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IRICHTER'Sa

MANUAL" HARMONY

J.C.aPARKER.I

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RICHTER'S

MANUAL OF HAKMONY:

PRACTICAL GUIDE TO ITS STUDY:

EXPBESSLT PREPARED FOR THE

CONSERVATORY OF MUSIC AT LEIPSIC

ERNST FRIEDRICH RICHTER.

TRANSLATED FROM THE EIGHTH GERMAN EDITION

UNIVERSITY, OF TORONTO

BOSTON: , \\_\\\ (

PUBLISHED BY OLIVER DITSON & COMPANY.,

NEW YORK : 0. H. DITSON & CO.-CHIOAGO : LTON & HEALY. \

»A Co.. In the Office of the Lib

of Congress, at Washington.

S&iared, according to Act of Congress, in the year 1873, by O. DITSON <fe Co., In the Office of the LflxaxilO

".•'//,

PREFACE TO THE FIRST EDITION.

THE chief motive for the publication of this system of Harmony is given
on the title-page. It was to furnish pupils through their course of study in
musical theory with some aid in illustrating and reviewing the principles
brought before them. The essential qualities of such a book the author
believed to be these : that it contain the substance and fundamental features
of musical theory in as condensed and complete form as possible ; that it
present these outlines together with practical directions and hints, to prepare
the way for later attempts in composition.

The book comprises, scientifically speaking, no theoretical treatise upon
Harmonics, but although, like every system of Harmony it rests upon a firm
foundation, it is devoted only to practical ends, which with the scanty means
now accessible it might be difficult to reach upon abstractly scientific prin-
ciples.

There has indeed been hitherto an eager inquiry for mathematical preci-
sion in musical rules, especially among the young, who, naturally opposed
to an authoritative creed, would fain have everything so clear as to be
beyond a doubt ; while on the other hand they are ever fearful of learning
to know and comprehend the blooming life of art by the anatomical knife j
nor is it to be denied, that in this regard there is a gap in musical literature,
which no one has yet been able completely to fill. All attempts of this
kind have thus far failed to produce a really tenable scientifically musical
system, in accordance with which all phenomena within the domain of music
shall be constantly regarded as necessary deductions from a single fundamen-
tal principle ; and all that the philosophers, mathematicians and physicists
have achieved in the matter is indeed worthy of notice, but has been 011 the
one hand too disjointed to form a complete whole, and on the other too
abstract, less serviceable for music than for other purposes, and whatever

IT PREFACE.

comprehension of musical matters it may have displayed, having but littlo
reference to the essentially musical, which for the musician is the chief point
in question. But all that has been laid down in musical manuals as a scien-
tific basis has thus far failed to hold good, partly because as the result of
individual and learned research it was also unable to form a complete system
with infallible deductions, and partly because as a fanciful structure it was
wholly wanting in scientific support.

(It may be permitted here to call attention to a work which may be able
to fill an evident gap ; T/ie Nature of Harmonic and Metrical Laws, by M.
Hauptmann.)

Yet rightly considered, this want is felt only by the riper and cultivated
musician, who loves to busy himself with theory; but for the less advanced
scholar is not so detrimental as to affect his immediate progress ; and the
skepticism above alluded to is to a certain extent no more to be heeded, than
'that childish disposition, which from overweening curiosity would fain come
at the primal cause of everything by questions that can seldom be answered
intelligibly enough to conform to the precise stage of his progress. In his
early course the musician has to direct all his energies to his technical for-
mation, as it will cost him time and trouble enough to reach the point whence
he may with greater ease meet his peculiar position as artist. It concerns
not here to ask Why, but more nearly How ; to learn from experience and
from the best models the necessity of certain principles, not to calculate it ;
afterwards, when culture, knowledge, capacity and calling demand, it will be
time to search out the why, and all the knowledge acquired by experience
will be an assistance not to be despised in discovering the musical laws of
nature.

With this practical object in view, the author has endeavoured to give in
a simple and clear manner an explanation of Harmony, and of the results
of observation and experience ; and as he intended the book for study, to let
the truths contained in it work foi themselves, without wishing to procure
for them %y a very learned garb or winning form, a large circle of readers.

PREFACE. v

Ii coniprises the whole doctrine of Harmony with hints of a rational method
of making exercises for its more thorough knowledge, and for the skillful
use of all the fundamental principles. These exercises extend as far as the
beginning of contrapuntal studies; the science of counterpoint itself will
follow in a later volume.

A word in conclusion to the young student, serious indeed, but well-meant.

A far distant goal is to be reached ; it is really this, that art has to
achieve. For this is needed an intense, untiring activity to grasp the funda-
mental principles of music, and to give vital shape to what is acquired and
recognized. They will be bitterly deceived, who, filled with the works of
our great masters, endowed with poetic minds, suppose they can pluck the
blossoms, without learning thoroughly to know and test technical means ;
who adhere to the idea that the sacred charm of beauty which overhangs a
work of art must suffer by the analysis of material, or that the natural forms
of the latter could never be developed into that essential beauty. No talent
has ever reached that height at which alone artistic efforts are successful,
without thorough knowledge (which for it indeed was easier to attain than
for the less gifted.) Practice without theoretical intelligence is not the
mark of the artist, it is merely the working of instinct, which will make the
want of a thorough culture continually perceptible. An ingenious thought
cannot dispense with form, and this it is which must be recognized and
learned. If this indeed comes often of itself with the invention, it is impor-
tant in music more than elsewhere, to analyze the thought logically as it
were, to remodel it into new shapes, and to change it in the most varied
manner. The knowledge of these things and skill in their use the man of
talent must acquire, and it can only be done when one is at pains to recog.
nise musical laws and what others have already discovered long before, and
seeks to imitate and further develope it. Earnest, persevering effort, and
above all a rational method for unfolding to maturity and for the creation of
vital works of art, will with musical capacity surely lead to the goal.

PREFACE TO THE SEVENTH EDITION.

THE methodical arrangement of subjects has been retained in the former
editions of the Manual. I have been the less induced to make any altera-
tion from the fact that, apart from my own experience, the book has been
foul d useful in more enlarged circles, as is proved by the editions so quickly
following each other. Having endeavoured, however, in each new edition,
to introduce improvements and additions in the exercises and explanations,
I have bestowed much care in revising the present one also. It contains,
nevertheless, no essential changes, so that with the exception of the first
three, all the previous editions, specially the sixth, can well be used with this
—a great advantage in schools where the book is introduced.

PREFACE TO THE EIGHTH EDITION.

THIS edition also contains no important alteration, only that I have
Endeavoured here and there by improvements of style to contribute to the
better understanding of single passages. For the friendly recognition of my
labours, as is best shown by the rapid succession and marked increase of
editions, affording me a pledge of the utility of my unpretending book, I
have to express my special gratitude.

ERNST FRIEDRICH RICHTER.
LEIPZIG, February, 1870.

TABLE OF CONTENTS.

PAftS.

INTRODUCTION,— SYSTEM OP INTERVALS, 19

SECTION I

THE PRINCIPAL HARMONIES AND CHORDS DERIVED FROM THEM.

CHAPTER FIRST.— THE TRIADS OP THE MAJOR SCALB, . . . .21

CHAPTER SECOND.— THE TRIADS OP THE MINOR SCALE, ... 40

CHAPTER THIRD.— INVERSIONS OP TRIADS, 47

CHAPTER FOURTH.— SEVENTH-HARMONIES. CHORDS o» FOUR TONES, . M

CHAPTER FIFTH.— INVERSIONS OP THE SEVENTH-CHORD, .... 59

CHAPTER SIXTH.— COLLATERAL SEVENTH-HARMONIES, .... 64

CHAPTER SEVENTH.— INVERSION OP THE COLLATERAL SEVENTH-CHORDS, . 78
CHAPTER EIGHTH.— SEVENTH CHORDS IN CONNECTION WITH CHORDS OP

OTHER DEGREES, 81

CHAPTER NINTH.— CHORDS OP THE NINTH, ELEVENTH AND THIRTEENTH, . 88
CHAPTER TENTH. — CHROMATIC ALTERATION OP THE PRINCIPAL HARMO-
NIES. ALTERED CHORDS, 91

CHAPTER ELEVENTH.— ON MODULATION, 102

SECTION II

INCIDENTAL CHORD-FORMATIONS. TONES FOREIGN TO THE HARMONY.

CHAPTER TWELFTH.— SUSPENSIONS, . .105

CHAPTER THIRTEENTH.— ORGAN POINT.— SUSTAINED PARTS, . . 123

CHAPTER FOURTEENTH.— PASSING NOTES.— APPOGGIATUBAS, . . .128

CHAPTER FIFTEENTH.— PASSING CHORDS, 188

CHAPTER SIXTEENTH.— MEANS OP MODULATION . . . .141

Viil CONTENTS.

SECTION IIL

PEAOTICAL APPLICATION OF HAEMONIES. EXERCISES FOE THEIB USB
IN PUEE PART-WRITING.

FAGH

CHAPTER SEVENTEENTH. — SIMPLE HARMONIC ACCOMPANIMENT TO A

GIVEN PAST, 151

CHAPTER EIGHTEENTH.— EXTENSION or THE HARMONIC ACCOMPANI-
MENT, . . . , . , . . 173

CHAPTER NINETEENTH.— FORMATION OF MELODY, .... 176
CHAPTER TWENTIETH. — FORMATION OP THE ACCOMPANYING PARTS, . 183
CHAPTER TWENTY-FIRST.— EXERCISES IN THREE-PART MOVEMENT, . 187
CHAPTER TWENTY-SECOND.— TWO-PART MOVEMENT, . . . .193
CHAPTER TWENTY-THIRD.— HARMONIC TREATMENT OF A GIVEN PART

IN MELODIC FORM, 193

CHAPTER TWENTY-FOURTH.— FIVE-PART MOVEMENT, . . . .202
CHAPTER TWENTY-FIFTH. — Six-, SEVEN-, AND EIGHT-PART MOVE-
MENT, "., Y . , 206

CHAPTER TWENTY-SIXTH.— FORMS o» MUSICAL EWDINGS, . . .113
INDEX OF SUBJECTS . 216

INDEX OF SUBJECTS.

Accompaniment, figured page 183 ; harmonic ace. to a given part, 151, 173, 195.

Afterstriking of harmonic tones, 121.

Alto, 23 ; Alto notes, Alto clef, 113.

Antecedent, 177.

Anticipation, 121.

Appoggtaturas, 128, 129, 134.

Arsis, 107, 138, 174.

Boss, 23 ; movement, progression of the same, 34, 36, 153, 205.

Cadence, 55, 81 ; whole, half, 178, 214; perfect, imperfect, 62, 214 ; in modulation, 148,

Cadence-formidce, 149, 150.

Cantus Jirmus, 196.

C-clef, 113.

Chorals as exercises, 175, 205.

Chord, 21.

Chord-formations, incidental, 105.

Chord of four tones, 54 ; see Seventh-chord.

Chord of tfo eleventh, 88, 90.

Chord of the Fourth-and-Third, 59, 61, 62; augmented, 96.

Chord of the Second, 59, 61, 63.

Chord of the Sixth, 47 ; augmented, 94.

Chord of the Sixth-and-Fifth, 59, 60, 62; as Suspension, 189; augmented, 97; in modula-
tion, 147.

Chord of the Sixth-and-Fourth, 48; in forming cadences, 53; in modulation, 143; a»
passing chord, 139; use of the same, 153; of the augmented triad, 92, 198; of th«
diminished triad, 155, 188.

Chord of the Sixth-Fourth-and- Second, see chord of the Second.

Chord of the Sixth~Fourth-and-77iird, see ch. of the Fourth-and-Third.

Chord of the Tliirteenth, 88, 90.

Chords, altered, 43, 91, 101 ; passing, 138 ; view of the same, 99. See also Triads, Seventh,
chords.

Chromatic alteration, 91.

Close, 32 ; authentic, plagal, 32, 213. See also Cadence, Whole cadence, Half cadence,
False cadence.

Close-formation, 40, 53, 55, 213.

Closing cadence, 55, 81.

Closing formula, 40, 41, 149.

Collateral seventh-cJiords, 64, 78, 86.

Collateral tones, harmonic, 128.

Collateral triads, in major 33 ; in minor 48

Compass of parts, 113.
9

10 MANUAL OF HARMONY.

Connection, 25, 73, 81 ; local, inward, 35.

Consequent , 177.,

Consonance, 17, perfect, imperfect, 17.

Contrary motion, 26, 135, 201.

Cross relation, unharmonic, 166.

Degrees, diatonic, 73

Dissonance, 17.

Dominant-harmony, see Triad, Seventh-chord,
in modulation, 144.

Doubling of intervals, 25, 39, 48, 58, 70, 94, 109, 111, 132, 203, 206.

Eleventh, 14.

Exercises for practice in harmonizing (principal triads in major) 30, (all the triads in
major) 37, triads in minor) 45, (inversions of the triads) 49, dominant seventh
chord) 58, (inversions of the same) 63, (collateral seventh chords) 73, (connection of
seventh chords) 74, (collateral seventh chords in minor) 77, (inversions of the same)
80, (false cadence) 85, (collateral seventh chords in connection with chords of other
degrees or keys) 87, (augmented triad) 94, (other altered chords) 98, (study of mod-
ulations) 103, (suspensions) 112, 119, (harmonic accompaniment to a given melody)
151, 152, 157, 163, 164, 165, 170, 171, 172, 173, (formation of melody) 177, (three-
part movement) 187, 188, 191, (two-part movement) 193, (harmonic treatment of a
given part in melodic form) 195, 199), (five-part movement) 202, 205.

Extreme parts, 23.

False cadence, 81, 214.

Fifteenth^ 14.

Fifth, 13,22; perfect, 15, 16 ; augmented, 15, 16, 75 ; diminished, 15, 16, 38, 60; fifth in
the seventh-chord, 57, ?0.

Fifth-progressions (parallel fifths), 26, 28, 51, 79, 97; open, 30, 79; concealed, 30, 37, 99,
158, 204; in passing notes and appoggiaturas, 133 ; in contrary motion, 201.

Fourteenth, 14.

Fourth, 13; perfect, augmented, diminished, 15, 16; preparation of the perfect fourth, 155
the same as chord, 189, 196.

Fourth-progressions (parallel fourths) in passing, 134, 136.

Fundamental harmonies, 21 ; chromatic alterations of the same, 91.

Fundamental tone, 21 ; in seventh chord 57.

Half cadence, 178, 213.

Harmony, System of, 21.

Interchanging, 47 ; see inversion.

Interval, 13 ; major, perfect, 14 ; minor, augmented, diminished, 15.

Intervals, division of, 17 ; view of, 16, 19 ; transposition (inversion) of same, 18. See also
Omission, Doubling.

Intervals, doctrine of, 13.

Interval, steps and skips, augmented and diminished, 156.

Inversion, 47 ; of triads, 47 ; of seventh-chords, 59, 62, 78 ; see also Interval.

Inverted intervals, 18.

Leading tone, 37, 39, 56, 76, 116, 159, 203.

Major triad, 22, 64.

Melody, formation of, 176; rhythmical formation, 177.

Middle parts, 23.

Minor triad, 22, 33, 64.

Modulation, 102 ; means of, 141 ; extension and completion of the same, 148.

MANUAL OF HARMONY. H

Motion, direct, contrary, oblique, 26.

Movement, one-part, 185; two-part, 193; three-part, 187; four-part, 23; five-part, 202,

six, seven, eight-part, 206.
Ninth, 14; major, minor, 15, 16.
Ninth-chord, 88, 118, 127.

Ninth-suspension, 1 18. *

Numbering, 34, 48, 53, 55, 59, 63, 111, 164.
Oblique motion, 26.

Octave, 13; perfect, augmented, diminished, 15, 16.
Octave progressions (parallel octaves), 26, 28 ; open, 30, 110, 133 ; concealed, 30, 86, 52, 84

158, 204 ; in contrary motion, 201.
Omission of intervals, 57, 73, 188, 193.
Organ-point, 123.
Part-management, 24.
Part-movement, 26.

Parts, extreme, 23 ; middle, 23 ; formation of accompanying parts, 183.
Part-writing, pure, strict, free, 24 ; pure, 137.
Passing, passing notes, 128, 134.
Passing chords, 138.
Period, 177.

Plagal cadence, 33, 41, 213.

Position of the chord, close, open, dispersed, 31, 32, 114.
Preparation of seventh, 70; of suspension, 107.
Prime, 13 ; perfect, augmented, 15 , 16,
Principal seventh chord, 54, 64.
Principal triads in major, 23, 33 ; in minor, 40.

Progression, melodious, nnmelodious, 155, 156 ; of collateral seventh-chords, 65, 73, 81.
Relation of parts, 1 73.
Resolution of the dominant seventh chord, 55, 61 ; of collateral seventh -chords (in major)

65; (in minor) 74 ; of suspensions, 106, 109, 116, 120.
Scale. See Triads.

Second, 13; major, minor, augmented, 15, 16.

Second progressions (parallel seconds J in passing, 134 ; with appoggiaturas, 136.
Second step, augmented, 44.
Sequence, 37.
Seventh, 13 ; major, minor, diminished, 15, 16 ; passing, 72, 173 ; preparation of, 70 ; same

without preparation, 72, 77, 153, 164.
Seventh-chord, 21, 54 ; Dominant-seventh-chord, 54, 57, 61, 82, 144 ; fundamental, 64 ; same

in passing, 139.

of the seventh degree In major, 68, 78, 90, 199.
diminished, 76, 79, 87, 90 ; same in modulation, 146 ; same in movement of

several parts, 206.
Seventh-chords, connection of, 73; same in connection with chords of other degrees, 81,86;

view of the same, 100.

Seventh-progressions (parallel sevenths) in passing, 134 ; with appoggiaturas 136.
Signatures, 53.

Sixth, 13 ; major, minor, augmented, 15, 16.
Soprano, 23 ; soprano notes, soprano clef, 113.
Style, free, strict, 24.
Sub-dominant triad, 23.

12 MANUAL OF HARMONY.

Suspension, 105, 109 ; in the Bass, 111 ; from below, 116 ; in several parts, 117, 198.

Sustained parrs, 123, 126.

Tenor, 23 ; Tenor notes, Tenor clef, 113.

Tenth, 14.

Thesis, 107, 138.

Third, 13, 21 ; major, minor, diminished, 15, 16. Same in seventh-chord, 56, 57, 60. (Set

leading-tone.^)
Thirteenth, 14.

Tliarough Bass notation, see Numbering.
Tones foreign to tlie harmony, 105.
Tonic triad, 23, 142.
Transition. See Modulation.
Transposition, 47 ; see Inversion.

Triad, 21 , major, minor, 22 ; dominant triad (in major), 23 ; (in minor), 40 : tonic do.
23; (in modulation) 142; subdominant, do. 23; doable diminished, do. 95;
major diminished, do. 95, 97 ; augmented, 43, 65, 92.
diminished, do. 34, 38, 43, 50, 65.
Triads of major scale, 21, 33, 46, 99 ; of minor scale, 40, 42, 46, 99 ; natural connection

of game, 22 ; view of 46, 99.
Tritonet 70, 168.
TweJJlh, 14.
Unison, 13.

Unison-progressions, 28 ; concealed, 162, 204.
Upper interval*, 18.
WhoU cadence, 218.

INTRODUCTION.

OF the elementary requirements included in the general science of music,
a knowledge of which must be assumed at the commencement of the study
of harmony, that which stands in the closest relation to it, the doctrine of
Intervals, will* be primarily discussed in a brief and concise manner.

Doctrine of Intervals.

By Interval, Intermediate Space, is meant the relation in which one tone
stands to another in respect of distance.

The length of distance is immediately determined by the number of de-
grees on which they stand apart from each other, and according to this rule,
that the lower tone be considered as on the first degree, and the higher be
numbered according to the diatonic degrees lying between.

REMARK. — By diatonic degrees is understood the series or succession of tones repre-
sented by the scale of any major or minor key.

Take for example g as the lower tone on the first degree, then the o above
is on the second, the e above on the sixth degree :

The numbering of degrees thus resulting is expressed as follows :

Unison of Prime. Second. Third. Fourth. Fifth. Sixth. Seventh. Octave.

14 MANUAL OF HARMONY.

Generally we count only to the Octave, and begin the series again with the
tones beyond, and so on with each new octave ; so that the ninth degree be
comes a second, the tenth a third, the eleventh a fourth, &c. ; in like manner
the fifteenth becomes an octave again, and the sixteenth a second.

Reasons, however, which find their explanation in the harmony system
and in theory generally, sometimes give occasion for naming tones lying
above the octave according to the actual number of degrees. The series of
intervals from the octave up will therefore receive the following double
designation :

Octave. Ninth. Tenth. Eleventh. Twelfth. Thirteenth. Fourteenth. Fifteenth.

Second. Third. Fourth. Fifth. Sixth. Seventh. Octave.

Longer distances of two tones are simply reduced to their relation in the
lower octave.

More Exact Designation of Intervals.

It is easily seen that the above representation of intervals is based upon
the diatonic scale of C major, and that the relations of the intermediate tones
are not touched upon. These are based in like manner upon the first tone
of the diatonic scale, whilst any tone of the scale may be taken as the lower
one ; by which the tones of the different degrees become changed, and also
in these slight variations will appear.

In order to obtain a clear view in these manifold variations, the following
rules may be observed :

•

The series of Intervals exhibited above, where the lower tone is the FIRST
tone of the major scale, and the series itself forms the scale, serves as the basit
for determining att the intervals. These intervals are all called MAJOR, some

PERFECT.

No chromatic alteration of these tones, whether upper or lower, changes
either the number or the name of the degree; only a more exact designation
becomes necessary.

MANUAL OF HARMONY.

For instance, if a sharp be prefixed to the Fifth * it will still be a Fifth,
only a more precise designation is necessary, as it is evidently become »
different Fifth from the original one.

Now, as such changes of intervals arise by raising or lowering them chro-
matically, the following terms are used, serving to denote them mort
closely .

1. Seconds, Thirds, Sixths, Sevenths, Ninths, which result from the ma-
jor scale by taking its first tone as a basis, are called major ; Primes, Fourths,
Fifths, Octaves, perfect.

2. Lower the upper tone of the major intervals a half degree, and we get
minor intervals.

3. Raise the upper tone of the major and perfect intervals a half degree,
and we have augmented intervals.

4. Raise the lower tone of most of the perfect and minor intervals a half
degree, and diminished intervals result.

To 1.

Perfect. Major. Mayor. Perfect. Perfect. Major. Major. Perfect. Major.

Prime. Second. Third. Fourth. Fifth. Sixth. Seventh. Octave. Ninth.

To 2.

Minor. Minor. Minor. Minor. Minor.

To 3.

Second. Third. Sixth. Seventh. Ninth.

Augmented. Augm. N.B. Augm. Augm. Augm.

Prime. Second. Fourth. Fifth, Sixth.

N. B. — Augmented thirds, sevenths, and ninths do not occur ic harmonic relation!
Augmented octaves are to be regarded as augmented primes.

MANUAL OF MARMOMT

To 4

Diminished.

Dim.

Vim.

Dim.

90-

±&

. Third. Fourth. Fifth. Seventh. Octave.

/ REMARK. —Diminished primes, seconds, sixths, ninths, are harmonically inconceivable,
/ excepting in melodic connections, t. e.t in relation to progressing intervals, not to those
sounding simultaneously.

Observation on the Formation of Diminished Intervals.

The reason why, in the formation of the diminished intervals, the lower tone was raised,
whereas a similar interval would result if the upper tone were lowered, lies in the peculiar
relations of all intervals in respect to inversion, of which more will be said hereafter.

Tabular View of the Intervals most in use.

PRIMES.
Perfect. Augmented.

Major.

SECONDS.
Minor.

Augmented.

-&-

THIRDS. FOURTHS.

Major. Minor. Diminished. Perfect. Augmented. Diminished.

FIFTHS
Perfect. Augmented. Diminished.

Major.

SIXTHS.
Minor.

Augmented.

-e-

SEVENTHS. OCTAVES. NINTHS.

Major. Minor. Diminished. Perfect. Diminished. Major. Minor.

Division of Intervals into Consonances and Dissonances.

When we speak in music of consonant and dissonant intervals, we under-
stand thereby not those which sound well or badly, as these terms might
well express ; but, by the former, such as stand hi a pure, satisfying relation
that needs no further distinct connection with other intervals as a neces-
sary consequence ; by the latter, such as point distinctly at something fur-
ther, and without it would give no satisfactory sensation.

Consonances include the intervals termed perfect, and major and minor
thirds and sixths.

MANUAL OF HARMONY.

The former are also called perfect consonances, the latter imperfect.
Dissonances are the major and minor second, major and minor seventh, and
ill the augmented and diminished intervals.
Hence results the following table :

I. CONSONANCES.

a. Perfect.
The perfect prime, perfect fourth, perfect fifth, perfect octave.

1 4N.B. 5 8

N. B. — The peculiar relation of the fourth will be explained later under the system o/
harmony.

b. Imperfect.
The major and minor third, the major and minor sixth.

-&-

II. DISSONANCES.

The augmented Prime, the major, minor and augmented Second, the di-
minished Third, the augmented and diminished Fourth, the augmented and
diminished Fifth, the augmented Sixth, the major, minor and diminished
Seventh, the diminished Octave, the major and minor Ninth.

Augmented 1

Major. Minor.

Aug. 2

Dimin. 3

Aug. Dimin. 4 Aug. Dimin. 5

==«

'or. Minor. Dimin. 7

Dimin. 8 Major. Minor.

— fe? jag [- ~ — g-

MANUAL OF HARMONY.

Transposition (Inversion) of Intervals.

As was indicated above, in determining intervals we reckon generally
from the lower tone. When there are reasons, however, for determining the
relation of two tones reckoning from the upper, we term them : Inverted t»-
iervals.

For example,

- d is the Fifth from g, but g the inverted

fifth from d. It is easily seen that the interval is not hereby changed.

It is. however, otherwise when the upper interval is transposed below the
tone which was originally the lower, that is, an octave. As this transposi-
tion is a matter of special importance in certain, kinds of composition, an
explanation may here follow.

The diatonic major scale thus transposed will assume this form :

Upper intervals. 1

3 4

5 6
n -&-

~(g-

JL 0&. ££i c* £> g g &.&. asu.

Lower intervals. 8

This gives the following series of numbers :

1234567
8765432

that is : by inversion the Prime becomes an Octave^ the Second a Seventh,
&c.

With the inverted major scale as a basis, the following may be observed
of all the intermediate intervals.

1. All PERFECT intervals when transposed an Octave, remain PERFECT.

2. All MAJOR intervals become MINOR, all MINOR MAJOR, the AUGMENTED
DIMINISHED, and the DIMINISHED AUGMENTED.

The following table affords a general view of all the inversions :

ORIGINAL
INTERVALS

INVERSION

PRIMES.

Perfect. Augmented.
,_G ^ ^_

Major.

& f

SECONDS.
Minor.

./Iw^TnentetZ.

ffi— — * — ^

OCTAVES.
Perfect. Diminished.

Minor.

SEVENTHS.
Major.

Diminished.
_

§•• 1

1: 1 1 H

i i ..

-3 t

I^u

i»- ^ ^* yr

MANUAL OF HARMONY.

THIBDS. FOOBTHS.

Major. Minor. Diminished. Perfect. Augmented. Diminished.

SIXTHS. FIFTHS.

Minor. Major. Augmented. Perfect. Diminished. Augmented.

FIFTHS.
Perfect. Augmented. Diminished.

b±

SIXTHS.

Minor. Augmented.

%+*=£=t^=i=

FOUBTHS.

Perfect. Diminished. Augmented. Minor.

THIKDS.

Major. Diminished.

Jfo/or.

SEVENTHS.
Minor. Diminished.

OCTAVES.

Perfect. Diminished.

Minor.

SECONDS.
Major.

PBIMES.
Perfect. Augmented.

-h

75-

An exact, thorough knowledge of this essential transposition of intervals
is not only important for exercises in double counterpoint, but facilitates a
comprehension of, and insight into, simple harmonic structure, wherefore the
Btudy of it is strongly to be recommended.

A few remarks may follow here.

The reason why in the first table of intervals (p. 1 6) all diminished inter-
vals were formed by raising the lower tone a half degree, and not by lower-
ing the upper, can be clearly seen from the above table of inversions. Since
diminished intervals result from augmented by transposing an octave, this

formation comes of itself. For instance : the augmented fourth

must necessarily produce the following diminished fifth : XL <a — .

20 MANUAL OF HARMON*.

Likewise the perfect fourth belongs originally to the consonances, since
by transposition it is changed to the perfect fifth, just as the perfect fifth
can produce only the perfect fourth ; and in general, a dissonance can never
result from a consonance by transposition. Mention is here made of this,
because in special cases, which will be noticed hereafter, the fourth has to be
regarded like some of the dissonances, which in former tunes induced many
theorists to pronounce it merely a dissonance.

Likewise it becomes clear that the augmented octave, as well as the
ninths, cannot be transposed, as they can never fall below.

Other kinds of transposition, as into the Tenth and Twelfth, which pro-
duce entirely different results, may be passed over here, as they have no
influence upon our immediate studies.

Since a complete and thorough knowledge of all the intervals is indispen-
sable for the studies in harmony which follow, written exercises in them, as
well as oral solution of given intervals, will greatly facilitate a proper con-
oeption of them, and should be repeated again and again.

SYSTEM OF HARMON ¥.

COMBINATIONS of tones, sounded simultaneously, and composed of differ*
cut intervals according to certain fundamental principles, are called in gen-
eral terms : Harmonies, chords.

The science of Harmony points out the nature and kinds of chords, and
teaches their natural treatment. This consists in the proper, natural con-
nection of chords one with another, i. e. in the transition, resolution, blend-
ing of a chord in and with the following.

SECTION I.

THE PRIMITIVE HARMONIES AND THE CHORDS DERIVED FROM

THEM.

Among the different chords which may serve as the harmonic groundwork
of a composition, we may easily distinguish such as appear independent
without a determinate relation to others, from those which clearly point to a
connection with other chords, consequently are not independent. Consonant
and dissonant chords.

To the former belong most of the Triads, to the latter the Seventh-chords.
Both kinds form the primitive harmonies from which all the remaining
chords are derived.

CHAPTER I.

The Triads of the Major Scale.

A Triad is formed by a combination of three different tones. The lowest
of these is called fundamental tone, to which are added its Third and Fifth,
for example :

22 MANUAL OF HARMONY.

But these triads, formed from c, g and a, exhibit another difference in
theJr intervals. While the triads of c and g are formed here with major Third*
and perfect Fiftlis, the triad of a contains a minor Third and perfect Fifth.

A triad with a major third and perfect fifth is called a MAJOR TRIAD, one
\with a minor third and perfect fifth a MINOR TRIAD.

Remark. — The explanation of other sorts of triads cannot follow until later.

As the diatonic scale makes up the substance of a key, and forms the
groundwork of the melodic series, so also the triads, which are built upon
the different degrees of the scale, will form the essential part of the har-
monic substance.

Natural connection of the triads of a key.

The triad based on the first degree of a key must indeed be the most im-
portant, as fixing the key ; with it, however, stand others in the closest rela-
tion, serving to explain its position.

Viewing the triad in its natural form as third above third, the Prime ap-
pears as the fundamental tone, the Fifth as the highest tone, the summit as
it were.

2. =1^=1 Fifth.

Prime.

. — Any further addition of a new interval would either alter the chord or double
tones already present.

The chord which stands in the closest relation to this must indeed as an
independent chord lie wholly outside of it, but yet rest upon one of its
tones. This tone can be found only in the extreme limits of the chord,
namely c and g. Therefore G, which is here the fifth, will become the root
of the nearest related triad, while c in like manner will form the summit, the
fifth of the other, whose root would be F.

The connection of these three chords can be best seen in this form :

In these three chords, standing in the closest connection, it is especially
to be remarked that their tones include the entire scale ; that they form the
outlines of the key, and that they are and must be the most frequently used
In practice, if the key itself is to be clearly and distinctly represented.

MANUAL OF HARMONY.

On account of their importance, special names have been assigned tbero.
The first chord, resting on the first degree of the scale, is called :

THE TONIC TRIAD,
the second, on the fifth degree :

THE DOMINANT TRIAD,
the third, on the fourth degree :

THE SUB-DOMINANT TRIAD.

Let these three chords be ranged in their order in the scale, and they will
appear thus, without showing their inward connection :

I. IV. V.

and they are also seen to be all major triads.

Application of the above Harmonies.

In applying these three chords, we will use here, as also with chords to
be treated of later, four-part harmony.

Remark. — The theoretical connection of chords can be, it is true, well represented in
its manifold relations, with three parts. It would however keep us longer from our prao-
tical object, and may therefore be left for special treatment. Four-part harmony will ever
maintain its importance as the foundation of all kinds of composition.

Every harmony is regarded not as a mere mass of tones, as often appears
in Piano-forte compositions, but we divide its ingredients into four special
parts.

The upper part is called Soprano, the lowest Bass, the two together the
extreme parts ; that next below the Soprano is termed Alto, that over the
Bass, Tenor, both together the middle parts.

The following is an arrangement of these parts in score, and the triad
appears thus :

ALTO.

TEKOB.

24 MANUAL OF HARMONY.

For the three upper voices special clefs are used, which are better adapted
to their compass than the Violin clef employed above, and of which we shall
speak hereafter.

To obtain an easier survey of the parts, we will adopt in our next exer-
cises the Piano-Forte arrangement of parts, and not take a separate staff for
each voice.

The distribution of parts in No. 5 will stand thus :

BASS.

These different parts will be considered in a double relation: first in
reference to the progression of each part by itself, then in its relations to
the other parts, both of which must be pure and well-constructed.

The result of these two conditions constitutes pure part-management.

This purity of harmony and progression is attained by seeking and prac-
tising what is natural and in accordance with law in the connection of har-
monies.

Hence arises what we term pure part-writing or severe style, which im-
poses rules and laws resulting from the nature of music itself, and whose
observance will affosd the surest basis for a subsequent free use of the
materials of composition. Exercises in this style render the judgment keen,
cultivate the sense of what is true and correct, and enlighten the taste.

R&nark. — So far as every composition should be the result of & right use of all availa-
ble means and of the purity (that is, natural expression) wrought thereby, the term pure
part-writing in the general sense would as a matter of courser equire no farther explana-
tion. In the narrower sense, however, something more is implied, which might be more
closely and hotter indicated by the synonymous expression : strict composition, strict style, in
contrast with the free style, which in its real meaning, as opposed to the pure, is not to be
understood as impure writing ; for this, however often it may occur, is in all cases to be
indicated as false, whereas the free could in the main be founded upon what is legal in the
pure.

As was hinted above, by the term pure part-writing in the narrower sense is understood

MANUAL OF HARMONY.

inch as in the natural development of all the relations of tones allows the fewest deviations from
what is legal, and only such as do not affect what is essential and fundamental.

If the idea of pure part- writing is thus in general determined, yet its limits are not yel
drawn ; and it is precisely this that creates all the more difficulties for the beginner, since
the limits are very differently fixed by theorists themselves. This difficulty has induced
many of them, especially some of the more modern, to say no more of pure part-writing
or strict style, but generally to commence at once with the free style and learn the harmo-
nic laws incidentally. Whether this compliance with youthful impatience, which does not
love to busy itself with the abstract, this tendency to premature living creation, before the
organic is developed into a creative faculty, can bring anything to real maturity, is not to
be farther investigated here.

It is to be hoped that those who follow the views of this book and let their studies con-
form thereto, as well as all who have to go through a strict school, will be convinced that
their freedom for future work will by no means be lost by what is forbidden them, but,
based on natural principles, will develop all the more fully and powerfully. Real master-
ship has ever learned to reach the greatest intellectual strength when under restraint,
whereas the wildest fancies frequently give evidence of mental disease and weakness. On
the other hand the scholar cannot be warranted, where rules are at stake, in making use
of principles based upon exceptions, such as may perhaps be found in the best masters, or
in general in wishing to produce compositions, when his business is to perform exercises
theoretically well.

The three chords thus far found, when applied in four-part harmony, will
lead to remarks and observations, from which certain principles and rules
are to be established.

Since triads contain but three tones, one part (interval) must be doubled,
when four are lo be used.

Each interval of the triad may be doubled,

but in most cases the root is the best adapted for this purpose, more seldom
the fifth and third, and the last, in many cases to be pointed out later, not at
all. All doubling is to depend on a good and correct progression of parts.

To accomplish the connection of two triads, the following rule is to be
observed :

When there is a tone common to two chords that are to be connected, it u
retained IN THE SAME VOICE.

MANUAL OF HARMONY.

In example a we find c common to both triads ; the Sopi ano, which had
the first c, retains it also as fifth in the next chord. So in example Z>, where
g in the alto makes the connection.

The other parts move to the nearest tone, as in a the Alto from g to a, the
Tenor from e tof, &c.

When no tone is found common to two chords, the parts must be moved
independently in such a way, that no one shall appear in PARALLEL FIFTHS
or OCTAVES with another.

In order to explain this faulty progression more fully, we shall first premise
what is necessary concerning the movement of parts relatively to each
other.

The movement of parts with respect to each other.
One part can progress with another in

direct motion (motus rectus),
contrary motion (motus contrarius) and
oblique motion (motus obliquus).

Direct motion takes place, when two parts ascend or descend simulta-
neously, e. a.

Two parts move in contrary motion, when one ascends, and the other
descends, e. g.

Oblique motion occurs, when one of two parts remains upon the same
tone, while the other moves, e. a.

10.

.I — & , t

MANUAL OF HARMONY.

These three kinds of movement occur promiscuously in chord connections.
Thus in example No. 7 1. the direct motion appears between Soprano and
Tenor, contrary motion between Soprano, Tenor and Bass, and oblique
motion between the Alto and the rest of the parts.

The above-mentioned faulty progression in parallel Octaves and Fifths can
only appear in direct motion, as for instance when two parts move thus by
Rteps or skips :

This is equally a fault with all the parts :

The following harmonic progressions contam both errors :

12.

In example a. there are parallel octave movements between Soprano and
Bass, in example b. between Alto and Bass, and in example c. between
Tenor and Bass. Parallel Fifths appear in a. between Alto and Bass, in b.
between Tenor and Bass, and in c. between Soprano and Tenor, as well as
between Soprano and Bass.

The mechanical means of avoiding these and similar erroneous progres-
sions, is, for cases like the above, the employment of contrary and oblique
motion in the parts, i. e. the voice which already stands an octave or fifth
from another, must either move in contrary motion thereto, or, if the follow-
ing chord contains the same tone, remain stationary. The other voices then
pass to the tones nearest them in the new harmony.

Thus in example 12 a. three voices must move, one remaining still ; in &
and c. contrary motion of all the parts to the Bass is to be employed, fof
instance :

13.

MANUAL OF HARMONY.

Remark. — The reason for this prohibition of the octave (that of the unison is included)
can be easily found in the necessary independence of the parts. To discover the reason for
prohibiting the progression by fifths is not so easy, however much one is convinced of its
necessity, and great pains have ever been taken to express it clearly and definitely. Let
the following view of this subject be examined.

If every chord-formation presents for itself an independent whole, which, however else it
may be shaped, yet in respect to its root and fifth principally, unites itself as it were into
a circle (the Seventh as an addition is here out of the question), and if harmonic connec-
tions are only produced when two chords become in a manner merged into and identified
with one another, it is obvious that two chords with their extremes, fifth following fifth,
do not become thus merged, but, when placed side by side, appear without any relation to
each other. This is easily seen by comparing the following formations :

Sevenths form essentially no new chord, nor can they be conceived of as outside the
circle of the primitive chord ; they only serve to mark more definitely the relations of two
chords, and to render the harmonic connections closer and firmer.

Now wherever the perfect fifth appears, it will carry in itself its character of demarca-
tion, and whether the other component parts of the chord (the contents as it were of the
fifth) or an added interval like the seventh, lie above or below it, the unpleasant effect of
the succession of two perfect fifths will always be traceable to the lack of connection, to their
isolated nature.

While speaking of the fifths of triads, it may he observed further, that in the case of
perfect fifths which arise from added sevenths, the law of preparation partly indeed of itself
prevents parallel fifths ; but in the case of the progression of such a seventh, forming a
perfect fifth with another voice, to a succeeding perfect fifth, the unpleasantness and want
of connection will be equally perceptible, just because this lies only in the second fifth,
which appears without connection, for example :

15.

But as far as tlie diminished fifth is concerned, which in the Dominant Seventh chord
under certain conditions can appear even unprepared, its entrance without preparation
even in parallel fifths perfectly justifies the views above expressed, since whenever it follow*
the perfect fifth, its connecting character is maintained, but when it precedes it, the latter,

MANUAL OF HARMONY. 29

to say nothing of farther laws of progression, at once departs from the uniting circle of
both harmonies.
Compare the following passages :

J_ j

j^-.,

asp

V \E3l

16.

Though passages like the following are often found in compositions of the stricter style-

17.

it is to be understood that the doubling of the diminished fifth (the/) requires a double
progression of the same, and the consecutive fifths are justified as lying in the middle
parts, but that the following.progressions could not be called pure :

18.

r — r

partly because they are too conspicuous in the upper part, partly because the above con-
dition of a necessary double progression is wanting, although passages like that in
No. 16 c., are often met with.

It becomes clear here also, why parallel fifths resulting from passing notes in many
cases do not sound as disagreeably as those discussed above, wherefore many theorists
allow them as faultless ; this however is not to be admitted unconditionally, since many
of them are based upon other false progressions (for example, upon concealed fifths) and it
is not to be denied that, when widely dispersed and of sufficiently long duration, their
unpleasant effect is obvious.

This is not the place to treat further of these relations, and much might be said upon
many points, as for instance the progression of the fifth in the augmented chord of the
Fifth and Sixth, which would lead us now too far away. We shall be led back to this
point in our practical exercises by individual matters.

JO MANUAL OF HARMONY.

If the meaning of the above explanation be too obscure for the beginner, it will never
theless with his advance in knowledge and practice and his necessarily oft-repeated study
rf the whole harmonic system, be soon understood.

The faulty progression of parts thus far mentioned, we call open fifth and
octave progression.

When in direct motion between two parts the second interval forms a fifth
or octave, it is concealed, e. g. :

Open parallel fifths and octaves are never admissible for harmonic connec-
tions ; respecting the value or futility of concealed fifths and octaves we
shall speak hereafter (chap. 17)*; for the present this must be left for oral
instruction, as, in general, with a proper conception of the exercises, there
will be no immediate opportunity for errors of this kind.

Remark. — The beginner will do well in writing his first exercises to pay no attention
whatever to concealed fifths and octaves, because, by too anxiously avoiding them, the first
principles of chord connection are violated, and other errors, much worse, may easily arise.
Many things will in the sequel bring us back to this point, and be especially examined
and discussed.

Exercises.

The use of the three principal triads musically in connection, observing
the rules thus far established, will be the next exercise.

We will select for this purpose some Bass progressions like the following :

on, ])° fV 1

zcpzzjr^:

1 & ..

& .. r^&_.

20. ^ \±t &—\-

0: I
3.

— -M4 — •

V I IV

4 —

'-&-

1 \ f? 1
M j

r\'» '| /£* 7

i<^

^1 >r> I

- 1

*-}• f

£r

? * I :~

1 — :

^^ 1-

-* — L

Remark. —These and all the lessons that follow, serve to indicate the manner and
method to be pursued in our practical exercises. They should always be continued as
long as the subject in hand renders needful.

The disposition of the three upper parts to be added in the first chord
will lead us to further important remarks.

MANUAL OF HARMONY.

We have already seen in example 5. that the disposition of the voices in
a chord may vary greatly. This disposition of the voices is called the
position of the clwrd.

Close and Open Position.

A chord is in close position, when the three upper parts lie so near each
•ther that neither the Soprano nor Tenor, if transposed an octave, would fall
between the other two, though the Bass be far removed, e. g.

12.

The first position of the chord a. is so changed in £., that the former e of
the Tenor is given to the Soprano an octave higher ; in c. the case is the
same with both tones g and e ; hi d. the c of the Soprano is reversed and
put an octave lower. In all the transpositions the distribution is changed,
but not the close position.

It is otherwise when the chord appears in open position (also called dis-
persed position,) which is the case, when either the Soprano can be placed
between the Alto and Tenor, or the Tenor between Alto and Soprano, so
that the close position shall result therefrom, e. g.

22,

In a. the chord appears in open position, by placing the g between Alto
and Soprano in close position, 6., likewise in c. and d. In /. the g of the
Soprano in the chord e. is put an octave lower between Alto and Tenor.

But the following disposition of the parts (No. 23) would not be an open
posi tion in this sense, for by transposing the Tenor the disposition of the

MANUAL OF HARMONY.

upper parts is not changed, &., and only the transposition of the Soprano
would give the true open position, c.

b=l=iE^

23.

bzzg— :

Although the open position renders the chord fuller, yet it should not be
always used, and for our first exercises is not compact enough to be clearly
seen, so that at present we shall give them in close position.

Remark. — It will always be better to write the examples at first in close position, and not to
use the open position until later, commencing with the exercises in the second and third section, where
it will be seen of itself to be needed. Beginning with the open position the scholar continu-
ally stumbles upon difficulties, which it cannot be his immediate object to overcome, and
ar« therefore much better avoided.

Usually the different positions do not appear singly, but occur promiscu-
ously, according as the movement of the parts requires.

When the position of the first chord is determined, those following are no
longer so free as regards distribution that any can be taken at pleasure, but
it is governed by the rules already given on pages 13 and 14 for connecting
chords.

This chord connection and movement of parts in the first exercise No. 20
can proceed thus :

24.

^•"••i "&r^*m* ~*&r 2? °*

C: I

The natural relation of these chords to each other becomes clear in the
above simple example, if their connection be closely observed ; but especi-
ally from the last two chords may be seen the close connection, how one
completes the other. The sensation of return, of rest, of satisfaction, which
lies in this combination, renders it suitable for forming the close. This form
of cadence through the dominant chord, which inclines to the triad of the
tonic, is called, when the latter falls upon the rhythmical accent or on a good
place as to time, the authentic cadence.

MANUAL OF HARMONY.

25.

•> z? »"

Another form of cadence, which is formed through the Sub-dominant
triad, as above in No. 20, 4th example, is called the Plagal cadence.

26.

IV I

Of these and other kinds of cadences we cannot speak at length until
later.

In order to become familiar with the succession of chords which arises,
when the Bass moves by degrees (as in example 24 F — G), it will be well
to write out the succession IV-V and V-IV in different positions and keys.

The triads of the remaining degrees of the Major Scale.

All the triads of the remaining degrees of a scale belong, to be sure, to
one and the same key, but do not point to it so decidedly, as e. g. the chord
connection V-I.

These triads are called, to distinguish them from the principal triads,

COLLATERAL TRIADS.

They are formed upon the second, third, sixth and seventh degrees of the
scale.

III

vn-

The triads of the second, third, and sixth degrees are seen to be minor
triads, as their thirds are minor and their fifths perfect.
The triad of the seventh degree is essentially different from the rest)

84 MANUAL OF HARMONY.

since it has beside the minor third a diminished fifth ; it is therefore called
the

DIMINISHED TRIAD.

As an easy mark of recognition we take for the minor triads small' letters
to number the degree on which each is built, to which we add an ° for the
diminished triad, as above vn°, a method of numbering introduced by the
theorist G. Weber.

Now the triads of the major scale collectively will stand thus :

28.

in IV V vi vu*

Remark. — The beginner must be very cautious lest he regard all these chords, when
they appear, as tonic triads, an error which greatly obstructs the understanding of har-
monic connections. As long as C major is the prevailing key, the incidental triads of G,
F, of d etc. are merely the chords of the several degrees belonging to it (the key of C major,)
and we are not speaking of G major, F major, d minor, since these keys do not appear
independently.

Hence arises an ambiguity in chords, which it is well to heed. Every triad can belong
to various keys. The C major triad may be :

C: I F? V G: IV

If therefore, in connection with this chord, we speak of C major (meaning, according
to ordinary usage, the key,) this is true only in the first case, where the C major triad
occupies the first degree, but in all other cases is incorrect.

Application.

In connecting these chords with each other, as well as with those previ-
ously fouud, no new rule is immediately necessary: much that is new,
however, will appear as we proceed.

The Bass can move either by skips or by degrees.

In the former case there will always be connecting tones (degrees com-
mon to two successive chords;) in the latter, the parts must move in
contrary motion, according to the above rule (p. 27,) in order to bring
out the natural connection of chords.

UAtfUAL OF HARMONY.

a. TJie Bass moves by skips.

6. NB. better.

II IV

II V

— <S7

II VI etc.

Skips in tho Bass, as in these examples from the secor i degree, can be
managed similarly from all the remaining degrees, so that tones common to
the two chords shall remain in the same voice.

In many cases, however, there are exceptions to this rule.

In example 30 at NB. there is a progression of parts formed according to
the above rule, which contains a concealed octave between Tenor and Bass,
and which is decidedly improved by the progression which follows. Though
the local connection of tones be wanting in the latter case, yet there is still
an inward connection, since the d of the Soprano hi the first chord can
easily be conceived of as doubled hi the lower octave, by which the connec-
tion becomes at once evident, as in 31 :

31.

Remark. — The reason why precisely this tone should be conceived of as doubled,
such might be the case with any other, is hased upon the fact that it is the fandamenUA
tone, that, in fact, which gives the entire chord its determinate character.

The unpleasant effect of the above-mentioned concealed octave consists io
this, that the upper part moves a whole tone ; and the effect is still more
itartling when the octave is contained in the extreme parts, as in example
32 in a. ^

«• „-*» * ~ *, c-

32.

MANUAL OF HARMONY.

By the contrary movement of the Bass in I. the progression can be im-
proved, also by the contrary movement in example c., although even here
there is a succession of concealed fifths between Soprano and Tenor. (See
the remarks under example 34.)

Remark. — In the cases given above, we are not speaking of absolute errors. When we
have entire liberty as to the movement of the parts, much can be avoided which we can*
not escape under other circumstances, e. g. in handling a cantus firmus, a motive; or when
other reasons exist, important as regards the composition. The corrections are here cited
only from an absolutely theoretical standpoint. Of the concealed fifth in 32 c. we shall
speak more particularly under No. 34.

The unpleasant effect of the concealed octave vanishes at once, when the
upper part moves a HALF TONE, e. g.

33.

b. The Bass moves ty degrees.

Here contrary motion is constantly to be employed, e. g.
NB. 1. better.

84.

=a=s=

-77-

—G

...a

—<y—

\ * 1

V vi

MANUAL OF HARMONY.

Remarks upon these Chord Connections.

Ill all the progressions used in NB. 1 and similar passages which follow,
it is better to double the third in the second chord, in order to avoid con-
cealed fifths. Their unpleasant effect is even more prominent, if the chorda
appear in open position, e. g.

•&L

35.

The progression in b. is preferable.

If these concealed fifths occur in the middle parts, they are, under certain
circumstances, sooner to be allowed, not being so prominent

In NB. 2 the doubling of the third in the second chord Li not always to
be resorted to, since hi general the doubling of the seventh degree (in
example 34 the b of the second chord) is to be avoided.

Of the use of this tone, called the leading tone, we shall speak more at
length in the exercises which follow.

Exercises to be written out.

37-§3E*

4 NB.

Tie fourth exercise gives occasion for some remarks.

The progression of the Bass here in the first four measures proceeds in a
regular, consistent manner. Such a regular harmonic or melodic progression
is called a Sequence.

MANUAL OF HARMONY.

This consistent progression of the Bass requires also an equally regular
movement of the other parts.

If we harmonize this passage on the above established principles of con-
necting chords by means of stationary tones, e. g.

this object will not be attained ; on the contrary, the progression must pro-
ceed in such a manner, that the first chord hi the second bar shall be in the
•ame position with the first in the first bar, so that the connecting tone d
ice* n*>t remain in the same part.

39.

NB.

IV ii vi in

So in the first exercise, on account of the sequehce, concealed octaves, of
which we spoke above, are allowable, if they are not in the extreme parts.
In the third measure in exercise 4. we find a chord not heretofore used.

The Diminished Triad.

It is based upon the seventh degree of the major scale, and is less inde-
pendent than the triads thus far found, as it points distinctly to one progres-
sion, caused by the dissonance, the diminished fifth.

The natural progression of diminished intervals can in general be con-
ceived of thus, that either both tones approach each other one degree (a.),
or that one or the other moves while the other remains still (3., c.), a method
of progression which only becomes plain in a real chord connection.

d. e. Inversion.

40.fc=z«

MANUAL OF HARMONY.

In the third which follows the diminished triad (d.) the triad of the first
degree c appears incomplete, the fifth being omitted.

Since according to the relations of intervals heretofore explained (pp. 18,
19) as regards inversion (transposition,) an augmented fourth results from a
diminished fifth, so their progression must likewise appear in an inverted
manner. See 40 e.

The fundamental tone, upon which the diminished triad is based, is called

LEADING TONE.

It appears again as third in the dominant-triad, and as fifth in the triad ot
the third degree.

vn°

Since the LEADING TONE is of itself very distinctly prominent, it is NOT
DOUBLED in simple four-part harmony.

So its progression should be to ascend a half degree, when the chord that
follows contains this tone.

The necessity of this progression lies in the melodic character of the
leading tone, preceding, as it does, the tonic of the scale by a half tone.
This is particularly observable in the dominant-triad, if the leading tone be
hi the highest part ; thus a. in example 42 is more satisfactory than b. and c

c. d. e.

IjC^i — ££ —

6"^ ^

£• ""

C^2

42.

This upward tendency is less decided in the middle parts, as in e?. In
many cases hi such chord connections, skips hi the upper part (in c.) are
positively unendurable ; and skips in the middle parts (in e.) are to be
employed, when the Bass progresses by contrary motion.

In example 39 in the third measure we have the leading tone doubled
and progressing contrary to the above rule. Both were on account of the
sequence contained in the example, which allowed no change either of
position or progression of the chords.

On the more Complete Formation of Cadences.

The cadence by means of the dominant chord noticed on p. 32 (the
authentic cadence) appears in the last examples in a still more definite form.

MANUAL OF HARMONY.

That is : as the natural relation of the dominant chord to tKc tonic triad
renders the two chords suitable for the formation of the cadence, so there is
observable in these examples a still further preparation of the same by
means of the triad of the second degree, which stands in the same relation to
the dominant chord, as the dominant chord to the tonic triad, e. g.

43.

Besides the triad of the second degree, that of the sub-dominant is also
well adapted to this form of cadence, e. g.

±4.

IV V

The forms of dosing (cadences) which result from this connection of
chords will assume a still more definite shape by a use of the chords to bo
explained hereafter.

CHAPTER H.
The Triads of the Minor Scale.

a. Principal Triads.

THE principal triads of the major scale were found upon the fast, fourth
and fifth degrees. On the same degrees we find also the principal triads of
the minor scale.

The relation, however, in which the dominant triad stands to the tonic
chord, as it is seen with special clearness in the cadence-form above shown,
necessitates the alteration of one tone of the minor scale.

The seventh degree, which according to the signatures of the minor key is
always a whole tone removed from the eighth degree, is raised chromatically
a half tone, so as to receive the character of the leading tone. e. g.

MANUAL OF HARMONY.

45.

NB.

By this means the dominant triad in minor is formed exactly like that in
major, thus :

A minor. A major.

a: V A: V

or to speak briefly :

The dominant triad, both in major and minor keys, is always major.
This is plainly seen by comparing the cadence-form of both keys :
C major. C minor.

i & £~ &

47.

That the sixth degree, however, of the minor scale is in a harmonic sense
not capable of any chromatic change by raising a half tone, as is often
required in a melodic relation, is proved by the plagal cadence a. (see p. 33)
which cannot be conceived of at all as in b.

in A minor,
a.

c: iv

The three principal triads in minor can be represented in their most
natural relation, as formerly explained, thus :

T x V

MANUAL OF HARMONY.

The minor scale, therefore, as a basis for harmonic formations, will stand

thus:

l t t 1 i 1ft ft

50.

Remark. — All other forms of the minor scale, as

51.
or descending :

52.

rest upon melodic conditions, which do not admit of the interval of the augmented secona,
found in No. 50 between the sixth and seventh degrees.

Abstractly these forms have no influence upon harmonic formation; yet the harmonic
sub-structure reacts upon the formation of the minor scale, as the following example*
show:

53.

The last case, where the descending scale has this very interval of an augmented second
6 — a flat, which in the sequel we shall carefully avoid in harmonic connections, is explained in
this way, that 6 was necessary as a component part of the chord, but ab, in order not to
destroy the minor character of the passage, which is strikingly the case with a, while in
the ascending scale (in the first example) this is already perfectly preserved by the minor
third eb.

b. The Triads of the other Degrees of the Minor Scale.
SECONDARY TRIADS.

According to the establishment of the minor scale, the secondary triad*
appear in the following form :

54.

n° NB. iv

VI vir

MANUAL OF HARMONY.

The second degree gives a diminished triad, as formerly the seventh
iegree of the major scale: likewise a diminished triad is found on the
seventh degree. The sixth degree forms here a major triad.

The third degree brings a new form of the triad.

It has a major third and an augmented fifth, and is called therefore

THE AUGMENTED TRIAD.

From the forced or strong connection of this chord with others of the
same key, it can seldom appear as the fundamental harmony of the third
degree of the minor scale. The following examples may prove this :

55.

!•

&. JO

vn°

Of these examples those under c. and e. will be the most practicable.
The introduction of this chord appears still more difficult :

56.

Its introduction is the most tolerable, when the augmented fifth is pre-
pared, i. e. is already present in the same voice as a member of the preceding
chord ^(in d.).

Remark. — There exists something peculiarly foreign in the chords of the third degree
as well in the major as in the minor scale, so that this harmony, even when it appears
simply as a minor triad as it does in the major scale, can with great difficulty be connected
naturally and effectively with other chords, and therefore seldom occurs.

Most of the practical chord-connections indicated above will occur in other
relations, and not allow the augmented triad to be recognized as the third
degree of the minor scale. The augmented triad, which is very often used hi
more modern music, belongs to the chromatically altered harmonies, which
will hereafter be explained under the name of Altered Chords. (See chap. 10f
Altered Chords.)

MANUAL OF HARMONY.

Application.

The principles already developed of harmonic connection and part move-
ment will be valid here also, and what was said above concerning the
progression of the leading tone, is eminently applicable to the connection
of the principal chords in minor, since the interval of the augmented second
from the sixth to the seventh degree in the minor scale, as well as from the
seventh to the sixth descending, is to be avoided as unmelodious, when the
two tones, which include the interval, belong to different harmonies, e. g.

57.

V VI VI V

In connecting therefore the chords of the fifth and sixth degrees, which
very often happens, the leading tone must always ascend, by which in the
triad of the sixth degree the third appears doubled, e. g.

58.

V VI VI

Hence it would be impossible to present correctly the example given
inder 57 6.; unless an intermediate tone were used, as thus :

69.

Eemaric. — In certain special cases practice deviates from this rule. It will be well,
however, to adopt the progression indicated above, for the reason that it should not be
overlooked, that every deviation from rules in practice has and should have a stated nutive,
whereas in numerous other cases the observance of them is still recognized.

MANUAL OF HARMONY.

Exercises for Connecting the Triads of the Minor Scale.
L 2.

Remarks upon these Exercises.

A chromatic sign over a Bass note without a figure, as e. g. in the third
measure of the first exercise, always has reference to the third of the Bass.
This raising of the third in the dominant chord, as very often happens in
minor, is the raising of the leading tone spoken of on p. 41.

In general, when the Bass has the root, the triad is not figured in Thorough
Bass writing, and there must be special reasons for figuring with 3, or 5, 8,

, 8

o' or fully with 5.

In the third and sixth exercises there is a reason for figuring with 5. The
introduction of the triad of the third degree in minor has here been attempted,
and it was necessary to indicate the elevation of the fifth, since it forms
likewise the seventh degree of the minor scale.

Where a 3 or 5 is givon with the first chord of some exercises, it has
reference to its position. On this point see remarks under exercises (p. 50.)

The principles thus far developed will be verified by filling out one
exercise. We take the first for this purpose.

NB.

61.

The first principle of chord-coonection (through connecting tones in
the same voice) is observed here throughout, and therefore in the third

MANUAL OF HARMONY.

measure (at NB.) the Alto makes the erroneous progression of an atig«
mented second from/ to g%.

To avoid this error (according to p. 44,) it will be necessary to let the Alto
move from f to e, the Soprano from b to g #, and the Tenor from d to 6,
thus.

(a connection of chords already explained in No. 31, where the tone-con-
nection did not take place in the same voice,) or : the Soprano retains the 5,
the Tenor descends from d to g%, and the Alto from / to e, by which the
close position is left, and this and the following harmony appear in open
position :

63.

Further remarks, rendered necessary by the difficulties of progression as
regards the chords of the fourth, fifth and sixth degrees, are in special cases
to be left for practical guidance.

Before we pass on to the further use of triads, we shall give a synoptical
view of the chords thus far found as follows.

View of all the Triads of the Major and Minor Scales.

Major.
64.

n° III' iv V IV vn°
in major.

in minor.

Major triidt are found

IV V

V VI

MANUAL OF EARMON7.

Afinor triads.

Diminished triads.

Augmented triads.

in Major :

in Minor :

ft . v~. .

U III VI I ,T

in Major. in Minor.

VII0
in Minor.

n°

CHAPTER HI.

Inversions of Triads.

Chord of the Sixth, Chord of the Sixth-and-Fourth.

THE use of triads and of all fundamental chords generally, is not limited
to this, that the root, as in all previous examples, shall lie in the Bass ; the
Bass can also take the third or the ffth of the fundamental chord. Hence
arise transformations of the fundamental chords, which we call

INVERSION, TRANSPOSITION, INTERCHANGING
of the chord.

Remark. — It may well be observed that we are here speaking only of moving the Bass into
another interval, and that the transpositions before mentioned of the other parts into close
tnd open positions and into various intervals by no means change the chord essentially

The Triad is capable of two inversions :

a. When the Bass takes the third of the triad, we have

SIXTH.

CHORD OP TBffl

Fund, chord.

Chord of Sixth.

65.

1=1

Third
of fund, chord.

48 MANUAL OF HARMONY.

b. When the Bau takes the fifth of the triad, we have the Chord of th*

SIXTH-AND-FOURTH.

Fund, chord. Chord of Sixth & Fourth.

of.

The Chord of the Sixth is indicated by 6 over the Bass note, the Chord
of the Sixth-and-Fourth by \ over the same, e. g.

H:-

OL 14.

0
0: I

Hereafter to indicate the root we shall use the letter, and to indicate the
degree, as formerly, the number, by which, as may be seen in example 67,
only the position of the root, not the casual Bass, is to be regarded.

Remark. — As the root of the chord of the Sixth and of the Sixth-and-Fourth in example
67 is still C and not the Bass notes E and G, so the chord itself will not be based on the
third or fifth, but still on the first degree, since these are by no means newly-formed chords,
but only by means of the Bass brought into another position, and are therefore derived
chords.

Application.

By using the inversion of chords, there results not merely a greater
variety in the management of the harmony, but the movement of the parts,
especially the Bass, becomes more flowing.

According to the rules given on p. 25 respecting the doubling of one
interval of the triad, it will be better in the chord of the Sixth also in four-
part harmony to double the root of the primitive chord, and the doubling of
the Bass tone in the chord of the Sixth (i. e. the original Third) or of the
third of the Bass (i. e. the original Fifth) can only take place when the
natural movement of the parts requires it, or when false progressions can be
thereby avoided. In accordance with what was said on p. 39, it may be
remarked further that the leading tone in like manner forms an exception to
this doubling, when it lies in the Bass.

It need barely be mentioned too, that the distribution of the three upper
parts depends only on their movement, but has no other essential bearing
upon the chord.

MANUAL OF HARMONY. 40

The Chord of the Sixth can therefore occur in the foil owing forms :

68.

The use of the Chord of the Sixth-and- Fourth is less frequent than that
of the Chord of the Sixth, and requires certain conditions, which will be
mentioned later. We find it mostly in the formation of cadences. The
Bass tone, the Fifth of the primitive chord, is the best adapted for doubling,
and the chord will appear in the following and similar forms :

69.

For connecting these chords with others, no farther mechanical rules are
needed than those already given ; in like manner we omit the mere mechan-
ical combination of two and three chords, and exhibit the application of
these derived chords in short pieces, which, however insignificant, contain
the form of a complete whole, and admit of a better estimation of single
in their relation to the whole.

Exercises.

1- 6

6 6 43

r r* — «• — = 4-f H-

7f>- rr (p ^ ^
2- 5 6

-4_f- . p ^__*q.____. «_4],

6 6

rv^L, 1 — & r-

— ~j — H~~" — ~! i ! H : —

:_^ — 9 . B jj ^ \ £ — 1_|

i — 1 1

3- 6 6

p_ j — -^ — T

6
664

<2 ^

r^"(p t) -'" — ^

„[ 1 C . j ^ ||.

4> 3 6 6

L 1 — | 1 1 (- 1 ^ — L LL

6 6
43 66 6 43

T It i 1 II

1 S3 & _d \ *3 - II

**^ XiJ t

~\ & O 1A \ & • • ||-

' t cJ & & ^

5. 666

6 66 6. 366 66

•^ ' - P ( ! i. ' 1 ' P ' & S3 l

"in 2? ^ ^ 1

\ lr \- " r I

4 U-L- . |-lt L_J— . -4 t-J

MANUAL OF HARMONY.

66 V 7. 36 5 66 43

Hf—

2? — /5 —

i rH ^?

? _.t .

: A j t— J— it=-

-y

— £L J

IOT — j^—

ZS 2

• #

9. 3 6

6 6 #

nzzztufcc — <g-+-^ f

•Jr-T^g^-T-i ^-F^^-^^tt

Remarks upon these Exercises.

The designating of the fifth in the first measure of example second, as well
as all similar indications hereafter, shows the position of the Soprano, con-
sequently that of the first chord. When there is no figure over the first Bass
note, it is to be understood that the Soprano most fittingly takes the Octave
of the Bass.

The diminished triad of the seventh degree appears in the second exer-
cise as a Chord of the Sixth. It is in this position that it most frequently
occurs. It may be remembered here that the root of this chord, being the
leading tone, is not doubled, instead of which in most cases the third is
doubled (the Bass tone in the chord of the Sixth.) The movement of parts
results at times in the doubling of the fifth also. The diminished triad of
the second degree in minor allows the root also to be doubled.

The progression of the diminished triad always depends on the movement
of the Bass. The natural tendency of the diminished triad in its funda-
mental position has been already shown on p. 38.

In most cases the Bass moves thus :

71.

and the other parts as follows :

MANUAL OF HARMONY.

It follows from the above examples, that the inversion of the diminished
fifth, namely the augmented fourth, in four-part harmony will not necessarily
have the same progression as was given above in two parts on p. 38 ; we see
in the first example and others b and f in the Soprano and Alto moving to c
and g :

The similarity in sound between this chord and the dominant-seventh-
chord, which is to appear later, frequently induces beginners to make the
diminished fifth descend, even when by inversion it has become an augmented
fourth ; this, as the above examples show, is only and solely necessary, when
actually as a diminished fifth it lies above the root, and a progression like the
following

is wrong on account of the parallel fifths.

Remark. — It may here be observed further, that parallel fifths, of which one is dimitt-
ished, and the other perfect, are allowable, if the diminished follows the perfect fifth, but not
the reverse, e. g.

good.

not good.

75.

Compare also Remark on p. 28.

The progression of the parts in the diminished triad takes a different
form, when the Bass passes to any other chord than the tonic triad. A few
chord connections may follow here :

vn° in

vn° IV

vn°

MANUAL OF HARMONY.

letter :

not:

Ill ^2=$:==-*' — ni

4l *•— Tsr-^ff

VII VI

not

^^!E|^f:3^^^FF
— T£=\\— v — ^-Hl-p^^ — FF

*f 2J

•-ex

vii ° n

and others.

The diminished triad of the second degree in minor admits of a different
treatment, since its root may be doubled. See p. 50.

A succession of two or more chords of the Sixth, when the Bass moves by
degrees, as in exercise 70. No. 3 and others, will compel one or more parts
to move in contrary motion to the Bass. e. g.

77.

66 66

The series of chords of the Sixth in the 5th and 6th exercises in No. 70
can be harmonized indeed in different ways, but it will be best, when the
regular Bass progression is retained in the other parts also, e. g.

6 &c.

Concealed octaves, as in the 2d and 3d measures between Tenor and Bass,
are not to be avoided in such cases. Hence we may conclude, that to INDI-
YIDUAL abnormal progressions, WHEN PLACED IN COMPARISON WITH THE
CONSISTENCY OF THE WHOLE, «* ? art not to attach that special importance

MANUAL OF HARMONY. 53

which is otherwise their due, since the formation of details, though to bo as
perfect as possible, will always be subordinate to that of the whole.

Remark. — Without doubt the principle just laid down can be easily misunderstood by
the beginner ; yet its statement was unavoidable, and, to escape all possible error, it maj
6e added further, that a final decision on these points belongs only to a judgment fullj
ripened by experience and practice.

The Signs used in Thorough Bass Writing.

The figures and signs in Thorough Bass are called in general, Signatures
Some of them have been already explained, as the chromatic sign so often
used in minor. The figuring of the Chords of the Sixth and of the Sixth-
and-Fourth was given on p. 48. A line through the figure (e. g. in exer-
cises 8, 9, 10 under No. 70 through the 6:0) is used when a chromatio
elevation of the interval a half degree is needed, instead of which, however,
a # or k| by the side of the figure is often used (e. g. 6# or 6b|, 5t|). Other
figures will be explained hereafter with their respective chords.

Formation of Cadences by irteans of the Chord of the Sixth-
and-Fourth.

In the exercises 70 we find, through the inversions of the triad, an ex-
tension and more determinate form of the cadence previously cited. It
appears namely, that the chord of the Sixth-and-Fourth of the tonic triad
before the dominant chord leads directly to the close.

79.

C: I V

The triad of the fourth or second degree often precedes the Chord of the
Sixth-and-Fourth .

BO.

C : IV I V

I V

54 MANUAL OF HARMONY.

While the chord of the Sixth-and-Fourth points so decisively to the close,
and has likewise so positive an influence when a modulation into foreign
keys takes place, its appearance is equally flat under other tircumstances, so
that its proper use is dependent upon certain conditions, which will be
discussed hereafter.

CHAPTER IV.
Seventh-Harmonies. Chords of Four Tones.

SEVENTH-HARMONIES are based upon the triads. They result from the
addition of a third to the fifth of the triad, forming a seventh from the

root:

7 7

Beside the different kinds of triads, the different kinds of sevenths also
will produce a variety of Seventh-harmonies.

General Properties of Seventh-Chords.

Seventh-chords are not as independent as most of the triads, but point
directly to one progression, so that they never alone, but only in connec-
tion with triads, produce any effect that is complete or exclusive. On the
other hand they render the relations of chords to one another closer, more
intimate, and by this property become particularly useful hi combining
chords and managing the parts.

The Dominant-Seventh-Chord in Major and Minor.

The most prominent of the Seventh-chords, and the one that occurs most

frequently, is the

DOMINANT-SEVENTH-CHORD.

also called the principal Seventh-chord.

Like the dominant triad it is based upon the fifth degree, and is formed
exactly alike in major and minor, namely from the major triad and minor
teventh.

82.

MANUAL OF HARMONY.

In the fundamental position it is indicated by 7 over the Bass note and in
our method of indicating by V7 :

C: V7 G: V7

The relation, in which the dominant triad stands to the tonic triad, haa
become generally clear through the cadence formation above exhibited (see
p. 33.) The close receives a still more decided character by the use of the
dominant-seventh chord.

The following chord-connection will show the form of cadence :

84.

Remark. — It should be observed here, that the triad which follows the seventh-chord is
incomplete; in both cases the fifth of the chord is wanting. The reason of thte will
appear from what follows.

The inward tendency of these chords to some point of rest, and their con-
sequent union with a triad, is called

RESOLUTION OF THE SEVENTH-CHORD, (Cadence.)

When the union of the Dominant Seventh chord with the Tonic triad
takes place as in No. 84 and similar combinations, it is called a
CLOSING CADENCE.

As regards the movement of the parts, the progression of the intervals
of the Seventh chord will furnish some important remarks.

First, we regard the closing cadence as the regular resolution of the
Domin ant-seventh-chord especially.

The Seventh as the essential interval of the chord is, from its relation to
the root, forced to a determined progression. Eegarding the progression
of the Bass, which contains the root, as given, an upward progression of
the Seventh will seem impossible :

MANUAL OF HARMONY.

even if a third part be added, as in b ; whereas its movement downward ia
fully satisfactory :

86.

Since the progression of the root a fourth upwards or a fifth downwards
is already determined, that of the Third and Fifth of the Seventh-chord
remains to be considered.

The Third of the Dominant- Seventh-chord is always the leading tone of the
Scale ; its natural movement is determined therefore from what has been
said heretofore concerning the leading tone (p. 39 ;) its progression is to
ascend a half degree, hence b. will not appear as natural as a.

87.

In example 87 b. the Third is given to the highest part, which makes the
strangeness of its progression especially palpable. This movement can be
tolerated, if the Third lies in a middle part, e. g.

88.

This descent of the Third (leading tone) is therefore to be employed
under the following conditions :
a. When it lies, not in the highest part, but in one of the middle partt,

tddom used.

89.

MANUAL OP HARMONY.
b. When the Bass progresses by contrary motion, e. g.

b. not.

90.

& 7? \ & 3»J H-

The reason for the second rule is evident, if we observe the concealed
fifths between the Alto and Bass in example b.

The movement of the Fifth in the Seventh-chord is free. While it for
the most part is forced by the Seventh one degree downward, yet there may
be reasons for allowing it also to move a step upwards, as is seen in example
88 b., where the d in the Soprano is carried to e.

If we condense the substance of these remarks, we obtain the following
rules for the regular resolution of the Seventh-chord, and for the cadence
especially :

/ The Seventh descends a diatonic degree, whilst

\ The root moves up a fourth or down a fifth ;

1 The Third is carried a degree upward, contrary to the seventh, whilst

I The Fifth may ascend or descend one degree.

*^_ -^- \

Remark. — With this progression of the Third contrary to the Seventh may be remembered
what was said before (p. 38) of the root and diminished fifth in the diminished triad. Both
intervals occur again in the Dominant- Seventh-chord.

Application.

Except in forming cadences, the Dominant-Seventh-chord, as we have
thus far learned to apply it, is seldom used in the middle of a piece, and then
only in such places as do not create a sense of complete termination.

This happens, namely, when the Seventh of the chord lies in the upper
part, forming an imperfect close, or when the Dominant-Seventh-chord falls
upon the accented part of the measure (Thesis,) since in a perfect close
(cadence) the tonic triad must fall there (see p. 33.)

Moreover the chord often appears incomplete by the omission of an
interval. This interval, however, can only be the Fifth, seldom the Third,
since the omission of the root and the Seventh would entirely alter the chord
and make it unrecognizable.

MANUAL OF HARMONY.

e. iddom : d.

/o I t*

01. /r

V, I V7 I

In a., 5., d. the Fifth is omitted, in c. the Third, in place of which the root
is in all cases doubled, restoring the closest connection with the following
chord by sustaining the tone, and thus allowing the tonic triad again to
appear complete, which in the former resolutions was not the case (see
No. 84.)

Concerning the omission of one interval in the chord we annex the
following remark :

From the movement of the parts a chord may appear incomplete ; the
omitted interval will generally be the Fifth of the fundamental chord.

Exercises.

7 6647

82. ^{f-

&—

pL 1_.

— (X — E

& pL j

2.
___ —

^j'tr

| • A^ '
6

6 6

7
—6> » _jj

Z IP 6* .... 1

— -i

i—* *!.

t— \ f- "I

^—J « 1

366

6 7

6
4 7

« .

MANUAL OF HARMONY.

These exercises need no further explanation. It has been formerly
mentioned that by 7 the Seventh-chord in the position thus far known is
indicated, also that the sharp under it, or in general any chromatic sign
which occurs without a number annexed, has reference to the Third from
the Bass tone (see p. 55.)

CHAPTER V.

Inversions of the Seventh-Chord.

As the form of the triad can be changed by the Bass taking another
interval than the root, this can take place likewise with Seventh-chords :
2 he first inversion results, when the Bass takes the Third from the root;
The second, when the Fifth of the primitive chord lies in the Bass, and
The third, when the original Seventh is given to the lowest part.
The inversions in close position appear thus :

93, Bi

A comparison of these inversions of the Seventh-chord with those of the
triad shows clearly their analogous positions :

94.

3(3)

sG 2)

These derived chords take their names from the order of their intervals :

Theirs* inversion is called: the Chord of the Sixth-and-Fifth,

The second: the Chord of the Sixth-Fourth-and- Third — or briefly Fourth*

and- Third,

The third: the Chord of the Sixth- Fourth-and- Second — or briefly tin

Chord of the Second.
Their figuring in Thorough Bass may be seen above in example 94.

MANUAL OF HARMONY.

We need only recall the fact here, that with these inversions, as formerly
with those of the triad, the only essential point is the position of the Bass or
lowest part, and that the other intervals may be variously distributed among
the upper parts, e. g.

<5*2-

05.

^=*&

.JSL.

E|3
— ^— T

ri_j^». ^

-U.

Application.

2%e regular progression (resolution) of these derived chords is hosed upon
that of the primitive chord.

As the dissonance, the seventh, established the progression of that in one
direction, so also with the derived chords, where the two tones, root and
seventh, either appear again, or by inversion become seconds, the tendency
to the same progression will exist.

or:

96.

Progression of the Chord of the Sixtl\-and-Fifth.

Since the original Seventh also forms a dissonance, a diminished ffth, with
the Bass tone in the chord of the Sixth-and-Fifth, whose progression has
been discussed above (p. 38,)

the resolution of the chord of the Sixth-and-Fifth will naturally be as
follows :

98.

MANUAL OF HARMONY. (ft

The progression of the root cannot be here as it was formerly given, aa
the G of the upper part is sustained and becomes the fifth ; this, however,
is only apparent, for the same progression lies at the foundation of this
harmonic connection, as is shown by the figuring G7 C in example 98.

Beside other causes, the chief reason why the Soprano or a middle part
cannot take the progression of the fundamental tones note for note, lies in
the character of these parts, which is better suited for the connection and
union of harmonies, than for their foundation, which belongs to the Bass.

Remark. — Irregular progressions of the root in these cases, such as might result from a
freer movement of the parts in certain relations, are not hereby excluded, only there must
be an inward connection and relation between the chords.

Progression of the Chord of the Sixth-Fourth-and-Third.

Beside the Seventh and its inversion, the diminished Fifth, or its inver-
sion the augmented Fourth, again appears here :

99. gi:

The resolution of this chord proceeds as follows :
a 6.

,tfB«gi__^egi „_

100.

G7 C G7 C

The Bass, the original Fifth, can move in both these ways.

Progression of the Chord of the Second,

This chord has this peculiarity, that the original dissonant intervals, the
Seventh and the diminished Fifth, can only occur in their inversions, aa
Second below and augmented Fourth.

The progression of this chord is the following :

101.

The resolution of the Chord of the Second therefore is through the Chord
of the Sixth.

It may be seen from these resolutions, that they are all based upon the
natural progression of the Dominant-Seventh-Chord, called above Cadence,
for throughout we find the root indicated Gj C or V^ I.

MANUAL OF HARMONY.

These resolutions therefore will of themselves form Cadences, only not of
so perfect a kind as those before mentioned, and as those are called perfect
cadences, so these are distinguished by the name imperfect cadences.

View of the Natural Progression of all the Inversions of the
Dominant-Seventh-Chord in Various Positions.

102.

JOLL

6
-k-

b. The Chord of the Sixth-Fourth-and-Third

F^=&
F-*--Hf

MANUAL OF HARMONY.
C. The Chord of the Second.

262 62 6

Exercises for Using these Chords.

66 32

6
4 7

103.

4 6

36 65

6 87

32 63

6 6

5 4 7

2 6

436 687

#
2 6

3 6

Ooservation. —The figures 8 7 in the last measare but one of exercises 2, 4 and 5 meav
that the Seventh should not appear at once with the chord, but follow after the Octave.

&4 MANUAL OF HARMONY.

CHAPTER VI.

Collateral Seventh-Harmonies.

WHILST with the triads three principal chords are necessary, in order to
establish the key (the relation to the tonic triad being the central point,)
with Seventh-chords only one principal chord is needed, the Dominant-
Seventh Chord, the contents alone of which make the key unmistakeable,
and whose natural progression to the tonic triad represents it.

Remark. — In view of the fact that the Seventh of the Dominant-chord is at the same
time the root of the Subdominant triad, the relations of the two tones g and /(as roots of
the dominant triads) to their common centre c (as tonic triad) becomes perfectly clear (see
above p. 22. 3.)

Beside this Dominant-Seventh-chord, also called Principal or Fundamental
Seventh-chord, Seventh-harmonies can be formed from the other triads in
major and minor, whose relation to a fixed key, to be sure, is undeniable, but
by no means so decided as with the former. They are termed :

COLLATERAL SEVENTH-CHORDS.

They are simply to be formed by adding to the triads a Seventh of the

root.

a. In Major :

:fc
104.

^y yj GS • •

^ % % — I — H

% — % — * " \\

IV, VI, VII °7

6. In Minor :

NB. NB.

We arrive here at the chord formations, which without connection with
dther chords sound more or less hard and therefore strange, because, as was
4aid before, their relation to a fundamental key is not as decided and clear
as that of the Dominant- Seventh- Chord. Their use therefore is somewhat
less frequent, but none the less adapted for giving variety and especial
coloring to harmonic progressions.

Amongst these collateral chords, the following kinds may be distin-
guished •

a. Major triads with major
seventh.

MANUAL OF HARMONY. 65

in Major.. ,,, in Minor.

105. fc=g

a; VI

NB. Mi/or Jn'acfc «?#/i minor seventh always form dominant chords of

the seventh.

in Minor.
b. Minor triad with

major seventh.

^^ not used as fundamental harmony.

a: i

C. Minor triads with minor
seventh.

in Major :

in Mino* ;

C: n7

d. Diminished triads with a minor
seventh.

r vi7 a; iv7

in Major : in Minor ;
-«-

C: vn°7 a;

in Minor ;

. Diminished triad with a diminished seventh.

f. The augmented triad with a major seventh,

as it is found on the third degree in minor, is indeed not impracticable, but

for reasons before discovered under the augmented triad, rare and ambiguous

Remark. — We shall find this chord again in the tenth chapter with a different basis.

Use of the Collateral Seventh-Chords in Major.

The Seventh, or its inversion, the Second, whether major, minor, dimin-
ished or augmented (the last applying to the Second only,) will always in its
relation to the root as dissonance incline to a progression.

This natural progression with the collateral Seventh-chords is none other
than that already found with the Dominant- Seventh, namely one degree
downwards towards the root, if the latter descends a fifth or ascends a
fourth.

Accordingly while the progression of the principal intervals of the chord
is found to be the folio whig :

106

sqz zz

MANUAL OF HARMONY.

no new rules are needed for the other intervals ; the Third will ascend one
degree, while the Fifth can progress in either direction.

6. c.

107.

Remark. — The exceptional progression of the Third in example 107 b. arose from thii,
that the concealed Octave, which would result from the regular ascent of the Third by OM
degree, e. g.

108.

1 J^ f2 ' ^J

e*— =
^

~\\

Ffr — &i^**- —

<£

~\\

was thus avoided. See p. 35, example 32.

But whether, through the movement of the fifth, the leading tone in the following chord
shall be doubled, as in example 107 c., or the following concealed fifths are to be preferred :

109.

will depend upon circumstances, to be judged upon in practice with reference to place and
position.

Natural Progression (in Cadence-form) of the Collateral Seventh-
Chords in Major.

a. of the first degree.

or :

not:

110.

.• not ,•

^*& o

MANUAL OF HARMONY.

with omission of the fifth:

SH^i

— g —

j 1 <fe

1 & &

L^-4

5?
&

6. o/ £fo second degree.

-—%=-

or;

C: n

without fifth:

not:

c. of the third degree:

not: fiotf;

C: in? vi

d. of the fourth degree (seldom with this resolution. )

^iS2Z=J± ± =d± — ^5±s:s

— &-

without fifth;

68 MANUAL OF HARMONY.

e. of the sixth degree.

without fifth :

CS-—T (T^^TT ~lT-ex I ' -|T~°'^Z

not;
G: vn°7 in

without fifth :

-&-

Remark. — The progressions here given of all the Seventh-chords are neither exhaustive
hi their positions, nor have they been presented as including all that/are possible.

The difficulty in forming such progressions lies only in the frequent occurrence of con-
cealed fifths and octaves. So all the remarks above annexed, as " not," " not good," which
refer mostly to the movement of the Bass, so far as it produces those faults in connection
with other necessary part-movements, are in many cases to be taken only from the theoretical
standpoint, whereas in practice, even in the so-called pure composition, such and similar
cases must often be judged according to the principles above stated (on pp. 52 and 53.^

As theory hitherto has not succeeded in establishing positive rules for all cases of the
kind, the true and the false, the admissible and inadmissible in this respect can only be
discerned by a thorough harmonic culture and a true musically formed ear. More on this
•abject will follow later.

Of the Peculiar Progression of the Seventh-chord of the
Seventh Degree.

In the above table, under 110, of the progression of all the Seventh-
chords in major, that of the seventh degree, similarly to the others, was
carried to the third degree, i. e. the progression of the root, as with the other
Beventh-chords, was to ascend a fourth, or descend a fifth. This progression
U the less frequent, and is for the most part used only where there is a

MANUAL OF HARMONY.

uniform movement of the harmony (sequence.) That one occurs oftener, OB
which the diminished triad, to which the Seventh is here added, is based (see
pp. 38 and 50), namely to the tonic triad.

Hi.

C: vu

That the relation of the diminished triad to the tonic triad is not changed
by the addition of the seventh, on the contrary is still more positive, ia
plainly seen by the above example.

It is to be observed also, that when the chord appears in the above
position, the Third of the following triad must be doubled (see 1115.,) aa
otherwise perfect fifths would result (see 112 a.) ;

112.

or a skip must be made as in &., a movement of the Tenor which not infre-
quently occurs, and which is very effective notwithstanding the concealed
octave.

It is a peculiarity of this chord, that its only satisfactory position is that
hi which the Seventh lies in the highest part, whilst the other positions, if not
impracticable, are yet more confused.

" '

Iffin

I V.

113.

Remark. — Whether the reason of this lies in the fact, that the Seventh, with the pro-
gression as above, has the character of the Ninth (as many theorists affirm that this chord
with its resolution is based upon the Dominant-Seventh-chord with a Ninth added,) which,
although resembling that of the Seventh, is yet more comprehensive, and does not admit
of a middle position, cannot here be further investigated

70 MANUAL OF HARMONY.

The Freer Treatment of the Third and Fifth in the Seventh-
Chord.

Different progressions of these intervals have already been used in the
above chord-connections. The Fifth moves in either direction, the Third
likewise at times a degree upwards, at others three degrees downwards. This
was generally hi view of avoiding concealed fifths and octaves. Apart from
these faulty progressions the Third especially may move differently still,
whence the part-movement often becomes freer and more independent, e. g.

a. I. not good: c.

114.

It is seen hi c. that this progression is possible in the middle parts also, if
the position admits of it.

The progression of the Soprano in b. is not good, because a skip of an
augmented fourth is produced by it.

The step from the fourth to the seventh degree is called the Tritone,
because it contains three whole tones. Upon this more in the sequel.

Other progressions of the fifth are only possible, when the Bass also
changes its usual progression as fundamental tone, as in general still further
progressions of the parts will result, when we seek for other chord-<joimec-
tions than those hitherto employed.

The Preparation of the Seventh.

We have thus far spoken of the progression of the Seventh-chords, but
not of their introduction.

The harshness of the entrance of many dissonances and especially of most
of the Sevenths in the collateral Seventh-chords renders a careful introduction
of them necessary, which consists in their "being prepared.

A tone is prepared, when it already exists in the preceding chord IN ONE
AND THE SAME TOICE as a harmonic tone, so that it can be competed by a
tie.

MANUAL OF HARMONY.

Such a preparation of a tone we had previously in the first chord-connec-
tions presented, e. g.

-« — — Ss-

115.

We may say here : that the c of the Soprano in the second chord is
prepared by the c of the first chord ; also the g of the Alto in the example
that follows.

But the necessity of the preparation of Sevenths lies not only in the
harshness of their effect when they are heard without preparation, but
specially in the character of the harmonic connection and union of two
successive chords, which is eminently peculiar to sevenths, and would not
appear without that preparation.

The preparation of the Seventh can be effected as follows :

116.

C: V I. IV V I^IV IV

C: in IVjvn

in vi

I vi7 ii IV vn °7 I

In all these examples the tone, which is connected by a tie with the same
tone following, forms the preparation of the Seventh.

In forming such a preparation the following rules are to be observed :

a. The preparation falls upon the unaccented part of the measure (Arsis)
and must

b. At least be of equal length with the following Seventh : it may I w
longer, but not shorter, e. g.

MANUAL OF HARMONY.

not:

. ..

. r .... u-

117

Remark. — The preparation of the Seventh forms one of the most important parto of the
harmonic system, and is to be managed and practised with great care, because upon it
depends the most essential feature of the inner, closest harmonic connection.

Although exceptions on this point also may be found in practice^yet it may repeatedly be
called to mind, that they are nothing else than exceptions, which cannot disprove the im-
portance of the principle of harmonic union, but can only be judged as a concrete case,
caused and intended by reason of its position and relations. (Page 44. Remark.)

These exceptions occur mostly with minor Sevenths, as the less harsh, like that of the
second and seventh degree, and are always tempered by a good progression.

But the Seventh of the Dominant- Chord, also called the Fundamental
Seventh, forms a special exception to the necessary preparation. It is that
whose effect, by its relation to the tonic triad, to the fundamental key, is the
least harsh and strange, and does not need preparation in all cases.

The following may be observed as to its farther use :

The Dominant- Seventh needs, to be sure, no preparation, but its free
entrance requires the presence of the roott if the progression is to be pure and
without harshness.

118.

Remark. — The so-called passing Sevenths, which naturally as such cannot be prepared
are regulated according to the rules for passing notes, which are explained afterwards.
Concerning passing sevenths, see Chap. 18.

The Seventh of the Seventh degree, also, in major and minor (in the
latter case the diminished Seventh-chord) on account of its peculiar char*
acter by no means requires preparation in all cases.

MANUAL OF HARMONY.

1- 3 T

Exercises.

7 66

•4,

/^v . . ^y

j<7 1 i

^ i

"1./V ZJ ! I .Kt (_

^ i /^? nd

Z3&3Z

. u & . ^

i <5»

267

The Connection of Seventh-Gliords with each other.

The progression or resolution of the Seventh-chords in the previous
examples was always through the triad of the fourth degree above, or, which
is the came thing, of the fifth degree below. Instead of the triad, a Seventh-
chord also of the same degree may follow.

The progression of the parts undergoes no change by this, only the Third
of the first Seventh-chord will in this case serve for the preparation of the
following Seventh, therefore not move, but be sustained, e. g.

120.

C: ii

Here the Third of the dominant-chord, J, forms the preparation of the
following Seventh.

The peculiarity of this harmonic connection is, that in one of the Seventh*
chords the Fifth will always be wanting. In example 120 the fifth of the
first chord was omitted. When several Seventh-chords follow each other,
theffth will be wanting' in each alternate chord.

MANUAL OF HARMONY.

121.

The following rule may serve for harmonic connections of this sort :
When two or more Seventh-chords IN THE FUNDAMENTAL POSITION succeed
each other, the fifth is omitted in the alternate chords.

Exercises.

3 6

6 5

122. ^p ^

. — ^ — & — i —

— T — 1 a —

2- 3 67 7

sSte^tess

6 J 2

-p— i — 1 — 4-

^S — ^—

6 7 7

-— i — 53 —

:
J It

3- 5 777

A^-^-f +-H-f-

J— «— J-

X _J

:-^-^-*

6 26

.^±^4^±.

i ^

7 7

- . I" Tf

Z fflp " e) ^
4 T

&d 5~»-
i ^ »—

6
65 7

• -f—&-\-&—3-

-UJ 1-—? 1

-^7 4^

-*-^-^-||

t-t--yfa ig • — " •!• 1 • \

=*wi — w-H-ir*

-^1 — ^tt

Use of the Collateral Seventh-Chords in Minor.

The use of collateral Seventh-chords in minor is more limited. Many
of them for Chord-connections, as used in major, prove unsuited, or indefi-
nite and ambiguous ; others in their cadence-progression result in difficult
and unmelodious intervals in the parts.

One form of Seventh-chord, as given by the first degree, produces no
progression analogous to the above, since the following combination is
inconceivable.

123.

" r— ' "I Gel 3^J •-•— 1-«

MANUAL Of HARMONY.

Remark. — Although progressions can be formed with the above combination of intervals.
aa thus :

124.

yet it would be difficult to prove that this was a progression of the Seventh-ohord of th«
first degree in minor.

The resolution of the chord of the Second degree is to the dominant, and
is very frequently used :

JV—J&.

125.

: n° V

not:

not;

A progression of the Seventh-chord of the third degree is not impossible;

126.

it is. however, ambiguous, and might be met with in 0 major oftener than in
A minor. (See: Altered Chords.)

It may here be observed that the fifth in this chord, as an augmented
interval, will always ascend one degree.

The chords of the fourth and sixth degrees are uncommon, as the progrea-
iion of the parts in the resolution is awkward and unmelodious.

-g-

good;

127.

a: iv7 vn

MANUAL OF HARMON'S.

-6L.

=f=

& —

1 — =*—

— — *-ff

128.

The forced effect of most of the above progressions is undeniable, and
makes them of little use. —

The seventh degree in minor furnishes an important chord, which is gen-
erally known by the name of the

DIMINISHED SEVENTH-CHORD.

A resolution of this chord like that of all the others is impossible, as it
would lead to the triad of the third degree, which was found above to be
doubtful and ambiguous.

Instead of this, its progression, as with the Seventh-chord of the seventh
degree in major (see p. 68,) is based upon the natural movement of the
leading-tone, upon which this chord rests :

129.

'$ —

c: vn

As the root of this chord (leading-tone) moves a half degree, so also the
Seventh descends a half degree, while the Third and Fifth move with the
same regularity as with other seventh-chords ; but the progression of the
Third in many positions (130 a.) is to be carefully observed, because it
easily leads to a faulty progression :

not:

130.

whereas the position of the Third in b. and c. gives more freedom.

Remark. — The natural progression of this chord, as of the Seventh-chord of the seventh
degree in major, to the tonic triad, has induced the older harmonists to trace its foundation
to the harmony of the Dominant-Seventh. They considered a ninth (major or minor) to be
added to this chord and the root omitted, whence resulted both chords of the seventh
degree.

MANUAL OF HARMONY.

In referring to what is said later in Chap. 9th concerning the chord of the Ninth, w«
would state here as the ground of our views, that that assumption as regards Ninth-chords
is needless and far-fetched, and that the simplicity of the harmonic system for practical
purposes would be preferable to any complicated theory.

As to the use of the diminished Seventh-chord, the following also should
be observed:

The diminished Seventh, the smoothest of all, needs no preparation (see
p. 72.)

Exercises.

131.

These, and all former exercises in this chapter, whose object naturally was
only to learn the mechanical use of the chords explained hitherto, and test
the established rules and remarks, for this very reason are in their structure
somewhat stiff and unwieldy, since the great number of seventh-chords
could appear here only in the fundamental position, and because the intro-
duction of many of them from our present standpoint, which did not allow
us the choice of other means, was difficult and could not but seem forced.

The following may yet serve for their illustration :

The root of these Seventh-chords moves throughout a fourth or fifth as in
cadences, as may be seen from the Bass part, only in the third exercise of
122 and 131 there appears to be an exception. In the fourth measure of
the third exercise in 122 the Bass tone remains stationary, but the progres-
sion of the root is still contained in both chords according to rule: 07~.Z)7.
The sustaining of the Bass tone was possible here, because we have already
become acquainted with, and may therefore use, the modifications t of tht
Dominant- Seventh-chord. The case is the same in tfae fifth bar of the third

MANUAL OF HARMONY.

example of 131, where the progression of the root takes place A7-d with a
sustained Bass.

In the second exercise of 131 the Seventh-chord of the third degree in
minor is used, and it may be admitted that with this introduction it will not
seem unnatural and harsh.

CHAPTER VII

Inversions of the Collateral Seventh-Chords.

By the inversion of the collateral Seventh-chords are produced the same
derived chords, which have already appeared with the dominant-seventh,
namely: the Chord of the Sixth-and-Fifth, of the Sixth-Fourth-and- Third
and of the Second.

The varieties of Thirds, Fifths and Sevenths in the fundamental harmony
effect no alteration in the treatment of the inversions. For although the
major Seventh becomes by inversion a minor Second, the diminished an
augmented (see pp. 18, 19,) yet their progression follows in the same manner
described above.

132.

No new rules are needed for the progression of any of these Seventh-
chords. That of the Seventh degree alone in major and minor requires some
care, as has been already remarked, on account of the easily occurring open
fifths.

Something may here be added concerning their treatment.

Progression of the Seventh-chord of the Seventh degree in major.

133.

All these transpositions of the chord are available, though the last, the
chord of the Second, finds its degree with most difficulty, since the resohv

MANUAL OF HARMONY.

tion into the chord of the Sixth-and-Fourth could seldom take place, and at
best as a passing chord.

We must not be deceived by the compact form, in which these chords are
exhibited in 133, as to their utility ; as was mentioned above, it only depends
here upon the Seventh lying above or below the root, and positions of the
Chord of the Sixth-and-Fifth and of the Sixth-Fourth-and-Third like the
following :

134.

seem consequently more satisfactory, because the Seventh lies above the root.
The diminished Seventh-chord requires a method of progression like the
above, e. g.

135.

Here also the third inversion, the chord of the Second, will prove the
least practicable, as is shown by the unsatisfying resolution into the Sixth-
and-Fourth, a chord that always requires careful treatment, of which what
is necessary will be said hereafter.

. That consecutive fifths, which result from the resolution of the chord of
the Sixth-and-Fifth and of the Sixth-Fourth-and-Third hi this manner :

136.

are to be considered faulty, has been already mentioned (p. 76.) As to
consecutive fifths of this sort compare also p. 29, No. 16, 17 and 18.

With this very manageable chord the position of the root relatively to
the Seventh makes no such essential difference, as is the case with the chord
of the seventh degree in major ; the seventh may lie above or below the root,
the similarity of sound between the augmented second and the minor third
always adding softness to the chord, and causing the former to be felt as
«uch only in relation to the key.

MANUAL OF HARMONY.

Exercises.

e e

6 5

137.

3 ' 1 3

66 6

25 65 2 6 2 6 5

| I 1 ^J^^^-j* *^^**'

6 4

5 5 2673 66

6
6 5

7 7

66
326264265

7 7

67736

8. 3

6 7367

?— ijiTrl l~ra:=|:

7 6

36 7 it S

___

10-

5 6 73 2 6

6 4

MANUAL OF HARMONY.

CHAPTER

Seventh-Chords in connection with Chords of various De-
grees, other than those before Used. False Cadences.

THE familiar rule, that the Seventh must in the resolution descend one
degree, is indeed completely confirmed in the chord-connections previously
shown ; it has, however, as little positive authority as other matters, which
under different conditions and relations, in the great variety of chord-con-
nections, are subjected to necessary alterations and deviations.

With the movement of the Seventh, or its inversion, the Second, all
depends on the progression of the root. If this, as in all cases presented
thus far, is such that without the descent of the seventh no intelligible and
satisfactory result would follow, then that rule would possess full authority.

The progression of the root, however, may entirely annul this tendency
of the Seventh ; it may either remain stationary or even ascend, e. g.

138. i^gg^Ef^f---- ;

This leads us to the possibility of connecting Seventh-chords with chords
of other degrees than those hitherto employed. We may adduce here a few
familiar kinds of chord-connections with remarks, that in trying new forma-
tions of this sort we may be able to proceed on critical principles.

We begin with the Dominant-Seventh-chord.

It has been said before that the resolution of seventh-chords as shown
thus far is called cadence, and that of the Dominant-Seventh-chord, closing
cadence.

When any chord but the tonic triad, which forms the closing cadence,
follows the Dominant-Seventh-chord, the natural tendency towards the close V
*<» either delayed or else wholly removed. The anticipation of the natural
result experiences hereby a disappointment, hence these combinations are
called

FALSE CADENCES.

In general, therefore, false cadences arise, where the progression of the
Dominant-Seventh-chord leads, not to the tonic triad, but to different chords.

MANUAL OF HARMONY.

A few instances we shall now explain.

1. The connection of the Dominant- Seventh-chord with triads other than
that of the tonic, where the Seventh descends one degree.
a. Connection with the Sixth degree :

in Major: in Minor:

139.

C : V7 vi

This combination (false cadence) occurs very frequently.
The effect of this progression with the inversions of the Seventh-chord is
not as decided, and therefore more rare :

in Major:

6
56

4
3

in Minor;
6
5 6

140.

C: V7 vi

b. Connection with the third degree :

a: V7 VI

141.

better position.

Remark. — Trials with the inversions of the chord are omitted here and in the sequel;
they are easily made.

This progression is more decided when modulation is employed :

7 6 1. 6 76

142.

In minor also the connection with the triad of the third degree is possible,
only the latter as a dissonant chord (through the augmented fifth) requires
that something follow.

7 6

# -

143.

a: V HI' VI

i. Connection with triads with the Seventh sustained.

MANUAL OF HARMONY.
a, With tjie sicond degree :

not: useless in Minor.

144. 3t=*Z±4

— *?==zz=r

- —

C: V7 ii

b. With the fourth degree :

in Major.

-7S-
<K V7 11°

in Minor.

145.

The connection of the Dominant chord with Seventh-harmonies of
other degrees, than those we have used, is also possible. A few of them
here follow :

6th Degree: 3d Degree:

or;

Minor:

3d Deyret.

146.

-27- -zr
C: V, vi7

far

V7 aV7

a: V

7 1JLX7 V7 U. Y7 U. Viy

When we modulate into other keys, the possibility of new combination*
is greatly increased, e. g.

a. With descending Seventh :

not: better:

U7' S—

!: V7rf:V7

b. With sustained Seventh :

C: V7 b: vn°7 a: V7 F: V7 a: V7 G: vii0

143.

:V7Eb:V7 C:V7Bb:V7 a: V7 C:V7 a: V7 G : %~^

3. Connection of chords with the Seventh ascending.
This case may occur in the ordinary cadence (V7~I) as well as with othflt
progressions of the Seventh-chord, (e. g. H7- V.)
a. By exchanging the progression with various parts.

MANUAL OF HARMONY.

149.

The movement of a third in the Bass renders the descent of the Seventh
impossible, as the concealed octave caused thereby

150.

is entirely erroneous.

This progression of the root is not to be used in the other parts.

151.

All these instances are faulty.

b. By sustaining the fundamental tone:

not:

152.

g> «g-

C: I V7 I

The root (G) serves here as the so-called sustained part. (See later.
Organ point) But it must be remote from the Seventh, and the following
progression would be wrong :

153.

^^g—^-pp
I^^^^Btt

MANUAL OF HARMONY.
C. By a chiomatic change, and modulation :

C: V7 G: V7

V, e: vn°7 C: V7 F#: V7

d. By contrary motion of the Bass in modulating into other keys :

ja „ o-^dza .„. „. — ,g» «••• ^z.

C: V7 by. vn°7 a: V7 d: vn°7 C: V7 F: V7

(See above, No. 149.)

The foregoing table of chord-connections gives only an indication of
possible combinations. Its object was to call attention to the variety of
harmonic progression.

Of the value of these and similar combinations criticism can decide only
in special cases, since their proper use becomes possible only by considering
their introduction, their progression, their rhythmical importance, and, in britjf,
their whole situation.

The particular character of a piece, the part-movement expressly formed
with reference to the motive or idea employed, and similar causes, may lead
to such harmonic connections; but to use them adventurously, for the
production of new and strange formations, in general for the sake of
appearing original, might in few cases so succeed that the object would not
be perceptible :

Exercises.

150.

MANUAL OF HARMONY.

2 6 73

4 7

S 5

A 66

*• fc 6 5 5

6 5

6 6

7 7

open position. 3 667

6 5

6
47

-&-

46 6

33425

6 6

6 64

5 4366

-g>~ «g

6 6

5 5

Remark. — The open position in the 5th exercise has reference to a part-movement
cited on p. 84 ; it can afterwards be abandoned.

The Collateral Seventh-Harn\onies connected with Chords
of other Degrees or Keys.

A few chord-connections with collateral Sevenths may follow here. To
cite all cases of the kind would be both impossible and inexpedient.
a. With regular progression of the Seventh.

157.

n7 ev V7 C : in7 IV m7 F: V7 C:

not;

better:

a:n°7 in' VI iv, V iv7 V

b. With free progression of the Seventh.

&c.
G: V7a:vii°7d-vn°7

MANUAL OF HARMONY.

not:

158.

jj mg^ & ITf -g jrr- £7 IT" . n ^F-» /6 "]T — i ^? fT

C:n7G:V7 C:ii7c.*vn7 C:ii7 a:V7 C: n7 d: vn°7

Remark. — The reason why the last example is not good, lies in the so-called crow
relation, an explanation of which follows farther on.

C. With Seventh sustained.

159.

C: n7 IV n7

The last succession of chords is often used. It forms a delaying of the
cadence-progression of the second degree into the fifth by means of the
chord of the Sixth-and-Fourth of the tonic triad introduced between them.
The chord of the Sixth also of the same triad often occurs during the
resolution of this chord, as in example c.

The diminished Seventh chord is often used in like manner :

1 •

160.

g: vnw7 U:l V

Here also the natural progression is only delayed by the chord of the
Sixth-and-Fourth.

The mechanical combination of such successions of chords may be left to
individual practice and investigation. Their use will depend upon the
insight acquired into the relation and connection of chords, and therefore
not be so lightly estimated, as might first appear ; in general it will stand
about in the same relation to composition itself, as technical studies and
preliminary exercises to the practical execution and performance of musical
works. Both produce readiness and skill, cultivate the powers, and render
the productions of genius possible.

Only it may be further observed here, that for the criterion of such com-
bination the relation of the Seventh to the root and its progression will always
be found sufficient. If this is pure and the movements of the other parts
commit none of the heretofore mentioned errors, the chord connection will
be serviceable for particular cases.

161.

Exercises.

L j_.

6 6

65747

MANUAL OF HARMONY.

6 75 26

7 66

76 5 64 5

y ' ~*^ JPI — | — ———__— 4.

6 6
547776

747

6 6
547

765

-1=^:

5 4 7

7^ 6

J8-

7 6

* 4 6 67

72635 4ik

Remark. — Many of the cases above cited could not yet be included in these exercises,
because they are based upon modulation, which is hereafter more fully explained (The
iixth exercise affords opportunity for modulation.) So too, many of these examples by
the use of modulation would have been smoother and less stiff and strange.

CHAPTER IX.
Chords of the Ninth, Eleventh and Thirteenth.

Most treatises contain lengthy discussions upon these chord-formations.

e views, whi^h can be maintained concerning them, are various and
ill lead to equally practical results. It may be said

MANUAL OF HARMONY. $9

either, that these groups of intervals are to be considered and treated
like real chords, as e. g. the Seventh-chord :

or, that as unessential chord-formations they either belong to the suspen-
sions, or result incidentally from one part being sustained.

In the first case, the explanation of their use, especially through their
inversions, becomes very diffuse, and, since in four-part harmony one or
several of their tones or intervals are always omitted, obscure, because they
are then easily confounded with other chords.

In the second case their explanation is very much simplified.

Remark.— Chords of the Ninth, as well as the others above named, are but relics of the
old so-called Thorough Bass system, which readily adopted every combination of tones,
however casual it might be, as a special chord, and taught its treatment, without arrang-
ing the many incidental chord-phenomena under a definite system, and thereby rendered
the entire harmonic system difficult and prolix.

Without being able here to discuss farther the intrinsic theoretical grounds
for classifying such formations as incidental, the possibility of simplifying the
harmonic system without real practical disadvantage has determined us to
take the latter view. (More upon this point in the second section.)

But in order to obtain a clear perception of them, we shall show the for
mation of these incidental chords, and add some observations.

If a Ninth be added to the Dominant-Seventh-chord, a chord results
which is known by the name of the Dominant-Ninth-and-Seventh-chord.

In major we find the major Ninth, in minor the minor.

In pure part-writing tiffs chord, like that of the Dominant Seventh itself
in similar relations, is used with a preparation of the Ninth or of the
and cases like the following, where both tones enter without it,

-e-

are to be condemned for their stiffness and lack of connection.
This preparation can be made thus :

MANUAL OF HARMONY.

better:

164.

How far the first examples may be regarded as Suspensions, the last as
other incidental chord-formations, can only be discussed later in Section
Second.

Remark. — From the chord of the Ninth in major they derive the Seventh-chord of iht
teventh degree, which we fully discussed before, also the diminished Seventh-chord from the
Ninth-chord in minor, in order to be able to form their cadence-progression similarly
to other Seventh-chords, affirming that these chords are themselves Dominant-Seventh'
chords with the Ninth added and the root omitted, e. g.

165.

'C: V7

Hence arises in the first this difficulty, that we must accept two chords of the seventh
degree in major, one, whose natural cadence is the following :

166.

the other as derived from the Dominant-Seven th-chord; whereas it still remains the
simplest course to point to the character of the leading tone, upon which the above chords
are based.

Many musical treatises admit also collateral Ninth-arid- Seventh chords,
rendering the theory of many harmonic formations still more complicated
and equally needless, since none of these tones are to be used without
preparation, and hence in their entire treatment and consequences differ in
nothing from suspensions.

What holds good in practice, as well as in a simplified theory of Ninth-
chords, will be in greater measure true of the Eleventh-and-Thirteenth*
chords.

The singular form of these chords in full is as follows:

167.

MANUAL OF HARMONY.

In pure four-part writing they can of course never be employed, since
oy the necessary omission of many intervals they will appear simply as
suspensions, e. g.

168,

and even with more than four parts they will not differ hi the least in character
from suspensions, and in the freer style, where they appear without prepar-
ation, they may be regarded as appoggiaturas.

p-~ — =1

£^

1 — HI;

CHAPTER X.

Chromatic Alteration of the Principal Harmonies. Altered

Chords.

The chromatic alteration of one or more intervals of the principal harmo-
nies has a double effect :

either : it results in a modulation,

or : it gives the chord a new form hitherto not used.

Let for example the major triad be changed as follows, and there result

a. Modulations :

169.

Through c$ the diminished triad of the seventh degree in D major or D
minor, or of the second degree in B minor,

Through efr the C minor-triad,

Through e\) and g\> the diminished triad of the seventh degree in Dfr
major and minor, or of the second degree in Bb minor.

The last two alterations are mere transpositions of the same triad into
other keys, namely Cb major and C# major.

b. New forms.

a. b. c. d. e. f.

170. <^i=&-

Of these the forms a, b, J,/can indeed incidentally occur by means of
collateral (passing) tones, but they have no harmonic value.

MANUAL OF HARMONY.

Not so with the forms c and e, which have harmonic (chord-like) meaning.

The first form of the triad (c) is known as

THE AUGMENTED TRIAD.

This chord we have already found on the third degree in minor (see p.
43,) yet, as has been mentioned, it seldom appears in this position, but
oftener as the triad of the first, fourth and fifth degree in major with the
fifth raised chromatically.

It is easy to explain as resulting from the passing note (ff$) to the follow-
ing note (a), as also its progression is fixed through this tone (##) as an
augmented interval.

171.

The inversions (transpositions) also of this chord are available :

6 6

172.

IV vii

Though these chords generally appear as passing chords or with prepar-
ation of the augmented fifth, yet they may enter free in a sudden change of
harmonies :

flin

*=E

:4=t
173.

Not only may the Dominant- Seventh, which happens the most frequently,
be added to the augmented triad, but also the major Seventh of the first and
fourth degree.

a. The augmented triad in connection with the Dominant- Seventh.

174.

MANUAL OF HARMONY.
JD, In connection with the Seventh of the first degree.

C. The addition of the Seventh to the augmented triad of the fourth degrte
thould be very rare :

176.

In all these combinations so far the cadence-progression of the Bass (e. g.
V-I I-IV &c.) has been employed ; but a few examples may show that the
chords here treated may be used with chords of other degrees and a different
Bass-progression.

177.

or:

These harmonic connections, sometimes strange and harsh in sound,
acquire significance only through the position which they assume, and par-
ticularly when to a certain degree they are brought about by an inward
necessity.

If it is the duty of a manual to point out the possibility of such harmonic

MANUAL OF HARMONY.

formations, its duty is likewise to warn the beginner against overrating the
value of such attractions, and in general to advise him, not to occupy himself
purposely with such uncommon harmonic expedients, before he is wholly
conversant with the treatment of the simplest harmonies, of simple pure
part-writing. Too early employment of them and a wilful searching for
peculiar effects obstructs a clear view and insight into simple harmonic
principles, even renders it impossible, and diverts the mind from essential to
secondary matters.

Exercises.

178.

Remark. — In the fourth exercise the augmented fifth was used even with the minor
triad of the second degree (at NB.,) which in this connection does not sound unnaturally.
This would correspond with the form/ above in example 170. Hence it is seen, that with
a natural movement of parts many new chord-formations may be obtained.

iz (which is also treated

From the form e of example 170 : iaxi

T72-

under the name : double diminished triad) there arises a harmony which is
much used, namely :

THE CHORD OF THE AUGMENTED SIXTH.
The first inversion of the above chord gives ;

179.

From its progression, which is determined by the augmented Sixth ,

the original chord here belongs to G minor, whose fourth degree, C minor,
through the raising of the root inclines to the fifth degree.

MANUAL OF HARMONY.

Wherever this chord appears with its natural progression, as shown above
in 179, the last chord proves itself to be the Dominant. This is verified by
certain harmonies formed like the chord of the augmented Sixth, the chords
of the augmented Sixth-Fourth-and- Third and of the augmented Sixth-and-
Fifth, whose construction is explained farther on.

Remark. — The affinity of the augmented Sixth-chord with those just mentioned, has
its origin in the source of the former.

The chord of the augmented Sixth has this peculiarity, that only its Third
(the Fifth of the original chord) can be doubled in four-part harmony :

180.

Of the other positions of the original chord (the so-called double dimin-
ished triad,) the jfirst (fundamental) may be used in three parts, though very
rarely ; the third (second inversion) also in four parts, but only in widely
dispersed harmony.

tetter:

181.

Remark. — The chromatic alteration of an interval of the minor triad is already included
in the formations in Nos. 169 and 170, and therefore needs no further investigation. Sc
the chromatic alteration of an interval of the diminished triad will result either in major
or minor triads, or formations, which are to be found in the examples above cited.

Thus the form of the triad in No. 1 70 d. will be like the following as found in C major :

better in open position

182. 3E:

C; vn°

In many books this chord is called : major-diminished triad.

Chords of this sort, if they may be called such, usually appear only incidentally in
})assing, and their progression follows relatively to their intervals, i. e. augmented interval*
ascend, diminished intervals descend, one degree.

The chromatic alteration of an interval of the Seventh-chord was partially

MANUAL OF HARMONY.

noticed above, where to the triad chromatically altered the Seventh also was
added (p. 92.) This was in the case of the augmented triad :

Among the other collateral Seventh-chords, the chromatic alteration of one
of them receives a special importance. It is the Seventh-chord of the second
degree in minor, which hi the following form produces chords that are often

The chromatic elevation of its Third

183.

a,:

gives the following inversions :

184.

Of these inversions the second is the most important, and is much used,
the others are rare.

The chord resulting from the second transposition is known as

THE CHOKD OF THE AUGMENTED SIXTH-FOURTH-AND-THIRD.

Its progression is based upon that of the original chord, i. e. as the seventh-
chord of the second degree leads directly to the dominant, so also here it
will be the case.

185.

a: ii °7

If the root be omitted hi this chord, we have the augmented Sixth-chord
already found above, whose progression to the dominant finds here its expla-
nation (see p. 94) :

omitting the root;

186.

or as compared with 179 in G minor:

chrom. elevation chord of augm. chord of augm.
mdam. chord: of the third: Sixth-Fourth <k Third: Sixth:

187.1

g: ix°7

MANUAL OF HARMONY. 9"

Remark. — It may here be further observed, that the formation of the chord of the aug'
mented Sixth-Fourth-and-Third can be reached also through the major-diminished triad
mentioned on page 95, by the addition of the Seventh: only that the resolution must ba
different, since that was taken on the seventh degree, while this is found on the second.

Instead of the root, the Ninth of the original chord may also be added,
whence arises the

CHOltD OF THE AUGMENTED SIXTH-AND-FIFTH.
Its foundation is the following :

Inveriiont:

root omitted a. & b. £ * v£

original chord: with ninth: & third raised: 5 3

188.

Of these chords, that which results from the first transposition a., the
augmented Sixth-and-Fifth chord, is the most available : the others are rare.

Its natural progression is likewewise to the dominant, but always produces
parallel Fifths.

189.

This progression of fifths, not classed among the most offensive, is avoided
either by a previous resolution of the fifth (the original, above-mentioned
ninth as a suspension,) as in the following example (a), or by a movement
of the same to the third, whence arises the augmented Sixth-chord (ft), or
most frequently by sustaining the third and fifth while the Sixth and Bass-
tone move, whereby the chord of the Sixth-and-Fourth is inserted before
the resolution (<?), and can be regarded here as a prolongation of the
suspension.

190.

Remark. — The addition of the ninth does not entitle this harmony to be pronounced a
Ninth-chord; the ninth has here the same character as a suspension as elsewhere, as is
clearly apparent from the progression a. ; the progression in 6. and c. also corresponds

MANUAL OF HARMONY.

precisely to the treatment of suspensions, so far as (like the fifth in the above chord) they
require preparation.

It would follow from this, that this harmony should have been first spoken of together
with suspensions themselves; yet mention of it had to be made here, because we are
treating of construction, and should not with the above-mentioned views ignore a univer-
sal method of naming this harmony.

191.

^ -i-_^ (yf L

In closing this chapter, we survey once more the wide field which it opens
for harmonic formations. We have discovered much that is universally
known and useful, much has appeared to us unavailable and worthless ; yet
nothing was manifested in its primitive state ; everything was trimmed and
subjected to change, to a certain degree, embellishment. This abandonment
of original form induces us to call attention again to what was said on p. 93.

It was indeed a long time before these harmonic transformations were
discovered, and still longer ere they were turned to general use ; and much,
that has hitherto proved useless, may still in time be brought to perfection ;
only it is not advisable, from a desire for originality, to direct all effort to the
invention of new harmonic forms, or to an exaggerated use of them and a
departure from original principles, lest the sound inner kernel be lost.

Since all these formations serve rather for the decoration and, we might
say, the more elegant carrying out of simple harmonic principles, one must
only use them with discrimination, or his work will be overladen and him-
self consequently roputed as void of taste.

MANUAL OF HARMONY. 99

In closing this representation of all the essential harmonies and their
immediate use, we annex further a brief view of the same, theii kinds and
derivations.

View of all the Chords belonging to a Major or Minor Key.

I. FUNDAMENTAL HARMONIES.
a. The triad. 6. The Seventh-chord.

A. Kinds of triad:
Mayor, minor, diminished, augmented.

Major triads
of the major scale: of the minor scale:

0: I IV V a; V VI

Minor Triads
of the major scale: of the minor scale:

C: II in VI ^ a: i iv

Diminished triads
*fffhe majorjscale: ^of the minor scale;

p=^-fe

O: vn° a: n° vn°

Augmented triad of the minor scale .

a: III
The other augmented triads see under II : Altered Chords.

Inversions (transpositions) of the triad,
a. Chord of the Sixth. 6. Chord of the Sixth-and-Fourtk.

^= -6—*—^—

100 MANUAL OF HARMONY.

B. Kindt of Seventh-chord :
a. Dominant-Seventh — or Principal Seventh-chord.
6. Collateral Seventh-chords.

a. Dominant Seventh-chord (major triad with minor seventh) :
in major and minor formed alike:

+* 0 : V? c: V? a;

b. Collateral Seventh-chords :

1. Major triad with major seventh

in major: in minor;

> g g — rp g

_gz «?

0: IjT' TV? a: VI^

2. Minor triad with minor seventh

in major: in minor:

'0: 67 ni7 V17 o; IV?

S. Diminished triad with minor seventh

in major: in minor:

* C: vn°, ' a.- n°7

4. Diminished triad with diminished seventh ^diminished
Seventh-chord)

in minor:

a: vii0 7
d. Augmented triad with major seventh

in minor:

MANUAL OF HARMONY.
Inversions (transpositions) of the teventli-chords :

a. Chord of the b. Chord of the Sixth- c. Chord of the
Sixth-and-Fifth; Fourth-and-Third; Second:

101

HI. CHROMATICALLY ALTERED CHORDS.
a. Tfie augmented triad formed from the major triad :

jn 7 * 7 7 _

C : I IV V

b. Chord of the augmented Sixth, formed :

1. from the minor triad with the root raised (so called double diminished
triad):

2. from the Seventh-chord of the second degree in minor (see the follow-
ing chords.)

C. Chord of the augmented Sixth- Four th-and- Tliird ;

d. CJwrd of the augmented Sixth-and-Fifth, — both formed from the
Seventh-chord of the second degree in minor :

With the ninth from

Raising of Second Root omitted the root and without

the third: Inversion: Clwrd of augm. Sixth: the latter:

102

MANUAL OF HARMONY.

CHAPTER XI
On Modulation.

THE term modulation has a varied meaning. Formerly it signified the
method of arranging the succession of harmonies to a given melody. In
the modern sense we understand by it the transition from one key into
another. The expression : transitional modulation, which is sometimes found,
would according to the original meaning of the word be no pleonasm.

The meaning of the term being fixed, it next becomes important to learn
to recognize and define every occurring modulation (transition into a foreign
key :) later, in the sixteenth chapter, we shall treat of the means of modula-
tion, whereby the capacity to recognize it will be made more complete.

A modulation takes place then, when a harmony appears, which is FOREIGN
to the previous key.

The former key is then wholly abandoned, and the harmonies must be
reckoned as belonging to the new key, until a harmony foreign to it appears,
which effects a new modulation.

Thus in the following example

192.

a modulation into D minor will ensue in the third measure, because c%~e-g~
bfc belongs no longer to O major, but unmistakeably to D minor, whereas in
the fourth measure it is doubtful, whether the triad of C, which is foreign to
the previous key (D minor,) belongs to O major or to the G major which
follows, whilst the modulation into A minor in the fifth measure is obvious.

The Dominant-Seventh — as well as the diminished Seventh-chord must
e?er be recognized as the chief means of modulation ; all other chords are
ambiguous, i. e. they may belong to several keys.

MANUAL OF HARMONY.

103

Thus the G-major triad belongs not merely to G major, but is also the
Dominant of C major and C minor, the Subdominant of D majoi, and the
sixth degree of B minor.

From this ambiguity it often happens that the modulation can only be
recognized from the chords that follow, as in general the decisive modulation
itself can only be formed with the Dominant-Seventh harmony and it*
derivatives.

A musical ear can of itself very easily catch at a modulation : it always
conceives of the foreign harmony as belonging to that key which is nearest
allied to the prevailing one.

Thus, for example, the major triad of D in

193.

viewed independently, would belong to the key of D major ; but in connec-
tion with G major it will at once be recognized as the Dominant of G major,
and the following chords only can determine what key is to predominate.

A few examples are annexed here for practice in investigating modulation ;
for further discussion of this subject see chapter sixteenth.

Exercises.

194.

0 : I G : V7 I C: IV V7 Id: vn° 7 I C: I 117 V I

65.26 45 26

II *• 6 6, • # 6^ 7h - 5 J

6 J8-

2 6

6-
4 —

104

MANUAL OF HARMONY.

# •

4 7

6 6
5 5

4 7 326

667

1K-

The indication of the modulation can proceed in the manner given in the
first exercise, by which the letters denote the key, and the Roman numerals,
as usual, the degrees upon which the respective chords are based.

MANUAL OF HARMONY.

105

SECTION II.

INCIDENTAL CHORD-FORMATIONS. TONES FOREIGN TO THE

HARMONY.

CHAPTER XII.

Suspensions.

THE simultaneous progression of each part to the following chord, especi-
ally when, as in our previous examples, it proceeds without any metrical
variety of movement, produces a certain formality and monotony in musical
phrases.

A new mode of linking and intertwining chords, and hence an inter-
esting variety of harmonic connection results when the parts do not progress
simultaneously throughout ; when one or more of them remain in their
place, while others are already forming the materials of the next harmony.

The best and most important method « of linking chords thus together
takes place through the

SUSPENSION.

It is effected by the delay of the movement of a part, which is expected
at a fixed time or even necessary, and that too hi such a manner, that that
voice which has to descend one degree hi order to take its place in the fol-
lowing chord, shall still linger upon the tone of the first chord, while the
others move to the second, and the former shall not pass to the harmonic
tone until later.

In the following harmonic combination

105.

106

MANUAL OF HARMONY.

the Soprano during the entrance of the second chord can remain upon c and
afterwards pass to b, as follows :

196.

So by delaying the Tenor in example 195 a suspension can be formed

197.

G? G? 35

The characteristic feature of suspensions is, that they/orm a dissonance
with the harmony with which they appear, and that they thereby effect the
harmonic connection, while through the expected resolution of the dissonance
they render closer the necessary relations between two chords. In this
respect they bear a resemblance to Sevenths, since like these as combining
intervals they are subject to preparation as well as resolution.

To be sure, the dissonance in a suspension does not always consist in an
interval's forming a dissonance with some one part : cases may occur, where
the suspension as interval forms a dissonance with none of the other parts,
but only through situation, position and progression the character of the
suspension predominates, as in example 397, where the tone of the suspen-
sion forms a Sixth-chord, and where only the unusual appearance, as well as
the whole position of the triad of the third degree, together with the pro-
gression of the Tenor, produces the character of a suspension.

The above examples furnish the necessary rules for the formation of
suspensions :

A suspension can be formed where a part descends one degree, under the
following conditions : it must

1. be prepared and.

2. be resolved.

Thus three points will have to be considered in a suspension : its prepara
lion, the suspension itself and its position, and its resolution (progression.)

MANUAL OF HARMONY.

107

a. The preparation.

The preparation of a suspension cap happen through either interval of a
triad. Also Sevenths are used for preparation, though less often; the
Dominant- Seventh the most frequently.

Preparation
through octave of the root :

198.

through the Third

-^^J-j-

5 -

7 6

-&-

C: I

I a:vn°7 I

II VI

through the Fifth:

I^Ez-iEi

9 8

9 8.

E=S=j^=

C: I G: V

vi C:I IV

I c:vn°7 i

through the Dominant Seventh:

C: V7 I

The preparation must be upon the arsis, the suspension upon the test's.
Also the rule mentioned above (p. 71) holds good, that the preparation may
be of equal or longer duration than the suspension, but not shorter.

t). The Suspension :

The entrance of the suspension on the Thesis has just been spoken of, its
Further position shall be explained more particularly.

The suspension can appear in either voice "before an interval of the triad,—
before Sevenths only in rare cases.

108

MANUAL OF HARMON*.

Suspension* before the Octave of the root :

190.

C: IV 1

before the Fifth seldom, only in certain positions :

1 4-

-,51—1 ,5. — nL-^^u-I LE

As to suspensions of the fifth, attention may be called to remarks under
example 197. Thus the first and third example will be wholly in the char-
acter of a suspension. When there is a Seventh in the chord, as in the
second example, then the dissonant character of the suspension comes out
at once.

That the Seventh can only seldom have a suspension follows from this,
that in most cases the latter must be formed by the perfect octave, which of
itself is only a doubled interval, but can never be in a dissonant position
(a,), unless as hi the following example b. the octave be diminished.

200.

MANUAL OF HARMONY.

109

In the first case the seventh will be always a passing one.
c. The resolution.

The resolution of the suspension, as was said before, takes place by the
descent of the same part one degree.

Remark. — Irregular kinds of resolution will be exhibited later.

It is here further to be observed :

The resolution-tone (that which is delayed by a suspension) must be con-
tained in no other part; only the Bass or lowest part can take it without
injuring the harmony.

C. not:

d. NB.

201.

In example a. the Tenor moves from a to c, which last is suspended in the
Soprano by d ; in example c. the Tenor takes g, which has the suspension a
in the Alto. Both these cases of doubling are incorrect, especially because
they are concerned with the third and fifth of the chord. In the example
d. at NB. it is the root that is doubled. The effect in this case is better,
particularly when consistency hi the movement of parts requires it, as in the
following phrase.

Soot:

Third:

Fifth:

202.

Remark. — It may be further observed here, that the doubling of the root always pre
supposes a distance of one Octave at least, and that to double in the unison is incorrect,
e.g.

only between Bass and Tenor or in the part lying next to the lowest the suspension may
appear even in such close proximity.

The lowest part, usually the Bass, has however, as that which determine!
the chord, a counteracting influence against the dissonance of the suspension*

110

MANUAL OF HALMONf.

incorrect:

so that doubling is admissible, if it be founded on a good movement of
parts, e. g.

_J^-L^=^

203.

The incorrect progression of the Soprano and Bass in the last example
becomes clear, if we remove the suspension, as a mere delaying of the
nnvernent, by which open octaves result.

204.

The same is the case with progressions by fifths, which are covered bj the
suspension :

205.

Here, however, the same considerations will govern, as are usually taken
into account in cases of concealed fifths, since position, situation, and progres-
sion will admit of such a part-movement, without the disagreeable effect of
fifths being prominent.

We briefly condense these observations in the following rule :
Suspension does not remove parallel octaves and fifths. The following
progression, therefore, will be erroneous :

206.

parallel fifths of this kind, however, are not to be rejected unconditionally,
provided the unpleasant succession be counterbalanced by the movement of
the other parts, so as not to be too conspicuous. It is impossible to give
positive directions on this point; to reject them invariably would be too
restrictive.

MANUAL OF HARMONY.

Ill

Suspensiors in the Bass, which generally occur before the third of the
chord (or, which is the same thing, before the chords of the Sixth or of the
Sixth-and-Fifth,) admit of no doubling in She other parts.

not:

207

Suspensions before the root and the fifth in the Bass seldom prove of use

not:

208.

The figuring of suspensions in Thorough Bass writing is partially con-
tained in the above examples.

If the suspension lie in one pf the three upper parts, the interval reckoned
from the Bass is given together with the resolution, e. g. ^ T 8 7 6 • ^e
other figures determine the chord where it is necessary, e. g. the chord of
the Sixth |£j the chord of the Sixth-and-Fourth \~^ or \^

If the suspension be in the under part, the incidental intervals of the

other parts are also indicated by figures, e. g. g Z!> or w^n the seventh-chord

5 —

4 — the lines that follow denote that the parts retain their tones while the

suspension is being resolved.

A suspension in the Bass is also denoted by a cross-stroke over it, and the
proper chord placed over the resolution-tone, which in respect to the latter
is more distinct, e. g.

209.

In the following exercises the former method is adopted, as most in use.

112

MANUAL OF HARMO.VY.

Exercises.

5- « 7857

43 76 5 5- 43

-. ^ ~«g- _

36 91

210.

ftS^fei

C: I V IV V7 I xi7 V7 I

f 6 - 9 8 7

3. 5 - 6

32-76 75

L JL« *

6- 7-
54 43

5 —

8 26 62 5

6 98 3-

5 —
4 3

7 J8*
4 - «

3-4

27 765 987

6 5
6 44

786 5-

'• ^ 43

5 - '#

- 6

'• <* *» i 6 JB 3h 6 2 I 4 3-

ft 6 66

5 °* 3 6 987SR9 t ' « I S ••

4 5 3_7

s — (51

76 4_ 5_ 6

5~ 76-326 434 765

^ In working out these and the following exercises it will be expedient to
divide the parts and writ© each upon a separate staff. This mode of writing

jfANUAL OF HARMONY.

113

in scoi<5 afrbrds a better view of the movement of each individual part,
beside being generally a useful exercise preparatory to reading from score.

It is, however, necessary here to write the parts, which in pure part
writing are always considered as vocal, hi the clefs which have always been
assigned to them, a knowledge of which is indispensable to every musician.
Familiarity with these clefs may soon be acquired by attentive practice and
comparison with those already known.

Remark. — A knowledge of the Alto and Tenor clefs is essentially necessary for under-
standing and reading scored, as many vocal and instrumental parts are written solely o!
partially in these clefs, and even the knowledge of the Soprano clef, which more rarely
occurs, greatly facilitates reading in the case of various instruments, which have a partic-
ular pitch.

The clef used for the three upper parts, Soprano, Alto and Tenor, is
called the G-clef.

For the lowest vocal part, Bass, the F-clef or Bass-clef, which has been
employed hitherto, still holds good.

The position of the C-clef always indicates c of the third octave, and for
the Soprano this c is placed on the lowest line, for the Alto on the third, and
for the Tenor on the fourth, e. g.

Soprano,

Alto,

Tenor-clef.
or~:

The ordinary compass of the voices in these clefs stands thus :

Tenor-fief.

114

MANUAL OF HARMONY.

Remark. — It is interesting to trace the origin of these differem clefs frun a very temple
basis, the so called Tablature (a staff of usually ten lines, on which the parts were all
written with especial indication of those lines, upon which the three principal, tones F C G
were to stand,) but a further explanation would carry us here too far.

The easiest method of fixing these clefs in the mind might be, to observe
carefully the position of the (7-triad in the different voices, by which the
intermediate and adjacent tones are easily found.

Thus the position of the (7-triad in full, with the root doubled, will be :

In the Soprano:
In the Alto:

In the Tenor, best in the position itemftj
of the chord of the nxth-and-fourth: 5^ZJL

We annex here the first exercise of 210, written out in these clefs:

•

TENOB

BASS.

To work out these examples with all due observance of the rules thus far
given, requires an easy, somewhat free movement of the part in respect of
position, since the necessity of a better distribution of the suspensions often
demands a change in that distribution of the parts, which we have hitherto
always endeavored to keep as uniform as possible.

Thus it will be clear when to use the open position of parts, which must
again be exchanged for the close position, whenever necessity and expediency
require it.

MANUAL OF HARMONY.

113

In thus shifting the positions of the mrts, these rules must be observed :
The parts, in passing from one to another (differing) chord, must never

move either by steps or skips, out of their proper place SIMULTANEOUSLY ;

only in single cases, where ONE and the SAME chord is transferred to another

position.

Either part may leave its position, when one or more are sustained upon one
tone.

The 8th exercise of 210, worked out as follows, will make this clearer.

BASS,

a _ c — 7 a"7 d *7 Bb Eb Bb U7 F 7
,. j — iv— 7 ii°7Bb:inV7 I IV I F:V7IBb:V7

r—-X= --—r---^

i "T I JULC I ~"

B. g c F7 Bb c g e Eb a°7 D 7 g

g: D7 i ir Bb: V7 I n 0.- i ir VIn°7V 7 I

Let the following serve to explain this :

The close position, in which this example begins, is in the fifth measure
abandoned for the open ; this in turn continues till the close appears again
in the eleventh measure.

116

MANUAL OF HARMONY.

This was effected by a freer movement of the Soprano and Tenor.^ The
former in the fifth measure moves away from its position to the Seventh
E\) (at NB.) a skip which may take place if the root is already there and
remains fixed (as F here in the Bass ;) BO in the seventh measure it leaves
its position by skipping to the fifth g, the rest of the chord being sustained,
by which the suspension falls into a better place. Finally the close position
is again reached by a free and better movement of the Tenor in the tenth
measure.

Suspensions from below.

Suspensions from below are to be regarded as such only in a few single
cases ; most progressions of this sort have originated in the suspension from
above hitherto treated, by a contraction (shortening) of the same, followed
by an upward movement, e. g.

213. 3fc= «!zt±

The suspension from below may take place in the progression of the
leading tone :

214.

and with many intervals, which ascend a half degree, especially with those
altered chords, that contain augmented intervals by elevation, Q. g. :

215.

It should be observed here that, as formerly, the resolving (harmonic)
tone can stand in no other part but the Bass.

Remark. — The last of the above examples gives us tte same combination of tones,
which resulted above (p. 64) as the seventh-chord of the first degree in minor, and which
wag pronounced useless as a fundamental harmony (seep. 74). That, used as above, it it
•imply to be regarded as a suspension of the leading tone, needs no farther explanation.

MANUAL OF HARMONY.
Other suspensions, especially those that ascend a whole degree,

117

in some cases evince of themselves what is unnatural in their progression ;
in others are pronounced by theory as not genuine or available in pure
part-writing, however often they may find their place in practice. Should
these improper suspensions be carried out in the manner above shown (213),
incorrect progressions would appear as their base :

Suspensions in several Parts.
Suspensions may occur in several parts at once :

Suspensions
in two voices :

in three voices :

218.

Also the chord of the Sixth-and-Fourth often appears as a double suspen-
sion, e. g. :

219.

Freer movement of Parts in Resolving Suspensions.

In our previous examples the preparation, entrance and resolution of the
suspension took place through two chords, since the parts not concerned
remained stationary during the resolution. The same may also take place
with three chords, by which the change of chord and the part-movement
become yet richer and more varied.

This happens when, during the resolution of the suspension, one of the
parts, gene -ally the Bass, or several at once, move and form thereby a
harmony.

8 MANUAL OF HARMONY

For instance by progression of the Bass :

820.

596 6 9 7 4 ,, 7

: V7 I — n7 V I I IVn7 Ia;vn°7 I

By progression of several parts :

221.

C : I

In all these examples the resolution of the suspension follows regularly
during the progression of the other parts to a new harmony, of which the
resolution-tone forms a part.

Remark. — By way of illustration of the view expressed in chapter ninth concerning
chords of the Ninth, it may be remarked here, that many passages, in which the Ninth
occurs, and which are recognized by many as Ninth-chords, may be explained in the above
manner, as in example 221 b., where the cadence-progression of the roots F-b is easily and
far more simply represented as a progression of a suspended Ninth by the use of three chords,
and leads to the same result, as is likewise seen in all the following examples :

Ninth suspension

with two chords : with three chorda :

222.

Concerning the unprepared Ninth we shall speak later tinder Organ point.

As supplement to what was said in chapter ninth it may be further added, that as an
trgument against independent ninth-chords may be reckoned also the impossibility of
transposing them together with the. root in such a way that the latter shall be brought into
Immediate proximity to the Ninth, as may always be done in the case of seventh-chord*

223.

MANUAL OF HARMONY.
9

iSL

119

9 &-

So four chords may be used with a suspension, provided it stands before a
harmonic tone, which is not contained in the other parts, e. g.

1 234

without tuspenaion:
1 234

224.

^^=30=5

~0-

5 6
4

-&-^~*^-&- -&- -&-

-i^sz.

Exercises.

3- 56

796 4474. .7 6

r . JQ. U r._. -_, U_ ^ /P

6 7 7

a25.

6 766 5

822 6-4 5-5 4

6 747

V M * V V «/ V* ^y W V | X |

36 97 47- 94-

6 6

4 4

2 3

966
6 7 5 47

4 2 6?b 96—4 6—6 7

5 £

2 6 76—46 —

R 46 66-

* 824 4 5

120

MANUAL OF HARMONY.

1- 5 •

t 0 f 43 9 7 36 7 4 6 3 74 7

8 5

5 47

3 25 _6—43

7 6 7-

7 9 6

Between a suspension and its resolution other tones may be inserted in the
same part.

These may be :

1. Tones belonging to the chord, e. g.

tr-z^ J%_ _^_ _^r- 1~3£: 3I^a=5 tc

2. Tones foreign to the harmony, appoggiaturas, e. g.

227.

-£2_T_

5r-^— «

A more complete explanation of these and similar passages will be given
farther on under the description of passing-notes and appoggiaturas.
Passages also occur, where the suspension has no resolution at all, e. g.

usually thus;

228.

They have resulted by elision from the following phr

ases

MANUAL OF HARMONY.

121

or:

-&-

JT7. — |F= f—
yEg=#=?=fe

Anticipation.

The anticipation of a tone, which is of less frequent use than the suspeu
sion, is the reverse of this, and consists in one or more parts allowing tones
of the chord next succeeding to be heard sooner than others, and before the
metrical structure would lead them to be expected.

Where notes are of long duration, and in slow movements, this method of
progression seldom or never occurs, since the harshness of the dissonances
that appear would amount to unintelligibility ; it is generally only in shorter
divisions of the measure that anticipation takes place, e. g.

Anticipation
in the Bass:

in the Soprano:

in several parts:

23O.

The resemblance of this part-movement in its metrical form to that known
in the general musical system as syncopation, is unmistakeable, only that the
latter is formed or acquires rhythmical value, not by the anticipation of chords,
but rather by their after striking.

Here also the movement of the parts may under circumstances be freer,
e. g. another harmonic tone may be anticipated beside that which was
intended for the entrance of the chord, as in the familiar closing phrase :

231.

As the reverse of anticipation may further be mentioned the afterstriking
of harmonic tones, which so far resembles suspensions, that here also prepara-
tion and resolution take place, but differs again essentially, since its character

122

MANUAL OF HARMONY.

impresses itself more upon the metrical and rhythmical movement, conse*
quently it always appears also in a longer series, whereas suspensions,
whether singly or in greater numbers, appear under totally different condi-

tions.

A series of such delayed tones would be the following in the Bass :
Allegro.

JL ^ ^ ^ J. «

Under this head also would be classed the unison passage in Beethoven's
Overture to Leonora (No. 3) :

833.

. i , T i i i- — •,. i — \ — -\

hsJ^^JsdaHFr^CT^

MANUAL OF HARMONY. 123

CHAPTER XIII.

Organ-point. Sustained parts.

A PECULIAR variety of harmonies and mingling of the same is produced
by sustaining one, and even more parts, upon one tone, and by the chords
thus incidentally formed.

We often find, especially in the Bass, as well at the beginning of a piece
as in the middle and at the close, where a cadence should appea*, a long-
continued tone, while the other parts, apparently without any relation to it,
continue their harmonic movement.

When this tone lies in the Bass, it is called

ORGAN-POINT;
when such long-continued tones occur in the other parts, we call them :

SUSTAINED PARTS OB SUSTAINED TONES.
Remark. — Many give to these last also the name Orgar-point, but not rightly.

The tones adapted for sustaining are the Tonic or Dominant ; both at one*
also occur.

Remark. — Attempts, which in later times have been made with the third of the triad by
many composers, sound unnatural and forced.

The harmonic connection as also the progression of the remaining parts
during the organ-point still takes place according to the established rules,
the lowest of them acting as guide to the harmony, and in general without
regard to the sustained tone.

A few examples follow first, before discussing in detail the mode of treat*
ing organ-point.

a. Organ-point on the Tonic :

I I J I * .

J -«- J 1

234. fl I i f rir r

=3^=

124

MANUAL OF HARMON*

6. oil the Dominant :

* 1

_z3_;-.^-|-a&< —

=g=iz±?r±=t=iiiii-

gB-i —

CZH

— —

_£L

c. or:

d. on both at once:

*. *.

In these examples the chords to which the Bass-tone does not belong
harmonically, are marked with a cross.

The following remarks may serve for the treatment of organ-point :

1. The entrance of the organ-point must be at a time rhythmically marked,

2. By a chord, to which the Bass-tone harmonically belongs,

3. The last chord of the organ-point must also harmonize with the same.
The first takes place at the beginning or end of a period or section thereof

and upon the accent ; the second and third usually through the root of a
triad, as in example 234 a. c. </., or as in b. through the chord of the Sixth-
and-Fourth.

It is further to be observed, that the chords foreign to the Bass-tone
should not follow one another too frequently, but often alternate with chords
to which the organ-point belongs harmonically. This is necessary in order
to avoid digressions, which would destroy the character of the organ-point,
which lies in the close union of different chord-connections.

MANUAL OF HARMONY.
Thus the following organ-point would be faulty in this respect :

125

235,

i •*

The part lying next to the Bass, in four-part composition the Tenor,
becomes in the case of organ-point the foundation of the harmonic move-
ment. Hence all the necessary progressions will depend upon this voice,
even though the organ-point might accidentally belong to the harmony.
Thus in example 234 a. the progression of the Bfr in the Alto (in the first
measure) is determined by the movement of the other parts, and not by the
fact that it is the Seventh of the Bass.

If the organ-point be upon the Dominant, as is often the case at the close,
there can be no plagal cadence formed upon it, as follows from the third of
the rules above cited, e. g.

KB.

236.

»JL>.

The plagal cadence may however be used, if the organ-point be upon the
Tonic :

237.

The end of the organ-point is to be heeded with full as much care as tho
entrance. In the above examples this always takes place with a cadence.
In this case there is no difficulty, except in passages like that in No. 236.
The organ-point, however, may pass sooner into the harmonic movement,
and then the third rule must be carefully observed, e. g.

126

238.

MANUAL OF HARMONY.

To break off in this manner would not be good :

4 uJ-rJ-iJ-.L ^-Jt

239.

vj J_htfiiig~ — atziijr=jiz=a=zmi=TF

J-* — x — U* — £ — tt

Sustained Parts.

Sustained upper and middle parts upon one tone after the manner of the
above-described organ-point are much less frequent than the latter, and
require greater caution in their treatment.

Sustained tones of this sort suit the character of these parts only when
the chords not belonging to them appear very seldom, since these parts have
not the power to act as a counterpoise against foreign chords, this being the
peculiar property of the Bass or the lowest part as that which determines
the harmony.

Thus the organ-point in example 234 «., when transferred to the highest
part, will sound very unpleasantly in the last measures :

240.

whereas the following, where the Dominant is the sustained tone, is betterr
for the reason that the last chords of the example belong to the same :

241,

MANUAL OF HARMONY.

127

As an 3xample of effective use of sustained parts and continued tunes, and
for the treatment of the same, may be cited a passage in the " Gloria " of
Cherubmi's Mass in C major, where the violins hold a long A^, while the
chorus and accompanying instruments below it carry on their peculiar
melodic and harmonic progressions ; also the D of the violins iw the intro-
duction to the Overture " Calm sea and happy voyage " by Mendelssohn-
Bartholdy. In both passages chords will seldom be found, to which the
sustained tone does not harmonically belong.

Here also may be classed the Trio of the Scherzo of Beethoven's A-major
Symphony, which is throughout based upon the A, that appears sometimes
as a sustained tone in the upper and middle parts, sometimes as an organ-
point in the lowest, and serves as a foundation through the entire piece.

Sustained tones in the middle parts are to be treated with the same
consideration as in the highest part. In instrumental compositions they are
always proportionately reinforced : in four-part harmony they occur bnt
seldom and not at too great a length, e. g.

242.

Remark. — As supplementary to what has been said of chords of the Ninth, may be
added the following.

In the above example b. we find, if the sustained tone be reckoned with it, a complete
Ninth-chord in inverted position with a regular resolution. It has been already oaid of
Ninth-chords that their transpositions cannot be so used that the root and ninth shall be
brought into close proximity, KS with the Seventh. That they may occur simultaneously
at a greater distance, as above, affords no reason for regarding them as independent
chords, when they only occur in the above relations, namely, with a sustained tone, whose
character it is to support harmonies which are foreign to itsejf, as e. g. is the case v^th the
following Ninth, which in reality forms no chord of the Ninth.

128

MANUAL OF HARfoONY.

When the harmonic progression is to be indicated by figures over the
organ-point, they must always have reference to the tone sustained in the
Bass, so that in many cases the usual figuring of chords becomes changed.

Thus the organ-point in No. 234 b. might be figured in this manner :

6 — 7
4-5

? «

4 4

7 7
4

8
647

4 2

244. 9h=? tz±

=£

This mode of figuring, being difficult to see readily and at the same time
imperfect, is only employed for special purposes, so that in scores, where
figuring is used, we often find with the organ -point the words " tasto solo"
indicating that in the usual organ accompaniment only the organ-point itself
is to be given.

CHAPTER XIV.
Passing notes. Appoggiaturas.

UNDER tones foreign to the harmony are especially to be classed passing-
notes and appoggiaturas.

The former result from filling out greater or smaller harmonic intervals
with the intermediate tones, e. g.

245.

The notes marked x are passing, those marked 0 are secondary harmonic
tones, that is, so far as we regard the first note as belorging to the triad
of (7 or A. e. g.

MANUAL OF HARMONY.

129

246.

The passing notes under a. in example 245 are called diatonic, those
under A. chromatic.

Passing notes move from one harmonic note to another ; hence they appear
not with the entrance of the chord, but after it, in subdivided parts of the
measure, and can only be used by successive degrees.

Appoggiaturas on the other hand, are those tones foreign to the harmony
which either appear, like a suspension, with the entrance of the harmony
(that is, in this sense, on the accented part of the measure,) and be close to
the harmonic note (247 a.,) or, like passing notes on the unaccented part of
the measure, serve as a melodic ornament to two notes of the same pitch
(247 b.)

247.

An appoggiatura, therefore, may enter "by SKIPPING, but must be next to the
harmonic note, as is seen in the examples in 247.

It is further to be seen from the above examples, that appoggiaturas can
be formed as well with the note immediately below the harmonic note, as
with that above.

The appoggiatura below the harmonic note, especially if struck upon the
accent, has this peculiarity, that it gladly forms a minor second to the
principal note, by which chromatic tones are produced, as may be seen from
247, ani phrases like the following could not be written :

248.

130

MANUAL OF HARMCNY.

This is especially true of appoggiaturas introduced by skips.

The case is different if they follow one another by degrees, by which they
at once assume the character of passing-notes. Thus the following succes-
sion of appoggiaturas a. need not of necessity be written as in b •

249.

Appoggiaturas below, not falling upon the accent, need only at times the
minor second. Thus example 250 a. need not necessarily be written as in
b.y while c. is not as good as d.

250.

This point does not admit of fixed rules, nor are they indeed essential,
inasmuch as every musical ear will surely determine what is right.

Remark. — The third of the triad suffers the appoggiatura to be a whole degree, soonei
than the fifth or octave. Since in the last case the appoggiatnra may appear likewise as
the seventh, decision must be made in accordance with what follows.

Appoggiaturas above the harmonic note, whether they enter free (by skips)
or as in 250, may form major and minor Seconds to the tone of the chord,
because they are always formed diatonically, and are therefore regulated
according to the key or modulation.

* * * * * *

*n * + /^ * _ __

251.

We often find figures where appoggiaturas above and below the chord-
note are used alternately, e. g.

B52.

MANUAL OF HARMONY. 13]

This is the basis of the following embellishment, which often occurs :

253. i

Passing notes and appoggiaturas may occur in all the parts. If it be in
we only by way of preference, this will contrast strongly with the rest, and
acquire an olligato character, while they serve as an accompaniment. If
this is not the case, then all the parts can be alternately made prominent by
such secondary notes, and gain thereby increased importance. In general
where the position and progression of a part is adapted for the introduction
of such notes, it is thereby made susceptible of greater melodic significance ;
but even here, unless the proper proportion be hit upon, a crowded and
confused effect may be the result

The following simple harmonic phrase

254.

by the use of these secondary tones might be written thus :

255.

132

MANUAL OF HARMONY.

__ J J J — J-T * r-ri J T-J *~

The passing notes and appoggiaturas are here marked by crosses x.

It may be seen in the above example that a phrase can easily suffer from
§uch an accumulation of tones foreign to the harmony, if it is executed in
quick Tempo, whereas a slow movement is better adapted to this style of
writing.

As has been already remarked in the case of suspensions, care must be
taken also in the use of appoggiaturas, that no part shall contain the har-
monic tone which in another is introduced by an appoggiatura9 e. g. :

256.

This can only happen when the harmonic tone is at least one octave
removed from the foreign note, e. g. :

-<&-

257.

According to the principles of doubling, the root or fifth is better adapted
than the third of the original chord for such a purpose.

In case of a quicker movement, however, and longer continuance of such
figures formed of appoggiaturas, there are other considerations, as the follow-
ing phrase will show, which indeed cannot be conceived of as a four-part
vocal passage :

258.

With regular passing notes the same considerations hold good as to prox-
imity to harmonic tones, and figures like 259 a. b. are not as pure as in c. d. «.

MANUAL OF HARMONY.

6. 3. d.

133

Here also more rapid figures sooner admit of this proximity, e. g. :

^I&^E

^-*

260.

Erroneous progressions with Passing Notes and Appog-

giaturas.

As it is the office of passing notes to fill out the interval wheie a skip if
made in the harmonic progression, care must be taken in changing the
harmony, that no false progressions arise, as in the following examples where
concealed fifths become open :

261.

Open octaves, formed with passing tones, may not occur, as the first of
them will be equally harmonic with the second :

tOn the contrary, in the following cases the passing notes do not cover the
en octaves, and are therefore faulty :

263.

Remark. — In instrumental composition, where strengthening and doubling i» intend*
inch octai 2s might he used.

134

MANUAL OF HARMONY.

Likewise the entrance or progression of an appoggiatura by direct motion
to be pronounced faulty, if it proceed as follows :

letter:

264.

The last example is better, for the reason that the octave progression is
covered.

Passing Notes and Appoggiaturas in several parts at once.

A direct motion of thirds and sixths is best adapted for passing notes in
•everal parts at once, e. g. :

865.

JP* 1

t '. r i

1 i i it

The free movement of parts with the aid of passing-notes may produce
also parallel seconds, fourths, fifths, sevenths of all kinds ; these require,
however, great care, and on account of harshness are admissible only in
tingle cases and under very favorable positions.

Progressions of fourths are good when another part takes the third
below:

266. dt— i

Single fifth-progressions, formed by passing-notes, are found sometimes in
food compositions, which, however, affords no ground for recommending

MANUAL OF HARMONY.

135

them in general as faultless (see remarks upon consecutive fifths on p. 27
and elsewhere.)

In like manner the harshness of successive sevenths is alleviated only by
favorable position, good progression of all the parts, and in general by
Tempo, movement, etc.

In contrary motion the varied intervals of passing notes often give tha
movement a new, peculiar coloring, and add greatly to the independence of
parts, only they should not be too crowded or appear in too many parts at
once. *

287.

Here also it will be found that those passing notes, which with others,
outside of the simple fundamental harmonic structure, form as it were an
inner new (passing) harmonic movement, are more natural and smoother
than those whose combination cannot be shown to be harmonic.

The value of such movements can only be judged of with reference to
their character and Tempo.

In regular diatonic progressions several parts at once may have passing
notes, e. g. :

268.

The main point in all such passages is, that at the change of harmony
which in the last example occurs at the half-bars, the parts shall be sa
disposed as to admit of a regular formation of their progression.

Appoggiaturas can occur in differen • parts \

a. in two parts :

186

MANUAL OF HARMONY.

in direct motion:

in contrary motion:

270.

=E i i^ ii
7-,-rr Trr-r 1

b. in tftee parts :
271.

v- -*_• »- f-nnr

C. in /owr parts:

272.

fiemark. — Most of the above examples can also pass for harmonic progressions upon
an organ-point.

It appears from these examples that for appoggiaturas also, in a direct
movement of two parts, progressions of thirds and sixths are the most
natural, while parallel seconds, fourths, fifths and sevenths always have a very
harsh effect. Thus no one could easily pronounce as good, appoggiaturas
like the following :

good _

273.

|r— i i i good

Appoggiaturas may also be of greater length than the harmonic note that
immediately follows them. e. g.

274.

SSZ3

MANUAL OF HARMONY. 137

As regards composition, the importance of the matters explained in chap-
ters twelve to fourteen inclusive is sufficiently great for subjecting them to a
careful examination, as a thorough knowledge of them aids essentially in
understanding the inward harmonic structure of a composition. — It yet
remains to speak of their relation to pure part-writing, the object of our
next study.

As on page 24 we spoke but generally of the term " pure part-writing,"
it here becomes necessary to limit the question more closely and present it
somewhat thus :

What application of these materials for composition is allowed by our next
object, practice in pure part-writing ?

It is undeniable that these materials especially adapt themselves to the
perfection and adornment of the parts.

If, however, our immediate concern be with the recognition and working
out of simple harmonic formations, then indeed whatever is adapted for the
perfection of the parts may properly be used, but all else, serving them
merely for ornament, must be put aside ; in brief, a distinction made between
the essential and non-essential.

With the non-essential must invariably be classed first of all :

Whatever is affected in harmony generally, so far as there lies at the root
of it no inward necessity ; unnatural introduction of harmonies little used.

These readily occasion superfluity, bombastic overloading of the piece,
and rather give evidence of a sickly or mentally weak condition, than of
originality and a fresh, free, strong and steady action ; again :

irregular employment of suspensions ; the use of sustained partst of anti-
cipated and delayed tones ; but especially :

appoggiaturas abruptly used and the figures formed from them, in short,
whatever is inconsistent with simple, good four-part song.

Vocal composition being generally accepted as the basis of all music, much
will naturally be excluded from it which is proper in instrumental works.

Although for practice in the use of harmonies and for the study of good
and pure part-movement, the writing of chorals or simple movements in
choral style is suggested as most serviceable, yet even this will not exclude
the use of those materials, so far as they serve not only as ornamental, but
also as perfecting the movement of parts.

|38 MANUAL OF HARMON*.

Herewith is particularly to be reckoned the use of suspensions, regular
passing notes and appoggiaturas.

From what has been said may now be estimated the strictness of pure
part-writing at the commencement of the study of harmony and in later
contrapuntal work, which prohibits much as inexpedient, unessential and
diverting from the main point, that in practice may readily be used at proper

times.

A complete understanding of all the subjects hitherto treated will be
greatly assisted by the thorough study of good compositions : for individual
experiment opportunity will be afforded in chapter nineteen in the third
section of this book, in which we shall recur to these topics.

CHAPTER XV.

Passing Chords.

PASSING CHORDS are those which like passing notes in several parts
appear in smaller subdivisions of the measure as real chord-formations, but
whose entrance and treatment deviate at times from the general rules of
chord-connections.

One species of these has been already seen in those passing notes and
appoggiaturas in three parts, which assume the form of a chord, e. g. in Nos.
271 and 272. So in one sense most chords formed upon an organ point may
be called passing.

There are, however, other cases of this sort, which we shall here explain.

As, hi the main, passing notes and appoggiaturas rest chiefly upon rhyth-
mical relations, it becomes necessary also, for the explanation of passing
chords, to glance at the different divisions of time.

It is known that in simple even kinds of time the natural accent falls upon
the first part of the measure, while the second has less weight.

Now if the harmonic progression be simply based upon the two divisions
of the measure, so the harmonies also, which fall upon the accented part
(thesis), must be regarded as the most important and aa the point alwayi
to which the chords of the second part are directed:

MANUAL OF HARMONY.

189

875.

In this sense the chords in the second half of the measure may be called
passing chords, although moving thus uniformly their character does not
•tand out so prominently.

That this has been so understood in theory, though seldom plainly ex-
pressed, is proved by the fact that greater care at their entrance has always
been bestowed upon the chords on the thesis, and much that was inadmissible
allowed to those on the arsis.

The character of passing chords, however, appears more distinctly in
harmonies which are assigned to the lesser divisions of the measure ; as in
the following examples :

270.

277.

The peculiar appearance of the chord of the Sixth-and-Fourth in example
276 a. and c., as also of the Seventh-chord in c. is to be explained only a$ a

140

MANUAL OF HARMONY.

movement of all the parts ly degrees in the character of passing notes to th*
position aimed at (the chord on the thesis of the following measure.)

These parts may appear still better in their character as passing, if one
part be sustained, e. g. the Bass 277 a., or the upper parts b. (see above

277.)

By the use of both methods arose the part-movement in 27 6 a.

If this condition (the movement of parts by degrees) be fulfilled, then all
chords may enter free, and find explanation in the chord which terminates.

278.

^ KB. KB.

_-J_ J?~*~iu -]\ J i 4i J J | i I it ^^^rT:

Remark. — The free treatment of the seventh before mentioned finds its warrant also in
this explanation of passing chords (see N. B.)

In the simple uneven kinds of measure the accent falls likewise upon the
first part, while there are two parts of less weight Passing chords will
appear thus:

279.

__LJt— 3 . |— I *> * , , v . * * | *i _

-p-

75 6

Smaller divisions of the measure may also contain passing chords, exam-
ples for which are not necessary after what has been said, neither for the
compound kinds of measure.

Here also the study of good compositions will serve to illustrate and
assist.

For individual exercise the following remarks may be in place.

All chords indicated as passing will either progress according to the known
rules of harmonic connection or deviate therefrom. In the former case, the
most frequent, no further remark is needed ; in the latter it will depend on
a flowing, melodious movement of the parts, as well independently consid-

MANUAL OF HARMONY.

141

ered, as in relation to one another, whether formations of this kind are to
be considered correct. It can only be said in general, that here also th*
movement of the parts by degrees will determine the character of the passing
chords, and that all such passages must be estimated with reference to the
rhythm, Tempo and character of the piece.

CHAPTER XVI

Means of Modulation.

THE term modulation has already been explained in chap, eleven.

Having there treated of the proper method of determining all modulations,
we shall now discuss the principal means of producing them.

The art of modulation consists in discovering such harmonies as stand in
relation to two or more keys, that through them we may pass from one key
into another.

Any modulation can be effected in different ways, and will serve various
purposes. It may be

first: sudden in appearing, of short duration — and passing, or

second : with longer preparation, seeking the new key as an end and acting
longer as a basis.

In the former case it will employ the simplest means, be decisire, but
leave the new key speedily, and of itself even have no determined validity :
in the latter, it is usually through various means prepared and carried out
by degrees, seeks to impress the new key upon the ear, and itself leads to a
finite conclusion. Thus in the following example

280.

6 2

6
4 7

§3:

C: F: V,

G: V,

a: V,

C: I

142

MANUAL OF HARMONY.

the modulation is pausing, changing often, without essentially leaving the
main key G major.

This kind of modulation is only adapted to the keys nearest allied, and
though others more remote may be reached by special and absolute methods,
their development must be guided by perfectly natural and organic connec-
tions, or they will appear unintelligible.

In the next example, however, the more remote key becomes the end,
which is gradually reached ; the original key is wholly abandoned, and the
new takes its place :

281.

C: Iib:vn°7Bb:I

This example shows clearly how the extended modulation, having the new
key as its end, makes use of the passing modulation in order to reach it ;
the rather, as it was not the purpose here to pass quickly into Eb major.

Unless these short phrases are employed as interludes between two pieces
of different keys, or as exercises, their use in composition must be in a
special manner, as upon this very formation of modulations rests in part that
also of periods and their connections. This is, however, an important branch
of the study of form, and has to do with the order of modulations in a com-
position, consequently is foreign to our present purpose.

Remark. — An explanation of this may be found in the author's work : " The principles
of musical forms and their analysis."

At present we take as exercises the formation of such modulations, in
order by this means also to promote skill in the use of harmonies and their
proper connection. f

In discovering the means of modulation, we pay no regard at present to
the kind of modulation, as they may serve for both kinds indicated above.

The first and simplest means will be itself

THE TONIC TRIAD OF THE NEW KEY.

If this triad, however, already forms a part of the first key, the intended
modulation will only be definitely determined by what follows, particularly
tf it be the dominant-harmony of the new key. Thus in the following

MANUAL OF HARMONY.

143

example in a. there will be no modulation perceptible, while in 5. first the
third harmony makes the key of G-major to be distinctly heard :

282.

In the case of remote keys, indeed, the effect of the minor triad as the
tonic may be more decided, yet this also will be followed by the dominant*
harmony for the sake of clearness (in a.) ; but the major triad is more
readily received as a Dominant (£.).

)==±x=te>=

I 1 •~~t "•

C: I /: i V7 i C: I in

C: I a: V I C: I e: V i

Though the tonic triad used as above for modulation be so unsatisfactory,
yet one position of it, the chord of the Sixth-and-Fourth, has the property
of rendering a modulation thoroughly decisive. For as this readily forms a
part of the closing cadence (see pp. 49 and 53,) with the same effect it
produces also a sense of modulation, provided it be not used like a passing
chord, but enter on the thesis. But also in this case the dominant naturally
follows, the modulation not being complete without it.

284.

C: I G:I

d : i V I

MANUAL OF HARMONY.
On the arsis it wiU not indicate the key so decisively.

285.

All the above examples, however, point to a still more effective means of
modulation ; this is the

DOMINANT HARMONY.

The triad as well as the seventh-chord of the dominant appears as the
most natural and best means for modulation, since by it (particularly as
regards the dominant-seventh harmony) the key is most unmistakeably
fixed.

The modulation through the Seventh-chord of the dominant may take
place without any intermediate chord in the following manner.

According to the principle that that harmonic connection is most intelligi-
ble of all, which is effected through similar or sustained tones (preparation,)
we may modulate from the tonic major triad through the dominant Seventh
chord directly into all the other keys, except those of the minor and major
third and the augmented fourth. From C major then we may pass to all
other keys, except Eflat, E and F sharp (whether major or minor, need
not be determined at present) in the following manner :

From G to d:

C — F:

C — G:

C — a:

286.

In all these examples the similar tones, connected by a tie, effect the tran-
sition to the dominant of the next key, thus from C major to d minor the
tones g and e, which become the Seventh and Fifth of the dominant-harmony,

etc.

MANUAL OF HARMONY.

146

Remark. — We need only hint that these modulations are attained alsD through othef
positions of the chords, e. g. :

C —

d: or:

.
-&-

If we wish to modulate in the same manner into the three keys not found
above, this may be done by the insertion of a chord (a triad is simplest)
which supplies the desired connection, e. g.

288.

From minor the modulation will admit of these forms :

a to b: a — d: a — e: a — F:

289.

_<«_ *W _^c

a — G:

Into the remaining keys C, Dfr, Eb> F# and Al? through a connecting
chord :

From a to C: a — D\): a Eh:

It is understood that this method of modulating is merely adduced as the
simplest principle, and that a modulation need not invariably proceed in this
manner ; also that as simple harmonic connections can be effected without a
sustained tone, the same will be the case with modulations, as e. g. the follow-
ing may take place without an intervening chord :

146

MANUAL OF HARMONY

From C

C — e:

— C.

291.

Still for the connection of harmonies, and of keys especially, it will always
be greatly beneficial to become thoroughly familiar with that principle, and
for this purpose to write out modulations from all the keys, bringing the
chords at the same time into the most varied positions, and to illustrate these
connections by playing them on the Pianoforte.

This mechanical practice will greatly promote facility in the use of all the
means of composition.——

There is another chord which shares with that of the dominant-seventh
this aptness for modulation. This is the

DIMINISHED SEVENTH-CHORD.

This chord, which in most cases takes the place of the Dominant-harmony,
will often prove better adapted for modulation than the latter, since its
appearance is less harsh, especially in cases where seventh and root would
have to enter simultaneously without preparation.

The following examples will show the use of this chord.

to B\): C — B:

C —

292.

This chord, beside the above application, exhibits still further capability
from its enharmonic nature.
The following chord, precisely similar in sound, but differently written :

293.

will belong to four different keys, namely : in the first form,/ minor, in the
second d minor, in the third b minor, in the fourth aj? minor.
Hence a fourfold modulation becomes possible :

Now as all the diminished Seventh-chords can appear in the following
thre* positions, as can be most distinctly seen on the Pianoforte :

MANUAL OF HARMONY.

147

295,

each of which, however, may by enharmonic change belong to four keys, WB
thus have modulations for all the twelve keys in minor, to which in many
cases may be added the twelve in major, as this chord may often be used in
major in place of the dominant-harmony.

As far as the intimate connection of all the keys is concerned, and the
variety of harmonic connection, it will here also be very useful to write out
diligently this method of modulation.

Although in composition itself this kind of modulation proves useful iu
many ways, yet it should be at the same time observed, that it ought not to
be employed too often, because with its facility of application it loses in
artistic value.

Of similar use, that is by enharmonic change, though not in so extended
a manner, is

THE CHORD OF THE AUGMENTED SIXTH-AND-FIFTH.
Its similarity in sound to the dominant-seventh chord :

296,

renders it well adapted, in conjunction with the latter, for modulating into
certain keys through an enharmonic change, e. g.

From C to b;

297,

Though we have been seeking above the means of passing quickly from
one key to another, yet, as it is not always the object to effect a modulation
quickly and decisively, we may to acquire readiness extend our exercises and
arrange them thus :

From one key to the other through the triads of different degrees :

From G to d through the triad of the third degree :

298.

148 MANUAL OF HARMONY.

From C to d through the .riad

of tJie fourth degree: of the fifth degree: of the sixth degree:

899- aC=S=S^

-&-

of the seventh degree:

•2-^— 2— &
-or ~z

75?- V&- _;

-&-

From C major to E through the triad

of the second degree: of the fourth degree: of the fifth degree:

800, *-^

These hints may suffice, in order to learn to form other modulations on
the same principles.

Extension of the Modulation and its completion through

the Cadence.

The above-described process of passing from one key into another, was
based upon the simplest and most natural means.

If we wish to extend further a digression into a new key, the above means
indeed will serve this purpose likewise, only we must not apply them so
abruptly and directly, but make use of the passing modulation mentioned
before, and introduce the new key only gradually. The use of the cadence-
formulas, however, will best determine the key we arrive at.

For this object the following kind of exercises may be employed, e. g.

Modulate from 0 major through d minor, a minor, G major to e minor.

This would be performed somewhat thus :

301. , ^ | __ _ _

o; vn

MANUAL OF HARMONY.

149

In adding the cadence the following should be observed :
If the modulation take place through the chord of the Sixth-aud-Fourth
of the tonic triad of the new key (see p. 1 43,) the following of the dominant
chord with its natural progression is sufficient to create a cadence, e. g.

302,*— g— f=

~o~

-or

In other cases the extended cadence or the familiar closing formulas will
be requisite in order to determine the final key. As the simplest of these
formulas may be used the following :

303,

•9r

in other positions:

i ,
' 1

-&-

647

9iE^:

If these cadence-forms be added according to the position of the last
chord of the modulation, the latter is completed.

This may be shown in some of the former examples.

The modulation from C to Eflat No. 288 ends there with the fifth in the
Soprano. To this is added the cadence in the position corresponding to tliat
last chord, e. g. :

15Q MANUAL OF BARMONY.

From C to Eft : Cadence :

304.

The following modulation from C to a in No. 286 would require a cadence
in this position :

305.7

>m C to a:

Cadence:

* #

The modulation from C to J7, using the cadence under No. 303 I. :
C to 2?: Cadence:

306, /

307. /

or from C to Z> \) ; Cadence :

~3«— J-|

6 3t>

»b

We conclude with another example of a more extended exercise:
From G through e minor, C major, b\) minor to A^ major.

808

From G through e minor, C major, &b minor to Ab major.

ztunrj:
%&=?"

Cadence.

These hints will suffice to enable one to form a variety of exercises.

OP HARMONY.

151

SECTION III.

PRACTICAL APPLICATION OF HARMONIES. EXERCISES FOR THEIU
USE IN PURE PART-WRITING.

THE following hints on the most practicable form of exercises in the use of
harmonies may serve at once to further illustrate, enlarge and complete the
principles thus far developed. For this object, single cases in given exam-
ples will furnish opportunity for more extended remarks.

CHAPTER XVII.

A simply Harmonic Accompaniment to a given Melody.

FIRST of all it may be observed that we are here treating solely of the
simply melodic progression of a part, and for the present leave all other
elements of a melody, as its metrical and rhythmic formation, out of the
question.

1. Harmonic accompaniment to a Soprano.

We select first the following simple exercise :

309, =rzfc±fz=i:

For the sake of facility we will add in the manner heretofore employed,
those fundamental tones which may serve in general as the harmonic basis.

310.

In every harmonic progression the movement of the Bats is the
important.

J52

MANUAL OF HARMONY.

We turn our attention then to this first, and write its progress!^ Ju

lows:

311.

SOPBANO.

BASS.
thus:

312,

The addition of the middle parts will not now be difficult :
313. C G C d G C

SOPBANO.

ALTO.

TENOR.

BASS.

The above may serve chiefly as an illustration of the exercises them,
selves.

The next will furnish occasion for studying the principles of a good Bass-
movement as well as a melodic part-movement in general, so far as the
simplest harmonic progression requires it.

Examples incorrectly written out will best serve our purpose.

Exercise with fundamental tones given.

Remark.— -In working out this and subsequent exercises, we shall for the sake of room
nse the Violin-clef, writing the parts on two staves; most urgently recommending, how
ever, for individual laborn the method of notation employed in No. 313.

MANUAL OF HARMONY.
Let this exercise be written out thus :

C F Gi C d

315.

153

There appears in this example no violation of the rules thus far known
for progression and connection of chords, and yet it is wholly objectionable
from the stiffness, weakness and lack of firmness in the Bass.

Excepting where there is an organ-point, a good harmonic Bass-movement
admits of sustained tones only when caused by the necessary preparation of a
tone, or counterbalanced by a decisive movement in the other parts.

The above example also twice contains the chord of the Sixth-and-Fourth,
which may afford occasion to say more of the use of this peculiar and diffi-
cult chord.

Of the use of the Chord of the Sixth-and-Fourth.

The infrequent use of the second inversion of the triad, the chord of the
Sixth-and-Fourth, arises from the fact, that its appearance is tied to certain
conditions.

In the first place, we find it oflenest in cadence formations, as the preced-
ing examples show.

Then it appears in the same character in modulation (see p. 142.)

It may enter abruptly too in both cases, but is not to be regarded as a
passing chord ; on the contrary, it must always fall on the thesis.

Beside these instances it appears most naturally as a tonic, dominant and
tub-dominant triad under the following conditions :

a. When the fourth is prepared :

b. When the Bass moves by degrees to the next new chord, or is sustained.
The following examples show the application :

316.

ffARMClTT,

In example a. it appears most naturally, because it is based upon the
Tonic, Dominant and Sub-dominant, while on other degrees (b.) it readily
produces a sense of modulation.

Used upon the arsis, it may also appear, beside according with the above
conditions, with a preparation of the Hass.

317.

As in all these examples the chord of the Sixth-and-Fourth appears either
as a passing chord (on the arsis) or as above in the character of a suspen-
sion (on the thesis,) its effect on the thesis with a preparation of the Bass is
much weaker :

fcs:

Often it appears also as a suspension itself, whereby the preparation of the
fourth is fully vindicated.

319.

MANUAL OF HARMONY.

155

In the second case still more decisively, as it appears in a chord that
«eldom occurs (that of the third degree.)

That the chord of the Sixth-and-Fourth, however, where the parts move
by degrees in the smaller divisions of the measure, can in passing enter
without preparation even, as :

320.

will need no further explanation after what is said in chapter fifteenth con
cerning passing chords, and after examples 276, 279.

Remark. — The frequent necessity of preparing the perfect fourth in the chord of the
Sixth-and-Fourth has induced many theorists to class it among dissonances.

In the division of intervals on page 17 of the introduction to this work it is classed with
the consonances, and the reasons for it are given on page 20.

The uncertain relation of the perfect fourth and the necessity of its preparation appears
only as against the Bass or lowest part, and in general only in the chord of the Sixth-and-
Fourth, since even in the chord of the Sixth-Fourth-and-Third this necessity of prepara-
tion does not always exist ; as regards the other parts, the perfect fourth is to be treated
precisely like any other consonance.

With actual dissonances this is not the case, for they retain their character throughout,
whether lying in the highest, lowest or middle parts.

The chord of the Sixth-and-Fourth of the diminished triad can seldom be
used in four parts, showing itself to be too imperfect.

321.

It will occur, however, in three-part harmony, where it often supplies the
place of the chord 'of the Second (see later : Three-part movement.)

Beside the condition of a good harmonic progression, that the Bass part
shall form a good and intelligible foundation for it, the second requisite ia

THAT THE PROGRESSION ALSO BE MELODIOUS.

Certain skips have always been properly classed as unmelodious pro-
gressions.

156 MANUAL OF HARMONY.

A succession of two fourths or fifths in the same direction e. g. :

322.31:

These skips are better thus :

Even skips of a sixth are more practicable as thirds in contrary motion, if
the position and compass of the parts admit of them:

better:

324.B

better:

Skips by augmented intervals are to be avoided as unmelodious, diminished,
however, are serviceable :

letter:

not:

better:

325.

Deviations from this rule often occur ; they find their explanation in the
formation of the melody or the peculiar character of the composition gener-
ally. The observance of the rule in theoretical study will always be very
advantageous.

A skip of a major seventh is wholly to be avoided ; but that of a minor
seventh is practicable only in an inversion of the same chord.

not:

The last in some such harmonic progression as the following :
not good: not: not:

MANUAL OF HARMONY.

157

These few remarks contain the chief features of a good melodic progres-
sion of parts, and for the next, simply harmonic, exercises particularly, will
prove sufficient. It should be further observed that these rules apply not
only to the movement of the Bass, but in general to all the parts.

The exercises given under 314 may with an improved Bass-progression
be written somewhat thus :

328.

328 b.

C Q O — F G G C

Gt C G G a d

-&-

1fc- I

G —

G d^ G a d>j

The next example leads us to explain an important and difficult part of
harmonic connection and part-movement

Exercise.

F b° C

G^ C

329.

-&-

The following incorrect solution may serve to illustrate:

C F b° C a dt GT C

330.

6 7

158

MANUAL IF HARMONY.

The errors here consist, first, in the doubling of the third in the Bass of
the second chord, which gives to this and the following harmony an awkward
position ; secondly, in the concealed fifth indicated between the fourth and
fifth measures, and lastly in the seventh introduced by a skip in the last
measure but one.

As to this last, it can only happen with the dominant-seventh, when the
root is already present (prepared) (see p. 70.)

\ttr

===j£ — -^ — d=

--B^-tt

$5=3—

0 _•*- .... , X
— h- 4J- 1 <5>—

4-0 — W
t-^

331.

The free entrance of Seventh and root is more endurable and less harsh
in contrary motion,

332.

but in direct motion either wholly objectionable, or only to be used in speci-
ally favorable progressions, when perhaps as in the first example of 333 the
root g is already present in the preceding chord, although in a different part

333.

-&-

The first of the above-mentioned errors shall be corrected in the sequel.
The second is more important, and leads us to speak in general

OF CONCEALED FIFTH AND OCTAVE PROGRESSION.

We have already spoken on p. 29 of the nature of these progressions.
Concealed fifths and octaves arise, when two parts progress IN DIRECT
MOTION from a different interval to a fifth or an octave, e.g.

Concealed Fifths:

334.

MANUAL OF HARMONY.

159

These fifths and octaves become obvious, if the skip made by one or both
parts be filled up with the intermediate tones, as is indicated above by the
black notes.

Since in all four-part harmony certain concealed fifths and octaves may
occur, without which the choice of chords as well as the movement of parts
would be very limited, but others again are to be avoided, it becomes neces-
sary first to examine more particularly the mode of their appearance. The
attempt to furnish positive rules for their use, sufficient for all cases, has
never yet been successful, nor could it easily be ; only general remarks
therefore are to be made, which nevertheless for special cases will afford a
standard of criticism.

Concealed fifths and octaves between two parts may occur :

1. when one part moves by step, and the other by skip ;

2. when both parts skip.
In the former case :

a. by degree in the upper, by skip in the lower part;

b. by skip in the upper, by degree in the lower ;

As to the position of the parts, relatively to both cases :

a. between the extreme parts,

b. between the middle parts and

C. between one extreme and one middle part.

Concealed Fifths and Octaves in the extreme parity
They are allowable, if the upper part move by step.

a. Fifths. 6. c. Octaves. d. e.

335.

It will be well also, if one part at the same time move in contrary motion
or be sustained, as in example 335 a., b., c. Not so if all the parts move in
direct motion (d).

Remark. — Though the above rule will suffice for many cases, yet it will not hold good
universally, as is seen in the above example 335 e, which is not to be counted among those
having a good part-movement, the progression from the Sixth-chord c being a very forced
one. '

Likewise should be called to mind what has been said on pp. 35 and 36 of the cadence*
forming Bass-progression, namely, that concealed octaves over the leading tone or general!/
over a half-degree are more tolerable than over a whole degree.

160

MANUAL OF HARMONY.

In the examples, above cited, the octave appears throughout as root of the
chord ; cases where it forms the third of the chord are more doubtful, and
are consequently to be used with greater caution.

not:

Even as the fifth of the chord it is not to be considered good :
337. ?EzEii^=±=i

Remark. — In case of a concealed fifth the lower part will always be the root of the
chord.

Concealed fifths in the extreme parts are forbidden when the upper par
moves by skip.

338.

& >^^ -&- -&- -«- *•— •

In all cases where a seventh aids in the harmonic connection, as in &., d.9 e.,
the progression of fifths seems more concealed and less harsh.

Concealed octaves in the extreme parts are not absolutely forbidden when
the upper part moves by skip.

b. not:

339.

Here also those cases, in which the Bass moves a half degree, are seen to
be the most endurable. What was said in 336 and 337 holds good concern-
ing d. and e.

Concealed fifths and octaves in the extreme parts are forbidden, if both
va*-ts skip.

MANUAL OF HARMONY.

161

340.

When they form merely transpositions of the same chord, they are not to
be regarded as errors, because they are really not then fifths and octaves
progressing to other chords.

341.

Concealed Fifths and Octaves in the middle parts.

Although the movement of the middle parts should be quite as pure as
that of the extreme, yet their position being greatly hidden by the latter
allows them also at times a greater freedom, especially with regard to con-
cealed fifths. Concealed octaves should be avoided here, for the sake of a
good relation between the parts, and the case of concealed fifths, beside the
rules before mentioned, must principally depend upon an otherwise good
harmonic connection. A few cases may be annexed :

342.

Concealed Fifths and Octaves between the extreme and

middle parts.

Here alco the points to be considered in such part-progressions are rather
to be found in a good and natural harmonic connection, than to be settled by
merely mechanical rules. A few examples may follow :

162

MANUAL OF HARMONY.

843.

not good: not:

djjbs-p I

^1=!-:

-^^

m. — i — i

1 1 & i

One particular case of concealed octave is specially to be mentioned, that
over the seventh) which in all the parts is to be avoided as erroneous.

844.

(Seep. 84.)

What was said of octaves, applies equally to concealed unisons. Between
Soprano, Alto and Tenor they should be wholly avoided, between Tenor and
Bass, however, according to the position of the chord and of the parts them-
selves to be regarded as concealed octaves.

The cases, in which concealed fifths and octaves may appear, are so mani-
fold, that it would be superfluous to cite them all, if it were at all possible.
We may rest satisfied with the foregoing considerations, adding thereto the
followiDg maxim, which indeed is not written for those beginners who are
still occupied with the technical or the purely mechanical harmonic structure,
without regard to the higher demands of art :

Avoid indeed concealed fifths and octaves as far as possible, but use them
without scruple in cases, where, on the one hand, by so doing, a goocf harmonic
connection results, or, on the other, considerations of a higher nature prevail,
as the melodious movement of parts, use of given motives, or others.

After this digression we return to No. 330, in order to correct the faults
already mentioned.

MANUAL OF HARMONY.

163

It will be hardly possible in this case to correct the concealed fifth found
there, which belongs to that class where both parts skip, because, even if the
Bass progression be in contrary motion, the evil appears again elsewhere.
e.g.:

345.

All that remains therefore in this case is to change the harmony itself and
denote the fundamental tones differently.
The change may be made as follows.

346.

8 r

347

8 7

Exercises.

847

— Q g Q

164

MANUAL OF HARMONY.

F G

Let the following exercise

S48.

.-fcl;

be filled out thus :

849.

The errors here are indicated by the figures.

The movement by skips of all the three upper parts in direct motion in
No. 1 is not good, being contrary to the first principle of all harmonic con-
nection and not at all necessary.

A skipping movement of one or two parts can only happen, when the liar-
monic connection (by sustaining a tone or by contrary motion) is preserved
in a third part.

No. 2 also has the same fault, which becomes here still harsher, because
seventh and root appear in direct motion without preparation, and thereby
arrive at an awkward position, so that one is pushed aside by the other.

It has already been mentioned (p. 72 and 158) that the free entrance of
the dominant-seventh cannot but have a harsh effect, unless the root bo
already present and can be sustained in the same voice,

Thus all the following examples exhibit an undesirable movement of
parts.

850.

MANUAL OF HARMONY.

165

A few of these and similar passages could be excused for weightier melo-
dic causes.

The following examples may further serve as supplementary to what was
Baid on p. 158 of the allowable free introduction of root and seventh in
contrary motion :

351,

The passage in example 349 No. 2 contains also another error, violating
the rule before mentioned (p. 153) under the chord of the Sixth -and-Fourth :
that the Bass must not move by skip from the chord of the Sixth-and-
Fourth.

The third error in example 349 consists both in the concealed fifth, which
is made all the more prominent by the skip of the Soprano in the same
direction, and generally in the distended movement of the parts.

The concealed fifth in No. 4 is faulty because it was unnecessary, as the
Tenor could move equally well from I to c. That in No. 5 is better, being
allowable with the movement of the Alto and Bass in an opposite direction.

Exercise No. 348 is better written out as follows :

352.

Exercises.

-A ^

352 b. =51
>=

# (7 — 6? — Da D G Di

DI G

166

MANUAL OF HARMONY.

filled out thus :

854.

gives us opportunity to speak of an error, called the

Unharmonic Cross-relation.

The unharmonic cross-relation (relatio non harmonica) belongs to tho
unmelodious progressions and in general consists in this, that a tone is imrne*
diatety followed IN ANOTHER PART by the same tone chromatically raised or
lowered, as here the g in the Alto by the g sharp in the Bass.

To avoid this error, the following rule is to be observed :

Immediate chromatic alterations of a tone should always take place in the
tame part exclusively, in which the tone occurred unaltered just before.

Much as this rule agrees with every principle of harmonic connection and
progression, yet there is scarcely one to which more exceptions are found in
practice.

Hence in manuals of later methods the doctrine of the cross-relation has
been strongly suspected, and instances cited where the unharmonic cross-
relations occur in a perfectly natural way, without investigating the cause of
tlidir not being regarded as erroneous.

A few of them may be here introduced :

855.

°- e.

MANUAL OF HARMONY.
* /

167

In all these cases the cross-relation seems to be formed not by the timply
harmonic progression, but either

in the character of appoggiaturas, as in a., b., g.,

or by the shortening (contraction) of harmonic connections which are
natural, though too minute for metrical organization, as in c., d., e.,f., h.

The first needs no demonstration, and it need only be added, that this kind
of cross-relation would occur mostly in smaller divisions of the bar, and the
above notation in half notes is rare and hence inappropriate, since by them
is expressed the simple harmonic foundation, and not those tonic elements
which serve for ornament.

The original progression of parts hi the above cross-relations resulting
from contraction is as follows :

358.

Compare these examples with tluse under No. S55 at c., d.t e^ h.

168

MANUAL OF HARMONY.

All these qualifications, by which cross-relations have become natuialized,
are not to be found in the following and similar cases, and such progressions
as these must be reckoned as erroneous :

357.

Entire freedom therefore in the use of cross-relations cannot be justified.

In all the above passages taken from practice, but apart from their con-
nection, there comes also the consideration of the Tempo, and the consistency
of a whole resulting from rhythmical divisions, serving to render these forms
not unpleasant, but rather, precise.

Under cross-relations is classed also a progression, known as the Tritone,
an explanation of which here follows.

Concerning the Tritone.

The tritone is contained in the diatonic major scale, and includes the dis-
tance from the fourth to the seventh degree, in the C-major scale the aug-
mented fourth f-b.

This interval from / to b embraces three whole degrees, whence also its
name :

358.

It is regarded as unmelodious and incapable of being sung, because each
of its tones demands a special progression, properly belonging to two distinct
voices :

- .

one of which must be disregarded in the progression, when the step is givea
to one voice :

in which case the melodic series would have to be formed thus:

361.

MANUAL OF HARMONY.

169

That this, however, is not the sole cause of the bad effect of this interval ia
shown by the very common inversion of the same, which would likewise
require a two-part progression :

362.

and which is equally intelligible and easy of execution, as the tritone is diffi-
cult and repulsive.

Remark. — It may be further observed here, that the tritone is based upon the diminished
triad and its progression, as is evident from the above example 362 (see p. 38).

The reason why this interval was formerly especially insisted upon as
erroneous, was this, that hi the simple harmonic form of composition then in
use it constituted the only augmented interval, which diatonically presented
itself. At the present day, with the extended use of all the resources of art,
it is simply reckoned among the augmented progressions, which in a pure
harmonic movement of parts are to be avoided as unmelodious, or at least to
be used with caution.

The points to be considered in the use of the tritone lie in its position and
appearance itself.

It may occur based

upon one chord (a) or

upon two chords (6.) e. g.

363.

pe— J

-1

/^
& 1

gy
~& —

^ H

If it occur upon one chord, its entrance is not unexpected and the ear is
prepared : in case of two chords, however, its forced progression is very
perceptible. Formerly it was also forbidden to use the tritone upon the two
major thirds, which succeed each other by a whole degree, e. g.

but not:

334.

can it be denied, that this progression in two parts has the same harsh

170

MANUAL OF HARMONY.

effect, while with three and four parts it is much softened particularly if not
appearing in the extreme parts.

365,

The reason why the interval from the fourth to the seventh degree of tho
minor scale, e. g. from d to g sharp, was not considered a tritone, is based
upon the view formerly taken of the minor scale itself and its harmonies.
The effect of this interval, being augmented, remains the same.

We turn back to our exercise 353 and try a better construction.

366.

"ZXjgzr g-r ^> i ^~H

&0.

Exercises.

366 b.

JO ^

I £?_

& !

-^—4" 1 »

• &

h— «5>

\ J

-T-^ I ff 1^-1

JB?

c —

2. Harmonic accompaniment to a given middle part.

This practice, which properly belongs to contrapuntal studies, cannot be
commenced soon enough. We shall introduce it at first, indicating the
roots.

MANUAL OF HARMONY.

171

ALTO. C

Exercise.

c F G a

367.

In working out this exercise, the sketching of the Bass again will be the
first and most important thing. At the same time, however, the Soprano
may be added also as the most conspicuous part. e. g.

368.

C G C F G a d'j G C

The foregoing may answer for three-part harmony. By adding the Tenor
it will appear thus :

369.

Exercises with a given Alto,
i 2

869 b. for

[?Cp

F g C^ d 91 G F

F B\) G

B\) G F g Ci F F G F C d

g G F d — g Ci Ai d

d d Ad

172

MANUAL OF HARMONY.

g D — 7 9 B\> c g Di g

The treatment of a Tenor part will be the same.

Exercise.
TENOR. G G a, g G Gi G

Sketch of the Bass and Soprano :

371.

In four parts :

372,

_<sz_

Exercises with a given Tenor.

372

G G a, d GI G G G C

a E a d

4 F^ — F T T— -F^— Hi

a, d

This practice should be continued, until the sketching of the Bass, as well
•s vhe management of parts generally, is perfectly pure and safe.

In closing this chapter it may be further observed, that for a good con-
struction of these four-part movements, a good position of the parts is

MANUAL OF HARMONY.

173

especially necessary. The limits of the parts themselves must not be
transgressed, nor the distance between them too great ; neither must they be
brought too near together, which, however, does not apply to two parts
meeting, e. g., on one tone.

Let the following rule be observed in this connection :

Of the three upper parts the distance from one to the next must not cover
more than an octave. The relation between Tenor and Ba$s, however, admits
of exceptions.

Remark. — Transferring these exercises to the Bass part would be useless, so far as they
would be precisely similar to the figured Basses used heretofore. They can be used only
tor free harmonic treatment.

CHAPTER XVIII
Extension of the Harmonic Accompaniment.

A given part in whole notes with harmonic accompaniment in half notet
alternating in the remaining parts.
This can happen
through two chords,

through change of position in one chord,
through suspensions.
The exercises may be indicated in the same manner as heretofore.

Exercise.

'— 7 &° G-j Or—i d GT G

373, :£zfc=2=:

The Bass may be sketched as follows :

374.

=a:

In the second and fourth measures there appear sevenths of collateral
Seventh-chords without preparation. These are called passing Sevenths*

174

MANUAL OF HARMONY.

They move from the root, and always full on the arsis. They may occur in
this manner in all the parts.

The addition of the middle parts to the Bass sketched above gives the fol-
lowing four-part harmony :

376.

267

2 6

8 7

The same exercise with a richer variety of harmony may be written thus :

376.

Written out.

— &-

46 - 8

The next exercise will show the use of suspensions.

*
_n * Bfr C d g F

378.

879.

PTnltfen OM< :

9 8

MANUAL OF HARMONY.

175

3=3

We pass over the exercises in the middle parts.

The use of the simply melodic progression in whole notes for exercise!
(cantus jirmus) was in order to exhibit the simple harmonic substance of a
measure, or, as in Alia breve-time, in its component parts (half notes). If
the exercise is to be in half notes, chorals may be selected for the purpose.

For individual practice, one can easily take the Bass from some well-har-
monized arrangement of chorals, and work it out for himself.

The mode of proceeding is shown in the next exercise.

cGCFb°OF'c"c a c^ d — T af$°

This choral, harmonized as above indicated, could be written out thus :

176

MANUAL OF HARMONY.

After sufficient practice and sureness in the treatment of simple harmony,
one may pass on to the further development of the part-movement by means
of passing notes and appoggiaturas.

To this end we shall say more of melody and melodic progression in the
next chapter.

CHAPTER XIX.

Formation of Melody.

WE are not to discuss here the invention of melody, but its formation,
and, what is very important for our harmonic study, the method of recog-
nizing and using by the treatment and formation of melodies that which is
essentially harmonic in them.

This will depend on the recognition and comprehension of the following
principles:

MANUAL OF HARMON*.

177

Every melody, however carried out and developed, has a foundation fully
as simple as those we have used as exercises in our last examples.

TJierefore every harmonic movement of parts, however complicated, may
be traced back to simple harmonic connection.

To see the truth of this, one must learn to discriminate between the
essential notes and what is extra and accessory.

For this we choose the analytic method, and seek to develop the following
melody, which we will set down in the simplest form with the fundamental
tones indicated as heretofore :

382, F - Bb F

Both melody and harmony are chosen with a view to simplicity, and the
latter may be introduced in four parts thus :

383.

-&- -&-

Before proceeding to the farther development of this passage, it will bo
necessary to premise what ought to be mentioned concerning the rhythmical
formation of a melody.

A melody may be either a musical phrase consisting of a greater or less
number of measures without any fixed limit, such as often occurs as the
theme, motive of a composition, or by means of counter-phrases, a separate,
distinct whole.

In the latter case it is called a period, and contains usually eight measure*,
having as counter-phrases two sections of four measures each. These
counter-phrases or sections are often called " antecedent and consequent."

178

MANUAL OF HARMON*.

The details of this subject belong to the science of form.
See the author's work : " The principles of musical forms."

It is clear from its complete termination that the above passage forms a
period, and it is first of all necessary to find the division into sections.

This division is very often found in the cadences which occur in the middle
of the passage, either as imperfect whole, half, or plagal cadences.

Such a half cadence (in general : a close on the dominant) we find in our
exercise in the sixth and seventh measures, and we may take the point,
where the sign f stands, as the dividing line of the two sections of the
period.

The first section, the antecedent, therefore would contain seven, the conse-
quent six measures, and must each be rhythmically changed to four measures.
This may be done thus :

884.

I I

2— x

By adding the harmonic accompaniment above chosen, we have a complete
musical period.

Likewise it may be seen at a glance that all further transformations into

different kinds of time,
arranged, e. g. :

e. g. into J, J, g or g

time, can be very easily

QOR -V 1 1

1 " j-2 "1 ' J !

i ! Ill i

885-fch|^ — *-:*-

*? \~ All '

CE3! ^

£ J

r 1 .»*

| & • * L<5}» I

y i *. s i

/j_ - - ,_ ^ T

£^4 f^-^-rf—f

— f-A~^ — ^-f311

vjj * — i tj — p

.0 _ ^

i I i^i* i

&c.

6 -j^— fa — 6 »— ;

=--^-1=$=

P^-r— ^"f—

b— ffi^1^—-?^— "

&C.

&c.

We pass now to the tonic variations of the melody and add thereto pass-
ing notes and appoggiaturas. e. g. :

1 — r

MANUAL OF HARMONY.

179

A still further use of all the accessory tones would give the following
form:

387,

Originally.

The bimple melodic progression underneath will bo easily recognized as
the foundation. That the upper melody, however, is carried out with refer-
ence to the original harmony, will bo at once evident, if we add the other
parts witu the few deviations required by the upper part :

Adagio.

388.

tayio. - ^- ^_^. j -g

1*0

MANUAL OF HARMONY.

As to the consecutive octaves in the middle parts in the third measure of
this example, it is to be observed that these may be considered faultless, when
they do not occur singly, but in a longer series for the purpose of reinforcing
and thus bringing out a harmonic and melodic progression. The movement
in this case is to be viewed as in three parts.

Blight as is the independent worth of this example, yet it is used here
merely to show of what development the simplest melodic and harmonic
phrase is capable.

The advantage of studying and discerning these melodic and harmonic
relations is too important for us to omit making another experiment in the
following interesting phrase.

The fundamental harmonic progression is quite as simple as those
exhibited before.

889.

.This passage will form a period; the middle close is easily found in the
half cadence in the seventh measure.
We pass over the various kinds of measure and select the following

arrangement :

890.

MANUAL OF HARMONY.

181

The upper part, adhering to the harmonic progression, may be developed
as follows:

The following passage from Beethoven's E-flat major-Quartett will show
how the other parts can partake of melodic development :

A comparison with No. 390 will show the melodic and harmonic changes.
A still further variation of the original melody from the same piece fol*
lows here :

MANUAL OF HARMONY.

The other parts appear with the following changes :

•.

These hints in regard to melodic development m&y suffice here and be left
for individual practice or special instruction.

Remark. — The mechanical character of this whole treatment must not lead astray ; for
certain as it is, that in composition the above is not always the mode of procedure
(although Beethoven in the subsequent variations of th's original melody must have in
part proceeded thus), so our only object here was, partly to place in the right light the
relations of our previous exercises to the practical side, partly to gain a clear insight into
complicated compositions themselves.

As concerning the accompanying parts, they resulted naturally from the
simple harmonizing and needed little change, snowing themselves, if subor-
dinate, yet not pn that account unimportant.

It now remains to speak of other modes oi ^.jrajarihaej*', which will be
done in the next chapter.

MANUAL OF HARMONY.

188

CHAPTER XX.
Formation of the accompanying Parts.

THE mode in which the accompanying parts partake of harmonic, metrical
and melodic development, is seen in the last examples of the foregoing
chapter.

There are, however, still other kinds of accompaniment, known as :
THE FIGURED ACCOMPANIMENT.

Jt is not suited to the character of vocal parts, and its use therefor must
be very limited. In the following investigation we shall treat only of instru-
mental music.

By figured accompaniment is understood that kind which arises from the
metrically uniform transformation of the simple chord-tones, e. g. :

Simple Harmony:

Figured Accomp't:
a.

395.

_§?_ -fc^^ ur i i .-f^j 5^**^ •»«Ltor "*i

&c.

The accompaniment under a. is harmonically figured. The figures that
lesult from it are also called broken chords. That under b. is metrically
figured, and that under c. melodically figured. The figures produced by this
last are formed of appoggiaturas and passing notes.

Each accompanying part can be used for such figuration, either alone or
in conjunction with other parts.

We take the beginning of the 382d example to try a few modes of accom-
paniment. The following further remarks may here be stated beforehand:

When the figures are repeated uniformly (e. g. in broken chords), all thi

184

MANUAL OF HARMON*.

rules for harmonic progression in a CHANGE OP CHORD, as well as for
doubling, are to be observed.

We cannot therefore write thus :

-m- -J-* * ^*^ **'

396.

but somewhat in this manner :

15=E

\ \

•-i

— i-

J^ ^ 4-

— ^?

In a change of harmony the last note of a figure and the first of the next
must not form a false progression with any other part. e. g. :

not:

better:

898.

The harmonic figuration enables us to arrange even one-part movements
with greater fulness. The examples may begin with the following :

899. In one part:

MANUAL OF HARMONY.

185

It is easily seen that these phrases are calculated for a single instrument
RS a violin or clarinet.

40O. In two parts :

%^-i---

-0 p ^

S^N*

; parts:
in the middle part:

in the lowest part:

f=j

£:

-^-'

in the highest part :

-$=2

-&-'

^--

After 'nese experiments with the above example, the figuring in four-part
movem nt will be equally easy to accomplish.

186

MANUAL OF HARMONY.

Instead of this we rather take as an example of varied figuring the follow*
Ing passage from the Quartett movement of Beethoven cited above.

401.

SEN!. i^=i=£=r= =3

pizz.

cres

MANUAL Of ITAKMONT.

187

Tho whole of this rich development rests upon the base given in Nos.
390, 391 and 392, and in all cases where there is a change of harmony, the
progression of parts is carefully observed. —

If one desires to gain a clear insight into compositions so elaborated, and
learn to comprehend their inner harmonic structure, it will be very well to
trace back pieces of this kind to their simple basis ; labor of this sort will
be repaid by enriching his knowledge on many points, and qualifying him
for individual productions.

CHAPTER XXI.

Exercises in Three-part Movement.

In our exercises thus far we have used with but few exceptions four-part
harmony, and although the same admits of greater fulness and seems most
suitable for harmonic connections, yet three-part movements also are of great
use, being particularly adapted for greater skill and variety in the manage-
ment of the parts.

We begin as formerly with exercises on a figured Bass.

188

MANUAL OF HARMONY.

():. — i — i—

rl i~i
.] /s1

[—

41 i ^— -

?> J J -

1 • ^

/^ 2

^^rH

Three-part harmony is indeed sufficient for the triad, but the movement
of parts will often result in the omission of one interval, as must of course
be the case with seventh-chords, though the omitted interval can never be
the seventh itself. Generally the fifth can be left out, as has already
occurred in four-part movement, and in many cases the root also ; the third
as the interval which determines the nature of the chord, can rarely be
omitted without producing a peculiar gap.

We will harmonize as follows, and annex a few remarks :

403.

8NB.

10 11 12

E | F

— ffi

— ^)—

— fca£

_LL

— » — ?->^ ^> ^

^"iTi " i*^~ 1- Tl- ^-

•««»

-fcP81

4
6 3

E£ S

6
6 5

6
5

[fl ...

+4—

z5 ~^ — 1" —

• / A/ g

__| J_

-^ g

— |

^ T

In the fourth measure at NB. we find the chord of the Sixth-and-Fourth
of the diminished triad e-g-bfr* It stands in place of the chord of the Second
Ifr-c-e-g, the root of which c is here omitted, for in four parts the passage
mmld stand thus :

MANUAL OF HARMONY.

189

404.

i-^*—
^ f f-

6
5 9

Compare remarks on p. 155 concerning this chord.

In the fifth measure a fourth supplies the chord. Though a fourth, to be
§ure, can neither in three-part, nor in two-part harmony, pass for a complete
chord, as is the case with the third and sixth, yet in those instances where
the chord of the Sixth-and-Fourth hi four-part harmony can be used on the
arsis as a passing chord, in three-part, for the sake of a better movement of
parts, the Sixth, or the third of the fundamental chord, can be omitted, so
that the fourth shall stand alone, designating here the root and fifth of the
original chord.

Sometimes in two-part movement the fourth will represent the chord of
the second, CFpecially in the case of a passing seventh, e. g. :

With four parts the above passage in example 403 would be thus, when
completed :

408.

By the skip in the Alto part in the eighth measure of example 403, tht
chord of the Sixth-Fourth-and-Third is made complete.

In the tenth measure appears a chord of the Sixth-and-Fifth. Really the
fifth here is only a suspension of the fourth, which, however, by the progres-
sion of the Bass becomes a third. With four parts this too is made clearer i

190

MANUAL OF HAEM01TY.

407.

The last measure of example 403 shows in the Octave F that the triad
y appear in such cases even without the third and fifth.
Il is seen in the first and second measures of the next example that the
movement of parts often requires the omission of the third.

408

-». — -

--st-tvJ-

^rji^i —
a — I

— i — <«•

The omission of the third occurs best upon the arsis, as here in the latter
part of the measure : on the thesis, therefore at the beginning of the measure,
the third must not be wanting.

Further exercises are to be left for special instruction.

Exercises in Three-part Harmony to a given upper part.

Tho following exerciae with the roots indicated is to be written out in
three parts.

191

400.=

MANUAL OF HARMONY.

Written out:

410.

33=£=-

without
root.

This work needs no explanation.

The choice of the middle and lower part will in general depend on tho
position of the chords. Thus in a low position the Tenor is better suited for
a middle part than the Alto ; likewise the Tenor can be taken for the lowest
part instead of the Bass.

For the following example the Tenor is selected as the middle part,
because its movement is more in company with the Bass, while the simple
song of the Soprano seems of itself more isolated.

The former exercise with a more extended harmonic development :

Co,

O—

}t at dD Gi

412. Written out.

-<G_

6 —

NB.

In the fifth measure at NB. what is really a suspension on the ninth

. appears through the position of the parts as a second, which must occur very

rarely and only between Tenor and Bass. It should be observed here that

there can be no suspension on the second at all, because the second of itself

192

MANUAL OF HARMONY

is based upon the inversion of the seventh, and conforms to the progression
of the latter, e. g. :

Inversion:

413.

—

Exercise in a middle part.

TENOR, d A B^ C ge° d — <ffi°7 d A
414.

The Alto is taken here as most convenient for the highest part.

415.

The same exercise with the following designation of chords :

dg A—i B\)G OF Bfre0 d B\>F g C° d A d

417.

^=1=

ids

W&— ^

= 1

[tn — 1 — t —

h ,^—

_^2 ,5) —

— w-if

4- p

(| '

i — H

_.fi_LL

6
6 4

6 7

6
|

— Ig oL_

3g fiL

=Mt

MANUAL OF HARMONY.

193

The last measure but one shows that even the sixth may be a suspension.
The former exercises, proposed for the four-part movement, can also ba
made use of here for further practice.

CHAPTER XXII.
Two-part Movement.

THE great barrenness of the two-part movement in a purely harmonic
relation renders it seldom adapted for other than contrapuntal labors, in
which alone it derives any peculiar importance, and even then is used in
movements of several parts e. g. in fugues. If indeed, for a simply har-
monic use, a metrical and rhythmical variety in the formation of the parts
will render a two-part movement tolerable, so the contrapuntal develop-
ment of two parts can alone free them from the monotony of numerous
consecutive thirds and sixths, and give it essentially that completeness which
every part-movement should have.

There must always be in this movement an omission of one or more inter-
vals. In triads it will oftenest be the fifth or the root. When Seventh-
chords are used, the seventh of course must not be wanting. Octaves and
fifths should seldom be introduced, as the effect is too bare : the fourth would
only be admissible in a few cases, where the chord of the Sixth-and-fourth
may properly stand, or when it occurs in place of the chord of the Second
(see p. 182.)

419.

sample: OF 6° 0 — F C a G C

• -r 1 Jfl T T 1^1 3T3 1 ^ 1 ^>J 11'

-a-f-2-f " : = : : :: l - l__| = Ji

'•itte/i out:

1 1 II

-^- -*- «

-7BT- --^-4-^-4 f j 4-« ^ «— «-

1 — |. — | — | — |. U-

368 3 6 63 3 1

Iff *K ^ —

-1 { \ 1 1 H-

194

MANUAL OF HARMONY.

The omission of intervals is plainly seen, on comparing the fundamental
tones in exercise 418. There will seldom be a confusion of harmony, since
each chord explains itself by its position, that is, by the harmony which pre-
cedes and follows it.

The same exercise with different harmony :

G O

C Co,

420.— E-<

Written out:

421.

— s 1

r~5 —

-22 =C

^ T

fe (ft tf» f "

U|fl p_|

5 —
6 ^^2 -

=9—^1

r-1 — F—

-r S

Mr— ^

E^ t=:I

• a. — .,

^ \ « fh =

2 -

-41

_^ 1 1 1

-1

4-C- 1 — U ,

Most of the exercises in the third section pass into the domain of counter-
point. The difference lies in this, that here the succession of chords is
prescribed and the part-movement remains to be carried out, whereas in
contrapuntal studies a knowledge of harmony and a safe use of it is presup-
posed, so that the series of harmonies can be left to individual choice.

These studies may therefore be considered useful as preliminary to those,
furnishing at the same time a view of the relation between harmony and
counterpoint.

The exercises in the following chapter are to be regarded in the sam«
light, though the restriction to a fixed series of chords is done away with.

MANUAL OF HARMONY.

195

CHAPTER XXHI.
Harmonic Treatment of a given Part in Melodic Form.

BT the melodic formation of a part is not to be understood here that
richer ornamentation exhibited in chapter nineteen, but we merely 'meun to
avoid by means of metrical variety the simple choral-like progression of our
previous exercises, and thereby afford opportunity for learning to develope
the parts better in the harmonic accompaniment.

The following exercise will make this clearer :

422.

The series of chords is left for selection when the exercise is worked out.
Although the kind of measure we have chosen will of itself produce a simi-
lar melodic movement in the parts to be filled out, yet special attention must
be given to their good progression according to the principles developed in
former chapters, if a free, skilful treatment of them is to be acquired.

Let the exercise be first treated in three-part harmony.

423.

This treatment needs no further explanation after the remarks under
three-part movement.

The harmonic treatment of this melody as a middle part will show its
many-sidedness, and may be recommended as a useful exercise.

To be able to retain the Alto voice, we transpose the melody for the sake
of a better position into F major.

196

MANUAL OP HARMONY

424.

The explanation of the unprepared chord of the Sixth-and-Fourth in the
fourth measure is found in the remarks on passing chords in chapter fifteen.
It arose incidentally from the progression by degrees in the Bass, and stands
here in place of the chord of the second. >

The treatment of the same cantus jirmus transferred to the Bass :

425.

This treatment displays one weak point in the third and fourth measures in
the harmonizing of the sustained a in the Bass. So the bare fourth in the
sixth measure is a very imperfect representative of a chord, unless it be
explained as a passing note.

If it be desired to develope the part-movement still further, passing-notes
and appoggiaturas can be used alternately in the parts to be added, e. g.

'•/• ^T

426.

7 6

MANUAL OF HARMONY.

197

JOL

3 7

Of the remaining treatments, that with the cantus firmus in the middle
part here follows :

427.

c.f.

-0—f-

i&i

6 9

The following may serve here as examples of four-part treatment :

428. Given part:

198

MA&UAl OF BARMON7.

429. Harmonized in four parts :
C.f.

NB.

In the fifth measure at NB. the skip of the Tenor to the seventh should
not be considered good for the reason that the Soprano simultaneously
makes a long skip in the same direction to the root g ; this can only be
justified by the position of the Alto.

In the same measure we find the chord of the Sixth-and-Fourth of the
augmented triad, whose original fifth is prepared, (p. 91 and 92.) It stands
here in the character of a suspension from below (see Suspensions, Chap.
XH., p. 116.)

The same cantusjirmus transposed into D :

nfe * *

"^,

l ^^ ^

BEi

_H 1 ; — ,

c./.

430.

MANUAL OF HARMONY.

199

N.B.

7 6 5

In the fourth measure are suspensions in three parts (see p. 117). In the
fifth and sixth measures the position of the Alto and Tenor is not good, as
they are more than an octave apart.

Of the remaining treatments, that with the cantus firmus in the Bass may
here follow :

431.

NB.

The introduction of the seventh-chord of the seventh degree in the fourth
measure seems confused here, because the root lies immediately above the
seventh (see p. 69.) In similar favorable positions it is well to use even the
chord of the second or VII? .

Moreover the progression here is not according to the movement of the
leading-tone, but in the same cadence-like form as with other seventh-chords :
C£° f#.__ (See pp. 68 and 69.)

The treatment of this cantus firmus with more movement in the parts can
be effected thus :

MANUAL OF HARMONY.

432.

- f & . ±. r (:

F -0- £=

— It

15 p, r.r, .- £

. ...

. r_^

NB.
-«? .« 5

:
—=-. — 1+

F [J L ,

6 66

5 25 74

:j» — j_4- -1 -^-l-| -| — ' P *

T — t — r— -

3 6 7

— ^ ff

:=z=rc

1 (? f> .. , .„._ fld^ ,.^ *... j_ j: |

1: f — ^ 0 -1 [

= tt

The progression of the seventh upwards in the last measure but one (at
NB.) is caused by the movement of the Soprano (see p. 84.)
The treatment of the cantusjirmus in the Tenor here follows :

433.

MANUAL OF HARMONY.

_|~ p -H- |~ -fa V-* ^-f^fSL

201
-*1 tf

Eg ! — E ! 1 [^_u-4— f-l

^fi

|pL — it—^-j:1"1"7 ' j L p H h

p.. * ^'-]^^^==:r=W — ^ — ^-1

— | E ! E — -1- — r — r—

6 6
# 43 6 47

# W T— | 1 1 1 ~=-r»- 1

^* 1 1

The third measure gives us opportunity to speak of consecutive fifths and
octaves in contrary motion.

According to the principle heretofore unfolded (p. 27, &c.) they are
equally faulty with those in direct motion, and it should especially be
observed of consecutive octaves, that they clog the free movement of the
parts. With consecutive fifths, however, the character of chord-partition is
very much softened by contrary motion, which is especially true of those
that move towards each other; whereas those moving asunder make the
separation or want of connection more perceptible. (See also example 430
in the 6th and 7th measures between Tenor and Bass.)

Compare the following examples :

434.

A glance at the treatment contained in this chapter shows plainly the
melodic formation of parts, and here lies the reason for regarding them as
contrapuntal labors ; for the essence of counterpoint in contrast with the
simply rhythmical harmonic movement, consists in this very thing, that it
requires the melodic movement of parts to be freer and more varied, but
with observance of the harmonic laws which constitute, as it were, the

inmost germ.

Throughout these examples, even where the parts move in quarter-notes,
the simply harmonic structure can be traced, so that they may serve for the
present to show the difference between the simply harmonic and the contra-
puntal development of a given part. The details of this subject can only
be discussed under counterpoint itself.

202

MANUAL OF HARMONY.

CHAPTER XXIV.
Five-part Movement.

SINCE already in four-part harmony the doubling of the intervals of a
triad is necessary, so in a movement in five or more parts the same will be
requisite to a still greater extent and even in Seventh-chords.

As in pure harmonic movement every part must preserve its independence,
so, to attain this, those intervals will be specially adapted for doubling, which
admit of a double progression. Now this, to be sure, may under certain
circumstances be the case with each interval of a chord, though sevenths are
the least adapted to it ; the doubling of these must therefore be necessitated
by the melodic progression, as e. g. in passing. .

Further remarks follow under the examples given.

435.

In writing this out we may, according to the position of the parts, take
either two Sopranos, two Altos or two Tenors.

436.
SOPRANO.

MANUAL OF HARMONY.

203

The same exercise differently constructed :
437.

G^^^Z.

80PBANO I. / i~~[fr

SOPBANO II.

ALTO.

TKNOB.

BASS.

The independence of the parts demands also, that in a change of chord
two parts shall not be sustained upon the same tone or in the octave. In
the above example in the first and second measures it is the case between the
second Soprano and Tenor, but not erroneously, because the same chord
only leaves its position, but does not change to another chord.

But the following passage

438.

should be corrected thus :

439.

-&-

£SE;

Remark.— This rule, however, often admits of exceptions where there are more parts, ai
other relations then present themselves.

That the movement of parts allows also the leading-tone to be doubled, is
seen in the third measure of example 437 between the second Soprano and
Tenor,

204

MANUAL OF HARMONY.

As was the case in four-part harmony, still more in that of five or more
parts will be seen the impossibility of avoiding concealed fifths, octaves and
unisons. It may be again mentioned, however, that here also the extreme
parts must progress in pure relation, and only to the middle parts is a greater
freedom allowed.

The following example contains various progressions of this sort

TENOR.

BASS.

lEssz=zE££i

— i 1 — _i —

The progressions of concealed fifths, octaves and unisons in this example
are indicated by a stroke. The open fifth in the eighth measure between
the second Alto and Bass need not be avoided, since with several parts the
diminished seventh chord can with difficulty progress otherwise.

From the eighth measure the first and second Alto might also move in
this way.

MANUAL OF HARMONY.

205

441

From the second Alto and Tenor in the second and third measures it may
be seen that the parts, especially the middle ones, may often cross each
other.

For practise in five-part movement chorals can be used to special advan-
tage.

The following may be annexed here :

CD^ G Z>7

442.

EI a 6° 6°7 E a

Exercises in five parts and more require a simple and natural Bass-pro-
gression, and the less artificial and difficult it is, the clearer and more intel-
ligible will be the succession of harmonies, which is all the more important
because very unintelligible progressions can easily arise where there is thig
fulness of chords and necessity for the free movement of the parts.

The beginning of this exercise is here given :

443.

At the repetition this series of harmonies may be used :

906

MANUAL OF HARMONY.

444.

CHAPTER

Six-, Seven-and Eight-part Movement.

THE necessity of doubling or tripling increases with the number of parts
added ; likewise their independent movement will require them to cross one
another. The simplest harmonic progressions become now the main con-
dition of the possibility of employing so many parts, and it must be observed,
that many chords are totally unadapted to this mode of writing, because
their intervals, being subjected to a fixed progression, cannot be multiplied,
as for example the altered chords and the diminished seventh-chord.

A few progressions of the triad may be given here.

Progression to the second degree :

4 parts:

5 parts:

6 parts:

445.

M ' '

&• rj

S3 & /^?

2ZZZZKZZZ£Z1

73 ™ - f?

tt . , „ J^

-«>- j -*-

cv — 1_

z* & *•*

-*- & ~^~

& & &

f & &

-ffl_
-e- -&-

-** ^ «H

^S * 0 & &

_& 5. ^

3 * 22=^

7 parts: 8 parts:

_0 tP-^ 221

-GL-

MANUAL OF HARMONY.
Progression to the third degree :

207

4-parts:

5-parts: 6-part*: 1-parto: 3-parfc:

Progression to the, fourth degree :

4-parte: 5-parts: 6-parts:

7 -parts:

&-parto:

Progression to the fifth degree:

4-parts; 5-parts: Q-part$: 7-parts: 8-parts:

• - •

<£££. &J L

~* ~^!L

We pass over further combinations, which it will be very useful to try
mth all the varied transpositions.

As an example of the treatment of part-movement, the choral under No,
442 is here given in six parts :

446.
SOPRANO T. &II.

ALTO.

TBKOR I. & II.

BASS.

=&=&&= &t

208

MANUAL OF HARMONY.

t— |

647

i e

^ ff *="&•

352 ... 22^

r5* r^

M if

• i tfr

i B^

«y 1

DEfi

1 I ^3

^ '•&

I I '

/r? Q^5

\ J~~6

r r

h^ I

i SC-

1 C

I 10 \

f f

f '

£ 1

....

' ~ I

*=ftt=|

^g — $—

r i^'l

— IH

sr*^ —
^^ff—

7 91

6 3 -

1 1 1

sl 5

._( C 1

^—v—

-& — j

f
^1 ' -J-

1 ^-

MANUAL OF HARMONY.

201

— w-

*— I

Since in chorus movements consisting of many parts, these are not always
employed simultaneously, as in an accompanied chorale, the harmony is some-
times hi three and four parts, and is worked up to a climax by the addition
of others.

The following examples will explain this kind of chorus-movement, and
especially serve to show also, that even in a composition consisting of many
parts, suspensions and passing notes can well be introduced, without impair-
ing its clearness and comprehensibility.

447.

SOPRANO
L&II.

ALTO.

TENOR
I. & II.

BASS.

=£:

MANUAL OF XARMONY.

AwoIL

TEKOB.

BIBS.

MANUAL OF HARMON?

211

In eight-part chorus-movements, where the customary four parts are
usually doubled, these are not always employed as eight independent parts,
which might result in overcrowding, but frequently two parts of similar
register in unison (e. g. two sopranos, two altos, or two tenors and two
basses in unison) so that the harmony often appears in four, five and six
parts. We find also the eight parts divided into two distinct choruses, acting
each by itself and in detached places.

As showing the peculiar movement which many of these parts must adopt,
the commencement of the above choral is here given in eight parts :

449-
SOPRANO I. & H.

ALTO I. & H.
TBNOB I. & II.
BASS I. & II.

212

MANUAL OF HARMONY.

Iii movements of many parts, divided into distinct choruses, the difficulty
of this kind of writing is met by making, not always a tonic, but often a
metrical distinction between the parts, where two or more choruses co-operate;
but it must always be assumed that the succession of harmonies shall follow
in the simplest manner and never by a sudden change. This is also under-
stood to be the case, when we speak of chorus and movements in twelve and
sixteen parts, and only single compositions of Bach are found, where eight
and more parts, including, however, instrumental parts, are treated obligate.

These hints with regard to movements in several parts may suffice here,
especially as further details, after a thorough knowledge of harmony, may
be left to individual study and taste for movements of this kind. As to their
application we would only remark further, that the use of the movement in
many parts above exhibited, and its mode of treatment within the assigned
compass, will occur for the most part in compositions for chorus, but not in
instrumental music, e. g. in orchestral works, as may be conjectured from the
participation of so many instruments of various kinds ; and that for these
last in most cases the four-part movement is sufficient, concerning the further
treatment of which reference can only be had to actual systems of instru-
mention, since the doubling relations, although often approximating the
method above indicated, must yet be subjected to other principles.

MANUAL OF HARMONY.

213

CHAPTER XXVL

Forms of Musical Endings.

DIFFERENT forms of ending have already been mentioned on pp. 32 and
83, likewise further remarks have followed in reference to the authentic
close pp. 40 and 53, but throughout the whole treatise there has been no
opportunity afforded of recurring to them, so that what remains to be said
of these and other forms of ending shall here follow.

We divide the forms of ending first into

the authentic cadence and

the plagal cadence.

The authentic cadence has the formula V— I, the plagal cadence IV-I (or
in minor : V-i, iv-i), as has been before observed.

Both forms are used not only at the close of entire pieces, but also at the
close of the chief divisions, of periods and their sections. The remainder
of this subject belongs to the doctrine of form (see Book quoted on p. 142.)

If the plagal cadence end a piece, it seldom stands alone, but follows the
authentic cadence ; so in a piece in minor it often leads to major, e. g. :

auth.
Cadence.

Plagal
Cadence.

450.

It is then often introduced, as in the above example, by a modulation.

Endings (cadences) are also divided into whole and half.

By the former we understand the same as by an authentic cadence. But
these we subdivide ml® perfect and imperfect.

Perfect whole cadences are those in which the Bass contains the root of
the dominant and tonic, and the Soprano likewise the root of the tonic,
e.g.:

214

MANUAL OF HARMONY.

not;

451.

When this is not the case, they are called imperfect, e. g. :

Tr~ " cX T"

T — (g T

ff=g^

452.

&C.

tz :

..-

£j

£t

/^"

If the Bass move from the dominant to another degree, they are- called
false cadences.

453.

&c.

Bi:

See examples p. 82-85.

Half cadences hare the formula I-V. e. g.

454.

They consist also in this, that the dominant triad ends the phrase.
Beside the tonic triad, chords of other degrees also may precede the
dominant triad in the formation of a half-cadence, e. g. :

455.

Under half cadences we include also those endings in the dominant key,

MANUAL OF HARMONY.

215

which are formed by a modulation into the same, not a decisive one, how-
ever, through the fundamental position of the dominant-seventh harmony,
but either through its inversions or the seventh chord of the seventh degree'
e.g.:

456.

0:vn°7C:V c: n°7

This is the case, however, only in relation to the key which has prevailed
immediately before.

For the further understanding of these kinds of cadence, those which are
found in the examples of this book may be compared.

In No. 388 in the third and fourth measures there is a half cadence
formed by n-V, which constitutes the close of the first section of the entire
period : in the seventh and eighth measures, however, a perfect whole or
authentic cadence.

In example 392 a half cadence is formed in the third and fourth measures
through I-V, and a perfect whole or authentic cadence in the key of the
dominant at the end. (Here therefore no half cadence, because the domi-
nant-seventh harmony renders the modulation decisive.)

In the choral written out under No. 446 the first strophe ends with an
imperfect whole cadence, the second with a perfect whole, the third with a
half in E minor (iv-V), the fourth with a perfect whole in G major, the
fifth also with a perfect whole in A minor, the sixth with a half in E minor
IV-V), and the seventh with a perfect whole cadence in G major.

In chorals the application of the various cadences is easily found ; for
larger pieces they furnish means for separating and connecting the smaller
and larger divisions, and are therefore to be used with great care, since upon
them the construction of a piece as regards form in a great measure depends.

A. B. KIDDER & SON'S MUSIC TYPOGRAPHY.

MT
50
R5352

1873
Miiak

Ri enter, Srnst Friedrich
Eduard

Manual of harmony. 8th
German ed.

306123

Richter,Ernst Friedrich
Eduard

Manual of harmony. 8th
German ed.

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Full text of "Manual of harmony; a practical guide to its study, expressly prepared for the Conservatory of Music at Leipsic"

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