No. 2. (Development is a free ren-
dering of I. T., which is
therefore not given again
in the Recapitulation.)
Ruhlau, Op. 20, No. 3.
Kuhlau, Op. 55, No.
I
tº
(Short C. P., one mea-
sure only.)
Kuhlau, Op. 55, No. 2. (C. P. onitted; mod. by
; C1.)
Haydn, Sonatina, in C.
Mozart, Sonata in C. (Irregular repetition of
I. T. in the Sub-Dom.
instead of Tonic.)
Beethoven, Sonata Op. 49, No. 1. (See 1st Note,
below. In the Reca-
pitulation the I. T. is in
1eft hand.)
NOTE. If a Sonata is written (i. e., begins ) in a minor key, the
second subject is usually in the parallel major key rather than in the
IDominant, *
NoTE. All the above-mentioned Sonatas and Sonatinas may
be found in the “Sonatina Album, ” Vol. 51 of Schirmer's Library, in
an inexpensive and compact form. #
Harnnonic Analysis.
356. The analysis of the Form has been shown above.
As soon as the form is outlined in any of the above exam-
ples, the pupil should turn his attention to the harmozzic
construction. Each chord should be marked according
AZAA'MOAVY S/MPZ///ZZ). 231
to the degree of the scale upon which it is founded (sim-
ply mark them as required in previous chapters); the
chords should be figured, attendant chords indicated,
modulating chords marked by the letter showing the new
key, and all Passing and Auxiliary notes distinguished
from the essential notes of the chord. -
ROnd O-FOrnin.
357. In § 352 it was stated that Form relates to the
manner of introducing different keys, and of treating the
subjects, repetitions, etc. In the Rondo-Form we may
expect to find a different design from that shown in the
Sonata-Form.
A chief characteristic of the Rondo-Form is the fre-
quent recurrence of the Subject or principal theme.
Another characteristic is the freedom of the order in
which the different keys succeed each other. In the sim-
plest form (there are several varieties of the Rondo)
there is but one subject, which is repeated several times,
an interlude occurring after each presentation of the theme.
Variety is imparted, ( I ) by allowing the interludes to
digress into various keys (often a different key for each
interlude ), and (2) by the varying treatment of the
theme in the repetitions. -
In the more elaborate forms of the Rondo there are
two, three, or more themes, and the requisite interludes
(also called episodes).
For examples of the Rondo, see the movements
marked ‘‘ Rondo ’’ in the list mentioned in § 355.
Also Beethoven, Sonata Op. 2, A maj., Zargo.
Beethoven, Symphony No. 5, Andante.
Beethoven, Sonata, Op. ro, No. 3, Æozzdo.
Exercises.
358. Taking the examples mentioned above, indicate
232 AAAA*//OAVY SAA/A/LA AF/A2 ZO.
the principal subjects, mark the keys in which the epi
sodes are written, and try and discover if there is a second
(also third) subject. Also mark the chords.
The Primary Form.
This form, though simpler than either of those already
shown, cannot well be explained without a digression, as
follows:–
Definitions.
359. A Phrase: – is a more or less complete musical
thought. Its distinguishing characteristic is the presence
of a cadence to complete it. The cadence need not be a
perfect one, a cadence of any sort being sufficient.
Phrases are usually of two, * four, or eight measures,
though they may be of three, five, six, seven, or other
odd number of measures.
A Pez-Zod. ... — is the next larger division, and is
formed from two Phrases, each phrase of course having
its own cadence. It is required that the two phrases
shall bear a certain relation to each other, the second ap-
pearing as a sequel to the first, responding to or complet-
ing it. When the two phrases stand in this relation to
each other, the first is called the Thesis (Proposition,
or Question), and the second phrase is called the Antith-
esis (Conclusion, or Answer ). The first phrase should
suggest or lead toward the second ; therefore, it should
not be complete in itself either with regard to the melody
or harmony — (should not end with a perfect cadence).
The second phrase, which completes the Period, may end
with a more pronounced Close. As phrases vary in the
* A Phrase of two measures is technically called a Sectionz. Four-measure
phrases are usually chosen to form the Thesis or Antithesis of a Period, though
there may be two Sections in such a Thesis or Antithesis.
AſAA’A/OAVY S////2/.../A'//º/), 233
number of measures, the Periods, being formed by the
union of two phrases, will vary also.
A Motive : *
of elaboration. It usually consists of but a very few
is a germ of thought, which is capable
notes, which have a distinct rhythmic or melodic effect.
These fragments of thought are repeated in different ways
and elaborated until they constitute a large part of the
material. Some compositions are largely developed from
motives, others from more independent melodies.
To illustrate the above definitions, turn to Kuhlau,
Sonatina, Op. 20, No. 1.
The Phrase is shown in the first four measures (also
in each succeeding division of four measures).
The Period is shown in the first eight measures
(also in the second eight).
The Motive is shown in the first three notes (a
rhythmic motive, consisting of a dotted sixteenth-note
followed by a thirty-second ).
The Prinnary Form. Also called Liedform, or
Song—Form. -
360. When two eight measure Periods are used in
conjunction, they form, under a certain condition, a small
Two-part Primary Form. The condition is, that the periods
shall stand in the mutual relation of Thesis and Antithe-
sis, or Question and Answer. Thus we have the principle
of Thesis and Antithesis illustrated not only in the con-
struction of each Period, but also in the relation of the
Periods to each other. To comply with this condition, it
is necessary to have the Antithesis of the second Period
similar to the Antithesis of the first Period, though the
Thesis of the second period may differ from the Thesis of
the first period. For example, see Kuhlau, Op. 55, No.
2, Cazzèaô2/e. Here the Antithesis of the second Period
234. A/A A&AZOAVY S////2ZZZZZZZZ).
cannot be exactly like that of the first Period, since the
first closes in the Dominant, while the movement (of
which the second Antithesis is the close) must end in
the key in which it began.
Many Folk-Songs, Hymn-tunes, and simple songs
are written in this form.
36 ſ. Where the two Periods do not stand in the
Relation of Thesis and Antithesis, they do not form the
Primary Form, but simply a Double Period, or Period-
Form. There are various forms of cadences found in
the phrases of the Primary Form, but a discussion of
them would extend beyond the limits of this volume.
In addition to the Two-Part Primary Form just described,
there are the Three-Part Primary Form, produced by inter-
polating a new part between the two periods of the
Two-Part Form (for example, see Beethoven, Op. 49,
No. 2, 7 empo d'. A/izzzzeżo. The new part extends
from the 8th to the 12th measure); and the Large Primary
Form, produced by employing phrases of eight measures,
producing sixteen-measure Periods. Phrases may also
be extended, abbreviated, or may overlap.
Exercises.
Refer to the examples given in § 355, and try to
analyze the themes, marking the phrases, periods, and
motives; trying to discover the relation of Thesis and
Antithesis in the phrases and Periods, thus forming
Period and Primary Forms where possible.
Conn parison of the Preceding.
With reference to the preceding, it should be noticed
that the Theme is the means by which the Sonata and the
Rondo-Forms are judged ; while the Phrase is the basis
for analyzing the Period-form and the Primary form.
UNIVERSITY OF MICH IGAN
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