Elementary Counterpoint

MT

55.G59E9" VS'lT'*

3 1924 021

"*"*

751 098

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original of this

book

is in

the Cornell University Library.

There are no known copyright

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EXERCISES IN

ELEMENTARY COUNTERPOINT BY

PERCY GOETSCHIUS,

Mus. Doc.

(Royal Wurttemburg Professor)

Author of "The Material used in Musical Composition," "The Theory

and

Practice of Tone-Relations,"

"The Homophonic Forms

Musical Composition," "Models of the Principal Music Forms," "Exercises in MelodyWriting," "Applied Counterpoint" "Lessons in Music Form," etc.

Fifth Edition

NEW YORK G.

SCHIRMER

of

Copyright, 1910,

By

G.

SCHIRMER J1946

Dedicated to

Sfomfe Samroarij IN

CORDIAL RECOGNITION OF HIS SIGNIFICANT CONTRIBUTION TO MUSICAL EDUCATION IN AMERICA

PREFACE. The present volume is intended its title

and expected

to cover

more ground than

implies.

In the author's mind

it

represents a course in

Harmony,

quite as

much

as in Counterpoint. It

owes

its

two courses

inception to the author's often expressed conviction that these

be separated; and also

of study cannot

to

a constantly strength-

ening belief that the most rational, quickest and best way to acquire a

thorough knowledge of the chords and their uses (the recognized purpose of the study of

Harmony)

to begin

is

with one part, to pass from that to

two, from that to three, and thus gradually arrive at

For not at

this reason, all

four-part harmony. of

Harmony

Such general

familiarity

and

full

is

may be

" Material," or Chapters III to

four-part texture,

therefore

point "; and

its

recommended.

gained by the study of Part II of

XXX

of

my

my

" Tone-Relations."

when approached

atized in these chapters, will have developed

itself

in this way, as system-

naturally into " Counter-

acquisition will fully prepare the student to undertake the

subsequent tasks in

homophonic and polyphonic composition.

THE AUTHOR. New

is

necessary, though a general knowledge of the chords will facili-

tate the study of this book,

The

full

an extensive Dreraratory knowledge

York, February, 1910.

TABLE OF CONTENTS. PAGE

Introduction

i

Tee Single Melodic I. row Leaps

Chapter

Exercise

Chapter

LT.

Line, Stepwise Progressions and Nar5

i

7

Wider Leaps

8 11

Exercise 2

Exceptional Progressions, and the Minor

Chapter HI.

Mode

Exercise 3

15

The Association op Two Melodic Lines. Rhythm. Fundamental Intervals. Major Mode

Chapter IV.

Corresponding 15 20

Exercise 4

Fundamental Intervals, Minor Mode

Chapter V.

22

Exercise 5

23

Exceptional Intervals

Chapter VI.

24 28

Exercize 6

Rhythmic Diversity.

Chapter VII.

Two Notes

to each Beat

VUL

Modulations

37 41

Exercise 8

Chapter IX.

Three Notes to each Beat

43

46

Exercise 9

Chapter X.

Syncopation, or Shifted Rhythm.

Ties.

Two and Three

Notes to each Beat

47 50

Exercise 10

Chapter

XL The

Tle, continued.

Rests

51

Exercise 11

Chapter XEL

56

Four Notes to each Beat

57 62

Exercise 12

Chapter XJH.

29

36

Exercise 7

Chapter

ir

Four Notes to each Beat,

as Amplified

Forms

63

67

Exercise 13 vii

TABLE OF CONTENTS

V1H

PAGE

Movement

Diversity of Rhythmic

Chapter XIV.

in the

Two

Parts

67

Exercise 14

Chapter XV.

72

Motive-Development.

Imitation.

The Small Invention

Exercise 15

73 81

Three-part Harmony, Melody Harmonization with Pri-

Chapter XVI.

mary Chords

83

Exercise 16

91

Secondary Chords.

Chapter XVII.

Sequences

92

Exercise 17

94

Modulation, Diatonic and Chromatic.

Chapter XVLII. Steps

Altered Scale96

Exercise 18

99

Chapter XIX. Contrapuntal Amplified

Harmony,

Three

Parts.

Simple

and ioi

Exercise 19

Chapter XX.

105

Three-part Counterpoint

106

Exercise 20

Chapter XXI. Parts

113

Motive-Development.

The

Small

Three

Invention,

114

Exercise 21

121

XXH. Four-part Harmony. Melody Harmonization. and Secondary Chords. Sequences

Chapter

Primary 122

126

Exercise 22

Modulation

Chapter XXHI.

126

Exercise 23

Chapter XXIV.

131

Contrapuntal

Harmony,

Four

Parts.

Simple

and

Amplified

132

Exercise 24

Chapter XXV.

137

Four-part Counterpoint (Analysis)

138

Exercise 25

Chapter XXVI. Parts Exercise 26

Appendix

145

Motive-Development.

The Small

Invention,

Four 146 149

151

:

EXERCISES IN

ELEMENTARY COUNTERPOINT INTRODUCTION. Music, theoretically considered,

tone.

more nearly resembles a

It

than any other art-creation lines are visible

The

motion.

;

altogether

consists

picture, or

Lines of

of

an architectural drawing,

the difference being that in the drawing the

and constant, while

music they are audible and

in

in

separate tones are the points through which the lines are

drawn and the impression which by the intelligent listener, is not ;

intended, and which

is

apprehended

is

that of single tones, but of continuous

Lines of tones, describing movements, curves and angles, rising, falling, directly analogous to the linear impressions conveyed by a picpoising,

—

The popular name

ture or drawing.

As

for

such a tone-line

" Melody."

is

several tone-lines are usually being traced simultaneously,

it

follows

that several corresponding melodies may, and generally do, appear together. pal, or

The term Melody, however, most prominent

When

is

applied specifically to the princi-

line.

a number of tone-lines are intonated together,

The

they should agree, or harmonize with each other. this

agreement

is

assured

is

commonly known #

Tones are associated

in

two

as "

it is

evident that

process by which

Harmony."

#

* different

ways

:

First, in vertical

or simultaneously, in solid bodies of tone, usually

known

second, in lateral order, or successively, in strands of tone which call Tone-lines, tically,

c-e-g,

;

we

in

some

tone-line (Ex.

cessively, give a tone-line or a.

Ex 1.

It is of the

a).

i,

melody (Ex.

Chord.

it

The same

i

may

tones, arranged suc-

i, V)

i. Tone-line.

ii

and

shall

arranged ver-

give a chord-body, or harmony, each separate tone of which

be a point

and

For example, the tones

or melodies.

columns,

as Chords

J

f

n

utmost importance that the music student should adopt

cultivate the habit of

apprehending music according to

this defini-

a System of Lines. The beginner, and the ordinary hearer, are inclined to regard music merely as a series of chords, a succession of

tion, as

i

;

ELEMENTARY COUNTERPOINT.

2

tone-groups, and to associate mentally only those tones that are sounded

together (simultaneously, as Ex. correct as far as

it

tionably the chord.

chords lines

is

surely a natural view,

But

The

an imperfect view.

is

it

music

all

is

and

unques-

object of the

simply, to fix (approximately) the points through which the

is,

run

This

i, a)<

goes, for the harmonic basis of

;

and unless these

lines are

grasped and traced,

— unless the

hearer can associate mentally the tones that follow each other, the true

purpose and significance of the whole tone-association

is

This

missed.

must be so, because the only evidence of Life in music lies in the motions which interlink the tones in flowing lines and these lines are, therefore, ;

the only tangible element in the art of tone.

The real musical picture then, is a delineation an image of sounding and moving lines. Quite aside, for the present, from the numerous qualtheir directions, their speed, their ities which enter into these lines, rhythm (freedom and variety of changing motions), their spaces, and even ;

—

their indefinable sensuous or spiritual attributes,

— the fundamental

fact

must be grasped that it is these lines which create the musical impression. The " music " lies in its melodies. Music is " tone-lines " and ;

the quality of the several lines determines the quality of the composition the vitality of the lines equals the

harmony which governs the

life

in the

music

;

and the degree of

association of the lines fixes the euphonious

—

its

pleasurable effect upon the natural

what

is

meant by apprehending music as a

standard of the composition, sense of harmony or concord.

To

more

illustrate

fully

fabric of tone-strands, tone-lines, or associated melodies, traced, not vertically

through the separate chord-forms, but continuously

chord to chord, Sonata. tical

—

let

(laterally)

from

us take a passage, at random, from a Beethoven

In this passage, the master, though certainly guided by his ver-

chords,

was

quite as surely impelled to trace a good, distinctly

lodious, effective tone-line in each separate part or register Lowermost

line.

Next higher

Ulle.

:

—

me-

:

INTROD UCTION. The

total result,

obtained by weaving these four different strands of

tone into one compact body (as follows

:

came from Beethoven's hand)

is

as

out of the chords, of course, but the " Music "

it-

—

it

^m

n

^

^ The music proceeded

and meaning in the Lines of tone. The chords were the means, the lines were the object, of the musical thought. The above musical image (Ex. 3 ) should therefore appeal self

manifests

its

finished beauty

and

life

to the finer sense of the listener in the forms noted in Ex.

apprehend each

line separately, first of all

;

and the

He should

2.

total

sensuous im-

pression should be gained by mentally combining these lines. # #

The tone-lines differ greatly in their length, and in the manner of their Some lines are long, others are often very brief. Sometimes the line is continuous in sound (legato), and again it may be inter-

presentation.

mittent (staccato).

In the

latter case,

which

is

very common, the inner

ear of the listener traces the complete line across the silent gaps, just as

the eye traces a dotted line as readily as an unbroken one.

Through the following convenient (and customary) method and its corresponding performance on the pianoforte —

tion,

of nota-

:

Chopin.

Ex. 4.

i^Mff^F

£-

4-

N—netc.

^rsfr>— SB

S'^hrtj

^y^ "Mr s

the hearer should distinctly trace the following five lines Uppermost Ex.

Next lower

line.

^rrfhnrc fr

r r

I

f

line.

J'

:

ELEMENTARY COUNTERPOINT. Next lower

m

a

*&=

a,,t ,

S

f|Hf^ I

Lowermost

Next lower.

SSSe ffi The

fr

*=tt

line.

I

-=!-=»-

student should carefully examine brief passages from the master-

component lines, one single prominent line (the " tune " proper, in the uppermost part) seems to be distinctly melodious, as for instance, in No. 37 of Mendelssohn's " Songs without Words." In others, at least two independent lines are discernible in a few, the entire bulk may be divided into distinct melodies, as in the Inventions and Fugues of Bach, and many passages in stringquartets, or symphonic scores (where the lines are written separately, of necessity, on independent staves). In many, finally, the bulk is very uneven, as if, here and there, single extra tones, or brief little lines, had been inserted among the more important, longer melodies.

works, with a view to resolving the given bulk into as

shown

in the

above examples.

In

many

its

cases, only

—

—

;

*

#

To some

#

extent, this principle of simultaneous melodies is present in

every grade, even the simplest, of music.

cises,

connect

It is impossible to

chords, as, for example, in a hymn-tune, or in the earliest

harmony

exer-

without tracing such tone-lines.

In four-voice harmony there are

four,

— known in vocal writing, and

familiar to the student (in church choirs or choral societies) as the so-

prano,

alto,

tenor and bass.

As a

rule,

so

much

preference

is

given to

the uppermost of these (the soprano), that the other singers scarcely realize, themselves, that they too are intoning " melodies " quite as surely as the soprano.

#

Counterpoint

is

— or

*

one of the technical processes of music writing.

object of contrapuntal practice

melody,

*

is

The

add melody to or more tone-lines

to enable the student to

to obtain an association of two, three,

that agree with each other harmonically

and yet are

dent of each other to present really different melodic

sufficiently

indepen-

lines.

Briefly defined

Melody

is

Harmony

a succession, or continuous is

which harmonize Counterpoint

line, of single tones.

a succession of chords or vertical columns of tones

is

in their simultaneous presentation.

the harmonious association of individually perfect,

but independent, melodies.

:

Par.

:

THE SINGLE MELODIC LINE.

x.

CHAPTER

I.

THE SINGLE MELODIC 1.

Counterpoint

association

is,

and each melody

dant, 2.

associated melodies.

is

in a general sense, is

harmonious,

good, by

Probably the latter condition

sideration, for the beginner,

is

alone,

must produce a

LINE. In good counterpoint, the

—

that

is,

reasonably accor-

itself. is

The first con-

the most important.

the correctness of each separate melodic

independently of the other, or others.

line,

5

Each

line,

sung or played

satisfactory melodic impression.

Therefore, the first point to be mastered by the student of har3. mony, or counterpoint, is the fundamental principle of good melodic movement. He must acquire the ability to judge the quality of a melodic line, and to avoid any tone-progression which is unnatural, that is, which violates the natural conditions of Melody (smooth, rational, congruous, well-balanced and interesting tone-succession).

—

4.

Should the student harbor any doubt of the existence of laws that

govern Melody, or of the possibility of distinguishing good melodies from inferior ones with scientific accuracy, let him compare the following

Ex

fan r^

with those shown in Ex.

2,

J i

^.J^t^n

or with any other examples in this book that

are given as specimens of correct, sensible melody. 5.

It is

not possible, in this necessarily condensed form, to state

all

of the condi-

which enter into the process of perfect melodic formation, a process which is But a few general rules may be ultimately subtle, and no doubt partly incalculable. tions

given, and these the beginner must carefully observe and follow, until his and experience shall enable him to control the finer and finest movements. 6.

Probably the most vital law of melody

is

that which

is

instinct

grounded

in

the relations and interactions of the primary harmonies of the key, and

which determines the direction of certain Scale-steps. Rule 1. The natural or inherent bent of certain Scale-steps must be These tendencies are respected, as far as is possible without monotony. as follows

:

:

:

:

ELEMENTARY COUNTERPOINT.

Par.

%.

The 7th step of the scale moves (naturally) upward. The 6th and 4th steps of the scale both move (naturally) downward. These are called the Active scale-steps. Their movement extends, one step that is Step 7 moves to step 8, Step 6 moves to step 5, and Step 4 moves to step 3, as a rule, though wider movements in the proper direction are possible. For example, in C major 7.

generally, only

;

f

Ex.

=t

i&

I

=F^

The other scale-steps (1, 3, move in any direction,

free to

5

—

and 2) have no such tendencies, and are that

is,

free as far as direction is con-

cerned. 8. When the active tones of the scale move one step, as here shown, they are " resolved " that is, their active tendencies are gratified, and ;

movement is finished. But it is always correct, when less decisive movement is desired, for each active step to move two steps at once, or, their

in other words, to leap a third,

—

proper direction, of course.

in the

Thus (C major) 4

i

Ex.

To

9.

Rule so that

ing

it

this

2.

it

will

fundamental rule there

5,

"pushing"

preceded by step

7, if

preceded by

may pass on up to

pass on up to step

8,

a

step

may

step 7

overcome,

by approach-

along the scale.

side,

pass on down to step 6

;

and step

4,

;

preceded by

step 6, 3,

may

5.

8-7-6-5, 5-6-7-8

and

3-4-5 are good.

:

|0O

a

a

1,

a

a

*

o

V 8

i

may be

direction,

from the other

it)

In other words, the progressions

Thus (C major) r\

one important exception

is

The natural tendency of each active move along the scale in the opposite

(so to speak, by

Thus, step

1

-*—*

lit ^m

7 ,

6

-*—*

*

' 3

4

4

*

6

6

j/»

:?^£

1

I

:

:

THE SINGLE MELODIC LINE.

Par. 10.

Observe that the successions 7-6-7, 6-7-6, and 5-4-51 cannot be manner, and should therefore be avoided, for the present.

10.

justified in this

Thus (C major):

Ex. 10,

i EXERCISE The

The aim

of this

first

Scale-line, lesson

is

j

j

1

j

11

I.

and Narrow Leaps.

to impress these

fundamental melodic movements

and habituate him to them (m case his studies, hitherto, have left this most important work unaccomplished). Therefore, he is required to write a very large number of original melodies, in all the major keys, strictly accord-

upon the

student's mind,

ing to the following directions

At present, only in major. Use chiefly the regular resolutions of the active steps, as shown in But do not neglect the irregular movements (Ex. 9). All wider 3. At no point should the melody leap more than a third. 1

.

z.

8.

be deferred 4.

Any

lar

Use

6.

The

tone

may be

repeated, anywhere.

See par.

must

20.

all

length of the melodies

is

optional, but

it is

illustration

may be

of

advisable to write in the regu-

forms of four or eight measures, closing with the keynote.

For

skips

until the next lesson.

the simpler kinds of measure. (from \ to g). The notes uniform rhythmic value, or of different lengths. See pars. 21, 22 and 23. 5.

Exs. 7 and

:

:

:

:

ELEMENTARY COUNTERPOINT.

CHAPTER

:

Par. xi.

II.

WIDER LEAPS. 11.

son,

is

The

leap of a third (called a narrow leap), used in the

But

always good.

require specific limitations.

Rule

Any wide

3.

skip

first les-

wider leaps are generally hazardous, and

all

The is

principal consideration

natural,

is

as follows

and permissible, when both tones

belong to the same good chord. 12.

IV

;

The "good

" chords are the primary triads

though more rare

also the II,

;

The chords on

and Dominant-gth.

on scale-steps

also the chords of the

steps

VI and

III,

I,

V,

Dominant-7th

and

all

subordi-

nate dissonant chords, are too inferior to afford justification for wide leaps.

Thus,

C

in

major

Good Chords. Ex. 12.

i

1ST -!S>-

IV

I

13.

Rare.

The C

y7

y9

m

Inferior.

~tst

VI

1

III

etc.

following wide leaps are therefore good, in either direction

major.

Ex.

13. IV

I

V

II

V9

V7

etc.

I IV

The following

are unnatural, in either direction, and must be avoided,

at present

C

major.

t.^m "

Ex.

VI

III

f

I

etc.

IV 7

14. Rule 4. Two or more leaps in the same direction, whether narrow or wide, are also strictly subject to this rule All the tones must belong to the same good chord. Thus, C major :

:

WIDER LEAPS.

Par. is.

All good.

a.

Ex. .

£1

I

5 .E^EE| V7 -

i*

v

The

J

#

1_

:

major.

Note.

In the

first

group, the

tone, reached with a leap in the

The

££ S

i^ m± C

Ex. 16.

following are faulty

U-g

J

'

IV-

first

same

skip

g) represents the I, but the next does not belong to that (same) chord.

(c to

direction,

leaping tones, arranged in such a manner, always remain in the ear,

up," so to speak,

— and give the

impression of a complete tone-body.

—

"

add

The above

measures sound thus

i in the same direction. ear ceases to " add up " the tones,

This rule applies only to successive skips

15.

The moment the direction changes, the

and judges each leap separately, according to Rule 3. All the faulty promade good by altering the direction. Thus:

gressions of Ex. 16 can therefore be

All good.

Ex.

17.

iIE Rule

16.

turns,

Ex. 18.

=t

5-

— changes

Thus

direction.

If

J

r

l

This

is

:

lffj ;fcE&

Notice, particularly, that this

maitis unchanged.

etc.

After a wide leap (beyond a third), the melody usually its

pr-r

<

17.

srrrna

t-°CP"-

distinctly

is

£§^£

not obligatory when the chord

shown

in Ex. 15.

re-

:

;

ELEMENTARY COUNTERPOINT.

IO

It is generally better

and

it is

to tum, however, after a wide leap, even in the

usually quite necessary

rectified in

Ex.

Par. 18.

when

the chord changes,

—

same chord

as seen in Ex. 16 (all

Exceptions do occur, however; see Ex. 20.

17).

»

A skip of

any width may be made towards (or opposite That is, the resoluof an active scale-step. tion of step 7 being upward, any leap down to it is correct. And, similarly, any skip may be made up to steps 6 and 4. In each case, the

Rule

18.

6.

movement

to) the resolving

melody, in turning after the leap, properly resolves the active step. following

movements are

Down Ex. 19.

to step

good (C major)

The

:

7.

Iw Up

all

N. B. to step

iP

6.

6

Up

N. B.

to step 4.

IIE

i

In the measures marked N.

B.,

—

an exception to a part of Ex. 14 is seen, skips When properly resolved, these progressions

apparently representing inferior chords. are perfectly good.

19.

6,

— up

If a

wide skip

to 7, or

down

the melody cannot turn, resolved.

made, along a good chord-line, contrary to Rule an exception is unavoidable. Either after the wide leap, or the active tone cannot be

is

to 6 or 4,

Thus

i 3^

Ex.

20

—

v*?

?

p

m^m).

i

?

?

It is usually better to respect

in the

the fundamental law (Rule

Therefore, groups

active step properly.

1

,

1),

and resolve the 2, 4 and 6,

3 and 5 are better than groups

above example.

20.

good:

Rule

7-

The

repetition of a tone, or the octave-leap, is always

WIDER LEAPS.

Par. ai.

Ex.

II

E:

21.

a

Uniform rhythm

21.

But

melody.

it

is

always safe, and generally predominates in a

incurs monotony, and, therefore, notes of various time-

At

values are effective.

least occasionally, a note of greater value, or of

than the prescribed beat, should be used.

less value

Rule

The rhythm

and always good, when the and the shorter (lighter) ones upon unaccented beats or fractions of beats. Thus, in regular rhythm: 22.

8.

is

regular,

longer (heavier) tones appear upon the accented (heavier) beats,

Ex.

22.

gl

+-*l

4=

If the

23.

&£^B

^n order

is

reversed,

—

if

\=x

heavy notes occupy

— the rhythm

light beats, or

and the result by recurrence, that is, by being repeated in the next measure, or some other corresponding measure. Thus (both from Schubert ) light notes

occupy heavy beats,

doubtful.

Still,

—

irregular

is

irregular,

rhythms may always be

rectified

:

23,

§|

i-

i=a

^^

Recurrence.

Irreg.-

EE Recurrence.

Irreg.-

EXERCISE Wider Write, as before, a very large material of this chapter.

but No.

Leaps.

number

Review the

2.

employing the

of original melodies,

directions given in Exercise

i,

and follow

all

3.

CHAPTER

III.

EXCEPTIONAL PROGRESSIONS. MINOR MODE. 24.

After thorough exercise of the basic principles of melodic move-

ment, the student

will better

may appear in tone-lines.

understand certain less regular

These, though peculiar, and rare,

traits that

may be fully

:

:

;

ELEMENTARY COUNTERPOINT.

12

with the voice

then with the eye

;

and unceasing reference always be 25.

;

;

always with close mental application

to the keynote,

— of which

with reference to scale-step

First,

the mental ear

must

Good.

Good.

2.

3.

(C major)

7

S

Good.

4.

IPNE

24.

few are specially the piano then

first at

;

distinctly conscious.

1.

Ex.

A

by the circumstances that attend them.

justified

noted below, and should be thoroughly tested

Par. as.

? ?

5-

?

III

Good.

6.

7.

??

8.

??

9.

??

10.

m

t ??

11.

12.

?

Good.

i

13.

14.

? ? ?

Good.

i

*

7

G roups

Explanation.

Group 4

8.

is similar,

group 6

III

7 J* 4

is

2

,

r-fi

and 3 are good, because step

7

a^f—fl

passes soon up into

not good, because the skip represents an inferior chord

Group

but worse.

is better,

1

Good.

15.

iIE step

(?)

because the

5 is doubtful, first

group 13 because step 7 does not reach step 8 at all ;

three tones represent the Dom.-7th chord, and the

Groups 7 to 10 are all doubtful, because step 7 makes an extreme leap in the wrong direction group 10 is the least objectionable, because step 7 recovers itself and ascends to step 8. Group 1 1 is parresolution of the last one (step 4) satisfies the ear.

;

poor and should be avoided it may, it is true, occur in the line of the Dom.-7 th chord but step 7 leaps in the wrong direction it is an awkward leap (augmented fourth), and, landing on step 4, it cannot recover itself. Group 12, on the contrary, is all right, see Ex. 19, group 13. Group 14 is considered good, see Ex. 19, group 2. Group 15 appears to violate par. 10; it is permissible, however, because the succession 7-6-7 appears as embellishment only, and not as essential melodic movement. ticularly

;

;

;

—

Second, with reference to scale-step 6

26.

1.

Ex.

£W-

25.

*->

.6.

4.

—

Good.

2.

Good.

3.

Good.

4.

? ?

5.

Good.

x

1

a

Good.

7.

???

8.

J

(?)

9.

J

J

f

??

10.

I

VI

VI

??

—

:

EXCEPTIONAL PROGRESSIONS.

Par. 27.

Ss

n. Good.

Good.

12.

IW

13.

Good.

14.

13

Good.

15.

Good. 3

Ps^B

t=F

Groups

:

and 3 are good, because step 6 reaches step 5 soon group 6 is good and in group 5, both tendencies are satisfied. Group 7 contains too many irregularities; group 8 is better, like group 5. Groups 9 and 10 represent an inferior chord. Groups 11 and 12 are justified by Ex. 19. Groups 13 and 14 seem to be adjusted by the resolution of step 7. Group 15 is right, for the reasons given in Ex. 24, group 15, which review. Explanation.

enough.

Group 4

is

2

1,

poor, because step 4 is not resolved

;

;

—

Third, with reference to scale-step 4

27.

Good.

2.

Good.

3.

Good.

4.

?

26.

Good.

6.

f?

7.

8.

i

Good.

*=?*

?

5-

P^ ^

Ex.

±e*

S 9.

??

m

10.

? ? ?

1

Explanation. Groups 4 and 5 are doubtful, because step 4 ascends and does not return to step 3 compare groups 2 and 6. Group 7 is too irregular. Group 9 has the bad leap from 7 to 3 see Ex. 14, No. 2, and Ex. 24, No. 13. Group 10 is very poor, like Ex. 24, No. 11, and for similar reasons. ;

;

28.

Rule

One of

9.

the most vital traits (possibly the supreme one)

of good, effective, comprehensible and significant melody,

ment

of the tones in uniform or similar groups or figures.

is

the arrange-

Thus, a figure

(usually a half-measure, whole measure, or two measures in length)

be reproduced as form,

repetition, sequence, or

— generally

in

may

some other closely corresponding

some corresponding rhythmic group.

For example Beethoven.

Observe the similarity of formation in the two figures marked a ; the second Also the agreement of b and b. Also the general is a sequence of the first. exact resemblance between figures a and b. Also the slight intentional differences, agreement being by no means necessary.

measure

See also Ex.

13, b;

Ex. 21

;

Ex. 23,

b.

:

:

:

ELEMENTARY COUNTERPOINT.

14

Such syntactic agreement (uniformity

29.

distinct, is

Par. 29.

of delineation), if perfectly

often a sufficient excuse for certain irregularities of progression.

For example

e

EE

i $

Ex.

28.

» i 2.

?M *!ilV

l

>"

3.

&

1

SEE L

J

In No.

1,

the poor progressions 7-6-7 and 5-4-5 are both justified by being

a blameless figure). In No. 2, the awkward by the repetition of the first figure. In No. 3, several poor successions are palliated, as sequences of the very first one, which is a sequences of the

first

movement from 4 up

perfectly

good

measure (which to 7

is

is

justified

—

figure.

THE MINOR MODE. The harmonic minor scale

30.

is

the 3rd and 6th scale-steps of the

derived from the major, by lowering latter.

C

minor corresponds to

major, but has e-ftat and a-flat, instead of e and a. the scale of

major.

Every rule given above applies to minor precisely as to major. That the rules which govern C major also govern C minor (not A minor),

is,

— with one Rule 7,

C

C

Comp. Ex. 29 with

10.

single exception, as follows

The movement from step 7 to 6, and reversed, from 6 to awkward interval (augmented second) which

gives rise in minor to an

it is

better to avoid.

Thus, in the so-called " harmonic " or true form of

the minor scale

C Ex.

|H ¥

29.

31.

??

minor.

$ L5

ZJ

is

*

I

These progressions, from 6 to 7, and from 7 to 6, are, in themby Rule 2, Ex. 9. But they must be avoided if the minor

selves, justified

scale

??

to be " melodious "

(

singable).

THE MINOR MODE.

Par. 3a.

IS

32. The remedy is simple, and very common, and consists in so " altering " the active step as to remove the unmelodious augmented in-

Namely,

terval.

lower the jth

group

(in the

down from 7 to 6 by an accidental and

in passing

scale-step,

;

(in the

group 8-7-6-5

This results

5-6-7-8 only), raise the 6th scale-step.

only),

up from 6

in passing

to 7

good

in

singable intervals, and changes the harmonic form to the so-called " melodic " form of the minor scale. Thus :

C

/Exceptional.

minor,

\

Ex.

SO.

7-6556+788^767

8

6

7

6

/

See Ex. 42. Otherwise, as stated, every melodic condition in major

is

absolutely valid

for minor.

EXERCISE

3.

'

Exceptional Movements, and the Minor Mode. First review every one of the given

a.

each one

to

C minor

(first at

examples that

is in

C

major, transposing

the piano, then with the voice, then with the eye

;

always

with close mental application).

Then

b.

transpose every original melody of

Exercises

I

and

2

to the corre-

sponding minor mode (that of the same keynote'). c. Also write a very large number of original melodies, in major and minor, applying the principles of this chapter. Before doing this, examine very carefully the melodies given in Exercises

4, 5, 6,

All these original melodies

and so

forth.

may be used

in the

CHAPTER

coming

lessons.

IV.

THE ASSOCIATION OF TWO MELODIC The

LINES.

which naturally governs the association of meloThe condition of consonance should prevail not to the exclusion of dissonance (as will be seen in a later lesson), for the latter, in its proper place and proportion, is precisely 33.

dies

is

principle

that of harmonious agreement. ;

as necessary and important in music as consonance. But consonance should predominate sufficiently to create the impression of " harmonious

agreement 34.

''

The

as the ruling condition.

contrapuntal structure

generally obtained in the following

— the

association of melodies

manner some single melody :

is

—

is

adopted

:

:

;

;

:

ELEMENTARY COUNTERPOINT.

i6 as leading part

—

in a sense, as basis or principal

melody (though

equal value and melody another

significance, associated

upon an equal

successive tones to each successive tone of the

first

each tone of the given melody, a tone it,

is

its

melody, in keeping

chosen that

new melody which results will The new melody is therefore in a

peculiar sense a product out of the original one, obtained, not

35.

this

so that the

agree, tone for tone, with the former.

tion or evolution

To

footing).

In other words, for will blend or har-

with the simple regulations of harmonious union.

monize consonantly with

must

careful adjustment of each of

by

tone-line is added,

it

melodies are to be of

forgotten that, in true counterpoint, the

never be

Par. 35.

from within, but by adjustment to

It is quite as correct,

it

by deduc-

from without.

however, to create both melodies together,

each in turn suggest the next melodic move to be made, and making each thus alternately dependent upon the other. This is what

at once, letting

the composer

no doubt unconsciously does,

The student

ultimately.

will

use both processes, but should adopt the former (working with, or " against," a given

36.

Rule

complete melody) for the present.

The

1.

" harmonious " intervals, those that are invariably

consonant and therefore acceptable for the union of two melodies, are the

Third

(or tenth),

major and minor

the Sixth, major and minor the

Octave

given, as lower tone,

we may add

or C,

its

octave.

D

point

it.

And

Ex.

31.

m r

low

If

is

Ex.

it

If,

C

for example,

either E, its third

or A,

;

its

is

sixth

given, either F, B, or D, will properly counter-

For

so forth.

to

illustration

10th. 8th. 3rd.

6th.

1

J:

r

r

r

r

r

m

5=J

r

r

1

r

If C is given as upper tone, either A, E, or C may be added to and the same rule applies to all other tones. Thus

it

be-

;

Given

32.

and

;

(or unison), perfect, of course.

4

i

Given

a

o

N

iJ

r 37.

These three

nH^

:

»

R

a

-J— r^

I

r

intervals are unquestionably permissible at

any and the task of the beginner consists simply in the three is the best at the moment.

single point of contact,

determining which of

o

THE ASSOCIATION OF TWO MELODIC

Par. 38.

LINES.

i;

—

for it 38. This choice depends partly upon the melodic movement, must be remembered that each part, the given one and the added one, must describe a faultless melodic line (see par. 44). But it also depends partly upon the underlying harmonic result, for the implied chord-successions must also be natural and rational.

—

For

39.

illustration of this

harmonic distinction

:

—

If the

C

tone

is

melody (in C major), the 3rd above (and 6th below) will produce the Tonic harmony. The 6th above (and 3rd below) will represent the Subdominant chord, or, possibly, the VI. The 8ve and unison exert no positive influence on the harmony, and be-

given, either in the upper or the lower

come therefore Thus:

ioth.

3rd.

Ex.

mI

solely a question of melodic preference.

6th.

Unis.

Octave.

3rd.

6th.

1

33.

:£-

IV

--

IV

1-

Note. For the tions." Or glance at

rules of

o

(VI)

good chord-succession, see the author's

"

Tone-Rela-

pars. 169 to 176.

Whether the major or minor form of the

40.

o

3rd, ioth, or 6th

is

chosen, depends merely upon the key, and therefore takes care of

Note may

The

i.

distinction

Note

In the

2.

first lessons,

have

See Ex. 41.

its

39,

If

that

;

is,

each separate note in the given part

companion, or " counterpoint," in the added

scheme may be permitted

An

part.

for

occasional excep-

good melodic reasons.

e.

the interval 8 (octave)

given melody, the result

is

Given melody.

34.

and between octave and unison,

the rhythmic form of the two associated melody-

correspond

tion to this adopted rhythmic

Ex.

ioth,

be

hereafter be dropped altogether, because they are identical.

lines will exactly (or nearly) will

between 3rd and

to

itself.

± W3l

&

is

applied to each successive tone of a

as follows

:

h^

-L

r

r

^i r

r

Added melody.

The agreement of complete

;

the

the added melody with the one that was given,

harmony

of the association

perceives at once that here

some

is

absolute.

is

But the student

vital condition is wanting, for

by

this

process nothing more has been obtained than an exact duplication of the

given melody.

No new melody

has been produced, and therefore this

cannot be called an association of different melodies.

:

:

:

:

ELEMENTARY COUNTERPOINT.

i8

The

42.

more ample

result is

if

A

X

IIE

35.

it is

the interval 3, or the interval 6,

f=f

is

Thus

used with each of the given tones.

Ex.

Par. 43.

5_4

7

f series of tones

But even here, though a new evident that the added melody

is

but

is

r f produced in each

more, after

little

-5*-

all,

1 case,

than a

precisely the

re-

same

one an almost exact duplication and therefore practically the same melodic product, merely As true counterpoint is to be no such shifted to other steps of the scale. artless multiplication of one and the same melodic line, but the harmonious association of independent and individually perfect melodies, the folflection of the given

;

;

tone-line,

lowing rule must be observed

Rule

43.

In order to secure the independence of the added mel-

2.

ody, the interval of the 8ve must be limited to single points, and not be

used twice in immediate succession. that of the 6th) tire phrase,

may appear

The

interval of the 3rd (and also

consecutively, but never throughout the en-

and, as a rule, not oftener than three (or four) times in direct

succession.

The

best result

evidently to be achieved by a sensible in-

is

Thus, as applied

terchange of these three different consonant intervals. to the above given

melody

8

.636.

.

8

I

XEx.

mI 'fff

36.

r?

1

Rule

44.

3.

The

For

melody, by

itself,

ones,

it

r

must be dictated by the rules of

this reason

is

it

r

1

correct melodic

necessary to play or sing the added

after the contrapuntal union

has been

effected.

Such a

wholly satisfactory.

Applied to the following

reveals several obvious errors in the

added melody, despite the

applied to Ex. 36,

test,

r

f

choice of contrapuntal interval (whether the 3rd,

10th, 6th, 8ve, or unison) progression.

i r

is

fact that each separate interval

is

consonant, and that the two melodies,

sung or played together, form a harmonious union

Ex.

37.•

A

I

U

-4 e

EfEEfE ?r

See also Ex. 40,

?

T e.

4-

4-

4-

I

1

:

)

the following counterpoints

Ex.

pp

K Given

r-r^^g

part, above.

jp^i 8

10

6

8

^

Given

re

8 1

ft:

•"Tl

6

6

J

I1SE"

C^l j-*-

1

part, below,

Given

O

1

may be added J-r-*

J

I

39.: t

19

«

*

VW I4

-

LINES.

Furthermore, given the following major melody

45.

38

;

:

THE ASSOCIATION OF TWO MELODIC

Par. 45.

Ex.

^

:

1.

1

FFf

part, below.

This brief example, simple as

it is,

6

L

^s 6-^3

6

3

I

f=

tTT

should already afford the student a very clear

conception of the principle of melody-association, or counterpoint, and an appreciaHe should compare these three given tion of its value as a technical exercise.

and observe how completely the added parts differ from each other and he may be sure that these are not the only acceptable solutions. Each added part should be played, sung (and conceived mentally, by eye, as usual), first alone by itself then the two melodies must be studied together, and the student must endeavor to solutions,

;

conceive their association, mentally, and obtain a perfectly clear impression of their

After doing very thoroughly.— slowly and thought— he — he must transpose them (by finger and by eye) to G minor. And,

union, fully,

their effect together.

this

finally,

must invert each one of them ; that is, copy it out, placing the upper lower, and the lower part an octave higher, than here written. '

46.

Further, a few inferior

and

faulty versions, with the

melody

tee Ex.

40. Given

part.

part an octave

"rrr^-ftrr

,

a,

same given

ELEMENTARY COUNTERPOINT.

20 Given

part.

i A i

i

,

1l££ 111 r

tf^"

'

r

S

8

8

The

Explanation.

'r6

r

|

[

xO

half of version

first

ny

j

j

,

'a

j

,j

k^J tj ^6 d is

.j

i 10

10

because the long succession

inferior,

mere

duplication.

objection partly attends the parallel lines (in 6ths) further on. e,

j

3

of (parallel) 3rds gives the added part the effect of

version

Par. 47-

At

The same

the beginning of

the added part uses the octave three times in succession, which results in

and defeats the purpose of the union of lines. but more objectionable. See Rule 2,

exactly similar melodic progressions

and 6ths in

It is like parallel 3rds

principle,

par. 43.

The

rest of version e is all

poor counterpoint, because of the

faulty,

ing of the added part, in obvious disregard of the laws of melody.

awkward

lead-

— Invert both

of

these versions, as before.

In manipulating a complete sentence,

47.

same

parts should not begin with the

And, as a

dependence.

rule,

(the keynote in both parts)

ample

;

it is

this,

it is

desirable that the two

beat, in the interest of greater in-

end with the octave of the tonic however, is not imperative. For ex-

well to

:

Given melody.

Ex.

41.

gm

J ^-i-H-

4lj~

T

m

r

r-r

V

JnN-rJ

r

J

J

J

{

r

J

J

J I

.

J

J ,i

i

rr-rrrr J^ 4^ 1 r^

i

I

J

J

i

j 3C

m-

r

5±

irrrr

r

Given melody.

EXERCISE

4.

Two-Part Counterpoint with Fundamental Intervals, Major Mode.

To

each of the following given major melodies, a second part

is to be added, in and as shown in Ex. 39. The given melody is to be used first as upper part, where it is written, and the counterpoint added below. This may be done on the same staff (as in Ex. 39), or upon a separate staff (with bass clef, as seen in Ex. 43, b and c). The use of two

corresponding rhythm, according to the above

staves

is

preferable, as

it

permits greater freedom.

Then the given melody is

written (or

two octaves

added part that

differs

rules,

is

to

lower,

part, an octave lower than where it with an and counterpointed above,

be used as lower if

necessary),

Several different versions of the added part should be

was seen

in

Ex. 39.

—

reasonably from the preceding solution.

made

in every case,

— as

—

•

THE ASSOCIATION 0* TWO MELODIC

Par. 47-

LINES.

21

1.

m

F

-P

-a

•-

3E

$

*

•

0-

f

4=t: i

m

r^mr^M^=^

-#=•

g

3SE

a

4.

&

P^^^^P^i

^^

mWIS

te ^m ~2

|

J

=1

#—•—=—»

—

-#

i

^t

P # trmr

I

o^q^ga

^-fr

55

&—

(2

£

i|fe

i

^

H« i

r

i

f

J

J- b

•-

pzj^^E^zpc

j=t

s)

&-

u.

fc^^^algg^ BlScCT:

1

ELEMENTARY COUNTERPOINT.

22

Par.48.

12.

ferf= iW

-(=-

**

I

[A

£ Melody 4

solution of

refer, after conscientiously

will

be found

Besides these, the student

is

to write a

— designing the melodies

counterpoint,

in the Appendix, to

own

completing his

1

^i

4:

which the student may

versions.]

number of

added See the Note following

original melodies with

together (as duets).

Ex. 52.

CHAPTER

V.

THE MINOR MODE. 48.

mode

As

stated in par. 30,

all

movement

rules of melodic

in the

major

are valid for minor, with no other modification than that they are

applied somewhat more strictly in minor (as far as the movements of the

Review, carefully, paragraphs 30, 31 and

active steps are concerned). 32, and observe the

rule of par. 32,

that, in minor, the 7 th step

succession 8-7-6-5

must be lowered

in the

descending

;

and the 6th step must be raised

the

in

ascending succession

5-6-7-8-

49.

Further,

all

the rules given in Chap.

IV

for the contrapuntal as-

sociation of two melodies, in major, apply without exception to

The

minor

also.

choice of fundamental intervals (3rd, 6th and 8th) for the counter-

point of a given melody It is

more

is

precisely the

same

in

both modes.

simply necessary, in minor, to guard the melodic progressions

carefully,

and to be sure that each

part, alone, is a perfectly accep-

table melodic line. 50.

Ex.

42.

Given the following minor melody

f^e

*—*p=±$t^=t

Its contrapuntal manipulation Given part, above.

Ex.

, t

1 1

1

43.

a

a

may

result thus

8

s

s

:

^y m m

i

a

mm

m*

n, =F5 e

:

"^_

I

a

'

3

a

a

10

a (e>

— THE MINOR MODE.

Par. 50.

vrmim m mW^ o6eea3

23

&=E +-*-

-*-+

36

^=^? f

§33

X3:

Given

c

part, below,

Given

$

& ** ±±X±J=?*= 68

3

^

_

3

3

8

6

3

4

&

part, above.

—

-*-*JH *iH

.,

l

-

a,

^

8386633383

Prf^pf^r^

-1

Vt-I—

^

-B-*-r-fi-

Explanation. In one instance only, there are four successive 3rds

This should be the

limit.

The added

parts

all

move

^ & 8

3

f—f-

1

8

m

(in version i).

with considerable

f1

eedom, but

are everywhere melodically correct. of measure 3 in version a, one note counterpoints two of the In version c the added part has a wider range than usual, and diverges farther from the given part (at one point, in the third measure, the two lines are over two octaves apart). This is entirely defensible, as long as the melodies are separately

At the beginning

given part.

perfect.

Compare

the three different added parts, carefully.

EXERCISE

5.

Two-Part Counterpoint with Fundamental Intervals, Minor Mode. Manipulate the following minor melodies, exactly according to the directions given in Exercise 4

:

—

1.

^^=^l^j T^rr

r

^#a

a

2.

S: tEt

s •=*I§F4^f=f=F

&-f-f=fc:*= :j

*

0=t

*=*

.

:

-?-»-+

& j

•

§^S§ gsf^

$ft

J

s

f^=gg3BPPB m

\*

\

\-

:

ELEMENTARY COUNTERPOINT.

24

gsm

*-

T»

gb^rt^

i

&& iPas

***

-zt

i B.&

-&-

solution of

Also

I

^F=^

&s=e ii&t

[A

Par. 51.

Melody

1

be found in the Appendix.]

will

number of original melodies with counterpoint, composing See Note to Ex. 52.

write, as before, a

the two farts together.

CHAPTER

VI.

EXCEPTIONAL INTERVALS. 51.

Greater freedom of melodic progression

may often be

obtained by

a few judicious exceptions to the above fundamental rule of harmonious

While the 3rd, 6th and 8ve are undeniably

contrapuntal association.

the most reliable, and must at

all

times constitute the real basis of the

contrapuntal union of parts, there are a few other intervals, mostly of a mildly dissonant character, which,

prove the

effect,

when used

in moderation, greatly im-

without in the least impairing the general harmonious

or consonant character of the sentence as a whole. 52.

Rule

4.

These secondary

intervals, of

somewhat exceptional

character, are

the perfect fifth, the

augmented fourth, or diminished fifth, and major seconds, or minor sevenths.

certain 53.

The

perfect fifth

represents the

It can, therefore,

never appear

is

very rare, and should be used only

Dominant chord

(

—

possibly,

occur only singly,

in inverted

form

when

it

more rarely, the Tonic chord).

— not successively.

(as perfect fourth).

And

it

For example

should

:

EXCEPTIONAL INTERVALS,

Par. 54.

m

Ex.

44.

±^SSTJi

—•-

i»r

S

±M «

b. I

i&--•

25

'•

Poor.

4

I

rrrrm

r

The augmented 4th, and its inversion, the diminished 5th, are common, and always good. In Major, they occur only in the chord the Dom.-7th, as union of steps 4 and 7. For example 54.

fairly

of

Ex.

±

3:

45.

t

;

-J-a>-=-

TTrf

r

:

r

>

is, copy it out, placing the upper part; an octave and the lower part an octave higher, than here written. Do this,

Invert this example ; that lower,

withoutfail. Observe that these intervals are used

55.

C

major,

—the

7th

and 4th

counterpointing the tones b

in

and/

in

scale-steps. " outward," into a a smaller one.

Observe, further, that the augmented interval generally strives larger interval

;

and that the diminished one draws

" inward," to

Or, observe simply that the correct resolution of each of these active steps takes

care of the melodies.

For further

Ex.

46.

illustration

j

iw Ftt

i£S^^ -7

1

:

r

J 1

^ r

r

>__— »

r

r

f

i

r=^

T

r

-1

The

slurs in this

example indicate where the chord remains unchanged,

— a circumstance which always

justifies

nearly every irregularity.

Note

this fact well.

Invert this example, as before, and the diminished 5th. 56.

Do

this,

it

will illustrate the

In minor, the augmented fourth and diminished

exactly the

same way,

at steps

treatment of

without fail.

4 and

7, in

fifth

appear in

the chord of the Dom.-7th.

r

:

ELEMENTARY COUNTERPOINT,

26

2,

:

P»r. 57.

But they also appear (though more rarely) in the union of steps 6 and possibly also in the union of step 3 and the raised 6th step in minor ;

(par. 32).

As

usual, the melodic resolutions

must be respected, whereby the

re-

noted in par. 55 will be observed. Thus (C minor)

sults

a-

4+

s-

4.+

M^wi\)rn *s^ +¥ i££V4&h 'cr y rii* ±~*H^^

Ex.

47.

\

v

v 11

11

major 2nd, are rare. They should be limited to the union of steps 4 and 5, as part of the chord of Possibly, though very rarely indeed, they may occur as the Dom.-7th. For illustration (C major and C minor, alike) steps 1 and 2, in the II 7 57.

The minor

and

7th,

its

inversion, the

.

Ex.

jfA ,

48.

,

n |JJ JJ j^|jJ JjJjlly I > rT -p-T. t rif r 7 7 |

|

-

,

Also write

Invert this example, as before.

C minor.

out in

it

Observe that the interval of a 7th draws " inward," and the

58.

terval of the

2nd " outward," as a

As

not sufficiently explicit.

This statement

rule.

usual, almost everything

is correct,

in-

but

depends upon the

The whole matter may be

proper resolution of the active (4th) step. stated thus:

In the interval of a

7 th,

the lower tone

(When

tone a chord-seventh.

This tone,

course, the chord-seventh.)

is

a chord-root, the upper

inverted, as 2nd, the lower tone

—

the chord-seventh,

is,

of

— generally

moves downward one step but it may remain where it is and it may make a leap (usually downward) when the chord remains unchanged. Thus (C major and C minor) ;

;

:

Ex.

i

Uj

,j-j

j

j

J^J

,

,

J-J

j ,

,

-*= i 7

e

•

-0

7

•

a

r

•

$

a

Good.

J

J,

J

J

.

i rJ'rV '

'

1

JLU ..M-J.J.J r 7

—

,y±,

' '

a

1

r

r

r

r

7

8

v

V

'

r

r

^ J-t-J

1

:

:

EXCEPTIONAL INTERVALS.

Par. 59.

The

:

slurs again indicate

27

where the chord remains the same, and thus

account for the apparent violations of the

Invert

rule.

the illustration of the treatment of the interval of a 2nd.

Also write out both versions

fail.

For general

59.

illustration

:

in

= =t

^

Cpt.

1

solution of Melody 5 will be found in the Appendix.] Also write, as usual, a number of original melodies with counterpoint, comlike Ex. 52. posing the two parts together,

[A

4.

—

CHAPTER

VII.

RHYTHMIC DIVERSITY. TWO NOTES TO A GIVEN BEAT. 62.

The rhythm

of the

that of the given melody.

added voice does not always correspond to That is, the counterpoint may not only be de-

vised " note against note " in exactly or nearly similar rhythm, as in the

preceding lessons, but

may

run in a more rapid rhythm of two (or more)

notes to each note of the given melodic part. 63.

When

this takes place,

—

— when

two or more notes accompany

a necessary distinction arises, with reference to the each given note, relative importance of the several tones in each group (or beat) ; for it is probable that not every single one of the added tones can be of equal har-

monic

significance.

In making this distinction, the tones are defined as essential and unesIn a group of two notes (against one in the other part), one is ususential.

:

:

:

ELEMENTARY COUNTERPOINT.

30

Par. 64.

and the other unessential in a group of three notes, there The distinction will generally be one essential and two unessential tones. is important, because the burden of contrapuntal agreement devolves, naturally, almost wholly upon the essential tones whereas the unessential ones slip smoothly between, with little or no responsibility. ally essential

;

;

64.

In thus qualifying the tones, the student

the rhythmic location of the tones fraction of the beat

is

somewhat more likely

accented fractions are apt to be illustration (the unessential tones

influenced largely

to

be

marked

For

x)

x

x

x

2z

Ex.

by

essential, while the un-

in with unessential tones.

filled

x

x

is

the one which occupies the accented

;

I

54.

r The d and

b in the first

As may be

measure are so-called Passing Notes.

seen, this counterpoint

(marked x) were

sential tones

all

m 1—r

55.

from which the conclusion

if

the unes-

— thus

j-j

i

Ex.

would be quite perfect

omitted,

Tj is

T^T

i

drawn, that these tones are unimportant,

unessential.

Invert these examples ; that is, copy them out, placing the upper part an octave lower, and the lower part an octave higher, than here written. 65. all,

But

this is not the only test.

the harmonic quality of the tone.

of the beat cannot be essential

cupies the accented fraction of

;

it

its

The most

reliable guide

A tone which

is

is,

after

foreign to the chord

must be unessential, even when it ocThis is seen in Ex. 54; all the

beat.

tones marked unessential are foreign to the harmony (chord) of the beat,

d in the second measure, and the d at the end of the third (These two ri^ Tr T ,

J1

t

|

i

i

i

«* *r uHi IPa&se£ ¥ 7.

n ^^ji^EfflfNa ^ * fel *s

*=• 11

«s

i

1

it.

p

**

^

ss [A

may

-*

b=t

Melody 6 will be found compare his own versions.]

solution of

carefully

2- :r,[

in the

Appendix, with which the student

Besides these, re-counterpoint the given melodies of the preceding Exercises, according to the rules of this chapter (with two notes to each beat). The student will do wisely not to neglect this additional task, for practice is here of the greatest value.

Also

write, as usual, a

number

imitating the style of Ex. 66.

of original melodies with counterpoint (as, duets)

"

MODULATIONS.

Par. 77-

CHAPTER

37

VIII.

MODULATIONS. necessary nor desirable that the added part, or

It is neither

77.

the given melody, should remain in the same key from beginning to

Modulations in

either, or in both, of the parts, are likely to add and smoothness of the counterpoint. Such changes of key may be made at any point in the course of a musical sentence, and may be of any reasonable duration, but are subject to certain fairly

end.

greatly to the beauty

strict conditions.

78. The most important of these is the limitation naturally imposed by the varying degrees of relation between the keys. Each key is a mem-

ber of the greater family of keys

;

each key has

its

individual place in

the system, and stands in perfectly definite relations to the other

mem-

bers of the key family. 79.

The proper index of any key in the system of keys is its Signanumber of flats or sharps it contains indicates precisely the de-

ture ; the

gree of similarity or of difference between

it

and

C

major,

— the

central

or zero key, the one which has accidentally been chosen for the plain

phabetic

letters,

without

flats

al-

The com-

or sharps to inflect their pitch.

parison of the signatures therefore exhibits the relative location of the keys, their degrees of similarity or difference, and, consequently, the de-

grees of relation or non-relation.

For instance, the two-sharp and three-

sharp keys are more nearly related than the two-sharp and the four-sharp, Also, the two-sharp key is or five-sharp (or any more remote) keys.

more closely located to the one-sharp, than scale), or any flat key.

The

to the zero (the " natural

whose signatures differ by no key is next-related and is also nextthe one-sharp key (which has only one sharp less) 80.

next-related keys are those

more than one to

it is

similar sign.

That

is,

the two-sharp

;

related to the three-sharp key (which has only one sharp more).

the two-sharp key

is

next-related,

the other key which has the called Relative minor,

Note. This it is

— most

Further,

closely related, in fact,

same two-sharp signature

;

namely, the so-

— or Relative major, as the case may

be.

rule of Signature-relations applies, strictly speaking, to major.

absolutely valid for both major and minor

modes

— to But

(those with corresponding sig-

natures), because of their very close proximity to each other in the system of keys.

r

:

ELEMENTARY COUNTERPOINT.

38

For

illustration

G major,

:

D

major

is

next-related to

Par. 81.

A

major, to F-sharp

and to B minor. And B minor (with the A major, Fsame signature) has the same group of next-related keys, sharp minor, G major, E minor, and D major. Further, the next relatives of a three-flat key are the two-flat keys, That is, C minor the four-flat keys, and the other key with three flats. is next-related to B-flat major and G minor, to A-flat major and F minor, minor, to

to

E minor,

—

:

and

to E-flat major.

major and

If the student is not absolutely familiar with all the signatures,

N. B. minor, he

will

do well to pause

here,

and not undertake any exercises

in

modulation

before thoroughly mastering this necessary item of musical knowledge. 81.

Rule

Modulations that are made during a brief melodic sen-

i.

tence (phrase, period, or double-period) should be limited to the next-re-

Thus, a sentence

lated keys of the principal or central key.

may

contain brief modulations into

E

A

in

C

major

G

minor (same signature), into

F

D

minor (oneflat keys). A sentence in E-flat major may exhibit transiently the keys any one, of C minor, A-flat major, F minor, B-flat major, or G minor, major or

minor (one-sharp keys), and into

major or

—

or more, or

all of

these.

For example, a phrase with a three-sharp signature, containing brief excursions into the keys of two and of four sharps (the capital letters indicating major, and the small letters minor)

mmm ^ WLL3

1=

"1

Ex.

67.

— i

i

m

LSUJJ

£.

«—

^

1 A-



^'B=S ir^ps£^ Good.

;

be introduced in the corresponding direc-

Ex.

S

but they should

;

too rapidly (as a general rule not quicker than eighth-notes)

(in

the lower part)

;

the

preceded by a leap, downward, and therefore confirms the

wide leap"

(par. 16).

The same

thing occurs at the begin-

ning of Ex. 71, in the lower part.

EXERCISE

8.

Two-Part Counterpoint, with Changes of Key. 1.

5

Manipulate the following melodies, in corresponding rhythm (as in Exercises

and 6, and examples

first

7

1

and

72),

modulating wherever possible or necessary.

three melodies , the * indicates where changes of key are to be made.

each melody twice,

first

1.

An

J J J

and then as lower

as upper

fe

Uh

d:

Use

part, as usual

-g>-

4,

In the

^n±+h±

5

ELEMENTARY COUNTERPOINT.

42

Par. 90.

a.

i s^y ^ =P$i

ffiEfcfS

j

1^^

Ji^py ™^--

^Efc^

t=t

B£

2:

IBs ^2=2^

•

s

3

Tg-j

£>

5.

Efe

W W-

a

s r^r^—

li^



T-&

i

—hR-.n r -

t

SS^^f

r

r

i

.

rr g»-

rer—w—r 1

r

Invert these as usual.

The

third version of the

loses its cohesion

and

above example contains too many

force.

are irregularly distributed

;

The

fourth version

the melody loses

its

is

rests

;

the melody

also inferior, because the rests

evenness of structure, and becomes

spasmodic.

112.

From

beats, yield

this

it

appears that occasional brief

the best results.

board) with Exs. 87 and 88

;

rests,

on corresponding

The student may experiment also with Exs. 79 to 83,

(at the key-

— introducing

rests.

J

— THE

Par. 113.

113.

*

CONTINUED. RESTS.

TIE,

—

Rule 4. A tied note may be followed By its proper stepwise resolution, if it is an inharmonic suspension (as in Ex. 86) or by any good leap, if it chances to be an :

1.

55

:

harmonic interval 2.

—

By the other neighbor of the resolving tone, leaping a 3rd, up or down as the case may be, as in Ex. 86, last measure (and Ex. 90,

3.

(as in Ex. 88).

By

a).

a repetition of the tied note (Ex. 90,

b).

The first of these methods is, of course, always good and always The second and third are peculiarly useful in quicker rhythms (of 3 or 4 notes to a beat). For illustration, Ex. 86 may be ac114.

applicable.

celerated from two notes to three in each beat, in the following

ways

:

a. (Double-neighbors.)

Ex.

^^Yrymmfn^n — ^=^

=Z5

go.

^r

z^^jr

j—

'r

r

(Repetitions.)

t.

-I-

ii

2=£

—

t

i 1

•-

i—m

c.

$r i

-=1

3S

I

-*

S

s-

(Rests.)

1

—

-4

Effi3= pt

&—&-

r^ffi^f

-

r

— fe^ •-

71

r d. (Alternating rhythms, par. 99.)

The

best form.

J^r^h±=^

TTTLL

*=£^

:

"1

T

ijuf

-m

-I

—

—

r

ELEMENTARY COUNTERPOINT.

56

(a

fe

and

Par. 114.

mixed.)

b

^tSi;%^~ j^m i

r

r

—

etc

t

r

Invert each of these examples as usual. Observe that these methods, Rule 4, apply best to the note which is legitimately a result of shifting the original essential interval forward ; not so well to the which creates an anticipation (Ex. 87).

tied as tie

EXERCISE Ties and Rests;

Add

1.

II.

Two and Three Notes

to a Beat.

a contrapuntal part to each of the following melodies, in a rhythm of two ties, as in Ex. 86.

notes to each beat, with

The

tie

need not be used in every group; the occasional omission of the

substitution of passing-notes,

99 (Ex.

is

not only effective, but often convenient.

=J=

Lu

|H*=^

r

fag

1

r

f—0-

|~G major. rn

-•

•

&

<

&

minor

*

P-

1 pa

-*-f-

always

r

^IE 'U-d-r-J-f^=py^r

it is

1 [~e

FU¥

i

and

82).

Each melody to be used as upper, and also as lower part, as usual. N. B. The student must remember that in case of embarrassment, permissible to fall back upon the process given in pars. 96, 97.

4

tie,

See par.

=F=S=

minor.

|

qc -p-f-r-

£

±j Pi

m

:

FOUR NOTES TO A BEAT.

Par. 115.

57

5.

i iSs

fEb

-4f

fc5=Mp=

^=^

min.

|~f

e£ee£-u-q- £

^§1

-=1— f-

-wc

=F

Each version thus obtained

2.

ma]."]

2=^=t

is

then to be quickened into a rhythm of three

notes to each beat, according to the above rules (pars,

four different forms of each should be written out

made at sight, at the keyboard. [A solution of Melody 3 will be found 3.

in the

;

m,

and

113,

still

— Ex.

At

90).

least

may be

other versions

Appendix.]

Besides these, write a number of original melodies with counterpoint, as usual,

composing the parts

together.

CHAPTER

XII.

FOUR NOTES TO A BEAT. When

115.

there will

four notes

be one

accompany one beat-note of the given part, and three unessential ones, or two essen-

essential tone

and two unessential ones,

tial

in

each group.

All the rules given in the

preceding chapters are valid, without exception or modification, for these still

quicker rhythmic movements

;

but the larger the groups, the greater

the likelihood and necessity of uniform figures, and of more definite for-

mations, in general. 116.

Among many

forms which four-tone groups are apt to assume,

the following figures are especially

'See In group

1,

the upper neighboring note

figure out of the essential tone

back to

e,

as the next beat

may

(e)

;

the

require.

(/)

is

:

so inserted as to create a 3-tone

final unessential

In group

2,

tone (d) goes on to

the lower neighbor

the same way. In groups 3 and 4, the double-neighbor the essential tone at once into a four-tone figure. 117.

of notice

^a^fe^=a

=p=i=

Ex. 91

common and worthy

is

is

c,

or

used in

so used as to transform

Applied to a faultless series of good essential intervals

:

ELEMENTARY COUNTERPOINT.

58

Par. 118.

Ex.

92.

r

r

The

results

may

be,

?-

— using only the above

figures

-—--

Ex.

Invert

all

of these, as usual.

At N.B., instead of g.

in the second

In many

measure of version

a,

the lower neighbor

cases, this choice of the half-step

It is left to the taste of the student,

decidedly preferable.

is

gsharp

for the lower neighbor

who

is

therefore should not

neglect to test the lower neighbor, and substitute the half-step (with an accidental)

where

it

sounds better.

The upper neighbor always 118.

Rule

I.

The

agrees with the scale.

direction of the figure,

when a double-neighbor

— of which the two are indicated version b of the above example, — depends mainly upon the location of the following is

used,

possibilities

in

es-

sential tones,

For example:

which should, as a

rule,

be approached

in a straight line.

:

FOUR NOTES TO A BEAT.

Pai. 119.

59

Good Ex.

94.

S-

±=pj

i rr

-j

^

J—,

'

i

r Poor.

Rule

119.

2.

It is usually

unwise to leap to the

first

(accented) tone

of a following beat, a/fer stepwise progression in the same direction that point.

This

up

to

In other words, do not interrupt a step-

important.

is

wise progression (in the same direction) at the junction of one group

with the next

;

if

a skip

is

make

necessary,

it

For

earlier in the group.

illustration Good.

2.

1.

^

f f

E^*

Ex.

95.

??

*a3

±

r-r

r Good.

^k^i^ S Bad.

m

^-j~

is

r ??

6.

y.

5^

W£

Iw8.

Good.

Good. 1

;

,

rt

1

Good.

>/

J7

^^j™^ r

The

ear follows

up a stepwise progression, and

group, the ear (mental ear) expects that

it

if it

extends to the end of

will continue stepwise into the

next

its

beat.

Compare groups 1 and 3, for an illustration of this cause of mental disappointment. Group 4 is wrong in any case, because of the rule in par. 71 (Ex. 59), which see. In group

6,

the c-sharp

D

is

preferable to

c,

because the essential intervals impart

minor. Further, the c is possibly the unessential lower neighbor an impression of compare note to Ex. 93 (N. B.). of d, and therefore sounds best as half -step,

—

ELEMENTARY COUNTERPOINT.

6o Observe

same

in the tion

is

that, in

groups 3 and

7,

there

is

a leap into the new group, but

direction as the stepwise tones that precede

generally good.

Group 8

very peculiar

is

Par. 120.

;

and

120.

4-

not

direc-

but correct, because of the dis-

tinctly unessential nature of the notes that cause the irregularities. fully,

it is

Such a change of

it.

Analyze thought-

test at the piano.

Other manipulations of Ex. 92

:

1

2:

IIS

T_f ££J

i Study these carefully.

f

!

i

\

!

' '

I

S Invert them

i all,

as usual.

jiff 1

#

:

FOUR NOTES TO A BEAT.

Par. 121.

In version It

I,

second measure, there

daring, because

is

It is permissible,

tones

however, because

so entirely unmistakable

is

groups

in that

a wide leap at the junction of the groups.

is

a skip to an inharmonic tone.

it is

61

See, again, par. 71 (Ex. 59).

Ex. 95, No. 8) the nature of the unessential and, further, because of the analogy between the

(like

;

measure and the next (each group beginning with a

compare par. 107, Observe that

" neighbor,"

—

last sentence).

and

in all of these versions,

in nearly all recent examples,

one of

the parts usually carries on the quicker rhythm for a beat or so, at the cadence.

Rule

121.

It is permissible,

3.

Ex.

97.

and

desirable, to use successive chord-

Thus:

tones occasionally.

4-

i

3

3ES

z±

3= (IV)

^

Im

^ rr

I

vl_ Invert, as usual. however, suggests " harmonic " figuration rather than " melodic " proand should therefore be used sparingly. Preference should be given to stepwise progressions, especially to such straight lines (fairly long) as are seen in

This

style,

gression,

many

places in Ex. 96.

Rule 4. Besides the " straight lines " just mentioned, the most desirable and necessary trait in counterpoint is the sequence, and uniformReview, carefully, par. 95 (Ex. 77, b) and reity of figures in general. flect that this requirement is more imperative in counterpoint with four For further notes to a beat, than in the preceding, less active, varieties. 122.

;

illustration

Ex.

98.

m

Tt

T

m

Sequence.

Emwj

V I

Ex. 95

Seq.

Seq.

f

(6)

Seq.

t± 1= I

1

A

minor.

1

— —— i

1

I

I

w* |

i— J I

J-*:

ELEMENTARY COUNTERPOINT.

62 Seq-

i

I

i

r-^

ir^

i

G

t_ L_J

fr

*

ei

r

1

r

Par. i22.

1

major.

Invert this, as usual.

EXERCISE Two-Part Counterpoint.

12.

Four Notes to Each Beat.

Add a contrapuntal part to each of the following given melodies, in a rhythm of without ties. Each melody is to be used both as upper four notes to each beat, and as lower part, as usual and several different versions of each should be ob-

—

;

tained.

Use two

staves, as

a

rule.

1.

m M ¥

^

§SE

PS * 'k MMii

p=t

-t-^s-

it

-&-

BtrE tfn r

— M^SMgun »-*-

r r r

J^tiT^r

tat

i

1 i 1

iS3 6.

Se ^

i 8

rQ

i fe

fr-r--

g

—

-«

«=-

r?

si-

m

—

I

~g»-

^g=t |g-l-f=^

al

p l

f

^l j

H

:

:

FOUR NOTES TO A BEAT.

Par. 123.

[A solution of Melody

2 will

be found

Besides these, re-counterpoint

and

7,

some

in the

63

Appendix.]

of the melodies given in Exercises 4, 5,

6

according to this chapter.

Also

write, as usual,

a number of original melodies with counterpoint.

CHAPTER

XIII.

FOUR NOTES TO A BEAT, AS AMPLIFIED FORMS. The

and 100 (which review) is aprhythm of four tones to a beat. Namely An original counterpoint of three notes to each beat, if smooth and faultless, maybe accelerated to a rhythm of four notes, by means of the tie 123.

principle of paragraphs 96

plicable also to the contrapuntal

:

and shifted rhythm. For example

ex.

99.

$r I ^^^=d i 3E&

'f 6

3

U

'*

'

a c.

(from

^

_fl.

may become

'

P

I 'C

j

j

6

>^"^

1

4+6

3

X

'

6

X

8

a.)

^S 4 J S

ZUHT}~F7

!

4.

r z, 3, 4, 7,

and

and 8

;

first

Par. 149.

few measures of the Two-part Inventions of Bach, Nos.

observe the manner of imitation (in every case in the lower part),

carefully analyze the formation of the contrapuntal associate.

In No. 10 of these Inventions, the imitation of the motive (second measure, lower part), is not in the octave, but a fourth below the original tones. From this it will be inferred that the motive may recur upon any steps of the scale which may prove to be convenient for the purpose. The imitation in the octave (upon the same steps)

is,

however, by far the most

common

at the beginning ; while other steps of

the scale are likely to be chosen for the reappearances of the motive from time to

time in the later course of the sentence.

In continuing the manipulation of a Motive beyond the

149.

first

Imitation (the point at which the above examples were interrupted), the

numerous, and the greatest scope

possibilities are very

the

these, however, the following design is

mended

and to the most

writer's imagination

freedom of the

may be

his facility.

natural,

and

given to

Among is

com-

one measure to a modulation into the Dominant key (or the relative key), using lines which proceed as naturally as possible out of the preceding to the beginner

measure,

— giving

:

After the

Imitation

is

finished, devote

decided preference to sequential figures (par. 95); then of the Motive in the

make two announcements first

first

new

key.

Thus, with the

Motive (beginning in the middle of the second measure of Ex. 114):

-i^aa

fe E

Ex. 1 16.

9

•***-

=P=p=

\ Sequence.

3

iii, 3=

if Episode

:

Modulation into

T^

•

*

Seq.

-4*=*=±

F

m

cont. associate.

fat

1 m

m

3*

D major.

1 New

>-

f-flr-f-fr=j^

^m

--¥ Motive

(in

D).

m — f* ^

I

-•

I

#

:

MO TIVE-DE VELOPMBNT. IM1TA TION.

Par. 150.

Motive

77

D).

(in

m

I jy?rfi3 =jg^^ Mod.

etc.

gfea Cont. associate.

Observe that the 2nd of these measures, devoted contain the entire Motive, but only figures from sage

is

called

an Episode.

how

is

completely "

is

Such a pas-

not only permissible, but necessary.

new

measure, as compared with the puntal associate

to the modulation, does not

derived by sequence.

Observe, further, that the sequences are not exact, and

remember that such freedom Notice

it,

" the

one

first

contrapuntal associate ;

and notice how, for

is,

in the following

variety, this contra-

not re-constructed, in the next measure, but corresponds to the

preceding one. Finally, observe

how

d-sharp

substituted for

is

d

at the beginning of the last

measure, in order to introduce another modulation (this time into the relative key,

E

minor).

The

150.

formation, and the length, of

optional, excepting that

before.

It

must,

—

it

like

must be the

in close

an Episode are

contrapuntal associate,

— be

refer to the line of either the upper or the lower part.

a perfectly

and this mayFor this reason,

natural continuation of the foregoing lines (par. 146-5) sequential formation

entirely-

keeping with what has gone

;

the most desirable.

is

Further, the continuation of Motive 2 (beginning with the 3rd

151.

measure

of Ex. 115)

might be about as follows

^

Seq.

^H =r=l r=5^ ^rferff L^j Ex. 17.

Episode

:

Mod.

into

A

minor.

1

m

i^g

-

Motive

&F

(in

A

JE^fif New

j

i

j=* i

gSsg m^

minor).

|jOP

^g

cont. associate.

ijEfe '

J

'

ELEMENTARY COUNTERPOINT.

78

Sequences.

Seq.

Motive (in

Analyze

Par. 152.

carefully,

A

minor)

and observe the agreement of

this design with the suggestion

given in par. 149.

152.

The

observant student will probably realize that a great part of the object

and the labor of this method of composition centres in the formation of the contrapuntal associates, or of the " counterpoint " in general and this is a task for which The difference between the past lessons in counterpoint must have prepared him. the preceding Exercises and the counterpoints shown in this lesson appears much greater than it actually is it is merely a difference in rhythmic appearance, and is not Close comparison with the rules and illustrations at all of an essential character. given in Chap. XIV will prove this. If any additional directions are necessary, they are comprised in the following general rule Be sure that some good interval appears (or is understood) at the accents, and at strong beats in general lead the two parts smoothly to these points, maintaining a uniform rhythmic effect, and alternating (or combining) the shorter note-values so as to obtain a good rhythmic form in each separate part. To test this rule, analyze the contrapuntal treatment of every measure in all of the Two-part Inventions of Bach. ;

;

:

;

153.

In pursuing the development of the Motive

still

further,

it

will

be necessary (before rounding off the complete sentence with a perfect cadence in the original key) to introduce a few more episodic passages, Some of these are necessary, modulations, and imitations of the Motive.

and determinable

;

though, in general, the details

may be chosen

with

considerable freedom, and will depend upon the fancy of the writer, or

upon the

specific nature of the Motive.

1.

For the beginner, a schedule like the following (embracing the most natural and effective The announcement of the Motive (in either part).

154.

entire sentence) will prove

2.

The

3.

An

4.

Two announcements

:

imitation of the Motive in the octave, in the other part.

episode of one or two measures, modulating to the Domi-

nant key. of the

Motive

in this

key (one in each

part). 5.

An

episode of one or two measures, modulating into the Rel-

ative (major or minor) key.

.

MOTIVE-DEVELOPMENT. IMITATION.

Par. 154.

6.

One

79

or two announcements of the Motive in that key (either

part). 7.

An

episode, modulating into the Subdominant key (or

its

Rel-

ative). 8.

One announcement

9.

An

10.

One

1 1

Episode, and perfect cadence. 6,

or 7

and 8, or

For example, the development and 116, may be continued thus, details

part).

or two announcements of the Motive in that key.

Note. Either 3 and

above

Motive in that key (either

of the

episode, modulating back to the original key.

all

of

of

these,

Motive

may 1,

be omitted.

given in Examples 114

— recommencing

with No. 5 of the

(end of Ex. 116):

Seq.

n tee

m Cont. associate.

Motive

(in

E

min.).

Sequences.

N^^ Ei Episode

:

Mod.

to

A

minor.

Si

^m-

ELEMENTARY COUNTERPOINT.

8o Motive

(in

Par. 154.

A min.).

Motive

9$4-i

J j

rr

Cont. associate.

=#*=

to C).

5^

4H^-W

^^S

(Mod

N. B.

^3=& =#£

*-^r Episode

N. B. :

Mod.

to G.

Seq.

Seq.

Perfect Cadence.

I

1 rail.

paring for Cad.).

m5t*

-

*

g

=T The

student will do wisely to copy out Exs. 114, 1 16 and 118, consecutively, so he can analyze the whole sentence without interruption. Observe, at * in the first measure of Ex. 118, the imitating of a figure that is not the Motive. Such episodic imitations are as valuable as those of the motive itself. Observe, at N. B. in the same measure, the brief rests. Also in measure 6, be-

that

in

fore the entrance of the Motive.

Observe, at N. B. in the 5th measure (of Ex. 118), the alteration 0/ one of the

:

MOTIVE-DEVELOPMENT. IMITATION:

Par. 155.

intervals in the given Motive. 6th.

Such

The upward

leap of a 4th

is

changed

8l to » leap of the

changes are not only permissible, but desirable, from time to time. Observe, at N. B. in the 6th measure, that the Motive enters in the third beat, little

instead of at the beginning of the measure.

Rhythm, and

is

permissible and effective,

if

This

is

called

Imitation in Shifted

carefully tested.

Observe, further, the addition of extra parts, and the duplication of the lower part in octaves, at the approach to the perfect cadence.

Analyze every

detail,

most minutely; especially

the- formation of the various con-

trapuntal associates, and the Episodes.

155.

A sentence

of this kind

is

generally

EXERCISE

known

as an Invention.

15.

Motive-Development in Two-Part Counterpoint. Manipulate each of the following Motives, in the manner explained above, according to the schedule given

in par. 154, as

small

INVENTION.

Each Motive should be developed twice, completely beginning with the upper part for the first solution, and with the lower for the second solution ;

1.

Lento.

3.

Larghetto

4.

Allegretto.

8 lower.

^

£te^ i 1E=£

±g=

&J1= m^^^

*=±hiz

STL „

a Andante con moto.

m=* iIHEa

ELEMENTARY COUNTERPOINT.

82 6.

7.

Adagio.

f

8.

ifem

9.

B®= im^

£

^us^3 *3r£U

-SH

L

l^Eg 11-

feE^

^p -J-*-

g3^ [A

I

jt J

fc=t

solution of

refer, after

J

*—*

Allegro.

«^ ifar— 2-j IE

Allegretto.

Moderato.

IO.

^^

Allegro moderate.

mpttfaH

ip^EE

Par. 156.

hs^=4mi

3E

No. 5

will

having made his

£e found

own

Lento.

Si in the

1

Appendix, to which the student may

version.]

Besides these, invent a number of original Motives, similar in character and length to the above (and to those of Bach in his " Inventions "), and manipulate

them

in the indicated

manner.

#

#

#

156. Nothing remains to be said about two-part counterpoint. The fundamental conditions which govern the association of two contrapuntal parts have been

amply explained and illustrated in the foregoing lessons. All the essential rules, and all the important methods of treatment, have been thoroughly rehearsed. It rests now with the student to continue the exercise of these methods in his own way, inventing thematic melodies and motives, and supplying them with contra-

— ;

THREE-PART HARMONY.

Par. 157.

83

puntal associates, in order to gain more complete technical

not

fail

For

to do.

if it

be true that technical

This he should

facility.

the

facility is

and

first

really indis-

pensable condition of fluent and effective expression (whether reproductive or productive),

it is

also true that two-part counterpoint constitutes the

tone-association; and, therefore,

its

command

groundwork of

To

every task in the fuller styles of harmonic and contrapuntal writing.

who has

the student

learned to think and feel the simultaneous progression of two parts,

carry two melodies side by side with perfect ease and consciousness, are possible

;

and

their

complete mastery

is

all

him only a question

to

all

the fundamental preparation for

is

who can

combinations

of time and, of

course, earnest effort.

#

*

*

For further details of the Invention, the student Author's " Applied Counterpoint," Chapter V.

CHAPTER

is

referred to the

XVI.

THREE-PART HARMONY. The next

157.

ment

step in contrapuntal study

of three individual melodic parts.

" Individual " these three parts

158.

certain extent

;

is

Review must

the simultaneous treatpar. be,

1.

each by

itself,

to a

been shown, does accompaniment." It in-

for the contrapuntal principle, as has

not rest upon mere duplication of parts, or "

volves the association and interaction of separately correct and satisfac-

At the same time, this individuality of each of the and limited by necessary consideration for the the other parts, and harmonious agreement of each with the

tory melodic lines.

parts must be controlled

movements others

;

of

their

independence should consist solely

in their personal melo-

dic formation, as melodies, and must not lead to conflict of harmonic

In a word, to repeat the fundamental definition, the parts are but harmonically unanimous.

formation.

to be melodically distinct,

159.

This statement admits of but one construction, and that

a harmonic basis

must

first

is

necessary

;

and

be defined, from point to

that, therefore, the

is,

that

underlying chords

point, as a general guide (at least) to

the melodic course which the parts are severally to pursue.

this

tain

—

coordinate though they will all be, Of the three parts, is likely to be the Leader for the time being. The reasons for will be understood when the time comes. It may be (is almost certo be) that the Leader is that one of the parts which has the Motive

160.

some one

:

:

.

ELEMENTARY COUNTERPOINT.

84 or

it

may

its

position

or

;

it

part, which attracts attenbe the one that is engaged in car-

uppermost

be, rather frequently, the

tion because of

Par. 161.

will

rying out some sequential design, which causes it to step into the foreground for a while. Be this as it may, the mind is inclined to give momentary preference to some single line, and to define the chords from that line (as, for instance, the upper line in Ex. 123). 161.

" harmonizing " of a melodic phrase is subject to

Such

one

sweeping rule

A

tone "

may " be harmonized by any

chord of which

a component

it is

interval.

That

is,

the tone

may appear

it

as Root, Third, Fifth, possibly as Seventh

some chord as Seventh or Ninth, however, only when moves stepwise downward, or in some other way that provides for its

or even Ninth of

;

resolution.

162.

C may

Thus, the tone

indicate, in

C

major, the following

chords As Ex. 19.

1

t

Root.

Third.

I

CI And, besides

its fuller

As Root. Ex.

g

VI

^

these, in

120.

J

1

f& T &

)

Min.

This

list is

any key

Fifth.

4-

rhprz

Min.

Maj.

-hi M T—r f^E Maj.

Seventh.

163.

o

significance, in

I

i

1

II 7

Third

9th.)

^m t

J

1?

IV

^ Ff Maj.

Seventh. (Not as

Fifth.

Min.

Dim.

Ninth.

not exhaustive.

The given

tone

may

also appear

as root, third, or fifth in several other chords of the seventh (as root, for instance, in the

The

Dom.-7th chord of

F

major and minor,

etc.).

task of selecting the proper chord would be formidable,

entire list of possibilities

were always valid

at every point.

if

this

But the

r

:

THREE-PART HARMONY.

Par. 164.

choice

is

C in

;

whether,

Ex. 120 would be treated as a major third, or as a

must depend upon whether it occurs in the neighborhood of And, consequently, the number of available

third,

A minor,

85

very greatly reduced by the ruling key, or tonality

for example, the

minor

:

or of At> major.

in C major or its vicinity, would dwindle down to the brief list given in Ex. 119. Hence, further, while Ex. 120 discloses an inspiring outlook for the

chords for the harmonizing of the tone C,

and

intelligent student,

resources,

clearly exhibits the infinitude of the composer's

and vindi-

also suggests the necessity of rational limitation,

it

cates the truly vital principle of tonality

and

key, as

temporary centraliz-

ing influences. 164.

so with

The same D, and the

restrictions apply to every tone rest

among

;

;

as in the case of C,

the possible harmonizations. there are

all

a very few probable ones, to which preference must be given, and which are to be singled out as

Thus, the tone As

first

choice.

D suggests only the following chords, Third.

Root.

J=i -S-

r C

The name

f-r—

r

II

V

means

V7

VII

)

& r

V7

V

The name VII

This more narrow, but more

individual step of a scale,

may be

is

Not

as 7th, or 9th.

1

" Dominant-7th, Incomplete.''

refers to the omission of the root.

165.

(

C major

Fifth.

i

Ex.

121.

in

f The term

" Incomplete "

not used in this book.

rational, choice of

tabulated as follows,

chords for each

—

for

(or minor) Step

Ex.

122.

1 3

1.

* I

Step '

Step

— 2.

II

J

3.

-g= I

Step 4. Step

5.

Step

6.

Step

7.

C

major

:

ELEMENTARY COUNTERPOINT.

86

Par. 166.

166. The application of this table to a given melodic succession, is made by simply defining, first, the scale-step which each melody-tone rep-

the given key, and then selecting one from the group of

resents in

For example Given the melo-

chords that are valid for that scale-step.

C

dic figure e-d-c, in

be harmonized and one inner part)

major

;

in the following

fore

ways

2.

z.

3.

J

may

there-

— as upper part, with a lower

3-

5-

4-

1.

U-U-i

J, J

J

f

CI

(

:

1.

Steps

:

these tones are steps 3-2-1 , and

V

J

i

-r

r

r

r

r

r

I

II

I

I

II

VI

I

J

JrH^

J

'

7-

V VI

I

I

V

VI

9-

8.

3

6

3

3

4,

5

,

±e!

I P

1

rrf

^m

=F=fr=

^E

i

are all good. Examine them carefully. Many others are possible, by substituting other (inverted) forms of the same harmonic succession, compare Nos. 4 and 5 or by modulating into related keys, as in Nos. 8 and 9.

The above

—

especially

;

The

following are faulty 2.

1.

i Ex.

—J

J

5th.

5th.

-> !

5th.

3.

J

J

J

5th.

4.

J^JJ

5th.

* 5th.

124.

5th.

*=E VI In the

IV

1 II

IV

IV

II 7

first group, the successive 5ths (in the outer parts) result from two causes from harmonizing step 3 with the VI (which is possible, but rare, according to the table in Ex. 122); and second, from the unnatural chord-succession, V into IV :

first,

(see Ex. 125).

The

and fourth groups.

IV,— Ex.

125).

latter succession is also responsible for the faults in the third

In the second group there is an awkward chord-succession (II into

:

THREE-PART HARMONY.

Par. 167.

From

167. in

Ex. 122 Of these

this

limited

by the

may be already aware. and including par. 176).

to

It is true, ultimately, that

168.

— when

lists

rules of natural chord-succession.

rules the student

few paragraphs (up

ployed,

appears, that the choice of chords from the

it

somewhat

is

87

If so,

he might omit the next

any chord-succession may be em-

awkward movements (correct melodic But the beginner must respect the following

the student shall have learned to overcome

conditions by perfectly correct contrapuntal

movement

in every part).

distinctions.

Some

corroborating the

chord-successions are natural,

conditions

created by the relations of the chords to each other, and to their Tonic

Others are more or

centre. 169.

progress

The

After the

is,

I,

—

After the V, of the

and awkward.

how each one of the six triads may which chords may come after each any chord of the same key or of any other key.

following table shows

that

;

less unnatural

—

either the

I,

or the

VI (which

is

the " parallel " triad

Possibly the III.

I).

After the IV, any chord excepting the III.

— the V 5th below), or the VI 5th above). (which own After the VI, — any chord excepting the and therefore should not chord bxitf — the IV, or the VI. After the After the II,

(a perfect

either

(a per-

fect

the I

"

lel

follow,

III,

dent must

kn&w

" paral-

inferior one).

either

For every one of these movements (and entific reasons.

is its

recede,

This, however, the facts,

is

prohibitions) there are satisfactory sci-

The stuand embrace every

not the place for their demonstration.

and must therefore memorize the

tables,

opportunity of putting them into practice, until they become a second nature to him. If his musical instinct is quick, his not,

he

will

170.

have to work a

little

mind

will all

the more readily assent to them.

If

harder.

Stated inversely, the following are the chord-progressions which

should be avoided :

125. ( All poor.)

S^ V

IV

V

After the VI.

-& in

VI

me^tm PPP After the IV. After the

After the V.

Ex.

II

\V

v

III/

IV

III

VII

II.

II

IV

After the III.

-sh

III

III

11

V111

vJ

:

:

:

ELEMENTARY COUNTERPOINT.

88 The

succession V-III

avoided, as a rule.

when

but the III

;

—

that

is stiff,

when

is,

is

a rare chord, and should be it is always possible

but not bad

;

the chord-3rd, or 5th, appears in the

part, instead of the Root.

Every one

171.

used,

good

is really

succession II-I

inverted forms are used,

lowermost

when

above unnatural chord-progressions can be

of the

of the two chords is inverted. For example, the be followed by an inversion of the IV, or of the II.

V may

the second one

This refers principally to the first inversion,

172.

which

6th,

The

Par. 171.

is

— the chord

of the

almost invariably good.

The second

inversion of any triad-form (the \ chord) is rare and hazwould be wise for the student to avoid all | chords, exceptThese are good. second inversion of the I, and of the IV

ardous.

ing the

It

'.

In other words, avoid the chord-fifth in the lower part, excepting in the I and IV.

For I chords, the following rules must be observed Leaps are not good, either to or from a £ chord (in the lower part)

173.

;

excepting, as usual, during chord-repetition. Six-four chords should not occur in direct succession.

For

lower part

illustration, this

is

faulty

X

Pr

I Ex.

126.

r

r

f

X

4-

r

r

etc.

¥e On

tt

the contrary, the following

& rrr i

i

J

\

Ex.

is

good

hftj=&hhh±a r^F=^f=T

^

1

1

127.

^t^-pf 174.

The

rules given for the

their Incomplete forms, limitations,

:

7

and

1

6

6

Hi

I3

4

V apply also to the V and V (and to V ) but more strictly, and with certain 7

9

8

;

on account of the resolution of the chord-7th and 9th, Ex. 49.) For (See par. 58, second clause,

stepwise downward. lustration

V

1

—

— il-

b

THREE-PART HARMONY.

Par. i7S

The

V7

•^^

ft

r^^t

g

r

r

89

H»

—

U r

'

W

'

'

=

f

r

*

•

^

f VI 7

IV,

The

Vs

Incomplete.

^

3^=1 gfcEt fTTTf iv 2

1

Group

3

is

doubtful, because of the inverted form of the VI.

In group

rarely inverted.

4,

the seventh of the chord

(f

;

The

II 7

is

treated like the

V, or into inverted forms of the

The

V

very

Like the

II,

it

As

already stated,

passes into the

other chords of the Seventh seldom occur as essential bodies,

The Ex.

.

is

I.

but often as descending passing-notes.

129.

7

That triad

in the upper part) remains

where it is this is always good, if the proper resolution follows. the term " Incomplete " signifies that the Root is omitted. 175.

1

II 7

Thus

:

h sJ ± 4-^ = f=^ r f

.

i

I—r

BEEEp: tr

r

r^

'

V Other Sevenths.

m

Ii5^ 176.

O^j

^t=

m-

^B

r*=f=T=*r-i IV 7

to major.

9.

V

III 7

I7

IV

IV

r VI 7

All of these rules apply, as usual, to the minor mode, precisely as

The

only modification

is

the occasional lowering of the yth scale-

:

;

ELEMENTARY COUNTERPOINT.

90

Par. 177.

and raising of the 6th step, according to par. 32 (Ex. 30), which view thoroughly. See also par. 184. step,

Transpose Exs. 123 to 130 to

C

minor,

particular reference to these paragraphs (32

good

at the keyboard,

— with

and 184).

In this lesson, the student will confine his exercises to the

177.

"

—

re-

" chords (review par. 12, Ex. 12),

will simplify the use of Ex. 122,

and

and

to

one key at a time.

This

of par. 169.

For illustration, a melodic sentence in C major as upper part each an essential chord-tone (that is, no passing-notes or neighboring notes, ;

tone

in these lessons)

I2

Steps 3

IIS

34-3

l6

ii-^

1

Ex.

-J-^-

F^

§33

.24321

V V7

V

I

beat, the chord-5 th

the next beat,

In

all

n

y

g is

g

is

u

^CT I

beat

omitted.

I

x

3,

doubled and/ is omitted. On the next In measure 2, beat 3, e is doubled and ^ omitted.

the

d

again omitted.

is

In measure

of these cases, enough of the chord

the object of the omissions

is,

is

3,

beat

1,

d

is

omitted.

present to define

it

beyond doubt

simply, to obtain the best melodic progressions.

Either of the three endings

This

V

V*>

3

"j.

I 1,

—

0V 7

IV

1 1

rii

N. B. In measure

On

3

=F

130.

j

4

5

is

good.

to be sure, a purely harmonic task; merely the defining of the

178. chords that are required or suggested by the successive melody-tones. But it acquires a certain contrapuntal flavor through the effort to give each separate part a is,

good melodic form.

This can be done by judicious choice of duplication, and of

omission, in the spelling of the chords, as seen in Ex. 130.

Sing, or play, or write

above three parts alone by itself, and it will be seen that something more is accomplished than the mere harmonic accompaniment of the given melody. Such practice is so beneficial, so instructive and so stimulating, that the student should make extremely thorough use of it, before undertaking the genuine contrapunout, each of the

tal

treatment of three parts.

THREE-PART HARMONY.

Par. 178.

EXERCISE

91

16.

Three Harmonic Parts, as Melodic Harmonization. Harmonize each of the following melodies, as upper and V, as s.iown in Ex. 130. the I, V, IV, Each melody in the same key throughout.

only,

—

V

—

Primary Chords.

part, with

"good" chords

Endeavor to make each part, separately, as melodious as possible. If the melody is high, one staff will suffice (as in Ex. 128); if low, two staves will Or, in any case, the student may use two staves, if he so be more convenient. desires.

4^^^

Several versions (at least three) of each melody should be made. 1.

(One

jp^^yU ±r

j J j

.

,

JJ;..

.

e

^fW^ a

1IE

-Kt~

J „

staves.)

1

mm

p=m

i=3t=J

Mil »—

3t±M

15":

iffi

fczfa±± iiffi

*~

tj *

s

<

I

N=

15:

[A solution

of

Melody 6

will

«U_j

J

^d

km $ ^ S^*

-j-

d=

1

±=*z -X

:*=£

V^

^ m m^^ >

-&—!*-

^4m

5.

g?

(Two

i-S

„

m ^=^

Either.

*±=i=±

!,

3.

ijj inJJ

i

2.

Either.

staff.)

be found in the Appendix.]

l

sr^ ^=*i

V

:

:

ELEMENTARY COUNTERPOINT.

92

CHAPTER

;

Par. 179.

XVII.

SECONDARY CHORDS. For the employment of the other, comparatively

179.

inferior (but

decidedly useful and effective) chords, the tables in Ex. 122, and par. 169,

must be applied

The

180.

the II 7 and

in their fullest significance.

best of these chords are the II and

its

inversions.

They harmonize

inversion,

its first

and

steps 4

and

2.

used chiefly as substitute for the I, after the V or V 7 It exis not inverted; that is, the Root always appears in the lower part, cepting in the succession of 6ths, shown in Ex. 132. It harmonizes step

The VI

1,

—

is

.

—

rarely step 3.

The

III

is

very rare.

It

harmonizes step

7

when

it

descends, stepwise,

to step 6. 181.

The

following groups illustrate certain specific applications

iU

±

(I Ex.

±i

Better than

131.

a

Ik II

To these, add In group

1,

7

VI

II

si

X

4EEH

V V

V

S II 7

III

Ex. 129, which was not used in the preceding lesson. the

VI

appears after the

V.

In group

2,

the

first

version

is

better

than the second one, because it is always better to change the chord at the bar, if posIn group 3, the III appears as harmonization of the descending ph scale-step sible. (in the line 8-7-6).

182.

especially

The treatment

Successive

first

when used

of the Sevenths

is

shown

in stepwise progression.

^ T=H

which review.

Thus

?-r-r

—p- $=$— —

-*

in Ex. 129,

inversions (chords of the 6th) are always good

f

:

Er^ l-

£

:

SECONDARY CHORDS.

Par. 183.

-f

^ j

i

j

1

j

1

f=r^

6

6 is

1

lies closer to

6

6

6666-66

6

better than group 2

the upper one.

long line of sixths

;

it is

r

-^ 3^

j=^t Group

J=± ±^k i

j

1

93

;

the effect

Group

is

3

is

more compact when the inner part Group 5 exhibits an unusually

also good.

good, because of the uniform parallelism of the outer parts

compare par. 107, last sentence. But observe the conduct of the inner redeems its independence by occasional contrary motion, and wide skips.

In sequential successions, almost any irregularity

183.

part,

is

which

excused,

For example, in the following, many of the conditions of par. 169 are set aside. It is mainly necessary that the first See par. 29.

as usual.

figure

regular (normal),

is

and

that

it

interlocks readily

with the first tone

of its sequence, in each part. For illustration I

3=i--

U=l=^

^

iEh

Ex. etc.

133.

#—p-

ffff

§_^=tE

I w

ga=^=j -r«

5-

=^=F

m ^ rjy f

etc.

^ ^ $*=?=£

S*

*

f=Fm.

^E? 4=£— — ^^ -r

F

h-

^rf

^TTJL

^

etc

— ELEMENTARY COUNTERPOINT.

94

m

Par. 184.

7-

Tj^J- IT^-J_j

J

^r

r

„

etc.

^

1

§# *=t

iM^fc r~r

N. B. The uppermost

r~r

f

etc

slurs indicate the actual figure

inner and lower slurs are merely noted to

show how

Examine every group very

(preceding) figure.

and

its

sequences.

The

the sequence interlocks with its

carefully, observing exactly the effect

of each system of slurs.

Any good figure will yield a number of sequences, but the points at which the sequence may begin must be those into which the figure itself runs smoothly.

good melodic movement are innotes of the major versions need never be changed, but the notation of steps 6 and 7 may need to be modiAs a rule, whenever step 7 descends, it must be writfied by accidentals. ten b-flat (in C minor). And where step 6 ascends, it must be a-natural 184.

In Minor, the

difficulties of

creased, especially in sequences.

(in

C

The

minor).

Transpose

all

of the

above examples (131, 132, 133) to C minor, and closely observe the

both as written exercise, and at the keyboard application of this rule.

Do

this

withoutfail.

Ex. 30, and observe that the present rule

is

;

First review, thoroughly,

more sweeping than

that of

the melodic minor scale.

EXERCISE Three Harmonic Parts.

17.

Primary and Secondary Chords.

Harmonize the following melodies, with the material of Use two staves.

Sequences.

this chapter.

Review

the directions given in Exercise 16. 1.

3! ie

m

fe±

m

— THREE HARMONIC PARTS.

Par. 184.

UMU

mm 2.

95

jWg

^^

W^S

i

*2

nil

vi

^ ,

6

7

I

1IESfebB

^f-*

£ ^^?!

-^-t

'"

i

VI

frUi^Li^a

*i

^^^

I

EBa£| feW^i^^ iN^u jjj^g s

^j^l^^U^ g^j a p sS3E glE^S 8.

—g—

-g

zi

'-#

-g

—

g*-

10.

Successive 6ths.

^

gj

& ==• )

I

1

&^ 1%-art J 'j

g

g|g

II 7

6

6

6

6

6

3M IPfcg^g^ 6

11-

6

6

6

6

n_i *——

Si i

»

VI

i

II

Sequences.

hS*

W^i ^

i

J~M

i^UJJ-Jl,U|iJlM^%^ v

p.

:

:

:

ELEMENTARY COUNTERPOINT.

96

Par. 185.

12.

^m

j.jj j,j

ii

ttt

[A solution of Melody 8 will be found Besides these, the student

may

in the

Appendix.]

re-harmonize the melodies of Exercise 16, intro-

ducing Secondary chords where possible. Also write a number of original three-part sentences, like the above, with Sequences, and with Successive 6ths.

CHAPTER

XVIII.

WITH MODULATIONS. The

185.

86, par. 88

rules for

and

par. 90.

changing the key are

all

given in par. 81, par.

Review the whole of Chapter VIII, but very

particularly the paragraphs mentioned. 186. 1.

As usual The keys which occur

transiently in a sentence should

be

next-

related to the principal key. 2.

The key may always be changed

some form momentary key. But chromatic modulations may be made at any point, easily, after

Tonic harmony has completed the

3.

chromatic succession itself

—

if

the

And the pres-

properly prepared.

is

of the

ence of the chromatic progression excuses almost any irregularity.

187.

The

first

melody of Exercise 17 may also be harmonized as changes of key

follows, with transient

^m rrVfj^ G

1

e

,

G

.

Ex.

m£:S

j

* DV

3fc

188. itself, it

When may

n~r J-U.J r

I

1

rUrtm Chrom.

I

GV

Q J

id

*—1-»

134.

°

I

the chromatic progression occurs in the given melody

generally be treated in one of these two ways

:

.

;

MODULATIONS, AND ALTERED STEPS.

Far. 189.

The

1.

:

of the two chromatic tones may be harmonized with a and the second tone with a Dom.-7th chord, or dimin-

first

triad,

ished-7th chord.

Or,

Each tone may be harmonized with some chord

2.

97

of the 6th (con-

firming par. 182).

For

illustration

F

b

a

Et>

fe

T-*—•—*-

=t i

^^^fTT^ v

v7

v 4 Ov

6

§

9 e

9 «V Ov

CI

CI

•

i

=£^ iijUuiJa f^rr-pr n=f^r^=f- 1

SE

^is^p^f^

2e

cv 7

^

=#F

In the first version, the transient keys are not all next-related to the original key nor does the melody end in the latter. The chromatic character of the harmony See pars. 88 and 89. Also glance at the Notes to Ex. 158, a. accounts for all this. In the second version, the lines of chromatic 6ths are so indefinite that scarcely possible to prove the keys.

They

are,

it

is

properly speaking, no more than

passing chords, and do not actually change the key, which remains C major throughout. At the same time, any of the intimated keys might be confirmed at once, by resolving the chord in some legitimate manner; this would, of course, change the

melody

at that point.

For

instance, version 2

may end

like version

resolving the last chord of the third measure as Incomplete Dom.-7th of

B

by simply minor.

Closely allied to this principle of very transient modulations

189.

(shown

1,

in

version 2 of Ex. 135),

is

the

common

practice of momentarily

by accidentals. This gives the chord a so-called but does not change the key.

altering certain Scale-steps

" altered " form

;

Of many possible Altered scale-steps, the following frequent and effective The lowered 6th Scale-step, in major. 1 raised 4th Scale-step, both in major and in minor. The 2. 190.

are the most

:

:

ELEMENTARY COUNTERPOINT.

98 For

illustration (in

C

Lowered 6th

i.

major)

Par. igi.

:

step, in Dom.-9th.

*.

In

IV and

II.

w

m1 nvrnvfl

Ex.

136.

U ^ ^^^H^H^ 3.

$

Raised 4th

step.

ahsME

IV

4.

(Raised 4th and 2nd.)

r

±±4+JIV 7

II

5.

II 7

(Raised 2nd, in Dom.)

f 11

Observe that a Tonic chord always follows the altered one, as resolution, and in confirmation of the principal key.

Observe that by lowering the 6th scale-step the chord of the diminished- yth becomes valid for major fas well as minor).

Observe that the raised 4th step occurs only in the II, IV, II', IV (Subdominant Also that it may be accompanied by the raised 2nd step, in the II. And in the V or V. that the raised 2nd step may occur alone, chords^.

—

—

Further, the raised 4th scale-step in minor

C-

Ill

minor.

Ex.

*

137.

11 7

IV

IV 7

IV 7

Observe that, here again, the raised 4th step occurs only in Subdominant chords (II-IV-II'-IV). though it is Observe also, that the Tonic chord usually follows, as resolution, perfectly proper to pass from these altered chords into a Dominant chord (measure 2), because the latter naturally moves at once into the desired Tonic.

—

191.

minor,

The lowering

—

Exercises,

of

—

"Altered " following

of the 7 th scale-step,

and raising

of the 6th, in

which such extended use has been made in all the minor is nothing more than an application of the same principle of

scale-steps.

See, again, par. 32 (Ex. 30), par. 184,

and the

—

u

•

:

MODULATIONS, AND ALTERED STEPS.

Par. 192.

Lowered 7th 7

Raised 6th

step.

step.

i^44^U=^^ rrrf

Ex.

138.

f

r

192.

In minor,

it is

only in the II (usually in Ex.

139.

99

FE F^?

v r

r

1

also possible to lower the its

chord of the

r^

-p-

6th).

EXERCISE

f

Scale-step, but

Thus

-

-=-

2nd

^ =

r=

w

18.

Modulations, and Altered Steps. Harmonize the following melodies, introducing changes of key wherever possible Use two staves, as a rule. In the first melodies, the * indicates where modulations are to be made.

or desirable, according to the above rales. six

2.

1.

pm^i±UM±¥^¥3i J-

3.

4

IE

i

i 2e=t

-*

*11 7

^=* *—

^^pg St^g^ i

-•

1a

faE

— —

-*—•-

*

Jij.J

j

G

m^ J|t^-j

min.

6.

#t

i

«S fct

£ ife

-*-

ifcfe

ELEMENTARY COUNTERPOINT.

IOO

Par. iga.

^

8.

>UhM

i

n #

«

i

^J

i

j

i

..j s=*

.j

:j

j.

i

6

j

:# 6

6

^

6

l

#f^^^^-^ Sequence.

#

Ut \mj^

i .

i

Seq,

Sequence.

-•

i

Jt3t

£—hr-

^r^rr

^

-et-

10.

^= »J — bJ

IISE

^j

J

j

J-j

J

i

b^=^ y^i

J

I

j

l

| ,

11.

Altered Steps.

u

*

,

#

*

^ ^¥ ti±

^Hn

SB

-zS-

* Various

13.

m [A

1

1

l^Ud^j

it

I

altered steps.

^ jy

solution of

Efl

step.

12.

iPSSEg

t

*

Ifa3 i^3^Si=? * Lowered 6th

=

Melody

Besides these, write a

fti^S^ ^^

gEjiai

7 will

be found in the Appendix.]

number of

with modulations and altered chords.

original three-part sentences, like the above,

:

:

CONTRAPUNTAL HARMONY.

Par. 193.

CHAPTER

IOI

XIX.

CONTRAPUNTAL HARMONY. 193.

The

consideration of melodic independence in the several parts

becomes more emphatic when the same given melody nately, as inner and as lower part.

The still

is

adopted, alter-

from that of the preceding chapters.

It is

the act of harmonization, and subject to almost exactly the

same

task differs but

little

But the attention is necessarily more evenly divided between the parts, and the melodic nature of the exercise is sufficiently emphasized to justify the designation " contrapuntal harmony." rules as before.

194. In the following, the given melody is placed in the upper part, and harmonized as before possibly with somewhat greater concern for the melodic movements of the other parts ;

±

tt i=^LM 4=

4=t

It is significant, that the

I

^

-r-

=t

*-4-

4 *z.-jL

3=

two outer parts alone, without the

-v—tinner,

i

form a perfectly

satisfactory counterpoint in this example.

195.

When

the given melody

placed in the inner part, the chords

is

are defined according to former tables (Ex. 122, and par. 169),

may be greater freedom in the choice. The tones required to complete the chosen chords

— though

there

tween the outer parts as to give good melodic especially necessary in the upper part.

subject to the rules of chord-inversion.

The

are so divided be-

results in both.

lower part

is,

This

is

of course,

Review, carefully, par. 173, and

Ex. 126 (in which the above given melody appears in the inner part).

For example

J

,

J

.

r*

JL-±

l

3=t

Ex. 1

141.

m^f=FF

nr

^^

4-d-

(#)

Here, the inner and upper parts yield good counterpoint, without the lower.

1

:

ELEMENTARY COUNTERPOINT.

102 196.

When

again, are

the given melody is placed denned according to the tables,

For the lower

part, the table of Ex.

Par. 196.

in the lower part, the chords,

— but somewhat more

122 should be thus modified

strictly.

—

:

CONTRAPUNTAL HARMONY.

Par. 198.

But the quicker rhythmic movement

198.

is not to be maintained must appear in alternating parts, as Examples 66, 76, 108, 109, which must also be reviewed.

(constantly) in any single part.

shown

IO3

in

It

—

See also Ex. 111. This manipulation of the original essential tones

199.

absolutely necessary

not only desirable, but

is

and the student must not consider the task of 3-part contrapuntal harmony fulfilled until he has so accustomed himself to the addition of unessential (embellishing) tones, that they will naturally suggest themselves at once, and even

or influence, the choice of the essential tones.

assist,

For

200.

;

illustration, Ex.

140 may be accelerated to a rhythm of two

notes to each beat in alternating parts, about as follows

mm f^CF^T

gEHbsS

9

Ex.

:

&

r

144.

s

§fc

Compare

this

*=»=

St

t3=

very carefully with the original form (Ex. 140)

;

and endeavor to

obtain other solutions.

N. B. Observe

that the

rhythm

of the upper

part

is

arways regular; that

quicker tones are applied in the upper part at the unaccented beats. in the

upper part only, because of

its

melodic prominence

;

it

This

is

is,

the

desirable

does not apply

at all to

the inner, or lower, part. It is, of course, also possible to quicken the rhythm of a simple three-part harmonic sentence to two notes to each beat, by shifting either one of the three parts See Exs. 78, 79, 80. This should not be considas shown in Chap. X. forward, ered as a valuable or effective resource, and its use, unless very moderate, is not

—

commended.

Still,

when

sional rests, as in Ex. 89

;

applied in alternating parts, as in Ex. 81

—

it

may be

;

or with occa-

permissible, especially at single points, where

no other form of amplification seems convenient.

Thus, with Ex. 140

^

:

ELEMENTARY COUNTERPOINT.

104

ll

t\r*=V

•

'

LJ^uj^3

I

I

5*

1 as •'

ij

»l

>

.

I

^M H

Ex. 144 B.

1(8

Par. 200.

.

^ etc.

U a

:

j

.

etc.

&

1

Further, the

*

yx_.

P'

1=

same model (Ex. 140) accelerated

beat in alternating parts 3

-T-T-

iTT*—-*= *rrr

Ex.

to three notes to each,

:

145.

m

^E

1

fcs:

§EgE

a

I

=P=S=

Manipulate this in other ways.

Observe, again, the regular rhythmic treatment

of the upper part.

Further, with four notes to each beat

Ex.

i

e:-

146.

v§

i

e5 £&

•-*-

—

?=

j

CONTRAPUNTAL HARMONY.

Par. 200.

J

i5fc= ^7~^g^ J

§g2

,

•fe=£ ^S ^?^

j

net

PS

s

I

N.B.

I

p?

I

fr

isi

^i#

=fefe

Compare

this carefully with

taken with the original. Also,

^

Par. 121.

^^^ ,

•#

p=s=Pi j

Par. 75.

I

I05

make

Ex. 140, and observe the degree of liberty that

is

Again, note the rhythm of the upper part.

a number of other versions.

Also, review par. 184, and transpose

all

the above to

EXERCISE

C

minor.

19.

Contrapuntal Three-Part Harmonv. 1. Manipulate Examples 141 and 143 in amplified rhythms of two, then three, as shown in Exs. 144, 145, and 146. and then four notes to each beat, z. Harmonize each of the following given melodies in the three ways illustrated first as upper part, where it is written; then as innet in Exs. 140, 141 and 143; and then as lower part, two octaves lower than part, one octave lower than written

—

—

;

written (possibly a

little less

sional eighth-note

may be

monic

any

versions, in

I

t=X•-

i

-d

$=±

melodic movements.

^ JJ-

2.

H

2

I -tfz =z:=l

m— tTt

j^ JjJjtob^^M^B i

An occa-

used, as broken beat, even in these original essential har-

part, to facilitate the

1.

I839=

than two octaves, transposed to another key).

=

f

I

ELEMENTARY COUNTERPOINT.

io6

w^ g

2,

|

V

J

J

J |

U^4^ I

Bb major.

Each of these simple harmonic versions

3.

of

iTJ JJ |

Par. aoi.

is

then to be manipulated in rhythms

3 and 4 notes to each beat, as indicated above.

[A

partial solution of

4.

Select a large

Melody 3 will be found in the Appendix.] number of finished sentences from Exercises 16, 17 and 18, and amplify them, similarly, to the quicker rhythmic forms shown in Exs. 144, 145 and 146.

CHAPTER

XX.

THREE-PART COUNTERPOINT. 201.

In the four preceding lessons, the association of three melodic

was explained and conducted on the basis of the chords which the individual tones of one given melodic line suggested or required.

parts

202. This is, strictly speaking, the only correct manner, at least for the determination of all the fundamental conditions because it is the Chords which constitute ;

harmonious music. The inharmonious effects which are more or less plentifully interspersed, in an effective and interesting musical sentence, are merely modifications or embellishments of the chords, and neither can nor should be accounted for in any other way. No matter how freely the dissonant particles are intermingled, the general impression must be an harmonious one for no music may be called good, or may be expected to produce an agreeable and acceptable impression, Inharmonious music is really not music at all, in unless it is harmonious as a whole. in the sense in which our reason, our instincts, and the judgment of the whole civilThe chords are the " accordant " tone-bodies, ized world, compel us to regard it. the proper basis of

all

;

which guarantee

this

necessary prevalence of harmonious

(as

is

the case in

when

effect.

And

therefore the

and melodically independent of each other genuine counterpoint) must be determined, fundamentally, by refer-

association of parts, even

individual

ence to the chords.

But there are other modes of arriving at a good harmonious distinctively contrapuntal in character than the simple harmonization of the given melody. When the student has cultivated his 203.

result,

more

sense of chord-succession sufficiently, and has reached that stage of progress at which the chords have become a part of his nature, and perform

he will find it possible and natural to cenupon the melodic movements of the parts, and will achieve a good result more quickly and surely from this point of view.

their functions automatically, tre his attention

:

:

THREE-PART COUNTERPOINT.

Par. 304.

In genuine counterpoint

204.

The

sion.

is

it

but the movements of the separate

above examples rule, there is

there are too

many

not the movements of the chords,

tones,

influence of the chords

is

107

that create the required impres-

felt

rather than heard.

In the

chord-changes, at regular intervals ; as a

a different chord for each beat, and therefore the chord-

and

is probably the most under such conditions a not even when genuine contrapuntal effect cannot easily be gained, copious inharmonic embellishing tones are added (as in Exs. 144, 145

movements

are too frequent

obtrusive.

obvious defect in such harmonic sentences

and

This

;

—

146).

The most

effectual method of diminishing such persistent chordand increasing the significance of the tone-lines as such, is impressions, upon each single chord, or, at least, upon certain (strong) longer dwell to chords and, in general, to vary the length of the chords. While the chord is stationary (or passive), the separate parts are unhampered, and can move about with greater freedom. (This is shown in Ex. 148.)

205.

;

In these unrestrained melodic movements, the parts hold each

206.

other in check, to some extent, not only by mutual agreement with the

underlying chord, but by harmony of movement among themselves. This latter element is of extreme importance, especially in elementary counterpoint,

and manifests

itself

most frequently

in the following

two forms

1.

Parallel 3rds, or parallel 6ths, between any two of the parts.

2.

Duplication of any 3-tone stepwise figure, in the opposite direction.

For example Parallel 3rds

and

6ths.

1_e

4 X

C

I

J--rn

TCTTTH

j-

in

^F¥f^l II

*

:

THREE-PART COUNTERPOINT.

Pai. 208.

Ditto.

3.

«

-si—=1-

-

J.—,r«—a

J

J

-

ti

±^UJ NHH^feJ^ BJ Jlj a a=l l^^moa •^-jpitt l

,js

1

1

In example a there are three irregular chromatic conditions, known as the CrossIn measure i, beats 3 and 4, the d in Soprano is followed by d-sharp in

relation.

Alto in measure 2, beats 3 and 4, c in Tenor is followed by c-sharp in Bass in measure 3, last beat, the Bass has f-sharp, followed by f in Tenor. When the chromatic succession is thus divided between two different parts, it is simply necessary that the Jlrst of the two chromatic tones should move stepwise, not with a leap. Observe that in example c the line of diminished 7ths is always ultimately ;

;

—

checked by a resolution into the relationship

229.

is

I.

absolutely necessary,

The

Such a return

and should not

to the

normal condition of chord-

be deferred too long.

pianoforte music of Chopin abounds in beautiful and effective chro-

matic chord-successions, often extending through * complete sentence.

phrase in Ex.

The

The

last

urged to analyze Chopin's pages very comprehensively and thoughtfully, for such experience as he may desire to gain with reference to this particular kind of flexible harmonic movement. At the same 1

58 illustrates

this.

student

is

must not neglect the equally faithful analysis of Beethoven, Schubert, MenSchumann, and Wagner. a few random extracts from Chopin Further,

time, he

delssohn,

—

—

ELEMENTARY COUNTERPOINT.

128

4M rn R-a^+w ^ f^^ Hy \]\ \ \\ pg^H Largo,

nw

Ex.

Par. aag.

p

r

etc.

par. 72-1.

159.

\

\

cl (!)

Lento.

Sequence. Susp.

tf p#=* Ies T

F

j-*j

-1

V

BI

*=t==F

IV

3==$

?mm

gj minor.

dSII 7

?

3t

EfeS

3.

?P£

Allegro.

£=*

137.

fc

V

rfM

s

Ex. 137.

« & Is ^^S!^feRJ=p^ n*MM ^ ^ m s Ex.

i

par. 190.

^=^^ 3=^

5#l£ P=

' I

cj

IV

I

B

II 7

J

* * ^— P

fet

x-m-

-

I

(dt)_V

AV 7_

I

I

U:

giK^Sf SF=t

1

X

par. 92-8. I

I

V

B V7

E V7 AIV

V7 D V7

b II

I

^

X

§ess A V 7_

:

MODULATIONS.

Par. 230.

P^

129

* *

i

—

W-f

*=£ 4*L

f-ff EIV V

AV 7

I

Allegro.

4.

—i^hf—

»

pot

BV Number

.

AV

BbV 7

The whole passage

f^p

7

is in

H

* btfr,T

fVg,,t

7

1

etc.

i>*

f

i

f

f

GV

AbV 7

7

C minor nowhere ;

GbV

is

ft

.

i

a

if

7

FV 7

there evidence of an

actual change of key, because the tones involved create the impression of unessential

In measure

passing-notes only.

Number

2.

This passage

is

2, beat 2, the /-sharp is a raised 4th step. so " contrapuntal " in character, that the individual

melody-lines cannot in every case be referred to a legitimate chord

forms are sure

Alto

3, is

present,

beat

2.

—

their

names are not always

In measure

a passing-note.

5,

beat

3,

definable.

the purpose

is

a I of

This

B

j

only the chord-

obvious

in meamajor; the a-sharp in is

Similar conditions prevail in Ex. 149, No.

3,

the Notes to

which should here be reviewed.

Number 3. In measure 2, beat 3, the ^--natural in Bass is merely a passing-note, which does no more than change the mode of the chord from major to minor (compare Notes to Ex. 149, No.

1).

legitimate lowered 6th step of

Bass

Measure 6

E

major.

is similar,

though here the

In measure

4,

beat

3,

c in Bass is a

— again

similar,

a passing-note only. Number 4. A succession of Dom.-7th chords, in fundamental form, and, consequently, with persistent parallel 5ths. See par. 107, especially the last clause. the

e-flat in

is

N. B. This paragraph (229), and the above examples, belong properly to the It is not the purpose of the present lesson to use any other than es-

next chapter.

sential tones (chord-intervals).

230.

For the

rules of altered scale-steps; review pars. 190, 191,

192.

In four-voice harmony their application

is

as follows, in major

and

:

ELEMENTARY COUNTERPOINT.

130

Lowered 6th

i.

yr

Ex.

r

step.

Major.

step.

fpr-f-f

r

160. C

Raised 4th

z.

J

—

,

i

IV

3.

V9

I

II 7

I

Raised 4th and 2nd.

fe^ i

II 7

i—

f=^T

i

J

jg

VI

I

5.

—

J

TfT

II 7

V7

IV

I

J-hL-iJ-^ • -•

iE

s #f-T-rr

^

i

I

IV

I

Raised 2nd step (in Dom.).

4.

i_J_

TTi

lr

r

i i i-u.^ ri- f T r=Ff

j-

j

gi^fE

Par. 230.

Lowered 6th and 2nd

V7 (

I

in Major).

??

J-jLIlJ-JijJ*==^ »

j

j

g

I r,V

When

i

»»

9

d=j= II

I

the 2nd step

is

raised in the

Dom.

J j

j

j

s

i IV

I

discords,

II

should

it

lie

1 I

above, not below,

the chord-7th.

Further, in minor r.

Raised 6th

step.

C

Minor.

step.

3.

Raised 4th step.

~pm**^M

Ex.

161.

Lowered 7th

2.

sp -" IV 7

V

" \

I

>

r

r

III

IV

i

^

n

F= I

II 7

1

IV 7

I

— MODULATIONS.

Par. 230.

131

Raised 4th and 6th.

4.

5.

j jj j„.d^ Mfe£ j

SB

V

IV

m

1

IV 7

I

V7

step,

rr

UM

i

F*

II 7

I

Lowered 2nd

II

I

I

Probably the most common of these are groups 3 and 4. Observe that here, unlike major, the altered chords do not always progress into the

I.

EXERCISE

23.

Modulations. Harmonize, again,

1.

all

the melodies given in Ex.

according to the above directions.

Do

this without fail,

18,

in four-part

harmony,

and thoroughly.

Harmonize the following melodies:

2. 1.

Major.

-•

i H=& l£P

d

±

Seq.

duz

^5

1

^^B^^^^ 4=3fe 1|=eS

i

j

i|

J

Seq.

I

maj.

Major.

=fe=

iIE f

g

*t

Seq.

m

E

maj.

3 ^ A

it

Major.

Seq.

4JJ: *t

fr=Nt«^g

I

ELEMENTARY COUNTERPOINT.

J2

Seq.

i

(

bfy

)

Par. 231.

Seq.

^S^EjS^^? ^g

HrfrSjt»=fc 3=3 Altered steps

(

^=F

*

^=ft=t

as^-^u

i=t

Melody

*-J

l

a»

I

^^

*)

\Ȥ=p

H

be found in the Appendix.]

[A

solution of

3.

Besides these, write a number of original four-voice sentences, with the

5 will

material of this chapter.

CHAPTER

XXIV.

CONTRAPUNTAL HARMONY. Review

231.

par. 193, the principle of

which

is

applied to the fourth

voiced texture also, and in the same manner.

In the following example, the given melody

232.

Soprano.

Review

i

placed in the

Given Soprano.

i.

Ex.

is

par. 194.

i=± ±

W

+-l-±

1—G=f

c

1

r

T= f

162. J-

I

j

§S£ ££

I^ o. ^

J

^^m

^Ul

^ JL

TT

la

J-

X

S=P

X r

f=

i I

Here again, as in Ex. 140, there is significant evidence of fundamental agreeas if, unconsciously, the Bass were counterment between the two outer farts, pointed to the Soprano alone, with more reference to general melodic agreement than

—

to the chords.

It is

probable that this

is

always preponderantly the case, in music of

:

:

CONTRAPUNTAL HARMONY.

Par. 233.

133

and good contrapuntal association guarantees the complete harmonious result, into which the two inner parts necessarily fall. This attaches a degree of importance to the Bass (or lowermost part), which the student is warned not to underrate, or overlook. Observe the movements of the lowermost part in many sentences in Beethoven, Mendelssohn and others. See the 5th Waltz of Chopin (A-flat, op. 42), measures 29-41 from the end. every kind for both outer parts, because of their prominence, are melodic leaders ;

;

their

233.

Review, very thoroughly, pars. T97, 198 and 199. The above may be amplified to a constant rhythm of two

^

simple harmonic version

notes to a beat, in alternating parts, about as follows

w ISSt

i= 1

1

*.

m

-J

UL

^^

Ex.

163.

j"3

§« ^E

Compare

this

HA m

very carefully with the original form (Ex. 162).

Observe, here again, that the quicker rhythm

unaccented beats,

234.

i

— with one exception,

Review

par. 195.

— In

is

applied, in the upper part, to the

in the first measure.

four-voice harmony, the given

melody

cannot conveniently be used in the same key for each of the four parts. A given Soprano is placed one octave lower for the Tenor; and a

The given Soprano is transgiven Bass, one octave higher for the Alto. posed either a 4th or 5th downward for the Alto and the given Bass a ;

4th or 5th upward for the Tenor. C, the keys will be as follows

For example,

—C — G or F Tenor — C Bass — G or Soprano Alto

F.

if

the given

Melody

is in

:

:

ELEMENTARY COUNTERPOINT.

134

The above given Soprano placed in

F major 2.

162, B-flat major)

Given Alto (transposed).

T=F d j

Ex.

1

i

Wr^

may

m

^ ±1

.

$ES

i-U. f m m ^=51 '

1

Z.

j

j

j.

=P=F

.4

i

m

^1

J.

j-

1 y^F* =t=t t=a

rr^=^ ±

«_

1

^=t=d= IE

therefore be

Thus

for the Alto.

fe 164,

(Ex.

Par. 235.

r

4=^

PM

4=

I

Here, the Bass agrees contrapuntally with the given Alto, as if these two parts were unconsciously conceived together. Note the parallel 3 minor), measure 17 to 25 42 to 46. " " Fugue No. 8 (Dft minor), last 6 measures. " " Fugue No. 5 (D major), measures 10 to 16 24, to the end. After finishing these, the student may analyze any example of 4-part counterpoint that he may find, in the works of Bach, Handel, Mendelssohn, Rheinberger and

Volume

II,

Prelude No.

1

;

;

;

other modern writers.

CHAPTER XXVI. MOTIVE-DEVELOPMENT. Review pars. 142 to 145. Also pars. 212, 213, 214, 215 and These all have bearing upon four-part counterpoint, also.

243.

216.

244. The rule given in par. 217 should be applied with still greater emphasis to a contrapuntal sentence with four parts. At least one of that is, heavier the parts should be restrained in its movements,

—

(longer) tones should occur frequently in one

and another

some

of the parts,

This may be seen, to

in contrast with the prevailing quicker rhythm.

extent, in Ex. 170.

Further, rests should be frequently introduced

whole groups of beats should be another, of the parts,

— so

silent

and the

is

in one,

and then

In this manner, the

stu-

reduced for a part of the time to three-part counterpoint,

result is all the

more

The development

245.

not only brief ones

that while four parts are unquestionably rep-

resented, they are not always active together.

dent's task

;

now and then

while subject to

all

effective.

of a Motive with four contrapuntal parts,

the general conditions of foregoing chapters, requires

a somewhat more definite system of announcement and imitation, at the

The following schedule must be adopted The Motive may first appear in any one of the four parts. And, if need be, a few intermediate tones may be added, with strict

beginning. 1.

regard to pars. 213 and 214.

*

MO TIVE-DE VEL OPMENT.

Par. 245.

2.

:

The second announcement

(first

next higher or next lower part,

147

Imitation) must appear in the

—

in the

Dominant key (com-

pare par. 212).

The

3.

third

announcement must be

in the original key, one octave

lower or higher than the first announcement, and therefore in a " parallel " part of the latter. 4.

The

fourth announcement must be one octave lower or higher than

the second one,

be the

last

— again

in the

one of the four

Dominant

parts, the

This

key.

will

always

one which has remained

unused.

Between each of these announcements duced,

if

brief episodes

may be

intro-

necessary.

For example, with the

first

Motive of Exercise

21

Andante.

& IIS Ex.

s

Motive in Tenor.

172.

i^^ 3

-d

TT

lr-f

—

M. in Alto (Dom. key).

1 w

*tki

tfJ^to £=^

M.

1 ¥ ^J ;

—

Episode: Mod. back to F.

—

a

1

-feg

in Soprano.

1

^J?^ f-3 l

~

'r

1

g

.

,*-•

—

'i

_L

Par. 245.

—

l r a*

vj •

>'

\

r

&

d^=

aJT-L Efisode

:

Mod.

to C.

M.

Episode

in Bass

Mod, to Subdom, and to

:

(Dom.

key).

orig. key.

.

i

*

JiL #

=F=i=2=

rt___

m-t

'i^

s=e

=c=r# 1—T:

dV7_ *—"—

_

molto rail.

Uj =

t

r

r

S

5F5R

I

r

_&_

^

^

i

gV_

_DI

a ^

FV_

FII

i

(bb min.)

n O^tJ

I

F

maj.

r

molto rail.

F?fli

"; t

r

&g rjr

I

Motive.

Ff^-J=?T3 HTl^ FI

S II 7

V7

^r I

I

MOTIVE-DE VELOPMENT.

Par. 246.

149

Analyze this (first without, and then with, the keyboard) most thoroughly. Observe that the counterpoint does not become " four-part " until the last part announces the Motive (measure 10). The four parts are then retained steadily to the end, excepting one measure rest in the Alto. This is somewhat contrary to the spirit of paragraph 244, but cannot be wrong, of course. In the second version of the ending, one additional announcement of the Motive is in the Tenor. The d-flat (in Alto) is, in both cases, practically the lowered 6th

made,

scale-step of

F

major.

The above sentence

is much shorter than any of the Inventwo voices, or with three voices, made in Exercises 15 and 21. Should a more extended form be desirable, the schedule given in par. 154 m ay be consulted, but will probably be utilized more as a general

246.

tions with

Compare

guide, than literally,

par. 219.

EXERCISE

26.

Motive-Development, with Four Contrapuntal Parts. 1.

Make

three

more complete solutions of the Motive manipulated in Ex. 172, (in same key) then beginning with Bass (C or B major) and

beginning with Soprano then with Alto (C or 2.

B

;

;

major).

Manipulate each of the following Motives,

Each Motive may be developed

in

the manner above suggested.

by placing the first announcement respectively in each of the four parts (in different keys, as indicated above, and according to the suggestions given in par. 234). Review all the directions in Exercise 21, No. 3.

1.

in four wholly different ways,

—

(Sopr. or Tenor, in Ab.)

Alto or Bass.

i te

Moderate

2.

Bass or Alto.

(Tenor or Sopr., in

HP^^ii

SSSSta ndante.

3.

e.)

.

Tenor or Sopr.

(Bass or Alto, in A.)

Allegro.

^-*!

j- j

I

j j

yj

j

j^-

^tv^

ELEMENTARY COUNTERPOINT.

ISO 4.

Sopr. or Tenor.

(Alto or Bass, in

c%.)

m

Allegretto.

±d ffi izjLA I

5.

Sopr. or Tenor.

Par. 346.

(Alto or Bass, in £.)

Andante con moto.

^j._nVTg '—'

[A concise solution of Motive 3.

be found

in the

Appendix.]

Besides these, manipulate again (with four parts) some of the Motives given

in Exercise 15 4.

5 will

i

*

and

in

Exercise 21,

Further, the student

may

— subject

invent a

to pars.

number of

213 and 214, if needed. original Motives, similar to the

above, and manipulate them in the usual manner.

This is as far as the study of Elementary Counterpoint need extend. For the continuation of his contrapuntal discipline, the student may take up the author's Applied Counterpoint, beginning with Chapter IV. But before doing is

so, or in systematic alternation

with the

latter,

he

urgently advised to pursue a thorough course in free composition, as

detailed in the author's

Homophonic Forms.

The End.

.

I5i

APPENDIX. SOLUTIONS OF SOME OF THE GIVEN EXERCISES. a.

As upper

part.

^JT]._ 3.

As lower

part.

-•=#=

a.

5,

Melody

1.

i.

tt

"TrUj 'Li/t^t —— — —

Exercise

As lower

As upper ~ rt

r

6,

5.

1

part.

e£*

^r 0.

Melody

CCfT

part, t

1^¥ Exercise

i

££3:

4s J

Igas

m

As upper

r

*r

IST TTf riff

part.

ie^#^p#ff rrf r

£. a.

As as

lower part.

J i Jig? i fr^J St^i**fi r>Lrrrfrfrrs rrrrr? '

d^+m • t j «

r fffr

1

m f^frf rr ^ f ,j

-

'

-111 ^

ri

1

j

^

_'l:*^g rrr f

APPENDIX.

152 As upper

a.

part.

^frff-rt-^ ZmrfMh&h Exercise

7,

Melody

6.

m^'.f As lower

i.

ti^m^^^^

part (transposed).

m s^e^S3S jge^g^^^^gE^^^^I -+-&

?gf:

a.

Exercise

Melody

As upper

part.

8,

11.

A^S PS

I

!

!

I"

^

HI

(B)g* />.

As

h

lower part.

*

^ m+ t^tF-f -*

it

-P-

*-•

BV

£

S -• p

--—-

t=5=P= tttf ±± j

APPENDIX.

mst^^g

153

i«-

1

1

)

gpijjj

^i^Ppj

M .

As upper

i

i

V7 .

part.

g=3

Ep=§=t=F

Exercise

9,

Melody

4.

and

pars. 48

g&falls£

184.

^eS

If ^t*±5 v ii 7

ferf

> ^t

«_

SEI ar**-*T-

*:

itt±=«t

1

^

^^

-ft

•H^

=r=^

§Sfe* SE

II

£.

As lower part

te^

4t J4

gg*

-9-

-f

2"

gffi

£

3t!t

-x

x

-,

--

l»

ei

e>

75H

s*

°

f^

1

VI

Sequences.

3.

J

(==&: 'JI*H -h i obPS3 YjW wrrrrtt % PS r P r pf 'J

l

I

'

^

'

'f

rP-

l=t

-g>-

t*

M

• d «-=-

1

APPENDIX. Version

Sequences.

4,

|_J^ J

J? Jtl,

159

J

1

J

J

.

1

J

K

1

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1

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1

1

i_

,

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f-^fh-H^rf Vrf ff f p-^ ^5 « £

^s

#=-«^

a

e

Version

a

a

i

•*-=-

7

1.

.

|

1

1

I

Exercise 18,

Melody

7.

Bfcfcltp:

Version

im

^rn s

ga-^j

—

:

J

J~T

Jl

TTfrTTT

^L^ F*W»

^r=

Sequences.

2.

t-rhr-hHJ

a*^

fe

W=

b il

f

' i= Jl.ii

u p

-•—# i

iJ

Version

3.

VCT ^ ^HWrfH i

^>

H

'-

r

i

*=r^Pt

sea l

ri

l

a

a comp. par.

75.

Sequences.

p

--rrr^r -

teg

&£

i!

z=*£

5±^

fe

^rT.

1»X"

^^H

^

—— APPENDIX,

i6o a.

As upper

Susp.

part.

Exercise 19,

Melody

3.

*-•

—

r

i

(Amplified to 2-tone groups)

J?.

p

-m J

n M

d kPjJ l.'-v

1

1

I

* 1 \

§&3 r^zm W^-^ a^

f

As

inner part.

Hp

ffi

•

1 v

—

\

r\

iteEfc f*¥ T-iHf-£=r (Amplified to 3-tone groups

rr

i©*-#-

3?

-•

—

P-

1

trr '1

*

i

1

gy

•

II 7

II

)

-*

J ,J

>

1

* 1

Isa

^

'

n

j.j

J

J

=*=4 ]

i

J

-7r

—

J

*

m-

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^

J

I

Jj-

wgg—g

5 T-\—t

arid

£.

—^>-»

I

#

—

*-

P^ *

p-

*F

a ±=-

-3-»h*

*—rr

« * • d_±

f

VT] rn rU jj J

r^d

-

ip?

cjr 11

11 7

J J W j J A>* j

^

I

fiL-.

r

I

uiru-»sj^

APPENDIX. As

161

s 3 ^^mm trnrnnm^ 6.

lower part.

S3 Sf=*=T t=f

3=E

§Se

*t

*=fc

IV

(II)

(Amplified to 4-tone groups)

i3§l

^ ^Bf$

-*=• j

^fc±i S

1-

i

^

11 7

i p

1

i

fi^f^rTT^7-

1

'L_fMr '

1

1

1

-

1S3E

Exercise 20.

^T3 r* fefw

¥ No.

Upper part

1.

S T*

given.

^-offl

T?=-=

£

#=F

1

s

j

i I-*

^^tfJ^Li^J^^^^ j~r

l

is

u f=r% ~

r i

-#-#•

^f-frr

^^

^-p^-p-Hfe^ =t=t

r

,

,

:.-=&

LJ

r

1

r

^t^3

i

APPENDIX.

162

m

No.

2.

Inner part given.

•

^m jh~i.

^

ff^

No.

3.

l

•-

La=*

y /^ffi?^— i

zrr

##

Lower part

given.

j

Pte MEf!Ejj*5t

JV r

N ^J 'J=jy

w

#-?C

r~

'^

^Eaa

yP^eg^

f=f=F^

s W^ffiH«S

_*J±_*

£

m

rFFf ^^u

d

i=t±

1

S-E

'

APPENDIX.

ffitT~»f-6

163

WT%

^rr-

w m

m=^=^^=r^

^ S5

%,.r^—i p I 9

Hi

oft

Exercise 21,

Motive

H

*

ji'

j

j j

j

§?

=P=i: 1

#-*-#

I

1 r

*±*

p

?EF

Lento.

Motive.

M.

6.

^W imit. in 5th.

o^^^

^^tirf/fe

Dom, M.

\J

j

^

j

71—

^

—f

>

rJ T

to Z>.

^

^

imm

_

r

,

Episode : Mod.

gfeaa^

9 &4

minor..

1

Interlude.

IE

*?

jt- r 1— J-PJJ]M Ui^Si fi ^5^,, .

I SIE

chord of

imit. in Sve.

Motive.

tz^^-^ CSS3 ^If-'fVF?

Episode: Mod.

to

(5

1

APPENDIX.

64

Episode: Mod. to G.

N.B.

g*^ >

jt

f

Motive.

S^*

=P5 anfc

i»rrrfri%

Motive.

^L:

-,

Episode

Cfcr

rf,'J^J^J^CT ^g "*

9*

[Motive.

l

'

Dom. chord

of

S

^

a minor"

Episode : Mod. back to

J

Mod. to

^

C,

and a minor.

JP'JJ?

w ^^r^ ftU

:

r

ii

*^

^

I^T^-B'^g J

m

Motive.

Interl ude.

Lf/f"

1T~*

48S

r-

w L^ \J

orig. key.

^

165

APPENDIX.

^ ii£

i

Motive.

(" Intentional " 8ves.)

litfgiillWP

111

Adagio.

^BlEfiFVf Exercise 23,

Melody

5.

fefa!l^l^* 4^9594 ^1^P?= s i4j

1

tj-

^^^^^^ L-LJkL-i—jl

t-tj.

f

APPENDIX.

i66

m

^ ^•^

J

I

i

§E=3i r

j

J

r

t

i.

The given melody

i

=E

"r

f

*r-

r

as Tenor part. I

Exercise 24,

Melody

i wit rf t

wHMitt yrrrr 1

j

j

1

J1

,

1

^£to|g = :

4

£ As Alto

part

IbMt'.'/i,^ .'ii U Jf 'V,i' \m^r^f V7

J

i

I

j

X.V

J

^T

Jii /l,

i

r

Et>V 7 _

Ji '§te

J

j

par.

f

(

f=F

,J |i

,j

V

^ Notes to Ex. 158a.

s«f=

wm m

^

^y

J ,

f 11 7

transposed.)

J

j

J.

tJ

j Ji»i

j

*B

t.

;

f

r

1.

|

J

J

-

J

Jl ?i,

i''rr' EPF I

APPENDIX. b.

The

\6?

given melody as Tenor part.

Exercise 24,

Melody

2.

Pfe

riPtf^^

f\t

\f

r



g)

£ Tonic organ-point.

j

APPENDIX.

168

As Alto

*.

£m

H-n-fTJ

FJ ^gi*

s

9 ^b * :

i

^ inl^^

dJ

part (transposed).

g

>

of=^g

frr

£

ftfca

r»

WiJF

r

Dominant organ-point

:^ f=p 4i^ ^ri^ ¥^^M^ p^f jrj ^TfjJ „

i

-

Sequence.

N.B.

-

(

vUJ3.

pA ;

'-

im

—&

±j=;t

^, J

, -S=#=

,

J J

f=^

o

r-

J

J-—

,

y—

,

gj

T^rrt^

fg

g

J

J

-

ir_j r !

—ODjM^OOJ: §s ^^ Each

-

tfiuTi

=H s -f

3-note,

altered seq.)

zi g f

2: S2:

:: i

part (transposed).

s>

* 1 1^2

i

T^i

!

jj-Mr-r ri ^ nr-4-r'P-r

As Bass

rf.

-

i

'

j.

r

j

=f=f

1

-U

^f-ff^B

of these versions of Exercise 24 is to be amplified, in the usual manner, to 2-note,

and 4-note groups.

APPENDIX.

169

Motive in Sopr.

^HJ-jP.^

l

Exercise 26, Motive

5.

ggj^w -

Motive

in Alto

(

Dom. key

).

§±£|g Wfr

mi?5=^ l^S^rry^^^^r^l Episode

:

Mod. back to

At?.

i^ SE Motive in Tenor.

^bife^—

r=

iN§

1

P

1

t-t-^-t

5

i" ^,

1

B

rH

9ijfcT=^'

-x ¥

T

Motive in Bass

(

Dom.

key).

^ &?

•

j?*:

I&fer* rff^

Bp^

S

p=p=

r4f

"

^

ritard.

^

r Dt>V 7 _

r

g

i

Motive. 1V1

^s

^

n

Jcr-J S3 i^s .

1

Largo.

1

—

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