Foote - Modern Harmony In Its Theory And Practice

781.3 *'68m2

781.3 F6Bm2 Foote $3-50

55-02341

55-023^-

ftodern Harmony in its

theory and

practice.

Keep Your Card in This Pocket Books

will

be issued only on presentation

of

proper

library cards.

Unless labeled otherwise/ books may be retained tor two weeks. Borrowers finding books marked, defaced or mutilated are expected to report same at library desk; otherwise the last borrower will be held * responsible for all Imperfections discovered. The card holder is responsible for all books drawn

on

this card.

Penalty for over-due books 2c a day plus, cost of notices.

Lost cards

and change

of residence

must be

re-

ported promptly.

Public Library Kansas City, Mo.

ODD

I

'>

Eighty-Second Thousand

AUGMENTED AND REVISED EDITION

MODEEN HAEMONY IN ITS

THEORY AND PRACTICE

BY

ARTHUR JOOTE

A.M.

AND

WALTER

R.

SPALDING

A.M.

Professor of Music at Harvard University

PRICE $3.50

THE AKTHUR

P.

net

SCHMIDT

BOSTON ISO

BOTLSTOK STBBET

CO.

PREFACE one not used to it, is the having a mental in other of the symbols written down sounds conception of the real is directed to the thing, not now Education the with eye. words, hearing As the practical way of working in that direction, in this to the symbol. the book from very beginning the harmonizing of melodies goes step by from figured basses. It is hoped that the illustrathe with writing step has tions quoted from many composers will be of help by showing^what material. harmonic our with done been actually For matters connected with acoustics ( 5, 13), the student is referred on to Helmholtz's book "On the Sensations of Tone," and to the essay *' Partial Tones" in Grove's "Dictionary of Music/' all.

The most

difficult thing, for

BOSTON, August 1905. ,

PREFACE TO AUGMENTED EDITION SINCE this work was published much has happened in music, surprising changes having come, especially as to an increasing use of dissonances. From the time of their first discovery as a factor in music until to-day the number has been enlarged by degrees, but never until recent years has there been a reversal of former standards in their use; the theory that there must be a considered proportion between consonance and dissonance has apparently been discarded. For example, polytonality is a direct contradiction of the belief held for centuries that music must not be in more than one key at a time.

Something of value will later appear as a residuum, but much will thrown away as without real worth, to-day we cannot foresee what the net result of the upheaval will be; but one thing is certain, that we must keep our old standards, if they can still prove their value, not being distracted from fundamentals by experiments. More than ever is it necessary for the student to have a thorough grounding in the harmonic principles that have stood the test of time. In Chapter LI the important Third-relationship of keys is treated fully, while in the following one will be found an analysis of the experiments and doubtless be

innovations of the last twenty-five years. There are also numerous additional exercises,

BOSTON, November, 1936.

TABLE or SHAPTEK I INTERVALS Consonance and dissonance, 7; Inversion, II THE SCAUES /

PACKB 1 9.

11

Circles of 5ths, 13; Relative minor, 15; Chromatic, etc., 17.

HE

TKIADS Chord denned, 18; Doubling

16; Tonic,

18 of intervals, 19;

Open and

close

position, 20; Similar motion, etc., 22; Consecutive Sves and 5ths, 24; Voice-leading, 27; Leading-tone, 28; Rules for triads,

29.

IV EXERCISES WITH TRIADS

V VI

IN

MAJOR KEYS

31

Directions as to figured basses, etc., 31'; Exercises, 34. EXERCISES IN HARMONIZING SOPRANO MELODIES

.......

Triad successions in major keys, 36; Exercises, 37. TRIADS IN MINOR KEYS . . Additional rules, 39; Tierce de Picardie, 42; Triad successions in minor keys, 43 Three- voice writing, 43.

36 38

;

VII EXERCISES WITH TRIADS VilL HIDDEN SVES AND STHS IX INVERSIONS OF TRIADS CHORD OF THE GTH

IN

MINOR KEYS

.

X

Doubling of bass with single chords of the 6th in major keys, 51 ; in minor keys, 53. XE CHORDS OF THE GTH IN SUCCESSION General directions as to doubling the bass, 57. XII THE 6-4 CHORD As a passing chord, 59; In succession, 60. XIII EXERCISES WITH 6 AND 6-4 CHORDS Harmonizing melodies, 63; Three- voice writing, 65.

XIV CADENCES

XV XVT

SEQUENCES Writing on four staves, CHORDS OF THE 7TH

44 47 49 50

54

57 61

66 69 71.

71

Resolution defined, 72; Dominant 7th, 72; Its resolution explained, 73] Rules, 75; Its entrance, 76.

XVII PASSING AND AUXILIARY TONES v

76

TABLE OF CONTENTS

V{

CHAPTER

XVIII EXERCISES WITH CHORDS OF THE DOMINANT TTH

,

.

.

.

.

78

Deceptive resolution, 79; Three- voice writing, 80.

XIX

XX XXI

INVERSIONS OF THE DOMINANT 7ra SOME SIMPLE MODULATIONS EXERCISES WITH DOMINANT 7TH CHORDS AND THEIR INVER-

83 84 86

SIONS Three-voice writing, 89,

XXII IRREGULAR RESOLUTIONS OF THE DOMINANT 7TH XXIII EXERCISES WITH THE SAME

XXIV

93 .

IRREGULAR RESOLUTIONS OF INVERSIONS OF THE DOMINANT 7TH

100 105

Allowable consecutive 5ths, 106.

XXV

IRREGULAR RESOLUTIONS OF DOMINANT 7TH CHORDS AND THEIR INVERSIONS XXVI LEADING-TONE CHORDS oP THE 7iH IN MAJOR KEYS ... XXVH EXERCISES WITH THE SAME XXVIII LEADING-TONE CHORDS OF THE 7ra IN MINOR KEYS (DIMINISHED 7TH CHORDS) Enharmonic notation, 122; Consecutive diminished 7th EXERCISES:

110 114 117

120

chords, 122; Cross-relation, 124.

XXIX

XXX

EXERCISES WITH THE SAME SECONDARY CHORDS OF THE 7ra Free treatment, 129; The strict resolutions, 134; In succession, 136; 138.

XXXI XXXII XXXIII

XXXTV

124 128 rules,

132;

Irregular

Accented passing-tone,

EXERCISES WITH SECONDARY 7TH CHORDS INVERSIONS OF SECONDARY 7ra CHORDS EXERCISES WITH THE SAME CHORDS OF THE 9ra

138 142 146 152

The C

clefs, 152; Dominant 9th, 154; Dominant 9th with root omitted, 157; Inversions of Dominant 9th, 161; Chords of the 9th on other degrees of the scale, 161.

XXXV XXXVI XXXVII

EXERCISES WITH CHORDS OF THE 9rH CHORDS OF THE HTH AND 13TH CHROMATICALLY ALTERED CHORDS

163 166 171

Neapolitan 6th, 176.

XXXVIII EXERCISES WITH ALTERED CHORDS

XXXIX AUGMENTED

CHORDS

Augmented

6th,

183;

179 182

Augmented 6-4-3, 186; Augmented

6-5, 189.

XL

EXERCISES WITH AUGMENTED CHORDS AND THEIR INVERSIONS.

194

Three-voice writing, 198.

XLI SUSPENSIONS XLII EXERCISES WITH SUSPENSIONS XLHI ORNAMENTAL TONES Passing-tones; Auxiliary-tones; Changing-tones; Appoggiaturas; Anticipation; Figuration.

199 212

217

TABLE OF CONTENTS

vii

CHAPTER

XLIY

PA

i~

1

I

1

'

better'

is

,

J.

\

than

.

I

T

A

Jt V

1

^

VI

Consecutive Sves and 5ths can also occur in contrary motion, being then open to in similar motion (but see the top line of p. 74, and p. 242). Sve, or 8ve followed by unison, produces the same effect (p. 24) a*

A

same objection as unison followed by an the

consecutive Sves.

*

simply a workable rule and does not cover find similar motion of all four voices In writing exercises it is well to indicate that a tone is chords by writing a tie connecting the two notes, but in

This

fifth, e. g.

is

we may

every possibility. If the bass descends a natural and suitable ( cf. note on p. 22 ). kept in the same voice in two successive playing to disregard the

tie.

HARMONY i

.1

i

Jf-J,

V

In example (a) contrary motion is indicated for the succession not a point of great consequence the reason for this prefer-

48.

ii-V.

ence

VI

It is

;

mainly in the two consecutive major 3ds which would otherwise between alto and tenor. The interval Et?-A, comprising three whole

lies

result

steps,

i r

-r

a TRITONE, the use of which was formerly forbidden

although such a rule

fa needIn this particun-V which excludes it sounds better (e/.60.) 1 In (6) the leading tone naturally ascends to the tonic, in whichever voice it may be, doubling the 3d in vi, in the succession V-vi (p. 41). In (c) we see that the leading tone may be forced to descend, in order to avoid consecutive 5ths (in this case between soprano and bass). In (cO is an instance of the leading tone descending (to the 5th of the triad), in order that the following chord may be complete. This is often of good effect with an inner voice (alto or tenor) in the succession V I. At page 253 tottl be found additional txercises* supplementing those on pp. 35, 37, 47, 65*

te called

lessly rigid, there ia no question but that the tritone lar case we can justly say that the succession

;

demands expert handling.

82, 92.

1

Chap.

For a more complete discussion of the matter, see Spalding's I,

7-8.

**

Tonal Counterpoint,"

HABMONY

CHAPTER IV EXERCISES IN TRIADS 49.

triads

BEFORE

proceeding to our

first

exercises,

and forming musical

in connecting major pay attention to

sentences, it is necessary to certain details, which are considered in the following

GENERAL DIRECTIONS. At present we

remember always write the soprano

clef,

tenor

and

shall use

that

and

but two

clefs:

we are dealing with four alto in

real voices, soprano, alto, tenor,

and

bass,

and

the

bass in the other.

In making notes have the stems of soprano and tenor to the right of the notes, pointed upward, with the tails (if any) turned to the right; the stems of the alto and bass to the left of the notes, pointed downward, with the tails turned to the right.

In the case of single notes on a staff, or of a group written as a chord if the note is above the middle line, the stem will be on the left, pointed downward, and if below the middle line, on the right, pointed upward; with chords, similarly, the question of whether most of the notes are above or below the middle line determines the manner of writing. -f-

t Ties are to be

made

as follows,

when two

r

voices are on

a

staff:

f-

curving upward when used with the upper notes, and downward when used with the lower notes.

t.e.,

50. Certain conventional signs have been for a long tune used to define the meaning called figured basses (i.e.. all basses other than triads in the fundamental position), where the other voices are not written out, and the chords are understood solely through the :>f

what are

HARMONF

32

and other signs employed. These figured basses were largely used in the organ parts the player was of oratorios, etc., at the time of Bach and Handel, and with their assistance

figures

expected to extemporize a full organ part. is no figure, 51. In this book, if an 8 is below the first bass note of an exercise, or there on the the soprano is to begin on the 8ve; if a 3 or 5 is below the first note, the soprano begins F

raised a under a bass note indicates that the 3d of the triad is to be chromatically minor scale. is done, e.g. with the dominant triad of the below a bass note, means that the note indicated by b, or ft, after a figure placed a figure ( 0, etc.) that the the figure is* affected by that accidental; and aline drawn through below a bass note note indicated by that figure is to be chromatically raised. Any figures thus indicated upward mean that the chord is to be constructed by counting the intervals means that the chord first from the bass. A figure 3 after any figure or combination of figures note continued as its root. An 8 followed indicated is followed by a triad with the same bass A line after a figure means that 7th. by a 7 indicates a triad followed by a chord of the the next chord. the note indicated by that figure is to be continued into

A$ or

ft

half step; this

AJ

r*

i

-J.

-A

Dlfc

S l I

^ J 2

7 J

J

C

see chapter on 7ths)

6

6 6

5

--

43

J.

33

HARMONY

A 87

93 26

6 3

4

7

3

9

-r I

6

4

1

I

1

5 3

In writing the next following exercises, remember that when the bass is given it is understood to be the root of a triad (e.g. the note C implies that the other notes of the chord are E and G). When, the soprano is given it is either root, third, or fifth of the triad as the case may be; the bass to be written must always be the root of whatever triad is chosen. 52. Write exercises without the aid of an instrument. After writing try to realize, by singing and playing, how the single voices move and sound melodically, as well as in relation to the chords of which they form a part. Also listen carefully in playing the exercises over, that the ear may be trained by degrees to recognize chord progressions and the leading of tlie The corrections made by the student himself, from a comparison of what he thinks voices. is the sound that he writes down, and the real sound that he afterwards hears, is of more value than any changes suggested by another person. 53. Naturalness and simplicity are desirable in constructing our first chord progressions; long skips in any voices are to be avoided, and indeed we should move largely step-wise, with occasional moderate skips. When the soprano moves over an arpeggio in repetitions of the same chord, the inner voices, and occasionally the bass, naturally skip, for that will be a musical leading of the voices. To avoid any misconception, let us say that all exercises in this work begin and end on the tonic triad; a piece of music, however, frequently begins with some other chord, although the final chord will practically always be a tonic triad. (Two cases of an unusual beginning and ending are here given; they result from especial reasons. The first of these introduces a dramatic moment in the opera; while in the second one the dominant 7th chord ending the piece represents an expectation (a question, as the title indicates) which is answered in the piece immediately following. In ordinary music one has little to do with such things.) Tristan

und Isolde," Introduction of Act EC.

^

etc.

M"BittendesKind" (from*Kinderscenen";

34

HARMONY' are to

Open and close position 54. These examples from 1 to 31 are for four voices, from one to the other in the same exit is well to accustom one's self to change in any voice, keeping rather in the medium ercise- avoid an extended use of the extreme tones and remember the 8ve and 5th m every find the always in voices; be careful spacing range'; a be present. there leading-tone whether also chord, noticing the soprano and bass given. In In examples 1-7, the alto and tenor are to be added to the other tones being the 3d and 5th; the from root, count chord upward each ascertaining and 5ths and the leading-tone, be careful to observe the rules given, as to consecutive Sves be used, and

never allowing voices to cross each other.

P en

-

HARMONY WlTH EACH CHORD CONSIDER THESE POINTS

WE

TIE

2.

T

8fi

I

AVOID CONSECUTIVE 8VES AND 5THS.

1.

CAN WE TIE ? SHALL THERE A LEADING

3. Is

TONE PRESENT? Only the roots of chords are given; be sure that the soprano begins on the right note. Open.

Close.

7.

8.

Open.

12.

13

Close -

-

Open.

Close,

Open.

14.

16.

15.

17.

Open-

NOTE.

At X consider the succession V-vi;

that the repetition of a root often makes

it

at $ that of

-Close-

n-V;

desirable to get variety

X we have this by the soprano (or,

at

point, if

not

HARMONY

36

the soprano, the other voices) moving to another interval of the chord; "n Ex. 19 we have a sequence, in which each voice must move with perfect regularity, measure by measure, i.e., progress by the same intervals (the leading-tone being therefore doubled at one place).

65. Before harmonizing melodies it is necessary to say something with regard to the relative appropriateness of the triads for use with the different tones of the scale. Triads I, V, IV, and vi are the ones most

used, ri and in less often and vn practically never, in root position, except in a sequence (see Ex. 19 preceding). Considering these triads singly, we shall find

that in the major scale those indicated as follows under the dif-

ferent degrees are the ones

most often employed, their

relative frequency

shown.

being also

It is the custom to denote major triads by a large Roman numeral (I), minor triads by a small one (11), augmented triads by a large one with a + after it, and diminished triads by a small one with a after it (III + ,

vii

)

;

the augmented triad appears

with the minor

first

scale.

A

7

after

Roman numeral means

a chord of the 7th (V 7 > Hi 7 ). In harmonizing melodies these signs will be much used to indicate the chords desired for

a

particular notes; similarly (G),

major keys and minor keys by small ones (e).

will

be indicated by large

letters

CHAPTER V HARMONIZING MELODIES IN MAJOR KEYS 66.

WE

triads in

must

what have proved to be the lest successions of it is not possible to give more than an approxrelative frequency and importance. When a note is

also see

major keys, although

imate idea of their

repeated in the soprano it is often well to change the triad; if a melody is built on the notes of a triad, it is likely that the bass will remain the

ame. I

is

followed

n

"

m

"

" "

IV"

v vi vii

This table

is

"

" "

by V, IV,

m (seldom by n).

vi;

"

V, vi

"

vi,

IV

I, vi,

" IV,

m,

m, n n,

V

"

"

(

V,I,ii(

"

"

"

(

"

to

m

n,

I,

vi,

,

IV).

V).

m).

(sometimes by IV). (seldom by I).

need not be considered.

applicable to triads only, not

I,

inversions.

87

HARMO:NT 2O.

Close.

Open.

IV

in

22. fe

Open.

I

V

u

in

Close.

IV

vi

II

I

IV

24.

V n 25.

IV

Open.

m

IV

_*_i

^ in

'

tT

j '

__ IV

.

IV

'

1

1

Close.

27. Open.

n

vi

V

28.

29. Andante

sostenido.

so. Larffhetto.

AECADELT

CHOPUT (Nocturne)

to-j-j-^ 31. j.

Allegro maestoso.

TSCHJLIKOWSKI

HARMONY

38

CHAPTER VI TRIADS IN MINOR KEYS 57.

As stated above

related to

it

(

27),

every major scale has a minor scale so closely same tones with one exception) as

(consisting of exactly the

The

to be called the Relative Minor.

third below the Relative Major,

e.g.

tonic of this scale

the scales of

is

always a minor a minor bear

C major and

manner G major and e minor, F major and d minor. and Minor Keys always have the same signature, and the raising Major of the leading-tone is in every case to be indicated in the music itself; e.g. Ab major and / minor would both have for a signature four flats, and EJj,

this relationship; in like

Relative

the leading-tone of / minor, would have to be written, whenever it occurred. 1 The student is to write out for himself a table of signatures of all the major

and minor keys,

e.g.

Major Keys

Signature

Relative Minor Keys

a (G to

G

e

(D

"be

sharped)

to be sharped) ,

etc.

68.

minor

The

triads erected

on the successive degrees

of

the harmonic

scale are as follows:

VI vn In classifying these triads

and sub-dominant

tonic

(i

we

find that there are

and

iv)

;

two major

two minor

triads,

triads, on the on the dominant and on the second degree

the sixth degree (V and VI) two diminished triads, and the leading-tone (n and vn), and one new and most distinctive triad, an augmented one on the third degree (III*). The minor scale is evidently richer in harmonic variety than the major, as it has three dissonant triads ;

(n,

vn, 1

III 4") as against one in major keys (the leading-tone triad).

Capital letters (0) are used to designate major keys,

minor keys (a).

and small

letters in italics for

HAEMONY

39

A

marked feature of the minor scale is the interval of an 2d between the sixth degree and the leading-tone. Although augmented this augmented 2d is often of great effect when used in a melodic way, 59.

it is

generally better avoided in chord-progressions, especially in the inner Much more latitude is allowed on this point in instrumental music

voices.

than would be advisable in unaccompanied music for voices, for the augmented 2d is somewhat difficult to sing in tune. 60. In writing exercises in the minor mode the chief new points to be observed are these: First, the introduction and resolution of the three dissonant triads (n, III + vn) Second, that no voice may move over the interval of an augmented 2d or 4th. The diminished triad (n) may be connected with the triads VI and rv, and almost always resolves to the dominant. ;

,

mm

=te

^ YI

We of

see

n-V

I

f V

11

iv

V

11

now

the importance of the recommendation as to the connection in the major mode (48); i. e. that the common tone is frequently

not prolonged into the second chord the soprano, alto and tenor then proceeding in contrary motion to the bass (especially in close position). Observe the unvocal progression below of the augmented 2nd, and the good and vocal interval of the diminished 5th. ;

Bad.

Good.

r^j

.

.

i

iLxj-

A ^ r

ft^S i

f

,0

r^i-f^r

H H

Observe ttat in. the resolution of this dissonant triad the bass ascends a fourth. When dissonant chords of the seventh are treated, we shall see that the most natural resolution of all dissonances is for their bass to ascend a fourth (or, the same thing, to descend a fifth).

The augmented triad on the 3d degree (III+) is a harsh dissonance, and hence not commonly used in root-position, except where a striking effect 61.

is desired, e.g.

HAKMONY WAGNER

:

" Parsifal" (Amfortas Motive)

g:

When i.e.

so used its resolution

is

the bass ascends a fourth,

sixth degree, generally to the triad on the

e.g.

11+

YI

but these resolutions are also good.

III+

III+

This mediant triad and, in fact,

all

IV

dissonant triads (those with a diminished

frequent and generally more effective augmented as chords of the 6th. The augmented triad is very useful in this inversion to introduce dominant harmony, e.g. or an

5th) are

much more

I

=^

11+

V

HARMONY

41

The diminished triad on the leading-tone in the minor mode (vn), corresponding triad in major, is practically never employed ; as a chord of the sixth, however, it is very useful and frequent. The bass is 62.

like the

may be

generally doubled, although at times the original fifth with good effect, e.g.

-tr2

y

r

-f>\r*r

i

iff'' (at (a)

we

see the bass doubled,

and at

(6)

doubled

the original

\~

'

fifth).

When

the dominant and sub-mediant triads (V and VI) are connected in the minor mode, the voices have to move along certain fixed lines 63,

in order to avoid consecutive 5ths

and Sves and the augmented

2d.

The

leading-tone always ascends to the tonic (or descends from it). Two of the upper voices must move in contrary motion to the bass, and the 3d -is always to be

doubled in the triad on the sixth degree, in four-part writing. Never Aug. 2d.

3d doubled.

Y When YI

YI

precedes

Y

Very bad.

Poor Aug. 2d.

Good.

YI

Y .the

same arrangement of voices

is

to be followed.

e.g.

P3P z

**

p-f^ll P-+^fV V YI

YI

HARMONY the melodic form of the minor scale is without the raised leading-tone ( 22). This is a survival of the old Aeolian Mode, which was identical with our scale of a minor with G, instead of G$. The minor seventh, when so used, is generally harmonized

64.

In a descending bass or soprano

often used,

i.e.

with a chord of the 6th,

e.g.

+

single

name

65. NOTE. It is not infrequently the case that a composition in a minor key is ended by a chord in the tonic major. This major 3d in the final chord has been long known under the of TIERCE DE PICARDIB (Picardy 3d); it waa much used by Bach, and as a characteristic

example the following

it

will

be referred to

is

given, from his great

later, in

the chapter

G minor organ

on.

fugue

:

modulation.

Before proceeding to the exercises that are to be written, there are given below two models; in analyzing them attention is drawn to thea points, which must be considered ia constructing every chord: 1. Are there tones that can be prolonged into the next chord? If BO, shall they be prolonged, or do we prefer to use contrary motion to the bass ? 2. If there are no tones that can be prolonged, in which direction shall the 8ve and 5th go ? 3. Is there a leading-tone in the chord ? 4. Is there an augmented interval to be avoided?

"We aave to avoid the Interval of an augmented 2d (measures 1-2). In close position the soprano note is not tied; in open position it is, the tenor then supplying the necessary 3d in the following chord by making the good and vocal skip of a diminished 5th to G$. Observe in each measure but the last the employment of contrary motion to the bass, to avoid consecutive 8ves and 5ths; also the progressions V-VI, and n-V, and the choice of open and close positions in

measures 3-4.

HAEMONY In Exercises 1-12 the bass Is given ; in 13-25 the bass Is given, and a few chords of the and 6-4 chorda are introduced ; in 20-25 the simple passing modulations of relative major and minor are introduced ; and in 26-36 we have exercises for harmonizing melodies. 6th

66.

As the fact that we have one augmented triad, and the interaugmented 2d and two augmented 4ths, affects the matter of

vals of one

triad-succession, for for

major ones

i is often followed

n,

the 3d of

n

is

m+

minor

which

scales a table is given

differs

from that

:

by V, VI,

n, sometimes by Ill-h (when

IY,

followed

by

usually in the soprano, the position being close). generally followed by V, occasionally by 1, 1H-K " n, rv (see exVI, i is

" V, i, n*. " I, VI, in-f sometimes "

IV

V

,

VI

iv.

The introduction

amples in

61).

IV.

"

V,

n*.

a few inversions (6th and 6-4 chords) will give more flexibility to our exercises. The student is referred for necessary information to *he introductory paragraphs of the chapter on the Inversions of Triads. At present the bass of the chord of the 6th (the 3d of

NOTE.

of

the original triad, cf. p. 20) is not to be doubled in any case ; in 6-4 chords the bass should always be doubled. Until these chords are quickly recognized, tneir notes must be ascertained by counting upward from the bass the 3d and 6th, and 4th and 6th respectively. Modulation is produced by means of a connecting succession of chords

containing one or more tones foreign to the original key but belonging to the new one (e.g. in going from C major to a minor we introduce G#, the

G major is made Our modulations

leading-tone of a minor, while the change from a minor to

by reversing the

process,

here are passing ones, so

i.e.

having

much

GS

so as hardly to deserve the

x

J

e.g.

-

J.

^

-

a few exercises with given bass be written for 1, 3, 6, 8, 10, 13, 14, 17, 18 (Chapter VII) following show how voices are doubled and omit-

It is advised that

The basses recommended. The

three voices. are

name,

ftr ^

67.

in place of G#).

of

Nos.

ted.

r r &*

m

3E

-r

HAKMCXKTY

CHAPTER EXERCISES

TRIADS:

VII MINOR KEYS

IN"

THE melody in the soprano should be made as varied and interesting is possible, and indeed good melodic movement in all the voices is desirable. Write in all necessary accidentals. Observe modulations in Nos. 20-25. At NB. 1

64.

cf.

2.

.

Close.

-c

x

,$i

u|

Close.

position

.

*

'

S

ft

4.

3.

(see

ES

65)

ft

ft

5.

Close-

Open

ft

5ft

7.

6.

NB.

8.

9.

2 f

10.

3

11.

-Close-

Open-

f 5

r Jt

rJ| r

f

.__

-|

|

-&

1

Open

n

T

.

^

.^ju

HABMONY 12.

Open

3

45

Close.

S

13.

i 14.

(Chant)

. 15.

3

6

16.

S 17.

6

(Chant)

* 2 19.

18.

3

fl

5fl

6

NB.

6

fl

JJ

4

20.

Open-

^S

-Close.

3

21.

Open-

-Close-

-Open-

22.

ppi

46

HAKMONT 23.

Close-

In harmonizing the following melodies, first ascertain the key (minor) of each exercise, and then the leading-tone, as well as the augmented skips that must be avoided. Chords of the 6th and 6-4 chords are indicated by those figures under the notes; Roman numerals show in particular cases the triads that should be used. Triads may sometimes be repeated; a .triad may be followed by one of its inversions, and an inversion may often be followed by its triad; the leading-tone is always preceded by an accidental in

minor keys.

26.

IH+

HAKMONT

4 successions of triads 1-4; 1-5; 1-6; 2-5; 3-6; 4-2; 4-5; 5-3; 5-6; 6-2; 6-4; are common often used. are in both major and minor keys; 1-6-4-5 and 1-6-4-2-5

CHAPTER

VIII

HIDDEN OCTAVES AND FIFTHS 6ft

starting

gression

two voices go in similar motion to a perfect 8ve or 5th, from some different interval, we have what is known as the proOne voice will necessarily move by skip, of hidden 8ves or 5ths.

WHEN

and sometimes both

will

do

so.

HARMONY

Prom these illustrations we see the reason of the name; one voice passes overtones which, sounded, would produce consecutive Sves or 5ths; these 8ves and Sths, being passed over and not sounded, are said to be hidden (or concealed). if

Hidden unisons are

less frequent,

although they sometimes occur between

tenor and bass,

or even between other voices 69. to

!N.B.

The student

70).

(cf.

is strongly

avoid these hidden intervals.

In

advised not to

make a point

of trying

the first place, questionable progressions of

this sort will seldom occur if the chords are naturally connected in accordance with the given directions; and, secondly y a good melodic leading of the voices will justify all but a few cases.

may, however, be stated that hidden Sves and Sths are more noticeable, and in the outer voices; we shall not meet with the worst progression kind, that of a 7th or 9th followed by an 8ve, until we come to chords of the 7th.

70. It

often poor, of this

when occurring

A summary of the

usual statements regarding these hidden intervals x is given on page 49 examples, however, we see the futility of constructing rigid rules that are not really observed by musicians.

;

in the following

=i

J

JL

J.

1 Notice the hidden Sves between outer parts in measure 1, and hidden 5tha between outer parts in measure 3 of each example also the two hidden unisons. ;

HAEMONT

49

NOTE. A condensation of the rules given in one of the most important manuals is as folHidden Sves are forbidden between soprano and bass except when (a) the bass rises a 4th (or falls a 5th) either from dominant to tonic, or tonic to sub-dominant, and at the same time the soprano moves by step; or (6) the second of the two chords is a 6-4 chord; or finally, (c) when the second chord is another position of the first. They are, however, allowed between any other two parts, excepting when a 7th or 9th moves to an 8ve in similar motion. Hidden 5ths between soprano and bass are forbidden except (a) in a progression from the tonic to the dominant chord, or from sub-dominant to tonic, in both of which cases the soprano must move by step of a second; (&) in a case like this; lows:

and finally (c) from one to another

position of the

same chord. Hidden 5ths are not prohibited

except between the outer parts.

CHAPTER IX INVERSIONS OF TRIADS Chords of the 6th } and 6-4 Chords

EVERY triad of a major or minor scale may appear in inverted To characterize these we emforms, there being two inversions possible. ploy the so-called figured bass, an old but excellent way of defining chords in speech and writing; musicians think and of chords their 71.

by

speak

Words

are saved,

for to say

inversion

and there

is

figures.

a most satisfactory clearness;

a chord of the 6th on D and a 6-4 chord on F, and second inversion respectively. ;

is

as plain as

first

In determining every chord, we in practice always count the intervals upward from So in the following table, all the triads are composed of a root, 3d and 5th; ,he first inversions, of a bass (not root) 3d and 6th; the second inversions, of a bass (not root) 4th and tfth. These first and second inversions of triads are called " chords of the 6th " and " 6-4 72.

the lowest tone.

(six-

four) chords."

HARMONY

50

The inversions

of triads

I

on various degrees of the scale are useful in modulation,

X

X

J

J

6

6 4

X

J

X

r

e.g.

X

X

X

X

r~r~~r~r~r r

Chords of the 6th and 6-4 chords must never be thought of as triads, but It will be seen later that their treatment differs in important points from that used with triads. Unless this distinction is sharply made, the student is likely to become confused in his mind. as inversions.

CHAPTER X CHORD OF THE SIXTH 73. IT is impossible to make absolute rules with regard to the especial treatment of this chord, as exceptional cases are so numerous; there is

harmony requiring more care, judgment, and good taste; but examples of the usual ways in which it appears will be given and analyzed, as well as some exceptions, a working scheme being deduced therefrom. What chiefly makes this chord difficult is that its bass is the 3d of the nothing in

be remembered that in triads that tone

is comThe question, therefore, as ,to doubling it becomes more complicated and difficult when the original 3d appears as the bass of the chord of the 6th, for we shall see that we can no longer

original triad, for

it

will

paratively seldom doubled.

usually double the bass, as

we

did with triads.

Reserve the term HOOT for the baas of the triad, the lowest tone of every inversion as its BASS simyly;

the

BASSES being

E and

respectively.

and e.g.

of chords of the 7th

C

ia the

BOOT

of

and

9th, thinking o*

HARMONY Now

74.

in succession.

51

these chords appear in two ways, either singly or two or more Our decision on the above point as to doubling the bass will

depend partly on mere sound, but even more on the melodic leading of the and the necessity of avoiding consecutive 8ves and 5ths and doubled In our discussion until 76, the major scale is considered. leading-tones.

voices

75. Wusn the bass of a chord of the 6th termine as to the doubling.

the tonic, the leading of the voices will de-

is

-*-j-^-J=

1 i

J

r

1

-J

^

'

r 6

When

the bass is the second degree, the chord, being an inversion of the leading-tone never doubles the leading-tone except in a sequence. (See Chapter XV.) then have these forms and others like them,

triad, 1 naturally

We may

r

r

,

j

i

J.

TrrTT J

J:

J

J

m but not.

<

r

,

6

When the bass is the 3d of the scale, it is generally preferable to double one of the other tones, inasmuch as the bass is the 3d of the tonic triad, and^therefore of itself stands out contpicuously as the one tone determining the major or minor mode for the time being,

m a 6

Although the melodic i

as

66

leatf'iig of the voices

TTTTT may

It is in this inversion that the leading-tone triad is

a triad

it is

f-

result otherwise, e.g.

impracticable in most circumstances.

most

useful, for

we have seen

that

52

HAEMONY

J

When, the bass

is

the 4th of the

we

scale,

J.

j.

J

J. j.

are guided entirely

x

x

J

J.

by the leading

x

x.

though it should be said that in minor scales this chord of the 6th the bass be doubled, on account of the augmented fourth present, which the addition of another dissonance, the diminished 5th.

I

""-

f7~g

,

I

the voices

is is

more euphonious if over-emphasized by

" j

1

I

is

I

a

little

\

Til

better than

JL

6

When

the bass

is

e

the 5th of the scale, the leading of the voices will decide; 1

(?)

X.

X

X

.

x

gas^^to

fC^ths^srifciifjdra::

6

when the

6th, it

is

6

rarely doubled when occurring singly

;

X

and

finally,

the bass on the 7th of the scale (leading-tone), should never be doubled.

i

Notice the doubled leading-tone in (a) in chords of the 6th, the leading-tone, when not a root or 3d of the original triad, may sometimes be doubled, for in this connection it seems tc lose its excessive prominence. ;

HARMONY

53

In minor scales the bass is seldom doubled when it is the tonic, the 2d degree, often when on the 3d, usually when on the 4th, very often when on the 5th, often when on the 6th, never when on the 7th degree (leading-tone). 76.

often

when on

With both major and minor scales, original triad is

if

a chord of the 6th

is

the inversion of a consonant triad, if the

probably be doubled only in case better voice-leading .results; dissonant, the bass of its inversion as a chord of the 6th is usually doubled.

the bass of the former

"will

64

HARMONY

CHAPTER XI CHORDS OF THE 6lH IN SUCCESSION

Two

or more successive chords of the 6th are often used, and we marked difference between them and triads; for similar motion of all four parts, generally impossible with triads on account of the resulting consecutive Sves and 5ths, is not uncommon with chords of the 6th. 77.

here note a

Examples of the ordinary ways

6

of so using these chords follow.

666

6

6

f^

/N

W/

6

y

II J.

J-

6

-J-

6

J-

-II

tt.j'LdLJ^.

T

jH ? f i

i

r

6

6

(o)X

I

j

f

f

i

i

i

\

^=j=^ f ^ r

T

1

r

i

i

A

XX

J-

^

XX X

X

J 6

666

J

J.

6

6 6

(a) we must not double the bass of the second chord of the 6th, as consecutive 8ves between tenor and bass but should double the bass in the third chord in order to avoid consecutive Sves between soprano and tenor, and 5ths between alto and tenor, all the voices in this latter case being in similar motion: in (&) this similar motion is avoided by the use of open position. In (c) we have consecutive 5ths between alto and tenor, which are of In (1>I

^s*-

f

;r

r

r~i

r

i

I

(5)

and

In

(c)

(c), *hile

we

should

-

r^r fi-j

used between a triad and a chord of the 6th of the same

harmony.

I

T

i

or subusually preceded in a cadence by a tonic, supertonic subthe sometimes by dominant triad (or the same as a chord of the 6th), 82.

mediant,

It

is

e.g.

HARMONY

60

J

J.

It is best to

J

avoid having two 6-4 chords in succession, although, this can

be of good effect in some cases when the bass moves by step.

Such a pro-

gression as this

S&=f=f=fjEE^

A A A

etc.

J.

6

6 4

4 is is

positively bad to enter

made

and ugly. In the following example, the second 6-4 chord more naturally, chiefly through the diatonic movement of

the bass.

m y^= etc.

J

i

J.J..LU 6 4

In this

from the Third Organ Chorale

r^=F 8 4

of Cesar Francfc

r-rr ^f -&

attention

is

called to the

J%J

J

same diatonic movement

J.

of the bass,

and

also to

HAKMOFT

61

the fact that the distinctive character of the 6-4 chord, as we chiefly meet with it, is negatived by the bass not being doubled on any one of the three chords. NOTE. On page 8 of the score of Franck's D minor symphony, and at the entrance of the trombones in the second movement of Tschaikowski's 6th symphony, are instances" of successive 6-4 chords; they are in these cases separated from each other by a single chord between, but the effect is none the less singular and worthy of note. For an illustration of these chords in succession with a diatonic bass, the student is referred to the seventh and eighth measures of the first movement of Mozart's C major symphony; and fora disci^sion of 6-4 chorda on various degrees of the scale, the sixth chapter of Prout's " Harmony " should be consulted

CHAPTER

XIII

EXERCISES WITH INVERSIONS OF TRIADS 83. REMEMBER that the following exercises are to be written without the help of any instrument; after writing, play them repeatedly, listening for characteristic points, and making changes after careful consideration. Play also the separate voice parts, to see whether the melodic progression can be improved. It is helpful to transpose exercises, and also to play them, reading from the bass alone; both of these things axe at first difficult, but important aids towards clear musical thinking. AM we are now dealing with chords defined by figured basses, let us say that it is, not enough simply to calculate the chords correctly hi a mechanical way. Always try to obtain varied melodic soprano and bass first of all, and then see how far the inner parts may be made interesting to sing and to hear. Monotony and stiffness are the worst faults; simple diatonic step-wise progression is preferable, skips being used with discretion. Bass notes without figures are, of course, the roots of triads.

1.

HABMCCNY

62

3

6

6

6

J

F^F

36

6

6 Close.

13.

Close.

56 14. (Cbant.)

6

58

66

*

HARMONY

63

16

16.

66

66

3

4

RELATIVE MAJOR AND MINOR KEYS 17.

Open-

t=i

-Close.

36666

4

656

6

6

84. In hannonizing melodies, it is to be remembered that especial attention must be given to the bass (45); we should tr> to have it melodious, preferring generally movement by step, rather than by skip, and avoiding awkward skips. An important gain resulting from the use of the chord of the 6th is that we can do away with pointless repetitions of the same bass tone, resulting from the repetition of a triad; in case the triad is repeated in root position, the bass may skip an 8ve, up or down, with good effect. 7-

6.

6.

J

I

t

i

8.

64

HARMOIST

The skip of a 6th is unnecessary and not so natural as that of a 3d (measure 1 and 3-4); skips of a 7th. (measures 2, 3) are so awkward and unvocal that they must rarely be used ; the monotonous repetitions in measures 4-5-6 can be improved by inversions; finally the 6 and 6-4 chords in measure 7 are excellent examples of what to avoid, each being in this connection.

J

weak and inappropriate

L

i

Every note can form a part of three different triads (but cf. 46 ) chords of the 6th 6-4 chords; the one to be chosen, in each case, will depend on the chords just preceding ,

following.

E.G. (Ex.22). or

or

or

or

In the following chords

by

exercises, certain triads are indicated those figures in most cases, though not always.

Open-

by Romajk numerals;

-Close.

6

VI 23.

24.

6

25.

Close.

in

vi

^

Open.

666 26.

and and

Close.

6

666

the 6 and 6-4

HAEMONY 27.

Open-

65

Close.

28.

GJTTQ

I

VI

6

31.

6

vi

Open.

$ 85. In three-part writing the 6 and 6-4 chords are to be complete, unless the leading of the voices is such that no ambiguity results from the omission of a tone (the chords marked X

are unmistakable.)

I rrrp-f r 1

fy

;

*=*

6664

6

sometimes the case that an inner voice must move by a larger skip than when four voices are at our disposal; we may also find it desirable to have voices move over the intervals of a chord, to give a sense of completeness (as at X X). It is

ES r

r

r

urr

6666

4

The basses first

rule

of examples

1, 2,

3

:

5- 6, 8, 10, 12, 13,

on page 29 cannot be strictly observed.

are advised for three-part writing; in this thf

HARMOlSnr

tit)

CHAPTER XIV CADENCES 86.

THERE

are

four

cadences

V

common

in

CADENCE is formed by the dominant lowed by the tonic triad;

triad

I

I

The AUTHENTIC

use.

(often with 7th added) fol-

I

the strongest form of this being preceded by a 6-4 chord with the dominant for its bass; the soprano may end, in the final tonic triad,

on either root, 3d or 5th.

1 r j

^ j 6

V-I

6

A few other forms follow,

r

-

i p

j

T7 _I

in which the

dominant triad

is

introduced differ-

ently.

^

4"^-

5&*

rrr r

6

Y

ffF I

HAEMONT 87.

by

The PLAGAL CADENCE

consists of the

tonic triad; the soprano ending on root,

IY

67

IY

I

(Observe that the sub-dominant

may

3d

I

sub-dominant triad followed or 5th.

IY

I

appear as a 6-4 chord.)

This cadence is familiar in church music, being often used as an additional close after the Authentic Cadence:

J

A

L

of Plagal Cadence in a major key, but with the sub-dominant triad a *' the very beginning of Mendelssohn's Midsummer Night's Dream" Overture. Authentic and Plagal Cadences are called Perfect when the soprano ends on the tonic; when it is on the 3d or 5th, they are Imperfect.

beautiful

minor one,

88.

example

is in

The HALF CADENCE may

in

many

cases be considered as a sort of

reversal of the authentic:

for

it

ends with the dominant

6-4 position.

It

triad,

may, however, enter

and

is

often preceded

hi other ways,

e.g.

'1

by the tonic in

HARMONY

68

the dominant triad. the usual definition of it being that it consists of any chord followed by the authentic This cadence may be fitly compared with the semi-colon in punctuation, state of suspense, for we feel that it does resembling the period; the half cadence leaves us in a These two cadences, not mark an ending, but rather a pause, or interruption of the thought. is from their property of balancing each other, are complementary. The deceptive cadence not unlike a

mark

of interrogation (?).

that its NOTE. Some theorists enlarge the possibilities of this cadence by admitting In many cases for its root. final chord 'may have other degrees of the scale (n, m, IV, TI) old custom was to such successions do have the especial effect of the half cadence, but the triad. According to more recent restrict that name to such cadences as end with a dominant marked by a X would be conopinion, however, all the passages in the following examples sidered to

be half cadences.

WAGBTER:

"

Tannhauser " Overture

(V)

(m)

(VI)

89. In the DECEPTIVE CADENCE the dominant triad with or without a 7th (often preceded by the 6-4 chord, as in the authentic cadence), is followed by an unexpected chord, which leads us in some cases to a change ,

of key.

A number of specimens are here given.

HAKMONT

tf<

4

-U_|_C-i_flU

'^

69

CX

^

_

^

I

^

CX

j

_.CggL

rprnrrr ^Tfyrn^fn^PrrF *

j.

(The student

p

y

*y7

*y

referred to the chapter

is

j.j. j.j.

on the dominant 7th

for further

illustration.)

These cadences are sometimes named differently; but the terms Authentic and Plagal and Half Cadence and Deceptive Cadence express what is meant. While it is a question with the authentic cadence as to how far the use of a preceding 6-4 chord is needed, there is no doubt that the cadence is thereby strengthened, are well established,

CHAPTER XV .

90.

group

A

SEQUENCES

sequence is a regular and continuous change of position of a definite group followed by at least two such

of notes or chords, consisting of the

According to its structure it will transpositions. or upwards downwards,

-J

-

j

^f

move, as a whole, either

JirLu

TT

i Ff

and must progress without interruption in the same general

direction,

every interval being repeated in each voice identically, although the differences between major, minor, augmented, and diminished intervals are commonly disregarded. This usual form of sequence (diatonic) is. termed a tonal sequence; one in which the intervals retain their quality of major, minor, etc., is called real, and is rarely used, being indeed difficult to man-

age,

and often impracticable,

so far as concerns a

good musical

result.

.

HAKMOOT

TO

entirely regular, that quality in it is so important as to cause the minor prohibitions against doubled leading-tones

As a sequence must be

and augmented skips to be

disregarded.

i J i i

91.

Sequences are made

much

stronger,

and

characteristic,

by an

in*

termixture of dissonances (7th chords and their inversions).

L*L *~>

>-A

-

w

PtTT TTT O

f^

P

N

^

fe|

TannMuser "

Oyerttire

Sva

8va.

etc. t

rl

i

(

^-rTT^ 137.

A

diminished 7th chord or one of

circumstances, be preceded or followed ished 7th chord or one of its inversions,

(a) (b)

its inversions

may, in some

by the same or another diminby a dominant 7th chord or one

of its inversions, or (c) by a secondary chord of the 7th chord, or one of its inversions (the secondary 7th chords very rarely in root position).

ES

J

T

r

i

r j^etc.

^^

J

\*

^^

J ^ J *

,

h

HAKMONT

124 (c)

J.

_*

JL

;

in such a

way

effect,

that a

g sometimes approached in modulation made; this, however, is of a good leading of the voices (cf. Ex. 2, is

so-called cross-relation is

provided that there

6, in Chapter

g__ 'cr

The diminished 7th chord

138.

good

T

is

XXIX). Poor.-

Good.-

JL

J

i

5^

:

CHAPTER XXIX 139.

6

EXERCISES WITH CHORDS OF THE DIMINISHED ?TH

7

$

7

t &

6

4

66A

HARMONY

125

i 367 4

*

6

ft

4

JV

6

6

6

"7

7

C b

Passing tones are indicated by the slur Open

5.

67

4

tl

dt

9

63

/~x,

Close-

-

"

7 5

7

6fi7

6J

7

$

^ jt

"7

/

6] 6 5

$

== 6

6 5

3

6

4

-Open-

7

7.

r

r

*

*

5

4 a

r

I

r

r

r

66 5

r

66 I

7

6

4

(Chant)

6

6

7

5

6

6

4

a ggt

Clofie-

sv

-dose.

-Open-

*$ 5

6 4

6

7

5

$

664: 4

2

6

6

6

4

fl

HARMONY

126 Close-

9.

3

Close -

-Open

4

E3=r\

4

fl

if

6

5

6677

667

7

$

6 5

^a-^-H= 6

65

4

4fl

Melodies to be harmonized; diminished 7th chords and their inversions x Write these exercises on four staves; introduce are indicated by the .

a few passing tones. 10.

Open-

SE

-

iE In

gr

0-

In d-

-Close.

x

^p

1

III+

11.

^

VI 12.

YI

vi 14.

Y

^

HARMONY

127 X

X

17.

fab 7 $F-m f

'

18.

(Chant)

In

In/.

19.

(Hymn

c.

^

tune)

Spg:

^ In

i

a.

Bass melodies to be harmonized with occasional diminished 7th chords

and

their inversions.

Passing tones are indicated

^ 21.

by

slura.

IV

CHAPTER XXX. SECONDARY CHORDS OF THE SEVENTH 140. ALL chords of the 7th, whose roots are on other degrees of the scale than the dominant, have been generally classed as secondary (or collateral) 7ths; they were formerly, with the exception of the leading-tone 1 7th, considered to be subject to a rigid rule as regards their entrance (the so-called preparation), this rule holding good with their inversions also. The strict observance of this academic rule has for a long time been disit should be remembered that rules of harmony have been gradually deduced, during the evolution of worthy modern music, from what has been actually written. The music does not spring from the rules, but the really important laws (better that word than rules) ever remain to guide us, though modified from time to time to meet

regarded

by composers;

of observance

the requirements of later developments. It is true that in music, as in other things, the. radical of to-day is the conservative of to-morrow; even our individual point of view is constantly changing, and still more is that the There was a time when the dominant 7th was not case from one generation to another. allowed to enter without preparation; other changes of feeling are going on in our own time, for we have seen e.g. during the last fifty years the old doctrine about cross-relations become

entirely modified.

141.

poser

Now

may

it is true that, where there is a choice in the matter, a comprefer to prepare such a 7th chord, instead of introducing it

1 It is because the leading-tone 7th is understood by all theorists to require no preparation that it has been discussed immediately after the dominant 7th; by some theorists leadingtoiae 7ths are not included among the secondary 7ths.

HARMONY

129

it is also the case that the chord progression is often such that necessary to have the preparation, as otherwise the leading of the voices would be awkward, or result in harshness. The point to emphasize is simply this, that by reasonable theorists and musicians this

freely,

it

is

no longer considered absolute, nor of sufficient consequence to stand against a better way of producing the result desired, if that way preclude the preparation of the 7th chord. The course to be taken will, in "every case, depend on the judgment of the composer; a few hints, however, will not be out of place, even though no really definite staterule as to preparation is

ment can be made. Good.

Fairly Good.

6 5 Fairly Good.

Seldom Available.

Fairly Good.

The following is given as an example of an unprepared 7th, where the chord of the 7th Of itself less harsh, having the interval of a minor 7th.

It is, indeed, difficult to see

why

the secondary 7th chords

nr

,

m

T "7iT ,

be considered essentially nmeh harsher than the dominant and leading-tone

ifl

(in major) should 7ths.

It is clear from the above fa) that the 7th (when without preparation) enters best in a 6-5 chord; (5) that contrary motion between root and 7th softens the harshness; (c) that the 7th enters best step--wise. The 4-3 chord

and the chord

of the

2d are not easy to introduce well without preparation.

130

HARMONY

The statements given later as to the resolutions of these 7th chords hold good, whether the chords be prepared or not. NOTE.

"Even in the last century the old law as to the preparation and progression of was often disregarded; and it would be absurd to fetter ourselves now by any Any essential discord may be taken without preparation." (From Prout's "Har-

these chords

such

rule.

mony.") 142. To illustrate the unrestricted way in which 7ihs may be used in free contrapuntal writing this example is given; some of the 7ths being passing-tones or appoggiaturas.

X

v

The student is advised to analyze the first Prelude from the "Well-Tempered Clavichord"; the manner of showing its harmonic basis being given in the measures quoted below. In the fine example from Wagner, observe which 7ths are prepared and which are not; also that in T the third measure from the end the IV chord in C major is chromatically changed. BACH: "Well-Tempered Clavichord,"

WAGNER:

1st act of

1st

Prelude

"Die Meistersinger"

HAEMONT 143.

To

turn

be conceded that

now all of

131

to the old strict rule as regards preparation: it will the following 7th chords are harsh, when sounded

alone, but that this effect is mitigated either the 7th or the root is prolonged

by

the preparation, through which in the preceding chord

from a tone

At the same time (i.e. one of the two dissonant tones is prepared). there are differences as to the degree of harshness: I 7 and IV7 being more markeS in that way than the others, because of the interval of a major 7th; 7 and vi 7 are smoother, with their interval of a minor 7th. It while II7 , ,

m

must not be understood from

this that I 7

and IV 7 are

less useful, for

that

very quality of extreme dissonance makes them perhaps even more interesting factors, as their resolution is doubly agreeable when it does come. Secondary chords of the 7th in Major Scales.

X

miA^j.

* Ete

i

Hi*

i

7

X

^

J.

A A

f

^

IW-P r

r

7

? *f-fg- J_ ^T

r=F

^ J A A (BE=

J.

HARMONY

132 NOTE.

of the 7th on the IVth degree of the major scale is not same manner as the others, the reason being that by the root ascending a 4th (or descending a 5th) we pKp-lT double the leading-tone, a thing only tolerable in a sequence.

Observe that the chord

resolved above in the

rr

_AJ It is

j

j

more symmetrical to have the root and 7th resolve as above, downward and the root upward.

in all of the chords,

the 7th moving

The

may be summed up as follows: PROLONGED IN THE SAME VOICE FROM THE PRE-

rule illustrated in the foregoing

Either

THE ?TH

is

CEDING CHORD;

Or THE ROOT IS SO PROLONGED, IN WHICH LATTER CASE THE ?TH USUALLY ENTERS DESCENDING BY STEP.

Notice that in (a) and (6) the 7th chord is followed by another dissonance (chord of the 7th); we see that the 7th chord is not necessarily resolved into a consonance, thereby acquiring a resting-point, but that we may have two or more chords of the 7th in succession

When ment

of

have so

these chords are prepared, as indicated above, this strict treat-

them results in something more rigid than anything with which we far become acquainted, when their regular resolution follows.

HARMONY

133

In the normal resolution

144.

THE TTH NATURALLY DESCENDS ONE DEGREE; THE ROOT ASCENDS A 4TH (OR DESCENDS A STH) THE THIRD USUALLY DESCENDS A 3D (BUT IS PROLOIsGED

(1) (2)

;

(3)

NEXT CHORD,

INTO THE

THAT BE A SECONDARY CHORD OF THE 7TH ALSO) ; THE 5TH USUALLY DESCENDS ONE DEGREE; THE ROOT MAY BE DOUBLED, BUT THE TTH MUST NEVER BE. 1

(4) (5)

IF

On examining the above examples, it will be found that the 3d cannot progress by as. cending without producing a bad leading of the voices, but we have in the following an illustration of an upward progression of the 5th, in which the effect is musical, and the leading oi the tenor unusually good.

In minor

145.

by the augmented

scales

Bad.

so that

and

VF

I

T

and rv7

are good

we

are restricted in applying the usual resolution,

intervals;

Good.

Good.

Poor.

Bad.

are impracticable resolved in this way, but

and extremely

Good.

n07

,

useful, e.g. OOJUDMAB.K: "Sakuntala * f Overture

etc.

The

7th, being

a

sensitive tone, is unfit for doubling.

184

HAEMONY BRAHMS: Song, " Minnelied

I

jfr+7

!

;Kf? 1

NOTE. The chord of the 7th on the second degree often enters in such a preferable leading of the voices is obtained by omitting its 5th.

way

that a

Are better than

U

-L-r-l

In a major key these 5ths would be consecutive perfect ones.

146. (a)

by the

The irregular resolutions are that The 7th may be prolonged into the next chord, the course taken

other voices also being changed,

JU

J

J

4^A

in which case the resolution (6)

it

may

is

either delayed, or

j

^

JL

+^^=i==

a

*

^ ^

& r

A

abandoned altogether:

sometimes ascend,

P

J.

A-

HARMOKT

135

x

c and

in this case the tone to

by another voice, (c)

The

root

(p.

which

94

7

it

naturally would have resolved is taken

113.)

may be prolonged into the next

chord;

"

4^L^ ^1 r-'i

(d)

The root may ascend by an

J

^

^

j

i

(

I

I

I

FT

r

J-LL^AJJ

r

!

J

t

interval other than the 4th.

J

J

A

secondary 7th chord may be preceded by a dominant 7th chord or one of its inversions, by a diminished 7th chord or one of its inversions, or by another secondary 7th chord ( 147) or one of its inversions; it may also be followed by any one of those chords. Most of these points have been illustrated in preceding examples, but for completeness the following are also given: v,

x j

x

v

j

i

^,

j

i

J iJ

N

fliJ

j

J

r T

r

r

'" 1 f

HARMONY

136

-*-

rr~T

T

cr-r

r

rr-r r~rr

X

X

i i X

rrnr?

j

X

rr r

r

j.

r-

^

SUCCESSIVE CHORDS OF THE SECONDARY ?TH

These chords of the 7th are frequently used in succession, the good and strong when not too many appear at one time (for it is easy to let this device take the place of something better, that would demand more thought on the composer's part). Excepting the sequence, there is no chord progression that is so fixed in its treatment as this; for it is obvious, from the structure of the succeeding chords, that there will in each one be a 7th to be prepared at the same momertt that the 7th in another voice, which has just been prepared in the preceding chord, is being resolved. 147.

result being

From the

leading of the voices in every alternate chord. N/-X

it

K

will also be the case that the root will be doubled

^

x

^^=H^^^L^T~f\=l flrHn f=3tt77^T=f-P==f&^Jiraii. 1 ^ \

I

i

,

1

*

I

*

v

I

I

k.

JiJ

'*-' f^C l^v ffigh* '

#-jy

[ l

K *

^i^j.

7777 77726

137

HARMOJiTY

Notice in the preceding page that the chords of the 7th are alternately complete and incomplete; that the sequence could be continued indefinitely, and comes to an end simply to make a rounded musical phrase; it is seldom that so many successive chords of this kind are found. At X observe the exchange of the 7th of the chord from alto to bass, and the resulting final resolution in the bass (cf. Inversions of secondary 7th chords). ( 150)

Whenever these chords seem too

harsh, it may be that a different arrangement of the voices will mitigate that effect. Do not be satisfied with trying one way, but write the succession so that the complete chord is the

and third of the group and so on, and also so that it is the second and fourth, etc., and then compare. The above example is more dissonant written as follows (a), and in (&) we also see that the question of open or close position must be considfirst

ered.

(*>,.,.

(*).

m

f f

J-

r

c

T-

c

i

E =t=r 777 8va

d

m^

WAGNEKJ Bie Meistersinger" Oyerture (VOK BULOW'S arrangement)

In the above splendid example, tae harmonic basis of th 7th chords

ia

of course thi

138

A great gain in freedom will be found now that we have added the secondary 7ths to our stock of chords, and in Chapter XXXII we shall see that still more plasticity is obtained by employing their inversions also. NOTE. Passing tones ( 103) may occur axe in this case called accented passing tones. ence in effect (0 indicating the passing tones).

on the accented parts

The

of the measure also, and following illustration will show the differ-

Accented and unaccented passing-tones are indicated in the exercises by short slurs; the student is recommended to introduce these tones in moderation, when that can be done with naturalness.

CHAPTER XXXI EXERCISES INTRODUCING SECONDARY ?TH CHORDS 148. WRITE at least some of the exercises on four staves. Write each exercise twice; preparing all the secondary 7ths, and the second tune finding out whether any of them may well enter without preparation, then comparing the two versions. When there are successive chords of the 7th, find the arrangement of voices by which the alternate chords will sound first

best.

2

86

7

ft

2

65

6

HARMONY 3.

139

(Chant)

366 5.

267776

6ft

7

(Chant)

6.

37 7.

(

J

6

Passing tones are indicated

7

"by slurs.)

36777777 777777667

i

HARMONY

140 12.

14.

For

tliree voices.

15.

Si 7

76

7

626

7

7

5

16.

7

2677

7

7

f

17.

367

466

42

tr

Soprano melodies to be harmonized. indicated- by the x.)

7666

i 7 ft

(Secondary chords of the 7th are

18. For four voices.

X

r\

In

_In a 19;.- (

In C.

Hynmr-tnne )

F^ InF-

r?-

r

I-' nj

J

rir-c^n

:

^ i

HARMONY

S

(Hy urn-tune)

20.

141

m

TII7

InD-

t^=Fl -In G.

In G. In C21.

(

Hymn-tune)

X

X

^ In F. 22.

23.

BASS MELODIES TO BE HARMONIZED

InC

HAEMONY,

142 27.

3E

29.

30.

(

Hymn-tone )

CHAPTER XXXII INVERSIONS OF THE SECONDARY SEVENTH CHORDS

FOR the use of these inversions without preparation, cf. 141. introduced in accordance with the stricter rules, we shall have are they the same preparation of either 7th or root as when the chord is in its un149.

If

inverted form.

but the root

will

The 7th

will have the same regular resolution as before, be prolonged into the next chord, being in an inner voice.

Free entrance, without preparation

*

J_

HARMONY

143

With the usual preparation

X

)

,

(o),

X.

^

r~r j^j_u 6

I

5

From the above it will be seen that may be prepared; that the 7th regularly

150.

root

either (6) the 7th or (a) the descends one diatonic tone.

In (c) is an irregular resolution, by which the 7th is prolonged into the next chord, the root ascending one diatonic tone; in (d) we see how these inversions are used in sequences. With all chords of the 7th, dominant, followed by an inversion leading-tone, and secondary, a 7th chord is often and an inversion is often followed by the uninverted chord of the of itself,

by another inversion of the same chord; the 7th is then transferred voice to another, being usually finally resolved in the last chord one from or inversion. The chord of the 7th, or any inversion, may be repeated, the 7th being exchanged in a similar manner from one voice to another. 7th or

X X

& The 7th its

X X

X X

r=f

6 5

6 5

tonic chord, occasionally ascends to the 3d in the following

resolution (prolongation) being taken

by another

voice.

144

NOTE, Attention must be called to a progression of frequent occurrence with both dominant and secondary 7th chords^ which demands great care. The fault that easily can be made is shown in. the following; musical and right ways of handling the chords being also indicated.

151. In the following illustrations we see what powerful and interesting factors the chords of the 7th are, and how effectively they may be used in succession.

BEETHOVEN:

Sonata, op.

2,

No.

1

J_ X

XX GBIEG: Gavotte from the Suite "Aus Holberg's Zeit"

HARMONY

^^E ~r~r~Y~^

145

'~ !

etc.

m Song, "let grolle nichf*

:

3747

T^f

T

3

3

CHOPIN: Prelude ( Op.

28,

No

.

4)

*

etc.

I *

77

6

^E

5

3

190 7

7

;" Joshua*

r=* 2(n7)

2(17)

1

HARMONY

146

152. Observe the following directions faithfully. With a secondary chord of the 7th } always be sure which tone is the 7th and which the root; with an inversion, count upward from the bass } ascertaining what the notes in the chord ARE as the chord stands^ and then what are the TTH AND ROOT OF THE

ORIGINAL UNINVERTED CHORD.

We have,

e.g.,

in

[-^: f*

the notes

F-A-C-D;

the original chord of the

was D-F-A-C, D leinq the root, and C the 7th. Write every exercise twice; first preparing all the secondary 7ths and their inversions, and the second time finding out whether any of them may 7th

enter to advantage without preparation; after this, comparing the

two

versions.

CHAPTER, XXXIII EXEECISES INTRODUCING INVERSIONS OF SECONDARY SEVENTHS 153. (Always find the root

and 7th

of the uninverted chord.)

1.

3

$67 3442 466^ 4

I ft

7

66* 6 ft

HARMONY

36664 543

277 676 4

$

75 53

6 5

7626767

6

67

5

4.

66776 54

7

4

J

6

5

76626 46^67$

6

3

5

-Close.

Open-

2

77

5

76

2

147

6 5

67

35

72266

266

532

7664

6 5

4

7

7

7'

66

^E

666 54

6

HARMONY

14:8

Q

fe

764 3

7

*

$

2

&U 5Bi #64666 J

7

'

4

ft

,

3454

3&2

7

7g 5 &

5

5

7tf

6

25tf4

7tt6-

6^67 342 4

75

313

7.

jN*

c iir

rr>

67

6

3

5

5

5ft

7

676

4 9.

J

6

f

4

26

6

6fc

6

6

7

J

6}

J

(Chant)

3

6

" i

sir 3

ei

4 2

6

!

7

g

76|^672

6

S

[jfa^hBi

262

76

2

I

'

2

HARMONY

149

SOPRANO MELODIES TO BE HARMONIZED (In each of these are secondary chords of the 7th and their inversions; some of them, though not all, are marked by the X.)

10.

(Chant)

In

Ine.

CL

InC-

-Ina.

s

11.

InBb-

-InF-

In g

12.

Close.

i 13.

Open,

fe

j

f r

Close.

X

-J

"^

L50 16.

HAEMOJSr

^

(Chant)

1 i

InB-

-InB

JL_^

18.

(

Hymn-tune )

Ihdx

rrrir -In

19.

(

J-l J r

r

IE

I.

J

J

gr.

Hymn-tune ) r

r

r

In

In d 20.

-

^Ia a.

In C.

e

-

In

G

HARMONY

-InD-

151

-In

xxx

A-

-In

-Ind

A-

-InD.

BASS MELODIES TO BE HARMONIZED (Introduce inversions of secondary 7ths in each exercise.)

21.

m 22.

23.

24.

25.

i 26.

SS

^

152

HAEMCXNT

27-

28.

29.

SE

m CHAPTER XXXIV CHORDS OF THE NINTH

WE

154. have now discussed the chords most used, and the student is advised to review the preceding chapters. It will be well to write on four staves, and to transpose some of the exercises, introducing passing tones (both accented and unaccented) and auxiliary tones in moderation. It is also recommended that a beginning be made in the use of the C clefs (alto and tenor). 1 THE STUDENT is NOW REAJDT TOR INVESTIGATION ON HIS OWN ACCOUNT, nr LOOK-

ING UP INSTANCES OF THE EMPLOYMENT OF VARIOUS CHORDS AND CHORD SUCCESSIONS; the works of the masters from Bach to Schumann exist in editions so inexpensive that it is easy to form gradually an adequate collection of them, and not to become acquainted with only the best literature, but to gain a living sense of harmonic as questions they present themselves in the music of the great composers.

The G clef has been used for aE the voices except the bass, and is in orchestral music (for the viola, violoncello, bassoon, trombones, etc.). 1

of the staff it is employed,

are consequently the

it

designates the tone

same as

f

:

and

;

alto

:

still

much employed

On

whichever

and tenor

i

ling

153

will

appear as follows, when written with these

clefs.

155. Before entering upon the subject of this chapter, we must understand the fundamental idea of the suspension and the appoggiatura. When, any tone of a chord is delayed hi moving to that tone of the following chord to which it would naturally proceed, by being prolonged -

into the following chord (of which

dissonance first

is

chord is

it does not form a harmonic part), .4 produced requiring a resolution. The tone referred to of the then said to be SUSPENDED, and is regularly resolved by later

proceeding upward or downward to

its

proper tone in the second chord.

$ 166.

An

with whicn.

it

APPOGGIATURA

is

a tone not suspended, foreign to the chord it is a tone dissonant from the chord,

occurs; in other words

and must move diatonically downward or upward

in its resolution. Dontle appoggiatnra

Stispensio^i

Efe

J

^

A 5

3

4

. 5

4 3

Passing and auxiliary tones have been defined

(

103, 104 t 147).

THE CHORD OF THE NINTH 157.

This chord

is

formed by adding another 3d to a chord of the 7th,

the chord of the 7th by adding another 3d to the triad. just as It clearly is possible to construct seven such chords in every major and minor key, but many of them have no harmonic consequence ; most of those which are available enter by means of suspensions, appoggiaturas, and

we formed

passing or auxiliary tones.

HAEMONY

154 158.

The dominant chord

of the

9th

is

the one chiefly employed, and

will thereproductive of admirable results. Our attention on other the 9th of chords consider we before directed to fore be chiefly it, 1 is usually 9th the which in It occurs scale. the (in of keys major degrees a minor one, Ex. 2), major, though occasionally chromatically altered to sometimes is being chroand in minor keys (in which the 9th usually minor, Ex. a to 4). major one, matically altered

properly used

is

.

2.

t

^ X

9th.

159.

As

there are five tones in this chord, one must be omitted in fourno doubling is allowable. The root and 9th must al-

part writing, while

if the 7th is omitted, the 9th appears rather as an appogior atura suspension (e.g. p. 165, Ex. 12, 13), the chord being hardly to be as a real chord of the 9th; the 7th being present, either the classed properly

ways be present;

3d or the 5th must be omitted, the result being more characteristic if we When the 3d is omitted, however, that note have the 3d in the chord. chord (3 and 4 seq.) the in following sometimes appears 3.

9th.

4.

3th.

chord of the dominant 9th, standing by itself, is even stronger in giving a feeling dominant 7th; it not only fixes the key but the mode (with the rare exceptions caused by chromatic changes, as mentioned above). It is an interesting fac* that *> chord is really a combination of the dominant and leading tone 7th chords. * A.

of tonality than is the

HABMONY

155

160. The 9th may be prolonged from a preceding chord, or may enter by step or by skip, not needing to be prepared; its customary resolution is one degree down, the root ascending to the tonic, the 7th descending one degree,

3d (if present) ascending cending or descending.

the

to the tonic,

i

J^

i

J

the 5th (if present) either os-

^^

^

jiH j-J-j i

and

TT

f- r

4

j

j

f-

i

j

i

r

i

i

JrJ:

,

=FlH ; =F 9th.

9th.

Ath.

9th.

9th.

9th.

In another common resolution, the 9th descends while the other voices remain stationary, the second chord thus being a chord of the dominant 7th.

1

_

-4-/r\-!

9th.

The 9th sometimes proceeds to another tone (not the root) of the following chord of the 7th, and may also be followed by another triad than the tonic (Ex. 12).

J 9th.

9th.

9th.

7 9th.

161.

The 9th not

'

infrequently resolves upward.

9th. 1

in this and similar cases (Ex. Strictly speaking, the chord of the 9th does not resolve and (&) ); the interval of the 9th does resolve, but the chord-resolution takes place

4 and 8 (a) finally

through the dominant 7th chord.

HAEMONT

156

J.

J

J

i

9th.

Instead of resolving upward to the 3d of the chord, tone an octave lower, making a skip of a 7th; 9.

it

may

descend to that

x

x it

r or

may

1O.

f

x

x

J V 9th.

it is

9th.

same harmony.

leap to another tone of the

In the following

fe

T

IJth.

9th.

used as a passing tone, in an ascending and a

descending passage. sfc

J.

Finally, the 9th

may be

irregularly prolonged into the next

(different)

chord; see Ex. 7.

x

12.x

9th.

Observe in Ex. 2 the minor 9th in a major key, entering by preparation; ia Ex. 4 the major 9th in a minor key, entering by skip; in. Ex. 3, 8 (a) the omitted 3d, which is given us in the chord of resolution; in Exu 5 (a) (6) the different resolutions of the 5th in order to avoid consecutive 5ths; that in Ex. 4, 8 (a) it may be properly considered an appoggiatura, and in 11 as a passing tone; that in Exs. 2,

some cases by a skip.

(

3, 6,

8

(&)

it is

suspended; that in

7. 9,

10

it

moves in

HAEMONT

157

Something should be said here concerning a view held by many theorists, espeEngland and France. It is briefly this, that chords of the leading-tone 7th in major and minor are to be regarded as chords of the 9th with the root (or "generator'*) omitted, and that the first inversion of the leading-tone triad is a dominant 7th chord with its root

cially in

omitted.

This opens an interesting field for speculation, and is to a certain extent justified by facts in acoustics, but hardly important to the student who is learning about chords and their uses. From a musical point of view, the value of this theory seems questionable when one considers that the tone F of the following chord of the 6th will nearly always ascend, and may even be doubled (in which latter case one F will ascend), neither of which things is true of the 7th in the 7th chord of which this chord of the 6th is supposed to be a part. .

1

J

i

1

,i

T

j *r* ,

It is

a fact that if the tones Frobe sounded, we almost

and then the low pleted

by the

additional tone; but this

is

feel as if

be played and sustained, the

first

chord were com-

rather of acoustic than harmonic interest.

most often the case that the 9th is placed in the soprano; may, however, be in either alto or tenor. The only thing absolutely 162.

it

[I

It

is

necessary is that in pure four-part writing the 9th shall always appear above and be distant at least a 9th from it, for the result otherwise will be

the root

excessively harsh.

Possible in instrumental music.

Bad.

9th.

in alto.

The above

are

all

good in minor keys

also.

All good.

HARMONY

158 A fine example of the 9th in the th "Meistersinger" overture ( 147).

alto,

with the 3d ahove

it, is

seen in the extract from

etc.

^

^X^

-

9th.

163.

Some examples

of this chord follow, illustrating various points

of entrance and of resolution.

J J ^3i!

WAGNER: "Lohengrin" *J

I

J

h

_K\14 J

)

f

CJ

I .

.|

J

..J

9th.

SCHUBERT: Sonata, Op. 42 9th.

,

P DEBUSSY: "La Demoiselle

_

r

BEETHOYEN: C minor Concerto

^^ ^^

JSPT'l^

^

BEETHOVEN: Sonata, Op. 53

9ttu

HARMONY

159

9th.

SCHUBERT: Unfinished Symphony

JL

9th.

Mrs. H. H. A. BEACH: 'llreflies**

9tb.

9th, :

"Die WaJtttre"

9th.

160

HABM02STY CHAD WICK: rt)I v r"+

c

Lovely Bosabelle"

/J

g^s^r

9th.

'

CHOPIN-:

B ? minor Sonata 1

MENDELSSOHN: Chorale

J-j

1

* -J 9th.

Toccata

9th.

In these

an

last three

examples the 9th appears in an authentic cadence.

We now have

fflustration of successive chords of the 9th, as well as one of successive chords of the 7th. but fair to say that they are to be regarded as specimens of an exceedingly free treatment of these chords; the question of pure part-writing does not enter. The extract from

It

is

m^

Debussy fe OP** *"*

'

j

1

J.

I

<

}

9

&

i

g?g^-

-r

i

i

J.

8

9

The chord

of the 9th on the super-tonic is often used hi a cadence as follows, and occawith the chromatic change indicated in (/), in which latter case it becomes a dominant 9th derived from the dominant key. sionally

J J ^

J

9

9

J

Q

BACH: Chromatic Fantasie

etc.

HAEMONY BACH: Preludio con

163

fnga. (Peters Ed. No. 207)

9th.

BACH: Well-Tempered Clavichord, Vol.

1,

22d Fugne

etc.

9th.

166. The secondary chords of the 9th are flexible in treatment, although great care must be taken that the leading of the voices is pure and musical; the inherent harshness of many of these chords is softened by the manner in which they are introduced, as indicated

above. It should be observed that the occurrence of the iidervaL of a 9th does not of itself indicate In the following the note G is a simple appoggiatura in one voice, and real chord of the 9th. the chord is really a chord of the 6th.

a

X

^--^^

1

CHAPTER XXXV EXEBCISES WITH CHOKDS OP THE NINTH 167. 1.

Y%~39

7

6

9 7

6

164

HARMONY

2.

39

1

96

35 4

75

67

7

3

2

3.

Open-

55

n 7

Open

1 3

6

6

6

$ 2

Close.

Adagio

6937 5

967 7

6

87

4

J-

HARMOlsrY

165

10.

Allegretto

Chords of the 9th are indicated by a x; in some exercises is to be omitted.

( e.

g.

the 7th 12.

13.

Close. I

s

14.

In

InC.

a.

16.

3t=3^

J

17.

r

i

f

i

i

ff

rj

No. 12)

HABMONY

166

-Close.

18. Close. Open.-

InG.

Inc.

InG.

21.

CHAPTER XXXVI CHORDS OF THE ELEVENTH AND THIRTEENTH

No

one can say what will be the future of music on the harmonic from the past there will be further development, at least in the direction of greater freedom in the use of chords. In the history of music we find at different periods the ecclesiastical modes giving way to 168.

side; judging

our present scale system, the mediaeval vagueness of tonality abandoned

modern

definite feeling, and a purely contrapuntal way of working the growth of harmonic understanding, into the methods know approximately when employed in the master works of Bach. the use of suspensions became common, when the dominant 7th was allowed to appear without preparation, when the authentic cadence came into

for our

developed,

by

We

ordinary use. During the last century freedom has been gained in the use of secondary 7ths without preparation, in the introduction of chromatic passing-tones, etc.,

and

of chromatically

changed chords, and in the manner

HARMONY

16T

regarding the tritone and the cross relation; the chord of the 9th has been granted its place, as an independent factor, in the family of chords. In)f

vestigation and experiment are still going on. 169. With the chords of the llth and 13th, however, we seem to have come to the end of independent chords. From our present point of view

they appear to exist mainly through suspension, or by means of appoggiaBut, although a discussion of them turas, and passing and auxiliary tones. might be left until later, in the chapters on suspension, etc., it seems preferable to

make a

brief statement here as regards their use.

CHORD OF THE ELEVENTH

same way that we get the chord of the 9th by the addition 3d to the chord of the 7th, so we obtain trte chord of the llth by adding another 3d to the chord of the 9th. A chord of the llth can theoretiis the case cally be erected on any tone of a major or minor scale but, as with the chord of the 9th, the chord of the llth with the dominant for its root is the one most employed. 170. In the

of a

;

7th.

9th.

llth.

rrri Observe thai in the examples given, the chord enters in the manner de169. scribed in 171. It is clear that two of these six tones must be omitted in fouris merely the 4th placed an octave higher; and part writing; that the llth often that it will consequently appear as a suspension (the 4th being rein suspensions as a dissonant tone that must be resolved) ; examples

garded

of this (a), as well as of the llth entering as (c)

and auxiliary tone

or upward.

(d) follow.

an appoggiatura

The llth

is

(b),

and passing downward

resolved either

168

HAEMOISY In the following example of this chord, with an unusual

for theorists to differ; for

7th, placed below

it is

resolution, we see how easy it ui also quite naturally explained as being a chord of the dominant

an inverted pedal (the tone :

D

of the soprano;

Novellette, Op.

cf.

21, !No.

the chapter on the Pedal).

S

X

ij 172. It

may

*

\t#

also occur together

as the llth is the

r P=

with a suspension of another voice j

xx

same tone

as the 4th (an octave higher), the 3d is of course omitted in the dissonant chord, and we must choose whether the 5th, 7th, or 9th is to be also omitted. .

x .

;:

" Tristan und Isolde "

3= llth.

MENJDEJOSSOHN: ~~

Choraa, ~

" For all the Gentiles " (" St Paul

l

Uth.

J

j

,.

j

*)

HARMONY

169

".Midsummer Niglit*s Dream** Overture

llth.

CHORD OF THE THIRTEENTH 173. By adding yet another 3d to the chord of the llth, the chord of the 13th. 7th.

9th.

we

obtain"

18th.

llth.

The addition of another 3d to the chord of the 13th brings us to the ton two octaves root, and therefore to the end of all possible chords, as we should then begin our

above the series of

3ds over again.

174.

This chord also usually appears with the dominant for

and is logically explained as resulting from a a passing tone or an auxiliary tone.

suspension,

its root,

an appoggiatura,

In four-part writing three of the seven tones of this chord must bf few examples are given of its most common use. omitted.

A

13th.

13th.

X

X

BEETHOVKST: 9th Symphony

x

lb (in-rorted.)

HARMONY

170 :

*'Der fliegende Hollander"

X

**

.

: Quintet from Die Meistersinger**

Intermezzo, op.

110.

-,

-.

ohLl

:

J I

r

;:

13th. i:

"Die Meistersinger" (p. 389)J

GEIEG: Song, "Eln SchTran"

X

I

>

1

,

X

A

t

.

etc.

'13th.

DEBUSSY: "Pellets

*

tf

et

M&isande"

J:

1

b* etc.

9th.

13th, 9th.

In the last example we have thfc chord used independently; a rare instance. It is given rather to show that experiments are being made in this direction; the result may tend to further emancipation of the chord of the 13th. :

X

"Des Abends," Op.

12,

No.

1.

9th. 13th. 7th.

(As this is for pianoforte, and the pedal sustains the other tones of the dominant loony, the chord may be regarded as a true 13th.)

HAKMONY

171

CHAPTER XXXVII CHROMATICALLY ALTERED CHOEDS 176. So far we have been dealing with chords of a definite tonality, which were classified mainly as triads and seventh chords (in either fundamental or inverted position) on the various degrees of the major or the minor scale. We must now enlarge our harmonic vocabulary by studying an important group of chords which are formed by chromatic alteration. The principle is this, that, whenever any voice progresses by a whole tone, the latter may be subdivided into semitones by the introduction of appropriate accidentals,

e.g.

A

may

176. Theoretically, any factor of a triad, or of a 7th or of a 9th chord be chromatically raised or lowered. Some of these formations will

from chords found, in a regular scale-series; some are used but as passing chords; while others are so frequent in inverted and rarely, that they are felt to have a definite identity and have received positions not

differ

appropriate names. 177.

The 3d

of triads

is

the factor which decides whether the

mode be

major or minor; either the root or the 5th may be chromatically altered, but those chords which arise from an alteration of the 5th are decidedly of the most importance, (1)

it

e.g.

In (1) we have a major triad may be used as a passing chord

which C-E-G

3

55$

55J

55$

f~ r

66

T

555

37 5|

6

6 5

2

HARMONY

180

26

666

i

$6797

5

7.

J

J

1

J

rnr nr876

1

88ft

6

6

55^4

6

3

8.

7b 65

5b

5

3$

4

6

367 4

sb-

Gfrazioso.

, Dfr, /, etc* The student should look up for himself examples of this modulation in standard compositions. (&),

two preceding chords, the augmented 6-5 chord is very common in th* a 7th chord with a diminished 3d) and also in the two other inversion* (4-3 and 2). Examples are cited of each. 203. LiVe the i

position (*.. as

WAGSTSB: Prelude to "Lohengrin**

=1 etc.

^ IB ttf^ pafflage

TUt

The 4

strildns

S-^T

wo fiM a chromatically altered

ebord placed in the

first

inveraioa

7th chord used in the fundamental pod*

would give a regular augmented

faifaoductory chords of Schubert's wonderfully dramatic aong **AiD example of ^h^ H chord in the second inversion.

Meer" famish

Here v& see anofibflr case of the enharmonic notation spoken of above, for D$is written Eb on account of the upward resolution. The 7th chord in its original position is

instead of

1(C)

HJL

rj|

The passage on a

The

"^ "^ I

Tntgh^ Blgo

^

origma^ 5tn

m

tlie

lms8

fa

obviously used as a 4-3 chord.

be explained as a normal augmented 6 5 chord

tonic pedal-point*

following passage gives us both the third inversion (chord of the 2d) and another second inversion, the original chord being

HARMONY CHOPHT: Nocturne, Op.

193 15,

No. 3

204. Now that the fundamental facts in regard to this chord have been presented, its use will best be learned by a careful analysis of examples from musical literature. few are cited and others should be sought

A

A

for.

thorough knowledge of all the augmented chords for an insight into the subtle harmonies of modern music.

is

indispensable

SCHTTBERT : Impromptu, Op.

142,

No. 2

" Bunte BIStter," Op. S9, No.

14

tr

The above passage is unique in its abundance of augmented harmonies, both in fundamental position and in inversions. Observe that the first two measures are on a double pedaL

GOUNOD : " Faust," Act I x

Faust," Act IH

*_

ffi|zfez4

^^pR

r^bS

rr

These last examples are interesting, the former on account of the downward resolution of the augmented interval, the latter for the combination of a suspended tone with the third inversion of lution.

an

altered 7th chord,

e.g.

Observe the subtle chromatic

HAEMOISTZ TSCHATKOWSKT: 5th Symphony ( 1st MoYement)

In the passage from TschaikowsH observe the bold downward leap of the Bb. JLK: New World " Symphony (2d Movement)

beautiful phrase of Dvorak, let the student ask himself what is thfl and also explain the notation. 205. In harmonizing melodies (Chapter XL, Ex. 7-24) It Is helpful to know that tfta augmented 6, augmented 6-4-3 and augmented 6-6 chords are frequently to be derived from inversions of the fourth triad, second chord of the 7th and fourth chord of the 7th, respectively, of the minor scale, their ordinary resolutions being the following (but qf. $192, 196 198,001).

In analyzing

*M

position of the chord

!__!

6+

64-

!

6+ 4

tf

I

!

frH

5

i

6+ 5

3

The student various

ways

is

reminded, however, that these chords are derivable in

ARE THEREFORE VEEY USEFUL

192, 196, 198); THEY

(

E?

MODULATION.

CHAPTER XL EXEEC1SES WrrH AUGMENTED CHORDS AND /6-K 6-k

INVERSIONS

<

206. AUGICENTEO triads'being marked by a X, the same method is pursued -with the aug mented chords. A distmction is thus made in figured basses between these chords and such at are indicated by f, 4 $ ( 194). In the soprano melodies some, not all, of the augmented chords

5 4 3

are

in a few of the bass melodies they are also indicated in the same wayv not being given in Ex. 7-10- Augmented skips are permitted in any voice-

marked by a X;

figures

HABMONT

6

7

6+

6+64546

ft

-

3

195

3

3

F-F 4.

1

3

1

4

6+ 6^

4

6t2

&f 4+

4

tf

6

6

6+67

65

4

5

4

6

a

6

$6

6+676 8*6 54 42

55

5 4

566

6 5

4+

e

6b

6-ff

4-

$

3

354

4

i

6+6

6+6

5

g

6.

3 7.

7

6 42

6 ebestj

6

6+

6

66 5

5

4$

4

(Hymn tune)

r

rif

J

ir

J i-n

196

HARMONY

197 14.

(Hymn

tune)

In Ab.

Ln/-

In/-

-InAfr.

15.

16.

~

J J ^^ 1

r \

f kV tor^

f*

i

-f b-y I

,

:

I

9fli

3.

(Hymn-tune)

^

HARMONY

238 Allegretto.

rfc!

5. (L

(Hymn- tune) f_

Ls

*-

l

7.

(Hymn-tune)

^JJi^ik^j^Luiru-jjij^rti

HARMONY

239

CHAPTER XLVH CHOSS RELATION (FALSE EELATION)

WHEN

a tone of one chord occurs in another chord, in a different and so soon that the effect of the one tone before the other appears to contradict it mind the from has not passed with its chromatic alteration, we have a CROSS RELATION. 252.

voice, chromatically altered,

1

1 The following cannot be properly called a cross relation, for the AJJ is an appoggiathe definition the simultaneous tura, not affecting the tonality; some theorists include in appearance of the altered and -unaltered tone in the same chord.

In fact the cross relations produced by the appoggiaturas in the next result in

a bad

effect*

TST tf.

Schumann's Andante and

variations for

two

pianofortes.

illustration

do not

HAKMOJNX

240

It is difficult to lay down definite rules as to usage; the feeling of musicians has become so modified of late years thai we may practically

say that no cross relation is forbidden that sounds tolerably well. 253. The harshest form of it is when the 3d in a tonic triad is major and minor in different voices in two successive chords, the effect not being altered

by the

we almost

for

interposition of

a passing-tone or of another chord:

get the feeling that two keys are used at the same time.

SCHTTBEBT : Impromptu, Op. 90, Ho.

1

BEAHMS: Symphony in F major

X

capricious shifting between tonic major and minor is a characteristic ot Schubert "Rosamonde"); in this illustration the effect is softened by the fact that Eb 254) ; Brahms simply is in the lower voice also, the change to EJ taking place in that voice, had two vital themes, which he intended to work together without regard to a temporary

The

(c/.

his song

roughness,

254.

The result is

generally good

when both the

original

and the altered

tone occur in the same voice, as well as the altered tone in the other voice also (a), or ( 138) when the chromatically changed tone is a new leading-tone in a modulation (6). There are many cases where a cross rela-

sounds better than it looks upon paper; we sometimes, however, may a change in one of the voices, for the sake prefer to avoid the effect by tion

of the slight

improvement

(c)

.

241

HAKMONT

m

*

J

ifa