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Table of Contents
(N. B. The numbers refer in every instance to the paragraphs)

Chap. I, Triads Page 4
The Primary triads in Fundamental Position, to harmonize a bass, i- To harmonize a soprano,*- The soprano
leaps, 3. Change of chord, 4, Bass repeats, 5- Rule for no common tone, 6- Cadences, 7_ Rale for common
tone, 8- Harmonizing first six tones of scale, 9- Tendency of scale steps, io_ Review primary triads, 11- First
inversion, 12- Successive Chords of the Sixth, 13- Second inversion, 14- Secondary triads in major, 16- Thirds
of sec. triads, doubling, 16- Rule for n-V, 17- Rule for n-I|, 18- Secondary triads in minor, 18- Acgmented in-
terval, Special rules for minor key, 20- Inversions of secondary triads, 21- Triad on Leading Tone,22- Permit-
fed Consecutive Fifths, 23- Three successive chords of the sixth, 24- Doubled third in successive chords of the
sixth, 25- Similar motion of all the voices, 26- The Sequence, 27- Sequence design, 28, 29, Sequence in mi -

or, 30- Phrygian cadence, 81_ The figuring (5 e), 32- General review, 83-

Chap. n. Chords of the Seventh Page 36
Chords of seventh formed, 34. Dominant Seventh, 35- Triad (vu) not independent, 36- Introduction of Dom.
7th, 37_ Resolution of Dom. 7th, 38- Inversion of Dom. 7th, 39- Licenses in resolution, 40- The Dom. 9th, 41-
Table of all the primary dissonant chords, 42- Use of Dom. 9th, 43- Leading-Tone seventh, 44- Diminished sev-
enth, 45- Secondary sevenths, 46- Cadencing progression, 47- Double function of Leading-Tone seventh, 48-

Cadencing sevenths in. fundamental position, 49- Significance of the Cad. res., 50- Tendency of IV, 61- Other

resolutions, 52- Introduction of sevenths, 53- Resolution, 64- Supertonic seventh, 55- Supertonic ninth, 56-
Various resolutions, of the secondary sevenths, 67- Freer use of the sevenths, 58- Mastery of conservative

usage, 59-

Chap. III. Alterations Paged
Alteration presented, 60- Rules for, 61- Application and exceptions, cross-relation, 62- Special alterations
in major, 63- Dim. 7ths by alteration, 64- Augmented Sixth, 65- Aug. sixth chords in harmonizing a melody,66-
Progressions compared, 67- Augmented sixth chords "not of the key", 68- No limit to resolution, 69-

Chap. IV. Modulation Page 12
Modulation by means of triads, 7O- Half and deceptive cadence, 71- Suggestions for harmonizing a choral, 72-
The tendency chords of a key,73- Modulation through the Dom. 7th, 74- Removes in the key-circle, 76- Mod.

by the Dom. 7th to next-related keys, 76- Modulatory inflection, 77- Reaching a new tonic, 78 - Passing
from key to key, deceptive resolutions of the Dom. 7th, 79,80- Modulation by the Dim. 7th, 81- Modulation by
the Aug. six- five chord, 82- Sequences, and use of any form of the Aug. sixth chords, 83- Modulation by the

Dim. 7th on the raised fourth degree, 84_ Sequences byway of the dim. 7th on raised fourth, 85- Modulation by
the Neapolitan chord, 86- Special intervals, enharmonic notation, pivot chords, (Ex.65).

Chap. V. Non -harmonic Tones --- Page 28
The Suspension, 87- The Preparation, 88- The Suspension itself, 89- The Resolution, 90- Passing-tone and

embellishments, 91- Appoggiatura, 92- Anticipation, 93- Comparing the unornamented harmony, 94-

Chap.VI. The French System of Figured Bass , Page 41
Examinations by eminent Frenchmen, 95- Significance of special figures and signs, 96-

Chap.VII. Examination Papers from Various Sources . Page 44

(in this list the numbers refer to the exercises, not to pages)
A fig. bass from Bachs "Thorough Bass" made "for his scholars", 642- Eight different basses on one choral,
Kittel (Bach's last pupil), 648- American Guild of Organists, sight-playing examinations from 19O7 to 1916,
644-677. Knox Conservatory of Music, 678-79- Cornell Conservatory of Music, 680-81- Oberlin Conservatory
of Music, 682-86-. Harvard University, 687-90. Columbia University, 691-93. New England Conservatory of
Music, 694-96. Royal Conservatory of Music, Moscow, Russia, 697-99. Trinity College of Music, London, 7OO-
703- Royal College of Music, London, 704- 14- Oxford University, 715-16- Cambridge University, 717-18-

Paris, The National Conservatory of Music, Chapuis, 719-21. Lavignac, 722. Gabriel Faure, 728-Gnflmant,7M-
Vincent D'lndy, (The Schola Cantorum), 725-27, Facsimile of M. D'lndy's solution of No. 726, Page 62.

A.V*. 11888*

Page 69

Keyboard Training in Harmony


Chap. in. Alterations
60. One or more tones of a chord may be chromatically altered without producing a modulation

or essentially affecting its original relation to the key. The alteration may be introduced chromatically

or diatonically, that Is the unaltered form of the chord may or may not precede the alteration. Fur-

thermore all such alterations are essentially melodic and the tone combinations resulting therefrom

should be considered ornamental variants of the original chord. In this sense only is it well to use

the term "altered chord." Certain combinations containing the interval of the augmented sixth are

usually termed Chords of the Augmented Sixth, another is popularly known as Neapolitan Sixth,
another the Diminished Seventh on the Raised Fourth degree, and so on. These terms are conven-

ient and are used in practically all the older treatises on harmony, but with the development of mod-

ern harmony along chromatic and horizontal lines and the resulting broader conception of the char-

acter of alteration in general these chords seem to have less claim to independence than was form-

erly accorded them. While this change of view point does not essentially change the treatment of

the altered notes it does simplify the subject of alteration in general.

61. In playing alterations from a figured bass it is best to observe the following general rules

although there are exceptions to them all.

Rules for Alterations
t. The alteration is never doubled.
2. The note which Is to be altered is not doubled unless one of these progresses stepwise

in the opposite direction.

5. Raised notes continue to ascend, lowered notes, to descend.
4. The alteration is made in one and the same voice.
6. Chromatic alterations usually follow the chromatic scale* which always lowers the seventh

degree and raises the fourth degree, while all others are raised in ascending and lowered In descend-

ing. (A good rule but frequently ignored.)








i s w g

i: o -e- -e-

(i) (j)


C(k) (D


e eXE
jgxco e


v: Good

Bad crotB- relation

62. Ex.48, A. The rules observed:- (a) Third lowered, introduction chromatic; (b) Fifth
lowered, introduction diatonic; (c) The note that is to be altered, correctly doubled (rule X).

B. Legitimate exceptions to the rules:- (d) Altered ton.- doubled in (so called) Nea-
politan Sixth -exception to rule 1; (e) (f) (g) rule t broken, but poor only as indicated; (h) Raited
note does not continue upward (rule 3); (i) (j) Altered note not kept in the same voice (rule 4).

C. Cross -relation (or false -relation). This not avoided by an intervening chord as at (1);
but aside from such open contradictions, which are obviously offensive, very little attention is now
paid to cross -relation, especially in modulatory or chromatic passages.

* Thu it mot the only form of chromatic scale in use.

HMD 1917 by The Arthur P. Hchll Oo.

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