Elementary Counterpoint

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EXERCISES

IN

ELEMENTARY

COUNTERPOINT

BY

PERCY

GOETSCHIUS,

Mus.

Doc.

(RoyalWurttemburgProfessor)

Authorof

"The

MaterialusedinMusicalComposition,"

"The

Theory

andPractice ofTone-Relations,""The Homophonic Forms of

MusicalComposition,""Modelsof thePrincipal

Music Forms," "Exercises in

Melody-Writing,""AppliedCounterpoint" "Lessons inMusic

Form,"etc.

Fifth Edition

NEW

YORK

(6)

Copyright, 1910,

By

G.

SCHIRMER

(7)

Dedicated

to

Sfomfe Samroarij

IN

CORDIAL RECOGNITION OF

HIS SIGNIFICANT

CONTRIBUTION

TO

MUSICAL

EDUCATION

IN

AMERICA

(8)
(9)

PREFACE.

The

present

volume

isintended

and

expectedtocover

more

ground than

its title implies.

In

the author's

mind

it representsacoursein

Harmony,

quiteas

much

asin Counterpoint.

It

owes

itsinceptionto the author's often expressed conviction that these

two

coursesofstudy cannot

be

separated;

and

also toaconstantly

strength-ening belief that the

most

rational, quickest

and

best

way

to acquire a thorough knowledgeof thechords

and

their uses (the recognizedpurpose

of thestudyof

Harmony)

is to begin with one part,to pass

from

thatto

two,

from

thatto three,

and

thusgradually arrive atfullfour-part

harmony.

For

this reason,

an

extensive Dreraratory knowledge of

Harmony

is

notatallnecessary,though a general

knowledge

of thechordswill

facili-tate the studyof this book,

and

is therefore

recommended.

Such

generalfamiliarity

may

be

gained

by

the studyof Part II of

my

"

Material,"or ChaptersIII to

XXX

of

my

"Tone-Relations."

The

full four-part texture,

when

approached

in this way, as system-atizedinthese chapters,will

have

developeditselfnaturallyinto"

Counter-point";

and

itsacquisitionwill fullypreparethe studenttoundertakethe

subsequent tasks in

homophonic

and

polyphonic composition.

THE

AUTHOR.

(10)
(11)

TABLE

OF

CONTENTS.

PAGE

Introduction i

ChapterI.

Tee

Single

Melodic

Line, Stepwise Progressionsand

Nar-row

Leaps 5

Exercisei 7

Chapter LT.

Wider

Leaps

8

Exercise2 11

Chapter HI. ExceptionalProgressions,and the

Minor

Mode

ir

Exercise 3 15

Chapter IV.

The

Association op

Two

Melodic

Lines. Corresponding

Rhythm.

Fundamental

Intervals.

Major

Mode

15

Exercise4 20

Chapter V.

Fundamental

Intervals,

Minor

Mode

22

Exercise5 23

Chapter VI. Exceptional Intervals 24

Exercize 6 28

Chapter VII.

Rhythmic

Diversity.

Two

Notes

to each

Beat

29

Exercise7 36

Chapter

VUL

Modulations 37

Exercise8 41

ChapterIX.

Three Notes

toeach

Beat

43

Exercise 9 46

Chapter X. Syncopation, or Shifted

Rhythm.

Ties.

Two

and

Three

Notes

toeach

Beat

47

Exercise10 50

Chapter

XL

The

Tle, continued. Rests 51

Exercise 11 56

Chapter

XEL

Four Notes

to each

Beat

57

Exercise 12 62

Chapter XJH.

Four Notes

to each Beat, as Amplified

Forms

63

Exercise 13 67

(12)

V1H

TABLE OF CONTENTS

PAGE

Chapter XIV. Diversityof

Rhythmic

Movement

inthe

Two

Parts 67

Exercise 14 72

Chapter

XV.

Motive-Development. Imitation.

The

Small Invention 73

Exercise 15 81

Chapter XVI. Three-part

Harmony,

Melody

Harmonization with

Pri-mary Chords

83

Exercise16 91

Chapter XVII. Secondary Chords. Sequences 92

Exercise 17 94

Chapter XVLII. Modulation, Diatonic

and

Chromatic.

Altered

Scale-Steps 96

Exercise18 99

Chapter XIX.

Contrapuntal

Harmony,

Three

Parts. Simple

and

Amplified ioi

Exercise 19 105

Chapter

XX.

Three-part Counterpoint 106

Exercise 20 113

Chapter XXI. Motive-Development.

The

Small Invention,

Three

Parts 114

Exercise 21 121

Chapter

XXH.

Four-part

Harmony.

Melody

Harmonization.

Primary

and

Secondary Chords. Sequences 122

Exercise 22 126

Chapter

XXHI.

Modulation

126

Exercise 23 131

Chapter

XXIV.

Contrapuntal

Harmony,

Four

Parts. Simple

and

Amplified 132

Exercise24 137

Chapter

XXV.

Four-partCounterpoint (Analysis) 138

Exercise 25 145

Chapter

XXVI.

Motive-Development.

The

Small

Invention,

Four

Parts 146

Exercise26 149

(13)

EXERCISES

IN

ELEMENTARY

COUNTERPOINT

INTRODUCTION.

Music, theoretically considered, consists altogether of

Lines

of

tone.

It

more

nearly resembles a picture, or

an

architectural drawing,

than any

other art-creation; the differencebeingthatinthe

drawing

the lines are visible

and

constant, while in

music

they are audible

and

in

motion.

The

separate tones arethe points

through

which

the lines are

drawn

;

and

the impression

which

isintended,

and which

is

apprehended

by

theintelligent listener, is not that of single tones, but of continuous

Lines oftones, describing

movements,

curves

and

angles, rising, falling,

poising,

directlyanalogoustothelinearimpressions

conveyed by

a

pic-tureor drawing.

The

popular

name

for

such

a tone-lineis "

Melody."

As

several tone-lines are usually

being

traced simultaneously, itfollows

thatseveral corresponding melodies

may,

and

generally do,

appear

to-gether.

The

term

Melody, however,

is appliedspecifically tothe

princi-pal,or

most prominent

line.

When

a

number

of tone-lines areintonatedtogether,it isevidentthat

they should agree,or

harmonize

with

each

other.

The

process

by which

this

agreement

is assuredis

commonly

known

as "

Harmony."

# * #

Tones

areassociatedin

two

different

ways

: First,inverticalcolumns,

orsimultaneously, insolidbodies of tone,usually

known

as

Chords

;

and

second, in lateral order, orsuccessively,in strandsoftone

which we

shall

call Tone-lines,or melodies.

For

example,the tonesc-e-g,

arranged

ver-tically,give a chord-body, or

harmony, each

separatetoneof

which

may

be

a point in

some

tone-line(Ex. i,a).

The

same

tones,

arranged

suc-cessively,give atone-lineor

melody

(Ex. i, V)

:

a. Chord. i.Tone-line.

Ex

1.

it

ii i J

f

n

Itis of the

utmost importance

thatthe

music

student should

adopt

and

cultivate the habitof

apprehending music

according tothis defini-tion, asa

System of

Lines.

The

beginner,

and

the ordinary hearer, are inclined to regard

music merely

as a series of chords, a succession of

(14)

2

ELEMENTARY

COUNTERPOINT.

tone-groups,

and

to associate mentally only those tonesthatare

sounded

together(simultaneously, asEx. i,a)<

This

issurelya naturalview,

and

correct as far as it goes,for the

harmonic

basis of all

music

is

unques-tionably the chord.

But

it is

an

imperfect view.

The

object of the chords is,simply, to fix (approximately) the points

through which

the

lines run;

and

unlessthese linesare

grasped

and

traced,

unless the

hearer

can

associate mentally the tones thatfollow

each

other, thetrue

purpose

and

significance of the

whole

tone-associationis missed.

This

must be

so,

because

theonlyevidenceofLifein

music

liesinthe

motions

which

interlinkthetones in flowinglines;

and

theselines are,therefore,

the only tangible

element

intheartof tone.

The

realmusicalpicture then, isa delineation;

an

image

of

sounding

and moving

lines. Quiteaside, forthepresent,

from

the

numerous

qual-ities

which

enterinto theselines,

their directions, their speed, their

rhythm (freedom and

variety of

changing

motions),theirspaces,

and

even

their indefinable

sensuous

or spiritual attributes,

the

fundamental

fact

must be grasped

thatit is these lines

which

create the musical

impres-sion.

The

"

music

" lies in its melodies.

Music

is " tone-lines";

and

thequality of the severallinesdetermines the qualityofthecomposition

;

thevitality of thelines equals the life inthe

music

;

and

the

degree

of

harmony

which governs

theassociation of thelinesfixes the

euphonious

standard of the composition,

itspleasurable effect

upon

the natural senseof

harmony

orconcord.

To

illustrate

more

fully

what

is

meant by

apprehending

music

as

a

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

ver-tically

through

theseparate chord-forms,but continuously(laterally)

from

chord

to chord,

letus take

a

passage, at

random,

from

a

Beethoven

Sonata. In thispassage, the master,

though

certainly

guided

by

his

ver-ticalchords,

was

quite as surely impelledto trace agood,distinctly

me-lodious, effective tone-line in

each

separate part or register:

Lowermostline. NexthigherUlle.

(15)

INTRO

D

UCTION.

The

total result, obtained

by weaving

these four different strandsof

tone into

one

compact

body

(as it

came

from

Beethoven's

hand)

is as

follows:

^m

n

^

^

The

music proceeded

outof the chords, of course,but the "

Music

"

it-selfmanifestsits finished

beauty

and

life

and meaning

in the Linesof tone.

The

chords

were

the

means,

the lines

were

the object, ofthe

mu-sicalthought.

The

above

musical

image

(Ex. 3)shouldthereforeappeal

to thefinersenseofthelistenerinthe

forms noted

inEx. 2.

He

should

apprehend each

line separately,first ofall;

and

thetotalsensuous

im-pressionshould

be gained

by

mentally

combining

theselines.

# #

The

tone-linesdiffergreatly in their length,

and

inthe

manner

of their presentation.

Some

lines are long,othersare often very brief.

Some-times thelineis continuous in

sound

(legato),

and

againit

may

be

inter-mittent (staccato).

In

the latter case,

which

isvery

common,

the inner earof thelistenertracesthe

complete

lineacrossthesilentgaps,justas

theeye tracesa dottedline as readilyas

an

unbroken

one.

Through

the following convenient

(and

customary)

method

of

nota-tion,

and

itscorresponding

performance on

the pianoforte:

Chopin.

i^M

£-

4-Ex. 4.

ff^F

N—

n-etc.

^rsfr>—

SB

S'^hrtj

^y^

the hearer should distinctlytracethe followingfivelines

:

Uppermostline. Nextlowerline.

^rrfhnrc

fr

r r I

f

"Mr

J'

s

(16)

ELEMENTARY

COUNTERPOINT.

Nextlower

*&=

a,,t

,

fr

f|Hf^

I

m

a

Nextlower. Lowermostline.

S

I

SSSe

ffi

-=!-=»-*=tt

The

student shouldcarefully

examine

briefpassages

from

the master-works, with

a view

toresolving thegiven

bulk

into its

component

lines,

as

shown

inthe

above

examples.

In

many

cases, only

one

single

prom-inentline (the "tune"proper, inthe

uppermost

part)

seems

to

be

dis-tinctlymelodious,

as for instance,in

No.

37 of

Mendelssohn's

"

Songs

without

Words."

In

others, at least

two independent

linesare discerni-ble; in

a

few,the entire

bulk

may

be

dividedinto distinctmelodies,

as in theInventions

and

Fugues

of

Bach,

and

many

passages in string-quartets, or

symphonic

scores

(where

the linesarewritten separately, of necessity,

on independent

staves). In

many,

finally,the

bulk

isvery un-even,as if, here

and

there, single extra tones,or brieflittle lines,

had

been

inserted

among

the

more

important, longer melodies.

# * #

To

some

extent, this principleofsimultaneousmelodiesis presentin

every grade,

even

thesimplest, of music. It is impossible to

connect

chords, as, forexample,in a

hymn-tune,

or intheearliest

harmony

exer-cises,without tracing

such

tone-lines.

In

four-voice

harmony

there are four,

known

invocalwriting,

and

familiar to the student(in

church

choirsor choral societies) as the

so-prano,alto, tenor

and

bass.

As

arule, so

much

preference is givento

the

uppermost

ofthese (thesoprano),thatthe other singers scarcely real-ize,themselves,thatthey too are intoning "melodies "quite assurely as

thesoprano.

# * *

Counterpointis

one

ofthe technicalprocessesof

music

writing.

The

objectofcontrapuntal practiceis toenable the studentto

add

melody

to

melody,

or toobtain

an

association of two,three, or

more

tone-lines thatagree with

each

otherharmonically

and

yet aresufficiently indepen-dentof

each

othertopresentreally different

melodic

lines.

Brieflydefined

:

Melody

is asuccession, or continuousline, of single tones.

Harmony

is a successionof chords or vertical

columns

of tones

which harmonize

intheir simultaneouspresentation.

Counterpoint

isthe

harmonious

association of individually perfect,

(17)

Par.x.

THE

SINGLE

MELODIC

LINE.

5

CHAPTER

I.

THE

SINGLE

MELODIC

LINE.

1. Counterpoint isassociated melodies. In

good

counterpoint, the

associationis,ina generalsense,harmonious,

that is,reasonably accor-dant,

and

each

melody

is good,

by

itself.

2.

Probably

thelatterconditionisthe

most

important.

The

first

con-sideration, forthe beginner, isthe correctnessof

each

separatemelodic

line, independently of the other, or others.

Each

line,

sung

orplayed

alone,

must produce

a satisfactorymelodic impression.

3. Therefore, the first pointto

be mastered

by

thestudent of

har-mony,

or counterpoint, is the

fundamental

principle of

good

melodic

movement.

He

must

acquiretheabilitytojudge thequality ofa melodic

line,

and

toavoid

any

tone-progression

which

isunnatural,

thatis,

which

violates thenatural conditionsof

Melody

(smooth, rational, congruous, well-balanced

and

interesting tone-succession).

4.

Should

thestudent

harbor any

doubt

ofthe existence oflawsthat

govern Melody,

orofthe possibility of distinguishing

good

melodies

from

inferior

ones

withscientificaccuracy, let

him

compare

the following

:

Ex

fan

r^

i

J

^.J^t^n

with those

shown

inEx.2, or with

any

other

examples

in this

book

that

aregiven as

specimens

of correct, sensiblemelody.

5. Itisnotpossible,inthisnecessarilycondensedform, tostateallof the

condi-tionswhich enter into the process of perfect melodicformation,aprocess whichis

ultimatelysubtle,and nodoubtpartly incalculable. Butafewgeneral rules

may

be

given,and these the beginner must carefully observe andfollow,until his instinct

andexperienceshallenablehimtocontrol thefinerandfinestmovements.

6.

Probably

the

most

vitallawof

melody

isthat

which

is

grounded

in

therelations

and

interactions of the

primary

harmonies

ofthe key,

and

which

determines thedirection

of

certain Scale-steps.

Rule

1.

The

natural or inherent

bent

of certain Scale-steps

must be

respected,asfaras ispossiblewithout

monotony.

These

tendencies are asfollows

(18)

ELEMENTARY

COUNTERPOINT.

Par.%.

The

7thstep ofthescale

moves

(naturally)

upward.

The

6th

and

4th stepsofthescale

both

move

(naturally)

downward.

7.

These

arecalledthe Activescale-steps.

Their

movement

extends,

generally, only

one

step; thatis :

Step 7

moves

tostep8,

Step 6

moves

to step5,

and

Step 4

moves

to step3, as arule,

though wider

movements

inthe properdirectionarepossible.

For

example, in

C

major

:

f

Ex.

i

&

=t

I

=F^

The

otherscale-steps(1, 3,5

and

2)

have

no

such

tendencies,

and

are

free to

move

in

any

direction,

that is, freeas far as direction is con-cerned.

8.

When

theactivetonesofthescale

move

one

step,ashere

shown,

theyare "resolved"; that is,their active tendencies are gratified,

and

their

movement

is finished.

But

itis alwayscorrect,

when

lessdecisive

movement

is desired, for

each

activestep to

move

two

steps atonce,or,

in other words, to leap a third,

in the

proper

direction, of course.

Thus

(C

major)

:

4

Ex.

i

1

9.

To

this

fundamental

rulethereis

one

important exception

:

Rule

2.

The

natural

tendency

of

each

activestep

may

be overcome,

sothatitwill

move

along

thescaleinthe oppositedirection,

by

approach-ingit(so to speak,

by "pushing"

it)

from

theotherside, along thescale.

Thus,

step7, if

preceded

by

step 8,

may

pass

on

down

tostep 6; step6,

preceded

by

5,

may

pass

on

up

to step 7;

and

step4,

preceded

by

3,

may

pass on

up

to step 5.

In

otherwords, the progressions8-7-6-5, 5-6-7-8

and

3-4-5 aregood.

Thus

(C

major): r\ a

|0O

a a 1, a a * o

-*—*

V

'

*

i

-*—*

^m

lit

7 8 , 6 3 4 6 6

:?^£

4

*

1

j/»

I

(19)

Par. 10.

THE

SINGLE

MELODIC

LINE.

10.

Observe

thatthe successions 7-6-7, 6-7-6,

and

5-4-51cannot

be

justifiedin this

manner, and

shouldtherefore

be

avoided,forthe present.

Thus

(C

major):

Ex.

10,

i

1 j j j 11

EXERCISE

I.

The

Scale-line,

and

Narrow

Leaps.

The

aimof thisfirstlessonistoimpressthesefundamental melodic movements upon the student'smind, and habituate himto them (m case his studies, hitherto,

have left this most important workunaccomplished). Therefore,heisrequired to writeavery largenumberof original melodies, inallthemajorkeys,strictly accord-ing to the followaccord-ing directions

:

1.

At

present, onlyinmajor.

z. Usechieflythe regular resolutions of the activesteps,asshowninExs. 7and

8. But donot neglect the irregularmovements(Ex.9).

3.

At

nopointshould themelodyleapmorethanathird. Allwiderskipsmust

bedeferreduntilthe nextlesson.

4.

Any

tone

may

berepeated,anywhere. Seepar. 20.

5. Use all the simpler kindsof measure. (from\tog).

The

notes

may

be of

uniform rhythmicvalue,or ofdifferentlengths. See pars.21,22and23.

6.

The

length of themelodiesisoptional,butitisadvisable to writeinthe

regu-larformsoffour or eightmeasures,closingwiththe keynote.

Forillustration

(20)

ELEMENTARY

COUNTERPOINT.

Par.xi.

CHAPTER

II.

WIDER

LEAPS.

11.

The

leapof

a

third (called a

narrow

leap),

used

in thefirst

les-son,is

always

good.

But

all

wider

leapsare generally hazardous,

and

require specific limitations.

The

principal consideration is asfollows

:

Rule

3.

Any

wide

skipis natural,

and

permissible,

when

both

tones

belong

to the

same good

chord.

12.

The

"good

"

chords

arethe

primary

triads

on

scale-stepsI,

V,

IV

; alsothe II,

though

more

rare; alsothe

chords

ofthe

Dominant-7th

and

Dominant-gth.

The

chords

on

steps

VI

and

III,

and

all subordi-nate dissonant chords, are too inferior to afford justification for

wide

leaps.

Thus,

in

C

major

:

GoodChords. Rare. Inferior.

i

m

~tst

1

Ex. 12.

1ST

-!S>-I IV

y7

y9

VI III etc.

13.

The

following

wide

leaps are thereforegood,in either direction

: Cmajor. I IV II

V

V

7

V

9 etc. Ex. 13.

I

IV

The

followingare unnatural,ineither direction,

and

must

be

avoided,

atpresent :

C

major. Ex.

"

t.^m

VI III

f

I

etc. IV7

14.

Rule

4.

Two

or

more

leaps in the

same

direction,

whether

nar-row

or wide, arealsostrictlysubjecttothis rule:

All

the tones

must

be-longto the

same good

chord.

Thus,

C

major

(21)

Par. is. a. Allgood.

WIDER

LEAPS.

I

£

1

Ex. .

5

.E^EE|

V

7-

IV-i*

££

S

#

v

' J

U-

g

J 1_

The

following are faulty:

C

major.

Ex.

16.

i^

Note. In the first group, the first skip(ctog) represents theI,but thenext tone, reachedwithaleapinthesamedirection,doesnotbelongto that(same)chord.

The

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

"add

up," so to speak,

andgive the impressionof a complete tone-body. The above measuressoundthus

:

i

15.

This

ruleapplies only tosuccessive skips in the

same

direction.

The moment

thedirectionchanges, the ear ceasesto "

add up

"the tones,

and

judges

each

leap separately,accordingto

Rule

3. Allthefaulty pro-gressionsof Ex. 16

can

therefore

be

made

good

byalteringthe direction.

Thus:

Ex. 17.

i

Allgood.

IE

t-°CP"-=t

srrrna

etc.

16.

Rule

5- After a

wide

leap

(beyond a

third),the

melody

usually

turns,

changes

itsdirection.

Thus

:

<

pr-r

If

J r l

lffj

Ex.

18.

;fcE&

£§^£

17. Notice, particularly,thatthis isnot obligatory

when

thechord

(22)

IO

ELEMENTARY

COUNTERPOINT.

Par.18.

Itisgenerally better totum, however,afterawideleap, eveninthesamechord

;

andit isusuallyquitenecessary

when

the chordchanges,

as seen in Ex. 16(all

rectifiedinEx. 17). Exceptionsdooccur,however; seeEx. 20. »

18.

Rule

6.

A

skipof

any

width

may

be

made

towards

(oropposite

to)the resolving

movement

of

an

active scale-step.

That

is,the resolu-tion of step 7

being

upward, any

leap

down

to itiscorrect.

And,

simi-larly,

any

skip

may

be

made

up

to steps 6

and

4.

In

each

case, the melody,in turningafterthe leap,properlyresolvesthe activestep.

The

following

movements

are all

good

(C major)

:

I

Down

to step7. Ex. 19.

w

N.B.

i

Up

to step6.

P

I

6 N. B.

Up

to step4.

i

IE

In the measures markedN.B.,anexception toapartof Ex.14isseen,

skips apparently representinginferiorchords.

When

properly resolved,theseprogressions are perfectlygood.

19. Ifa

wide

skip is

made,

along a

good

chord-line,contraryto

Rule

6,

up

to 7, or

down

to 6 or 4,

an

exception is unavoidable. Either the

melody

cannotturn, afterthe

wide

leap,or theactivetone

cannot be

resolved.

Thus

:

i

p

Ex.

20

3^

v*-??

m^m).

i

? ?

It is usually better to respect the fundamental law (Rule 1), and resolve the active step properly. Therefore,groups1,3and5are betterthan groups 2,4and6,

intheabove example.

20.

Rule

7-

The

repetitionof atone, orthe octave-leap, isalways

(23)

Par.ai.

WIDER

LEAPS.

II

Ex.

21.

E:

a

21.

Uniform

rhythm

isalways safe,

and

generally predominatesin a

melody.

But

it incurs

monotony,

and,therefore,notes of various

time-values are effective.

At

least occasionally,a noteofgreatervalue, orof

lessvalue

than

the prescribedbeat, should

be

used.

22.

Rule

8.

The

rhythm

is regular,

and

always good,

when

the

longer (heavier) tones

appear

upon

the accented(heavier) beats,

and

the

shorter (lighter)

ones

upon

unaccentedbeats orfractions of beats.

Thus,

inregular

rhythm:

gl

^n

&

+-*l Ex.

£^B

\=x

22. 4=

23. If the order isreversed,

if

heavy

notes

occupy

lightbeats, or

lightnotes

occupy heavy

beats,

the

rhythm

isirregular,

and

the result doubtful. Still,irregular

rhythms

may

always

be

rectified

by

recurrence,

that is,

by being

repeated in thenext measure, or

some

other

corre-sponding measure.

Thus

(both

from

Schubert

):

§|

i-

i=a

23, Irreg.- Recurrence.

^^

EE

Irreg.- Recurrence.

EXERCISE

2.

Wider

Leaps.

Write, as before, a very large number of original melodies, employing the material of this chapter. Reviewthe directions given in Exercisei,andfollowall

butNo. 3.

CHAPTER

III.

EXCEPTIONAL

PROGRESSIONS.

MINOR

MODE.

24. After

thorough

exercise ofthe basicprinciples of

melodic

move-ment, the student willbetter

understand

certain lessregular traitsthat

(24)

12

ELEMENTARY

COUNTERPOINT.

Par. as. justified

by

the circumstances that attend

them.

A

few

are specially

noted

below,

and

should

be

thoroughly tested; firstatthe

piano

;

then

with the voice; then with the eye; always with closemental application

and

unceasing

referencetothe keynote,

of which

themental ear

must

always

bedistinctlyconscious.

25. First,with reference to scale-step 7

(C

major)

:

I

1. Good. 2. Good. 3. Good. 4. ?? 5- ?

S

Ex. 24.

PNE

III 6. Good. 7. ?? 8. ?? 9. ?? 10. (?)

t

m

i

i

11. ??? 12. Good. 13. ??? 14. Good. 15. Good.

i

r-fi

a

^f—fl

IE

7

*

7 J* 4 III

Explanation.

G

roups 1,2 and3 aregood, becausestep7 passes soon up into step8. Group4isnotgood, becausethe skip representsaninferiorchord; group 13

issimilar,but worse. Group5isdoubtful,becausestep7doesnot reach step8atall

;

group 6isbetter,becausethefirstthreetones representtheDom.-7thchord,andthe

resolution ofthe last one(step 4)satisfiestheear. Groups7to 10 arealldoubtful,

because step7makesan extreme leap in thewrong direction

; group10istheleast

objectionable,becausestep7recoversitself and ascendstostep8. Group11 is

par-ticularly poor and should be avoided; it may,it is true,occur in the line of the

Dom.-7th chord;but step7leaps inthewrongdirection;itisanawkwardleap

(aug-mentedfourth),and,landing on step 4,itcannot recover itself. Group 12,on the

contrary, is all right,

see Ex. 19,group 13. Group14 isconsidered good,

see

Ex. 19,group2. 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

melodicmovement.

26. Second, with referenceto scale-step6

:

1. Good. 2. Good. 3. Good. 4. ??

£

x

5. Good. Ex. 25.

W-

1

4.

*-> a .6. Good. 7. ??? 8. (?)

J

J J

f

I 9. ?? VI 10. ?? VI

(25)

Par. 27.

EXCEPTIONAL

PROGRESSIONS.

13

n. Good. 12. Good. 13. Good. 14. Good. 15. Good.

3

I

W

S

s

t=F

Ps^B

Explanation. Groups 1,2and3 are good,because step 6 reaches step 5soon enough. Group4ispoor,because step4 is not resolved; group 6isgood;and in

group 5, both tendencies are satisfied. Group 7 contains too

many

irregularities;

group 8 is better,

like group 5. Groups9 and 10 represent an inferior chord.

Groups 11 and 12 arejustified byEx. 19. Groups 13 and 14 seemto beadjusted

bythe resolution of step7. Group15 isright,forthereasonsgiveninEx.24,group 15,whichreview.

27. Third,with referencetoscale-step

4

:

Good. 2. Good. 3. Good. 4. ? 5- ?

P^

Ex.

26.

^

±e*

S

i

6. Good. 7. f? 8. Good. 9. ?? 10. ???

1

m

*=?*

Explanation. Groups 4 and 5 are doubtful,because step 4 ascends and does not return tostep 3; comparegroups2 and6. Group7 is too irregular. Group9

hasthe badleapfrom7to 3 ; see Ex. 14,No.2,andEx.24,No. 13. Group 10 is

verypoor,likeEx.24,No. 11,andfor similar reasons.

28.

Rule

9.

One

ofthe

most

vital traits(possibly the

supreme

one) ofgood, effective,

comprehensible and

significant melody, isthe

arrange-ment

ofthe tonesin uniform orsimilargroups orfigures.

Thus,

a figure (usuallya half-measure,

whole

measure, or

two measures

in length)

may

be reproduced

as repetition, sequence,or

some

othercloselycorresponding form,

generallyin

some

corresponding

rhythmic

group.

For example

:

Beethoven.

Observe the similarity offormation in the two figures markeda; the second

measureisasequence of thefirst. Alsotheagreementof bandb. Also the general

resemblance betweenfiguresaandb. Alsotheslightintentionaldifferences,

exact

agreement beingby no means necessary.

(26)

14

ELEMENTARY

COUNTERPOINT.

Par.29.

29.

Such

syntactic

agreement

(uniformityof delineation), if perfectly

distinct, isoftenasufficientexcuseforcertain irregularities ofprogression.

For example

:

i

e

Ex. 28.

EE

$

i

2.

»

M

il

l

?

*!

V

>" 3.

&

SEE

1

L

J

In No. 1, the poor progressions 7-6-7 and 5-4-5 are both justified by being sequencesof thefirstmeasure (whichisa blamelessfigure). InNo.2,the awkward movement from4upto7isjustified bythe repetition of thefirst figure. InNo.3,

several poorsuccessions arepalliated,assequencesoftheveryfirstone,

whichisa

perfectlygoodfigure.

THE

MINOR

MODE.

30.

The

harmonic minor

scaleis derived

from

themajor,

by

lowering the 3rd

and

6thscale-steps of the latter.

C

minor

corresponds to

C

major, but has e-ftat

and

a-flat, instead ofe

and

a.

Comp.

Ex. 29 with the scale of

C

major.

Every

rulegiven

above

applies to

minor

preciselyastomajor.

That

is,the rules

which govern

C

major

also

govern

C

minor

(not

A

minor),

with

one

single exception, as follows

:

Rule

10.

The

movement

from

step 7 to 6,

and

reversed,

from

6 to

7, gives rise in

minor

to

an

awkward

interval

(augmented

second)

which

itisbetter to avoid.

Thus,

inthe so-called"

harmonic

" ortrue

form

of the

minor

scale

: Ex. 29.

|H

C minor. ?? ??

¥

L5

$

ZJ

*

I

31.

These

progressions,

from

6 to 7,

and from

7 to 6, are, in

them-selves,justified

by

Rule

2, Ex. 9.

But

they

must be avoided

ifthe

minor

scaleisto

be

"

melodious

"

(27)

Par. 3a.

THE

MINOR

MODE.

IS

32.

The

remedy

is simple,

and

very

common, and

consists in so "altering " theactive step as to

remove

the

unmelodious

augmented

in-terval.

Namely,

inpassing

down

from

7 to6(in the

group

8-7-6-5 only),

lowerthejth scale-step,

by an

accidental;

and

inpassing

up

from

6 to 7

(inthe

group

5-6-7-8 only), raise the6thscale-step.

This

results in

good

singableintervals,

and changes

the

harmonic form

totheso-called " mel-odic"

form

ofthe

minor

scale.

Thus

:

C minor, /Exceptional. \

8^767

6 7 6 / Ex. SO. 8

7-6556+78

See

Ex. 42.

Otherwise, as stated, everymelodic conditionin

major

isabsolutely valid forminor.

EXERCISE

3. '

Exceptional

Movements,

and the Minor Mode.

a. Firstreviewevery oneof thegivenexamplesthatisin

C

major, transposing each oneto

C

minor(firstatthe piano, thenwiththevoice, thenwith the eye;always

with closementalapplication).

b.

Then

transpose everyoriginal melody of Exercises I and 2 to the

corre-spondingminor

mode

(thatof thesamekeynote').

c. Also write a very large number of original melodies,in major and minor, applying the principles ofthischapter. Beforedoingthis,examinevery carefully the

melodiesgiveninExercises4, 5, 6,andsoforth.

Alltheseoriginalmelodies

may

be usedinthecominglessons.

CHAPTER

IV.

THE

ASSOCIATION

OF

TWO

MELODIC

LINES.

33.

The

principle

which

naturally

governs

the association of

melo-dies is that of

harmonious

agreement.

The

condition of

consonance

should prevail; notto the exclusion ofdissonance (aswill

be

seenin a

laterlesson), forthelatter, initsproper place

and

proportion,isprecisely

as necessary

and

important in

music

asconsonance.

But consonance

should

predominate

sufficientlyto createtheimpressionof "

harmonious

agreement

''as the ruling condition.

34.

The

contrapuntal structure

the association of melodies

is

(28)

i6

ELEMENTARY

COUNTERPOINT.

Par.35.

as leading part

inasense,asbasisorprincipal

melody (though

it

must

never

be

forgotten that, in true counterpoint, the

melodies

are to

be

of

equal value

and

significance,associated

upon

an

equalfooting).

To

this

melody

anothertone-line is added,

by

careful

adjustment

of

each

ofits

successivetonesto

each

successive toneof thefirst

melody,

in

keeping

with the simple regulations of

harmonious

union.

In

other words,for

each

toneofthegiven

melody,

a toneis

chosen

that will

blend

or

har-monize

consonantly with it, so that the

new

melody

which

resultswill

agree, tone

for

tone,with the former.

The new

melody

is thereforein

a

peculiarsense a

product

outoftheoriginalone, obtained, not

by

deduc-tionor evolution

from

within,but

by

adjustment

to it

from

without.

35. Itis quiteascorrect,

however,

tocreate

both melodies

together, atonce, letting

each

inturn suggest the next

melodic

move

to

be made,

and

making

each

thusalternately

dependent

upon

theother.

This

is

what

the

composer

no

doubt

unconsciously does,ultimately.

The

studentwill

use

both

processes,

but

should

adopt

the

former

(working

with, or

"against," a given

complete

melody)

forthe present.

36.

Rule

1.

The

"

harmonious

" intervals,those that are invariably

consonant

and

thereforeacceptableforthe

union

of

two

melodies, are the

Third

(or tenth),

major

and

minor

;

the Sixth,

major

and

minor

;

and

the

Octave

(orunison), perfect, of course. If,for

example,

C

is

given, aslowertone,

we

may

add

toiteitherE,itsthird; or

A,

itssixth ;

or C, itsoctave. If

D

isgiven, eitherF, B, or

D,

willproperly counter-point it.

And

soforth.

For

illustration

: 10th. 3rd. 1 6th. Ex. 31.

m

J:

8th.

m

5=J

1

r

r

r

r

r

r

r

r

r

If

C

isgiven as

upper

tone, either

A,

E,or

C

may

be

added

to it

be-low

;

and

the

same

rule applies to allothertones.

Thus

: Given : Given: » R a a o o

4

i

N

iJ

nH^

-J—

r^

Ex. 32.

I

r

r

37.

These

three intervals are unquestionably permissible at

any

single pointof contact,

and

thetaskof the

beginner

consistssimplyin

(29)

Par.38.

THE

ASSOCIATION

OF

TWO MELODIC

LINES.

i;

38.

This

choice

depends

partly

upon

the melodic

movement,

forit

must be

remembered

that

each

part,the given

one

and

the

added

one,

must

describe afaultlessmelodicline(see par. 44).

But

italso

depends

partly

upon

the underlying

harmonic

result,

for theimplied chord-suc-cessions

must

also

be

natural

and

rational.

39.

For

illustration of this

harmonic

distinction:

Ifthe tone

C

is

given, either inthe

upper

or thelower

melody

(in

C

major),the

3rd

above

(and

6th

below)

will

produce

the

Tonic harmony.

The

6th

above (and

3rd below)willrepresent the

Subdominant

chord, or, possibly,the VI.

The

8ve and

unisonexert

no

positiveinfluence

on

the

harmony,

and

be-come

therefore solely a questionof melodic preference.

Thus:

3rd. ioth. 6th. 6th. 3rd. Octave. Unis.

I

1

Ex. 33.

m

:£- 1- -<s>-IV IV (VI) o o

Note. For the rules ofgood chord-succession, see the author's "

Tone-Rela-tions." Orglanceat pars. 169to176.

40.

Whether

the

major

or

minorform

ofthe 3rd, ioth, or6thisto

be

chosen,

depends merely upon

thekey,

and

thereforetakes careof itself.

Note

i.

The

distinction between3rdand ioth,andbetweenoctaveandunison,

may

hereafterbe droppedaltogether,becausethey areidentical.

Note

2. Inthefirst lessons,the rhythmic formof the two associated

melody-lines willexactly (or nearly)correspond; thatis,each separatenoteinthegiven part

willhaveitscompanion,or"counterpoint," intheaddedpart.

An

occasional excep-tion tothis adopted rhythmic scheme

may

be permitted for good melodic reasons.

See Ex.39,e.

41. Ifthe interval 8 (octave) isapplied to

each

successive tone ofa givenmelody, the resultis as follows:

&

±

Given melody.

h^

-L

^i

Ex. 34.

W3l

r

r

r

r

Addedmelody.

The

agreement

of the

added melody

with the

one

that

was

given, is

complete

; the

harmony

of the association is absolute.

But

the student

perceives at

once

thathere

some

vitalcondition is wanting,for

by

this

process nothing

more

has

been

obtainedthan

an

exact duplicationof the given melody.

No

new

melody

has

been

produced,

and

therefore this

(30)

i8

ELEMENTARY

COUNTERPOINT.

Par. 43.

42.

The

result is

more

ample

if theinterval 3,or the interval6, is

used

with

each

ofthe giventones.

Thus

:

I

X

A

5_4

-5*-1

Ex. 35.

IE

f=f

f

7

f

r

But even

here,

though

a

new

seriesoftonesis

produced

in

each

case,

itis evidentthatthe

added melody

isbutlittle more,after all,

than

a

re-flection ofthegiven

one

;

an

almost exact duplication;precisely the

same

tone-line,

and

therefore practically the

same

melodic

product,

merely

shifted toothersteps of thescale.

As

truecounterpointis to

be no such

artlessmultiplication of

one

and

the

same

melodic

line,butthe

harmoni-ous association of independent

and

individually perfectmelodies, the

fol-lowingrule

must be observed

:

43.

Rule

2. In ordertosecure the

independence

of the

added

mel-ody, the interval of the

8ve must be

limited to single points,

and

not

be

used

twicein

immediate

succession.

The

interval of the

3rd (and

also

thatofthe 6th)

may

appear

consecutively,but

never throughout

the

en-tirephrase, and, as arule,notoftenerthan three(or four)timesindirect succession.

The

bestresultis evidentlyto

be

achieved

by

asensible

in-terchange ofthese threedifferent

consonant

intervals.

Thus,

as applied

tothe

above

given

melody

:

I

X-8 .

.636.

I 8

i

Ex. 36.

m

1

r?

r

r

r

f

r

1

'fff

44.

Rule

3.

The

choice of contrapuntal interval (whether the 3rd, 10th, 6th, 8ve,or unison)

must be

dictated

by

therules of correctmelodic progression.

For

this reason it isnecessaryto play or sing the

added

melody, by itself, after thecontrapuntal union

has

beeneffected.

Such

a

test,applied to Ex. 36, iswholly satisfactory.

Applied

tothe following

ones, it reveals several obvious errors inthe

added

melody, despite the

fact that

each

separateinterval isconsonant,

and

thatthe

two

melodies,

sung

or playedtogether,

form

a

harmonious union

: Ex. 37.

I

A

U

-4

4- 4- 4- I

1

EfEEfE

e

?r

?

See

also Ex.40, e.

(31)

Par.45.

THE

ASSOCIATION

OF

TWO MELODIC

LINES.

45.

Furthermore,

given the following

major

melody

:

19

I

*

1

Ex.

3

8

-

VW

)

4

«

the following counterpoints

may

be

added

:

I

J

J-r-*

1

C^l

Ex. 39.:

t

pp

r-r^

^g

j-*-^

Givenpart,below,

Givenpart,above.

K

jp^i

O 8 6 6 •"Tl 6 L

I

J 10 8

^

6 6 6-^3 1 1 1. 8

r

e 3

^s

I

ft:

1SE"

FFf

f=

tTT

Givenpart,below.

Thisbrief example,simple asitis,should already affordthe studentavery clear

conceptionof the principle of melody-association, or counterpoint,andan apprecia-tion of its value as atechnical exercise.

He

should compare these three given solutions,and observe

how

completelytheadded parts differfrom each other; and

he

may

besure that these are not the only acceptable solutions. Each added part

shouldbeplayed,sung (and conceivedmentally,byeye,as usual),firstalonebyitself

;

then thetwo melodies must be studied together,and thestudentmust endeavorto

conceive their association,mentally,and obtainaperfectlyclear impressionof their

union,

their effect together. Afterdoingthisvery thoroughly.

slowlyand

thought-fully,

hemusttransposethem(byfingerandbyeye) to

G

minor. And,finally,he

must inverteachone of them; thatis,copyitout,placing theupperpartan octave

lower,andthelowerpartan octavehigher,thanherewritten.

'46.

Further, a

few

inferior

and

faultyversions, with the

same

given

melody

: Ex. 40. Givenpart.

"rrr^-f

tee

, a,

trr

(32)

20

ELEMENTARY

COUNTERPOINT.

Par. 47-Givenpart.

1

i

,

A

i

i

, j

j

n

y

,j

j

j

.j

i

r r '

'r

r

tj

l££

tf^"

111

| [

k^J

3 'a 8 8 S 6 xO

^6

10 10

Explanation.

The

first halfof version

d

isinferior,becausethelongsuccession

of (parallel) 3rds gives the addedpart the effect of mere duplication.

The

same

objection partlyattends theparallel lines (in6ths) further on.

At

thebeginningof versione, theaddedpart uses the octave three timesin succession,which resultsin exactly similar melodic progressions and defeats the purposeof theunionof lines.

It is like parallel 3rds and 6ths in principle,but more objectionable. See Rule2,

par. 43.

The

restof versioneis allpoorcounterpoint,becauseof thefaulty,awkward lead-ing of theaddedpart, inobvious disregard of thelawsof melody.

Invertboth of

these versions,as before.

47. In manipulating a

complete

sentence,itis desirable that the

two

partsshould not begin with the

same

beat, intheinterest of greater

in-dependence.

And,

as arule,itiswell to

end

with theoctave ofthetonic (thekeynotein

both

parts); this,

however,

is not imperative.

For

ex-ample

: Given melody.

J

J

J .

J

I J

J

,i

Ex. 41.

g

4-T lj~

^-i-H-

i

m

r

r-r

V

r {

r

r^

rr-rrrr

m

JnN-rJ

J J J i

J^

I

J

J

i

j

m- 3C

4^

1

irrrr

Given melody.

r

r

EXERCISE

4.

Two-Part Counterpoint with

Fundamental

Intervals,

Major Mode.

To

each of the following given majormelodies, asecond partistobe added,in

correspondingrhythm, accordingtotheaboverules,andasshowninEx.39.

The

given melodyis tobe used firstasupper part,whereit iswritten,andthe

counterpoint added below. This

may

be done onthe same staff (asinEx.39),or

uponaseparate staff (with bassclef, as seen inEx. 43, b andc).

The

useoftwo

stavesispreferable,asitpermits greaterfreedom.

Thenthe givenmelodyistobe usedaslower part,an octave lower thanwhereit iswritten (or twooctaves lower,ifnecessary), andcounterpointed above,

with an

addedpart thatdiffersreasonablyfromtheprecedingsolution.

Several different versions ofthe added part shouldbe

made

ineverycase,

as

(33)

Par. 47-

THE

ASSOCIATION

0*

TWO

MELODIC

LINES.

21

1.

m

• i *

i

f

0--P

F

4=t:

$

-a

•-r^mr

^M^=^

m

3E

-#=•

3SE

g

a

&

(2

&—

I

4.

£

P^^^^P^i

#—•—=—»

i|fe

^^

-#

i

m

W

IS

o^q

^ga

55

^-fr

te

^t

r

if

J

J-

b

P

trmr

•-^

i

pzj^^E^zpc

1

#

j=t

^m

~2

|

J

=1

s)

&-u.

BlScCT:

fc^^^algg^

(34)

22

ELEMENTARY

COUNTERPOINT.

Par.48. 12.

i

W

ferf=

-(=-I

**

£

4:

^i

1

[A

solution ofMelody4willbefoundintheAppendix,towhichthestudent

may

refer,afterconscientiouslycompletinghis

own

versions.]

Besides these, the studentistowriteanumberof original melodieswith added

counterpoint,

designing the melodies together (as duets). SeetheNotefollowing

Ex.52.

CHAPTER

V.

THE

MINOR

MODE.

48.

As

stated inpar. 30,all rulesof

melodic

movement

inthe

major

mode

are valid forminor,with

no

other modificationthan thatthey are applied

somewhat

more

strictlyin

minor

(as faras the

movements

of the

active steps are concerned).

Review,

carefully,

paragraphs

30,

31

and

32,

and

observe the ruleof par. 32,

that, in minor, the 7th step

must be lowered

in the

descending

succession8-7-6-5;

and

the 6th step

must be

raised in the

ascending

succession

5-6-7-8-49. Further, alltherules given in

Chap.

IV

for thecontrapuntal

as-sociation of

two

melodies,inmajor,apply without exceptionto

minor

also.

The

choice of

fundamental

intervals (3rd, 6th

and

8th) for the counter-pointof agiven

melody

ispreciselythe

same

in

both

modes.

Itis simply necessary, in minor, to

guard

the melodic progressions

more

carefully,

and

to

be

sure that

each

part, alone, is aperfectly

accep-table

melodic

line.

50.

Given

the following

minor melody

:

Ex.

42.

f^e

p=±$

t^=t

*—*-

m*

m

m

Its contrapuntal manipulation

may

resultthus:

Givenpart,above.

Ex. ,t 1 1 1

n,

i

=F5

m

^y

s

m

a e a 8 s I

"^_

a 10 a a a ' 3 a (e> 43.

(35)

Par.50.

THE MINOR

MODE.

23

m

W^

m

&=E

vr

mim

-*-+

&

+-*-§33

o6eea3

36

f

^=^?

X3:

^

**

3 68 _ 3 3 8 3 1

±±X±J

=?*=

^

$

Givenpart,below,

c

Givenpart, above.

^

&

-*-*JH

*iH

., la,

-8386633383

Prf^pf^r^

-1

Vt-I— 8 6 3 8

-B-*-r-fi-

4 f—f-

m

^

&

Explanation. In one instance only,there arefour successive 3rds(inversioni).

This should bethelimit.

The

added partsall

move

with considerable f1eedom,but

areeverywheremelodicallycorrect.

At the beginningof measure3 in versiona,one note counterpoints twoof the givenpart. Inversionctheadded part has awider range thanusual,and diverges fartherfromthegivenpart (atonepoint, inthe thirdmeasure,thetwolinesareover

twooctavesapart). Thisisentirelydefensible,aslongasthemelodiesare separately

perfect.

Comparethe threedifferentaddedparts,carefully.

EXERCISE

5.

Two-Part

Counterpoint

with

Fundamental

Intervals,

Minor

Mode.

Manipulate the following minor melodies, exactly according to the directions

givenin Exercise4:

1.

^^=

^l^j

T

^rr

r

^

#a

a

2.

I

s

•=*-

S:

0=t

§F4^f=f=F

tEt

*=*

s •

&-f-f=

fc:

*

=:j * J .: $ft

-?-»-+

§^S§

j

gsf^

&

f

^=gg3B

P

PB

m

\*

\

(36)

\-24

ELEMENTARY

COUNTERPOINT.

Par.51.

g

s

m

T» *-

^F=^

I

i

i&t

&

s=e

gb^

rt^

i

i

as

&&

P

-zt

***

i

B.

&

-&-[Asolution ofMelody1 willbefoundintheAppendix.]

Alsowrite,as before,anumberof originalmelodieswith counterpoint,composing

thetwo fartstogether. SeeNotetoEx.52.

CHAPTER

VI.

EXCEPTIONAL

INTERVALS.

51. Greater

freedom

of

melodic

progression

may

often

be

obtained

by

a

few

judiciousexceptions tothe

above fundamental

rule of

harmonious

contrapuntal association.

While

the 3rd, 6th

and 8ve

are

undeniably

the

most

reliable,

and must

atall times constitute the real basisofthe contrapuntal union of parts, thereare a

few

other intervals, mostly of a mildly dissonant character,which,

when

used in moderation, greatly

im-prove

the effect, without inthe least impairing the general

harmonious

or

consonant

character ofthesentence as a whole.

52.

Rule

4.

These secondary

intervals, of

somewhat

exceptional

character, are

theperfectfifth,

the

augmented

fourth, or

diminished

fifth,

and

certain

major

seconds, or

minor

sevenths.

53.

The

perfect fifth isvery rare,

and

should

be used

only

when

it

representsthe

Dominant

chord

(

possibly,

more

rarely,the

Tonic

chord).

Itcan, therefore,occur onlysingly,

notsuccessively.

And

it

should

never

appear

in inverted

form

(as perfect fourth).

For

example

(37)

Par.54. Ex. 44.

m

EXCEPTIONAL

INTERVALS,

b. «

25

I

i&-±^

SSTJi

±M

'• Poor. 4 I

r

-•

•-r

rrrrm

S

54.

The

augmented

4th,

and

its inversion, the diminished 5th,are

fairly

common,

and

always good.

In Major,

they occur onlyinthe

chord

of theDom.-7th, as

union

of steps 4

and

7.

For

example

:

±

-J-Ex. 45.

3:

-a>-=-t

;

r

TTrf

: >

r

Invertthis

example

;thatis,

copy

itout,placing the

upper

part;

an

octave

lower,

and

the lower part

an

octavehigher, than here written.

Do

this,

withoutfail.

55. Observethat theseintervalsareusedincounterpointing the tonesb

and/

in

C

major,

the 7thand4thscale-steps.

Observe,further,that theaugmentedinterval generallystrives "outward,"intoa

larger interval; andthatthediminishedone draws"inward," toasmaller one.

Or,observesimplythat the correct resolution ofeachof these active steps takes care of the melodies.

For

furtherillustration:

Ex.

46.

i

j

1

r

J 1

^

w

Ftt

r

r

r

f

r

>__—

»

i

£S^^

-7

T

i

r=^

-1

r

The

slursin this

example

indicate

where

the chord remains unchanged,

a circumstance

which

alwaysjustifiesnearlyeveryirregularity.

Note

thisfact well.

Invert this example, as before,

and

itwill illustratethetreatmentof

the diminished5th.

Do

this, withoutfail.

56. In minor, the

augmented

fourth

and

diminished fifth

appear

in exactly the

same

way, atsteps

4 and

7, in the

chord

ofthe Dom.-7th.

(38)

26

ELEMENTARY

COUNTERPOINT,

P»r. 57.

But

theyalso

appear (though

more

rarely) inthe

union

ofsteps 6

and

2, in

minor

; possibly also inthe

union

ofstep 3

and

the raised 6th step

(par. 32).

As

usual,the melodic resolutions

must be

respected,

whereby

the re-sults

noted

inpar. 55will

be

observed.

Thus

(C

minor) : a- 4.+ s-4+

M^wi\)rn

\

i££V4&h

Ex.

47.

'cr

y

rii*

±~*H^^

*s^

v v 11 11

57.

The

minor

7th,

and

itsinversion,the

major

2nd, are rare.

They

should

be

limited tothe

union

of steps

4 and

5, as partof the

chord

of

the Dom.-7th. Possibly,

though

veryrarelyindeed, they

may

occur as

steps 1

and

2,inthe II7

.

For

illustration

(C major

and

C

minor,alike)

:

jf

A

, ,

n

|JJ

|

JJ

j^|jJ

|

JjJjlly

I

Ex. 48.

-p-T.

t

>

,

r

r

T

-rif

-7 7

Invertthisexample, asbefore.

Also

write itoutin

C

minor.

58.

Observe

thattheinterval of a 7th

draws

" inward,"

and

the

in-terval of the

2nd

" outward," as a rule.

This

statementis correct,

but

notsufficiently explicit.

As

usual, almost everything

depends

upon

the proper resolution of the active (4th) step.

The

whole

matter

may

be

stated thus:

In

theinterval of a 7 th,the lower tone is

a

chord-root,the

upper

tone a chord-seventh.

(When

inverted, as 2nd, the lower tone is, of course, the chord-seventh.)

This

tone,

thechord-seventh,

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 -0 •

a

r

• 7 e 7 a Good.

i

J

J,

J

J .

JLU

..M-J.J.J

,y±,

J-t-J

1

''

rJ'rV

r

r '

r

r

' r r ' r

r

1

^

1 7 a 7 8

v

V

(39)

Par.59.

EXCEPTIONAL

INTERVALS.

27

The

slursagainindicate

where

the

chord remains

the

same, and

thus

account

forthe

apparent

violations of the rule. Invertthisexamplefor

theillustrationof the treatmentofthe interval ofa 2nd.

Do

this,without

fail.

Also

write out

both

versionsin

C

minor.

59.

For

general illustration:

Given

the following

major

melody

:

.-.E

prfm

E§E§

Ex.

so.

^^

1

Itsmanipulation

may

resultthus

:

<* Givenpart,above.

mktiu

i

i

"w^m

Ex.

61.

C

f

t/'r

f

r

r

1

-

J

J

-*

j

-n

i

J

j-i

ijpP^l

^

P

.ivonTWrf KaIaw <^^^

Givenpart,below.

60. Further, in

minor

:

MvV.^t

Jit^

M

m

Ex. 52. v 11

^•—

|

mm

J-Jr^Q

giT^

¥

-TJ"

r

rrfr^r

Note. Thereisnottheslightestevidence that either of thetwo parts,inthese

twoillustrations,wasa" given part." Evidently,theywere conceivedtogether,under

theconstant influence of thetwovitalrequirements,

(1) perfectmelodic formationofeachpart alone,and

(2) goodintervalsatthe points of contact, to ensureharmoniouscooperation.

Invert

both

ofthese examples, withoutfail.

61.

Rule

5,

veryrare. In minor,itisalso possible touse a

(40)

28

ELEMENTARY

COUNTERPOINT.

Par.61.

steps 6

and

7 only.

They

are subject to the usualrules (given in par. 58).

Thus

: Ex. ~~ "

I

Aii'j

hU

\

J

J

j

i'

^

I

-gi-53.

w

EXERCISE

&

Fundamental and

Secondary

Intervals;

Major

and

Minor

Modes.

1. Manipulate Ex. 38andEx. 42again,accordingtothislesson.

2. Also afewofthe given melodiesof Exercise4andExercise5again.

3. Also the followinggiven melodies, according to former directions, and the

roles ofthischapter :

ft

m

w

r

i

r

J

j j

1-^

1 Q O 4.

ftfrr

nr

r

fir

r

^U^hAM^

*=&£

<f77HfrTTgg£

^m

w

r

frrFrr

^

fj

a

a

o

&

e) I

*-±±

-^

zp-

I

g

|

^J

Jl^JD

l

P^Hl

=S=^"c

-<=-'

i

(41)

Par.62. 9.

RHYTHMIC

DIVERSITY.

29

^

S$E

Si

i

«=f

10. Itt

n

, * =i=P=p:

FT*

rm

te

11.

%£H^r

am

2=

s

I* I* ?-

ft

S=p:

«

r

a~~

ira

•-=-12.

i

fc

-J

m

Cpt.

i

k>=

1

e

^

=t

[Asolution ofMelody5 willbe foundintheAppendix.]

4. Also write,as usual, anumberof original melodies with counterpoint,

com-posingthetwoparts together,

likeEx. 52.

CHAPTER

VII.

RHYTHMIC

DIVERSITY.

TWO

NOTES TO A GIVEN

BEAT.

62.

The

rhythm

of the

added

voicedoes not always

correspond

to

thatofthe given melody.

That

is,the counterpoint

may

not only

be

de-vised"note against note "in exactly ornearlysimilar rhythm,as inthe preceding lessons,but

may

runin a

more

rapid

rhythm

of

two

(or

more)

notesto

each

noteofthegiven

melodic

part.

63.

When

this takesplace,

when

two

or

more

notes

accompany

each

givennote,

a necessarydistinctionarises, with reference tothe

relative

importance

oftheseveraltones in

each group

(orbeat);forit is

probablethatnot everysingle

one

ofthe

added

tones

can

be

ofequal

har-monic

significance.

In

making

this distinction,the tonesaredefined asessential

and

Figure

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