Theory and Practice of Musical Composition

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40.M39 1854

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THEORY AND

PRACTICE

MUSICAL COMPOSITION BY

ADOLPH BERNHARD MARX, DOCTOB OF MUSIC, MUSICAL DIBECIOB Or THE tTHITEBSITT OF BERLIN,

ETC.

TRANSLATED FEOM THE THIRD GERMAN EDITION, AND EDITED BY

HEERMAlSr

S.

SAKONI.

FIFTH AMEEIOAN EDJTION,

WITH AN APPENDIX AND NOTES, BY EMILIUS GIEAC, OP THE

CONSERVATORY

OP PARIS.

NEW YOEK: PUBLISHED BY MASON BROTHEES. 23 PARK ROW.

Entered, according to Act of Congress, in the year 1851, by

MASON & LAW, In the Clerk's Offlce of the District Court for the Southern Distiict of

''

New

York.

Entered, according to Act of Congress, in the year 1854,

bf

MASON BROTHERS, In the Clerk's Office of the District Court for the Southern District of

New

York,

PUBLISHERS' ADVERTISEMENT.

A. B.

Marx

holds such high rank in

Gennany

upon

as a writer

the subject of Musical Composition, that any recommendation of his

great

work

to those

who

are at all acquainted with the musical

rature of the land which

be superfluous.

thoroughly

work of

It is

scientific,

is

emphatically the

home

lite-

of music, would

without a rival as a treatise upon this subject,

and yet adapted to popular comprehension.

this character in the English

language has been so

A

much

sought after in vain, as to lead to the present translation, which embraces two books,

Book

Book

I.

viz.

The Elements

II.

of Musical Composition.

The Accompaniment of a given Melody

reference to Chorals

The

:

and

People's Songs.

translation has been

edition,

made from

closely as possible, securing, at the

American student,

pared by the Editor.

with especial

(Volkslied.)

the third improved

and great care has been taken

tion to the

;

to

German

follow the original as

same time, the necessary adapta-

—and an Introduction has

been pre-

Ilxtraot

of a Letter recevoed from JiB.. A. B. Maex, ly the PiibUshers. Berlin, June 23, 1852.

Gentlemen,

Your

my

communication, and the copy of a translation of

polite

work on Mubical Composition, have been received through

*****

Messrs.T- Edwards,

thanks.

Sandford,

&

Co., for

which accept

I find that your translator (as far as I

am

my

warmest

able to judge from

a somewhat imperfect acquaintance with the English language) has done his work very ^jrac&aWy and successfully; and I beg

you to express honored

my

to him, as also to the eminent

work with

their approval,

my

men who have

sincerest thanks,

and

also yourselves to accept the same, for the very elegant style of the edition.

AUTHOR'S PREFACE.

The

true problem of a treatise on

Art may be thus expressed

TJiat it should transmute the most thorough

knowledge of Art into

and immediately

pil,

the consciousness

him

incite

and

and comprehensive

sensibilities

of the pu-

to artistic activity.

Neither abstract knowledge nor technioaHnstruotion can ever secure

artistic culture,

or even prepare the

opposed to the essence of Art

and

;

way

for

it

;

both are

the fault of the old

it is

teachers, as I have elsewhere proved, that they have not risen

above

As

this unartistie

tendency, or been willing to depart from

the achievement of the

vaded mind,

is

artist,

bom' of

his

own

not an abstract thougHt, but an embodied

spirit,

united in as intimate and inseparable a unity as the soul and of man, so

must the

most

and impressive

way

living

to bolder

science of

Art continually

truths,

from which

it

and more joyous achievements.

it.

free, truth-per-

body

strive after the

should lead the Both, however,

should be accompanied with that certainty, reposing on the convictions of experience,

and that ardent

ments and progress, which,

in

characteristics of a true artistic

my

desire for

new

achieve-

opinion, are the conditions

and

life.

This principle, in connection with contemplation on the essence

by observation and artistic activity from an early youth, strengthened by a view of the historical deve-

of Art, matured

period of

lopment of telligent

in

my

art,

and by the growing approbation of the most

and continually enlarging experience,

first

and second

treatises, is still

my

—

law.

in-

this principle, as

That the

inter-

author's preface.

6 change of theory and sence, of traries,

law and

practice, of

though

mated, and

liberty, of

form and es-

formerly, — —may become more

melody and harmony

as

still,

in reality united,

fertile of results,

my

was

principal

aim

called conliving, ani-

in the present

In this view, notwithstanding the gap in the formal, or

work.

rather merely nominal separation of the Elements from their ac-

companiments, I consider

an essential improvement to have

it

placed the further development of passes and harmonic figuration after the

and not before and

all

where they are immediately applied,

choral,

and more copious treatment of the secular melodies,

for the freer

This, however,

where they are not needed.

it,

further improvements are to be tested

by the

intelligence of

the professor, and the experience of teachers and pupils.

I would gladly

ofiFer

to

younger teachers, or to such as have

not yet had opportunity for extensive experience, an intimation of

my

method of teaching

;

certainly not with the presumption of

being able to say any thing

new

or important, but, as a duty, un-

assumingly to impart what I have to others.

however,

is

the insuflSciency of

all

immediate intuition most strongly cates

and only when

;

Precisely here,

writing to supply the place of

Not books, but

felt.

edu-

life,

quickened and wrought on by

life is

can books perform their mightiest and most beneficent namely, to unite the experience and intelligence of

many

life,

office,

lives

;

to

give support and a rallying-point, so that every isolated existence

—always most whole

—may

limited in

its

immediate activity in relation to the

not forever perish

;

that every worker, unadvised

and unquestioned by the mute Past and Present, may not be forced either to begin his task anew, or follow in the gloomy path

of transmitted usage, in order to be not wholly without support.

Often and long enough has the want of this reciprocal action of doctrine and felt.

Even

own

ers attempting with seurs, while their

the least

skill for

able composers

made itself most painfully we been obliged to see teach-

in our artistic science

life

in our

times have

words and books

to

form

own examples proved them composition

who

;

artists or connois-

to

be wanting in

and, on the other hand, there are

venture to neglect,

if

not to treat with dis-

dain, every pedagogic, psychological, or other assistance, even to

own

explain the science of their

are easily recognized prejudice

is

by

The former

execution.

skill in

their deficiency

The

not so the latter.

;

only too widely diffused, that an able or even a dis-

tinguished composer, must of necessity, and without further pains,

be also an able teacher

;

while yet the indispensableness of fur-

ther qualifications in a teacher

is

so easily seen, that pedagogic

science long since offered to explain,

proved, (as in the cases of that artistic ability

W. A.

and experience has often

Mozart and L. V. Beethoven,)

and the capacity

to teach are not so often or

may

so necessarily united, that the one

The teacher

the greatness of the other.

be safely inferred from should, indeed, possess

—should

the cultivation, the spirit, and the soul of an artist,

himself an

artist,

—

but, besides this,

he should not be wanting

be in

the full vocation, the dexterity, the experience, and the capacity

of the pedagogue.

found or attained,

Seldom

as this many-sided fitness

make us

reflection will not fail to

either

is

confess

its

necessity.

My the

method of

first

teaching, both in theory and practice, has from

verbal instruction only so

much

is

to acquaint the scholar with the

him

Of pure

been directed in conformity with these views. at first premised as

method of

to the point of artistic effort.

From

his teacher, perceives

what

While the scholar who to observe

and what

is

less gifted

—

will

its

to miss in the

—thus pre-

almost of themselves grasp

the next necessary, or next possible point, or understand

The

out diflaculty from the course of lectures.

kept from the beginning in his future

life.

artistic activity,

The teacher

peculiar

familiar with

form of the tune, the more able and diligent scholars pared among the

of notes,

first series

(the major diatonic scale,) the instruction assumes

and permanent character.

and direct

instruction,

the

necessary

is

—

in the

also remains fresh

with-

it

scholar

thus

is

atmosphere of

and

active,

has no longer cause, either in his work or his meditations, to

and fear'

the old disheartening dissension between Art and Science.

With

single scholars, or even with

teacher's side,

two or more, who

and watch the movements of

his pen, or

sit

at the

who

often

8

author's preface.

unexpectedly take the pen into their own hands,-^-to

must give

teacher

advice, or instruct

a work already begun

;

how

instruction has

—

sooner he

is

—the

more

pecially in the greater tasks of the

corrected at leisure, thus enabling

him

may

be taken up and

at once to perceive the

discrepancy of his error with some part of his work.

where

individuality

and

tion give the last decision in the it

its

my

scholar, es-

fugue and sonata forms, pro-

vided they have but one tenable position,

He

of

—the

successful, in

The mistakes of the

opinion, is the teacher's work.

not hold

fertile

anticipate the teacher,

able of himself to discover an explanation or an ex-

pedient-^to accelerate his progress

science,

the

for all these purposes this sys-

been proved most agreeable and

The more the scholar can

results.

whom

to proceed with

to explain, to improve, or to avoid

such and such a dubious point,

tem of

them how

subjective sensation

moment

In

artistic

and

voli-

of artistic creation, I do

advisable that the scholar should wholly avoid errors.

should be thoroughly tried and tested, and have opportunity

to conquer himself

progress

;

by

his

own

might.

A vanquished

error is a

an error merely suppressed threatens a return.

TABLE OF CONTENTS. MUSICAL NOTATION". PAOa IHTRODUCTIOK

.

.

15

PAKT FIRST.—TONES AND NOTES. Chaptee Chaptee Chapter Chapter Chapter Chapter Chapter Chapter

II.

The Tone System The Note System

III.

Abbreviations and other accidental Characters in Music

IV.

Elevation and Depression

V.

The Measuring of Tone- relations The Tone Species, Sexes, or Modes The Keys

I.

VI. VII.

VIII. Relation of

18 19

Keys

.

.

.

24 38

.

.36

.... .... .

41

44 46

BOOK FIRST. ELEMENTS OF MtTSICAL COMPOSITION. PART FIRST.—COMPOSITION FOR SINGLE PARTS (MONOPHONIC COMPOSITION), Chapter

ulation,

:

;

3.

II.

;

III.

Retrospection, 59.

Invention of Monophonic Phrases, 61;

Formation of Passages, 63

Chapter

;

;

ation of the Tone-chain, 66

Chapter

63.

The first Formations 1. The Tone-chain, with its Species, 63 ; Tone Reg54 The Major Scale, ih. Analysis of the Scale, 66 3. Rhythmical form-

I.

;

Discovery of New

1.

The Design and

Formation of Phrases, 64 Means, 67.

3.

;

4.

its

Efficacy, iS.^

Periods, 66.

PART SECOND.—COMPOSITION FOR TWO PARTS CDUOPHONIC COMPOSITION). Chapter Chapter

I.

II.

The Duophonic Composition, derived from the Monophonic, 73. The Duophonic Composition, derived from Natural Harmony, 74 77; Melodic Application,

ner of arriving at

it, ii.

Application,

Harmonic Designs, 78

dence,

Chapter

ib.

;

3.

;

3. Application,

;

ib.

III.

The Duophonic Composition,

81.

4.

The Cadmce,

79

;

6.

ii.

;

I. ManHarmonic

The

;

Half-Ca-

10

TABLE OF COin^KTS;

Chapter IV.

Compositions of two and three parts, 84

Retrospection, 87

;

Compo^

;

tiona of threo parts, 89.

The Double Duophonic

Chapter V.

Composition, 90

PART THIKD.—HARMONY OF

Application, 93.

;

THE.

MAJOR

SCALE.

Chapter I. Discovery of the necessary Harmonies, 94, Chapter H. Examination and Justification of the Harmony, 99 A. The Four Voices*, ifi. ; B. The Connection of Chords, 100; C. Harmonic Besi^ns^ ib: ;~ D. Faulty Pro-;

gressions, 101;

1.

Octave Succession (Consecutive Octaves),

Succession (Consecutive Fifths), 102 of the Dominant, 105.

;

E.

ib.

The Dominant Chord,

2.

;

103

Quint or Fifth F.

;

The Triad

Chapter TIL The Accompaniment of given Melodies, 107 j A. Limitation to those means which were found in the Ascending Scale, ib.] B. The Descending Scale, 109.

PART FOXJRTH.—THE FREER USE OF THE CHORDS IN OUR POSSESSION,

113.

I. Harmonic Designs, 114 A. Development of a Single Chord, ib. ; H, Combination of Major Triads, 115 1. Designs of Nearest Connection, ib. 3. Designs Of Remote Connection, ib. C. The Combination of Minor Triads, and of Minor and Major Triads, 116 D. Harmonic Designs froiA adding the Dominant Chords 117; 1. The Dominant Chord preparing the end, ib. 2. Other Chords in connection with the Dominant Chord, 118; E. Extension of the Harmonic Designs by means of Rhythm, 118 F. Formation of Harmonic Passages or Sequences, 119 Prelude, 120. Chapter II. Freer Harmonization of given Melodies, 122 A. Freer use of Triads B. Free introduction of the Donunant Chord, 125 ib. Freer Treatment of the Dominant Chord, 127 Doubling of intervals in the Dominant Chord, 128 Covered

Chapter

;

;

;

;

;

;

;

;

;

;

;

;

Octaves and Fifths,

;

129.

PART FIFTH.—INVERSION OF CHORDS, Chapter Chapter

I.

II.

Enumeration and Appellation of the Inversions, 132 Free use of the Inversions, 136

New

A.

;

131.

;

Figuring, 134.

Designs and Passages,

B. Combination of Inversions with Fundamental Chords, 133

;

C. Preludes

t&.

and Final

Cadences, 140; D, Avoiding faulty progressions, 141; E. The Diminished Triads, Chapter III. Employment of Inversions, &c., 143. Chapter IV. Close and dispersed Harmony, 144 Retrospection Modulation, 147

ib.

—

;

PART SIXTH.— HAHMONT OF THE MINOR SCALE. Chapter Chapter

I.

II.

Formation of the Minor Scale, 149. Harmonization of the Minor Scale, 151

;

Nona-Chord (Chord of the

Ninth), 152.

Chapter HI. Nona-Chord, ished Septime Chord,

continVfed,

Chapter IV. Freer use of the Melodies,

i5.

;

3.

154; Inversions of the Nona-Chord, 155

163

;

2.

Dimin-

New

Chords, 157

;

1.

Major Melodies, 158

;

3.

Minor

Licenses of the Dominant Chord, 160.

PART SEVENTH.—MODULATION INTO FOREIGN KEYS, Chapter

;

ib.

161.

Modulation from one Key into another, 162 1. The Dominant Chord, The Nona-Chords, 168 3. The Septime Chord, ib. ; 4. The Diminished

I.

;

;

TABLE OF CONTENTS. Septimo Chord, 169;

The Minor

7.

Cmaftek

5.

The Diminished

tft.

;

6.

The Dominant

Triad, 170

;

Triad, 171.

new means

Introduction of

II.

Triad,

11

Ascertainment of Digressive Melody, ternal Characteristics, 174

;

to the Harmonization of Melodies, 173 ib.

1.

;

External Characteristics,

B. Discovery of all eligihle Chords, 175

;

t£.

;

2.

;

A. In

C. Application

of these means to Indigenous or Digressive Melodies, 177.

Chapter

III.

Formation of new passages with the aid of Foreign Chords, 186 1. Pas2. Indigenous Passage, 190 3. Successions of Nona;

sages of Dominant Chords, 189

Chords, 191;

4.

;

;

Indigenous Passage of Nona-Chords, 192

Septime Chords, 192. Chapter IV. Variable modulations, 196 B.

The Dominant Chord,

A.

;

;

5.

Successions of derived

The Diminished

Septime. Chord,

ib.

;

199.

Chapter V. General Order of Construction, 201 A. The first perfect Construction of a two-part Composition, ib, ; B. Second two-part Construction, 303 C. Further ex;

;

tension of Modulation, 304

The

D.

;

Interrupted Cadence, 305.

Chapter VI. Abrhpt Modulation, 207. Chapter VII. Order of Modulation for more extended Compositions,

21Ij Passages of

Phrases, 313.

Chapter VIII. The Pedal-point, Chapter IX. Hetrospection, 220

215. ;

A. Development of Harmony,

ib.

PART EIGHTH. -DISPLACEMENT OF CHORDS,

228.

Chapter I. Suspensions from above, 228 Suspensions of fundamental Tones, 334. Chapter II. Suspensions from below, 236 A means of Connection, 238 Fifths niiti gated by Suspensions, 244 Octaves covered by Suspensions, 245. Chapter III. Anticipated Tones, 346. ;

;

;

;

PART NINTH.—THE Chapter Chapter B.

The

Chapter

The

I.

PASS,

248.

Diatonic Pass, 249 Participant Tone, 360. Chromatic Passes and Assistant-tones, 263; A. The Chromatic

II.

;

Pass,

I'A.

Assistant-tone, 256.

The

III.

results of Passes, 358

The Superfluous

;

Triad, 260.

PART TENTH.—THE TREATMENT OF MORE OR LESS THAN" FOUR VOICES, Chapter Chapter tion,

ib.

I.^

II. ;

266.

Triphonic, Duophonic, and Monophonic Compositions, 366.

More-than-tetraphonic Compositions, 271; A.

B.

The

The Polyphonic Composi-

Double-choired, or Poly-choired Composition, 376.

BOOK SECOND. THE ACCOMPANIMENT OF GIVEN MELODIES. iNTRODUCTIOIf, 381.

PART FIRST.—THE ACCOMPANIMENT OF THE CHORAL, 283. Chapter

I.

General Conception of the Melody, 285

the principal points of Modulation,

Chapter

It.

Disposition of the

ib.

;

Harmony,

B.

;

A. Confirmation of the Key and of Cadences, 390.

Summary

297.

TABLE OF CONTENTS.

12

Chapter III. Simple treatment of the Choral, 305. Chapteu IV. Higher treatment of the Choral, 310 B. Application to the Choral, 314 tion,

ib.

B. Fhrase-repetition,

;

ib.

;

;

1.

;

Technical

A. Character of the Toicei, 311 Difficulties, 318

;

aim of Choral treatment,

3. Artistic

j

A. Tone-repeti310.

Chapter V. The Canlus Firmua in other Voices, 831 A. The Cantus Firmua in the Alto, 322 B. The Cantus Firmus in the Tenor, 333 G. The Cantus Firmus in the ;

;

;

Bass, 334.

Chapter VI. More and

less

than four Voices,

less

treatment, 328

;

voiced treatment of the Choral, 327 1.

i6. j

The Duophonic

treatment,

The Choral with more than four Voices,

B.

A. The Choral with

;

ii.

;

2.

The fTriphonio

330.

How to acquire facility in the Harmonization of the Choral,

331.

PART SECOND.—CHORALS IN THK ECCLESIASTICAL KEYS,

338.

Chapter VII.

r.HAPTER

monic

The

I.

Point, 342

foreign Tones,

A. The Melodic Point, a.; B. The HarC. The Essential Tones of every Key, 344 D. Admissibility ot £. Transposition and Signature, i&. F. Modulation into other

Ecclesiastical Keys, 341;

;

;

ib.

;

;

Keys, 346.

Chapter Chapter Chapter Chapter Chapter Chapter

The Ionian Key, 34T. The Mixolydian Key, 349. IV. The Dorian Key, 350. V. The aiolian Key, 352. VI. The Phrygian Key, 354. VIL The Lydian Key, 35S. II.

IIL

PART THIRD.—THE SECULAR NATIONAL SONG, Chapter ib,

2.

;

General Conception of the Melody, SdO

I.

Character of Keys,

;

1.

358.

Consideration of Voice-region,

ib.

Chapter II. Plan of the Harmony, 381; 1. The Measure or the Quantity of the Harmony, ib. 2. Number of accompanying Voices, 364 ; 3. The Form of the Harmony, 366. Chapter III. Harmonic Figuration, 367 Discovery of its Designs, t&. ;1. Monophonic Designs, ib. 3. Duophonic and Polyphonic Designs, 363. Chapter IV. Execution of the Harmonic Figuration, 370 ; A. The Harmonic Point of 1. Retarded Resolution, ib. ; 3. Octave and Quint-Succession, 371; View, ib. B. The Melodic Point of View, ib. 1. Consistency of Execu3. Passing-tones, 373 2. Firm Connection, ib. tion, 373 Chapter V. The Exercise of Harmonic Figuration in Passages and given Melodies, 375 1. Passages rediiced to Harmonic Figuration, t&. ; 2. Accompaniment of given ;

;

;

;

;

;

I

;

Melodies, 377.

Chapter VI. Passing-Tone and Bye-Tone, 379 382

;

;

Help Tones,

381; Trills, Turns,

8ic.,

Passing or Transient Chords, 384.

Chapter VII. Introduction of Passes and Help-tones into Figuration, 385 A. FiguraB. Figuration of the Bass, 387 C. Figuration of a tion of the Upper Voice, ib. ;

;

;

Middle Voice, 389

Chapter

;

Application, 390.

VIII. Application of these

means

to Artistic

APPBITDIX, The Figural

Prelude, 401.

Accompaniments,

392.

ELEMENTS OE MUSICAL NOTATION. Br THE

TRANSLATOB.

PREFACE TO THE ELEMENTARY PART.

The

indefiniteness of the English language, in everything

concerning Music, makes

it

a task of extreme

difficulty to

write an Elementary Treatise, corresponding to a theoretical

work of any

foreign,

and particularly German author.

German musicians have made Music that

is

it

absolutely impossible to do

lating their

The

so thorough a study,

them

justice in trans-

works with general terms, which at every step

are subject to modifications and contradictions. It is this consideration

of this tise,

work

which has induced the Translator

to prepare the student

the chief object of which

such terms as

may

by an Elementary Trea-

is to

give exact definitions of

occur in this or other works of the same

author, and the exact meaning of which

it is

absolutely ne-

cessary for the student to know.

In order to avoid the introduction of indefinite terms, or

arguments upon them, as much as possible, the Translator has thought

it

best to convey the necessary information in regu-

lar didactic

form ; and

if

comparisons and arguments cannot

be absolutely avoided, they will be possible.

made

at least as brief as

INTRODUCTION.

" Music ear,"

is

is

the art of combining sounds agreeable to tbe

the general definition given of the word.

Not every sound, however agreeable cal sound

;

nor

It follows, then, that

sic.

to the ear, is a musi-

a combination of such sounds always

is

our

first

Mu-

task must be to distin-

guish musical sounds, or sounds agreeable to the ear, from

such sounds as constitute Music.

We know that the afiected

by Music.

ear

is

the organ which

Every vibration of means,

lision of bodies, or other

air

is

most directly

caused by a col-

sufficient to affect the ear,

we designate by the general name of

SOUND.

We

know,

also, that

voice, as well as

Music

is

produced by the human

by instruments of various kinds

—

Flutes,

These instruments distinguish

Trumpets, Violins, &c.

themselves from each other by the quality of their sounds. Finally,

we

perceive on one and the same instrument, that

the sounds produced upon

it

vary in regard to pitch.

Thus,

for instance, are the sounds produced on the shorter strings

of a

Harp more

string. call it

When we

acute than those produced on a longer consider a sound in this respect,

we must

16

TONE.

We

have, therefore,

many

the longer or thicker strings are called low shorter or thinner strings are called high. voices,

The

different tones. ;

tones of

those of the

Thus of human

we say that the tones of a man's voice, in general,

are lower than those of a boy's or girl's voice

the Flute, Violin, Trumpet,

we

;

the tones of

say, are higher than those

of the Bassoon, Double-bass, and Horn.

We

say " in ge-

neral ;" for since every voice and every instrument can pro-

duce many tones,

man's

it

can occur that the highest tones of a

voice, for instance, are higher than the lowest tones

of a girl's voice, &c.

Every tone or sound

to

be produced, must be produced

within a certain time, therefore must

fill

a certain space of

time,—^a longer or shorter space, definite or indefinite.

This time, or space of time, accorded to a tone or sound,

is

called its

DURATION.

We

say, therefore, of a tone

:

it

has a definite or inde

finite duration.

If

we cause

the gradual production of a series of tones or

sounds of certain duration, according to some regulating law, in any fixed and continued, i.e. repeated, time-mo-

ments, we call this regulation of time-succession,

RHYTHM. Where such regulation

does not take place, the tones have

either

no certain duration, or follow in no regular succes-

sion

we say

A

;

that such tone-succession

succession of toneS; which

is

is

unrhythmical.

formed according

to

any

17 particular plan, and at the

same time rhythmically regulated,

(whether agreeably, expressively, &c., or not,)

is

called a

MELODY.*

A piece of is

Music can

consist of a single tone-series,

—

it

then called

Monophonic,

Or

it

one voice.)

(for

can consist of two, three, four, or more, simulta-

neously progressing tone-series

Duophonic Tetraphonic

(for (for

two voices)

then called

Triphonic (for three voices)

;

four voices)

it is

;

or Polyphonic (for

;

many

voices.)

Each

series of tones, however,

upon some instrument,

is

called

a

TOICE The simultaneously-meeting

whether sung or produced

.

tones of different voices

must

stand to each other in some reasonable, corresponding relation.

This relation

is

called

HARMONY And

of all these essentials

:

.

tones and sounds, tone-suc-

cession and rhythm, melody and harmony, does

MUSIC consist.

*

A mve concise definition of Melody will be given at a later porioc'.

FIRST PAET.

TONES AND NOTES. CHAPTEE

I.

THE TONE SYSTEM. Tone

is

a sound of certain height or depth, (pitch.)

We know

already that there are

of the various tone-gradations

Music, however, not

A

of.

all

is

many

tones

;

the mass

absolutely innumerable.

these tone-gradations are

In

made use

part merely of these tones are actually and fixedly

employed.

These tones constitute what

is

called the

TONE SYSTEM. This tone-system contains above one hundred tones.

would have occasioned much

name

for each of

them

;

and

classification of these tones

difficulty to fix

this

It

a particular

has been the cause of the

under seven

DEGREES. These degrees have been named

C—D—E— F—G— A—B. And

all tones

them.

have one of these names, or one derived from

CHAPTEE

II.

THE NOTE SYSTEM. For

the designation of tones,

we make use

of a series of

characters, called

NOTES. It

would be tedious for us

eical Notation.

We

Mu-

must content ourselves with communi-

cating the facts, that after five lines

to enter into the history of

many changes and

modifications,

have been fixed upon, on which, or between which,

the tones are indicated

by open or

filled circles,

or ovals, ac-

cording to their pitch and duration. 1.

Where

these five lines are not sufiBcient, additional lines,

called

LEGER LINES are introduced, which, not being continuous, are easily distinguished from the lines of the stave.

2.

Here

^=1=1=4

^

-

4 j 4

w« have introduced

the leger lines, in order to designate

20 those high or low tones, which are above the highest or the

lowest tones capable of being designated within the stave.

We

might now read and write

all

we

notes, if

what meaning to attach to any particular note. words,

we must

sponding

to

fix

only

knew

In other

upon some point, or some note corre-

a certain tone, by which we can be guided in the

designation of the others.

For

this

purpose we have certain characters, called

CtEF s, Of such clefs

which indicate the tone represented by them. there are three in use

The

G-clef, or Treble-clef

The

C-clef,

The

F-clef, or Bass-clef.

1.

has this form,

:

—THE

;

and

G-CLEF

fc

and indicates that upon the the tonei g, (the lowest

g

line inclosed

by

lower circle,

its

of the Oboe, or the fourth

/f

of a

six-octave Piano-forte, counting from the left to the right,) shall be represented.

French composers of former times,

placed this clef upon the it

first line

of the stave, thus

imperative to consider the note upon

tive of the tone g.

At

it

making

as the representa-

present the G-clef

is

invariably

placed upon the second line of the stave, and the notes pre-

ceded by

il

it

would accordingly be named thus

s^s gab

:

m

FGAB CDEFGAB CDEFG

21

By means many

of additional leger-lines,

upon

additional tones

this stave

we migtt

;

designate

but since the read-

ing of such notes would be a very troublesome task, another

character has been invented, in the shape of a wave, or dotted line

:

8-

which, with the figure 8 before

indicates that the passage thus

sung an octave higher than

The

and the

it,

it is

marked

succeeding

it,

to be played or

written-

leger lines below the stave can be avoided, if neces-

by substituting another cM.

sary,

is

S

More of

this,

however,

anon.

THE C-CLEF,

2Its

most usual form

fold one.

is

Indicatiag the tone

A,

B

* A

and

:,

'(jj^)

upon the

names of the notes succeeding

'

,

use

its

it is

is

a

three-

used

as Soprano-clef;

in which case it is placed

the

this

first line it

of the stave, and

are fixed accordingly

DEFGAB CDEFGABC

B

B, as Alto- clef.

As such

it is

placed upon the third line of the stave, and

the notes succeeding

,jmm.

it

are called

:

^^B

3 V

-iD

z E

^ «

^ =

CDEFGAB CDE

22 C, as Tenor-clef.

As

sueli it IS

placed apbn the fourth line of the stave, and

the notes succeeding

it

are called

^

:

.^wi-it^

6."

m

1^

A It is

m CDEFGAB DEFGAB

^-f?

B

hardly necessary to add, that additional leger-lines

can be employed in the C-clef, as

3 It

.

—T HE

-well as in the

G or i^-clef.

F-CLEF.

has generally this ^f;, or some other similar form,

and indicates the tone

exclusively

f$

upon the fourth

.

line of the stave,

to the notes succeeding it the following

now placed

It is

names

and thus gives :

23 8.

3: The above appear 6hus

^

=£

passage, if written in the Treble-clef, would

CHAPTEE m. ABBBETEATIONS AOT) OTHER ACCrDEIITAL CHAEACTEES rw MUSIC.

We

have already mentioned the character which trans-

The same

poses a tone-series to the octave above. ter is

charac-

used for the transposition of a passage into a lower ocIn such case the wave-line

tave.

to be transposed.

is

placed below the notes

For single notes the

figure

8 will be

suffi-

cient.

A

similar facilitation consists in

employing the words

alV-ott«va, or aZZ'S^*, which, if placed above the notes, indicates that the higher octave is to be added to the notes

thus marked intended.

m

;

if

Thus

placed below the notes, the lower octave ia the following passages.

12.

:c

m

:•:

$

-$

might be expressed in

this

manner : all'Sva.

m

13.

all'Sya.

,

m

fcti:

25

Other abbreviations,

like alia

3za

(ter^£), alia

6S

{sista),

&c., will need no further explanation. Finally, there are certain characters intended to save the

notation of a passage partly. If a passage is to be repeated two, three, or four timeSj it

written but once, and the words

is

his,

are placed above to

it.

— —quater, ter,

In addition to the above, the passages

be repeated are often inclosed by curves, or dots

n

X4.^

:

26 If a passage

is

to be repeated, the

end of which expe-

riences an alteration in its repeat, the part to be altered is

enclosed by a curve, and the words

placed above

marked

volta), are

In the repetition of such part, the passage

it.

1^ is omitted, and the player has to pass on beyond

the repeat, where the words to guide

1= (prima

him.

2S

(seconda), should be placed

The words prima

volta,

and seconda

volta,

stand here for 1st and 2d, time, and thus explain the mystery.

The words Da similar meaning,

capo, (D. i. e.,

"

C,

or

B. c,

or d.

c.,)

have a

to repeat."

If the repetition goes merely to a certain point, where the piece

is to

be ended, the point

is

marked by the word

Fine, (end,)

and

is

for the sake of clearness

a pause

placed above the end note

;

:

and instead of the simple

D. C, the words D. C. aljine (from the commencement

to

the end), are placed at the point where the repetition is to

take place. If the repetition is to begin at a certain point in the dle of the piece, that point is

and instead of sign, are used.

d.

mid-

marked thus

c, the words

d. s., (dal segno,)

from the

27

There are in use facilitation,

still

we might

more characters of abbreviation and

say,

but these not being absolutely ne-

cessary for our immediate purpose, vre shall give their meaning -ffhen they occur.

CHAPTER

IV.

ELEVATION Aim) DEPEESSION.

When we

compare our notes and tones, as far as we know

them at present, with the key-board of a Piano-forte, we find that

we do not know yet

the tones of our system,

all

and that consequently we cannot represent them by notes.

We have

reference to the upper keys, or black keys of the

Piano-forte.

We

have permitted

this

pleteness, in order to obtain a basis sily arrive at the

Our

wanting tones and characters.

tones, thus far, if succeeding each other in regular

rotation, are

by no means equidistant from each

Beginning from

c,

for instance,

we

between the two, however, there

The same a and

A

temporary incom-

from which we can ea-

relation exists

other.

arrive at the next tone is

room

d;

for another tone.

between d and c,/ and g,

g and a,

b.

diagram of these relations

achieving our object. c as the first tone its octave, will

;

will

We have here

aid us materially in

accidentally mentioned

and on examination the

series

from c to

be found so satisfactory to the ear, that we

shall adopt it at once as the

normal tone-series for our ana-

lysis, being, in addition to

the above, the only one of the

seven tone-series at present within our reach, which pletely satisfactory.

Here, then,

possible intermediate tones are

is

is

com-

a diagram in which the

marked by a mere

dot, for

29

we have no other means

the simple reason that, at present,

of designating them

C—d—ef—g—a—b

We

repeat, again, that this succession of tones ;

we

c to the other,

der, or to use

for

will call the

perfectly it

were,

whole diagram a lad-

a technical expression derived from the Latin

" Ladder,"

(^scala,)

we

will call it

A SCALE

.

Having once adopted the term " scale," that

is

and since we ascend, as

satisfactory to the ear

from one

word

c

we should

call the

it is

but natural

intermediate tones

DEGREES, and the distances from tone to

tone, or

from degree to de-

gree,

STEPS When we now

compare the

.

different steps,

we

find that

those admitting of an intermediate tone are larger, must be larger, than those

tone.

We

which do not admit of an intermediate

will distinguish these different species of steps

by the terms " whole steps," or " steps," and " half steps."

We find, further,

that our scale contains five steps, and

two half steps, distributed in such a manner, that from the first to

the second, from the second to the third, from the

fourth to the fifth, from the fifth to the sixth, and from the sixth to the seventh degree, are steps to the fourth,

and from the seventh

half steps, as in the following diagram 1

16, c

;

:

—e-f—g—a— 1

d

i

1

and from the third

to the eighth degree, are

1

1

J

h-c.

30

We

stated In a former paragraph that ottr taking c as the

basis of a scale,

We will

was merely accidental.

remember

that a succession of tones, in order to be a scale, must be a

regular succession, in which the steps and half steps are

And now we

distributed according to the above diagram. will

attempt to form a scale from any other tone.

We

take

accidental

;

g-,

which the student

may

again consider merely

the reason, whereof, however, will soon become

The regular

apparent to him.

when we take the degrees,

g—a,

succession

as they follow from

6, c, d,

e,/,

g

;

attended to

is

g

to g, thus

:

or thus,

,17.

i but on striking these notes on the Piano, and comparing them with our last diagram (No. 16), we soon discover that the steps

from the sixth to the seventh, and from the seventh to

The

the eighth degree, are different from our diagram.

and

g

are correct, but

the/

is

/ degree is necessary to make And now we we could

find

it

our scale complete.

There

the very tone

original/",

we

we need

being absolutely indis-

new tone upon

this

from the

is

The/ degree

g-.

we place

distinguish

e

Yet the

return to those intermediate tones, for which

no name.

between the/ and pensable,

we want.

not what

it

;

and

place this

in order to

mark

# before

it.

This character

is

called a

" sharp," and conveys

the idea, that the tone before the representative of which

it

31 is

as

placed, has been it

made more

sharpened,

acute, elevated

were.

The

scale of

G, with

amendment, would present the

this

following appearance

18.

i It is

now a

C in

the scale of It is

correct scale in every particular, differing from

but one point, that of pitch.

time now to give the reasons for taking the tone

experiment upon.

The student

the fifth tone of our ori-

ginal scale, and in taking again the fifth tone of our scale, d,

one more sharp will be

the scale of

dent

may

to

will perceive that one tone

G was

only required an alteration.

g

all that is requisite to

D correspond with that of

Thus

G.

new

make

the stu-

pursue his course, adding sharp to sharp, while we

begin at a different point, probably to meet him at some point where

We

sion.

we can

explain his doubts, or remove his indeci-

have simply

to add, that in the course of his la-

bors, if he pursues the plan

we

indicated,

suming his task from the fifth tone of the

i.

e.,

always re-

last scale, he will

soon discover tones which are not in our original scale;

but in following the above directions, he cannot

fail in

com-

pleting his scale.

We

have succeeded so well in constructing a scale up-

on g, the

fifth

tone above

c,

that

we are warranted by

at least, in attempting the formation of a scale fifth

tone below

it,

upon f, the

c.

Let us again write our degrees in regular succession, beginning

with^

32

19. rf;

^

J

J

r

Comparing the steps of

gram No. 16, we

f-r^

this tone-succession

with our dia-

find that while in the scale of

by

the seventh tone which required being replaced it is

now

the fourth tone which

demands a

we must

bear again in mind, that

from the original

h,

we

was

We

preserve the regular sue

course to the intermediate tone below it

it

another,

modification.

cession of the degrees, and b being too high,

tinguish

G,

it,

we have

and in order

re-

to dis-

place a

b before

This character

it.

is

called a

"

flat,"

and conveys

the idea, that the tone before the representative of which is

placed has been lowered, depressed—^aWewed, as

With

it

pearance

the scale of

F would

it

it

were.

present the following ap-

:

20.

m

*=

The elevated tones have

the word

as/ sharp, g sharp, &c. The depressed tones have them, as h

Taking

flat,

fifth

a

flat,

above

g the

" sharp"

afiSxed to

name "flat"

affixed

C, fifth

fifth

tone to construct our scales upon,

G,D,^,E,B,Fi, below

to

&c.

would give us the scales of

Taking

them,

fifth,

Cit,&c.

would give us the scales of

C,F,Bi>,E\>,Jl\>,Di,

Gk

33

That some of these

scales should be alike in sound, yet

different in appearance,

we know when

Enough

need not trouble us.

to use the one or the other,

that

and enough to

remember that we issued from the same point

two

in

differ-

ent directions, and that our impulse has carried us over

ground previously gone over from the other point.

ai.

il

FfaT.

iFLaTi

§FILOTini3

.l.fHfiilSI'.i

In order to avoid the unnecessary accumulation of characters in the notation of

a piece of music, the sharps or

flats

incident to the scale or key in which a composition has been written, are merely placed at the beginning of the piece, or

at the beginning of each stave, and are called the signature

of a scale or key.

by

This signature

certain characters, (of which

until another signature occurs.

of music, flats its

fied.

we have then

to

is

we

valid until shall

it is

recalled

speak directly,) or

During the course of a piece

remember how many sharps or

key requires, and what tones have been thus modi-

34

The

fact of there being in existence incidental flats

and

sharps, leads us to suppose that there are also accidental

sic,

These occur in almost every piece of mu-

and sharps.

flats

and

piece

is

arise

when the composer leaves the key in •which the

written, either temporarily or permanently, without

changing the signature, or when a tone of a foreign scale introduced without afiecting the regular key. the sharp or

good imtil

flat is

it is

is

In such case

always placed before the tone, and holds

recalled

—

i. e,',

until the modified tone ia re-

placed by the original one, or until the end of the measure ia

which the accidental occurs.

The

neutralizing a sharp or flat is called this

character used for

a " natural," and has

form H

It is placed before the note to

be neutralized, and holds

good to the end of the measure* in which

There are

also instances in

or depression of a tone

point of pitch.

is

it

occurs.

which the incident elevation

not sufficient to reach the desired

Double sharps (X) and double

have been introduced in such cases.

flats,

The former

elevates

the tone an additional half step, the latter depresses the same ratio. tural

(tlfc^)

is

We need hardly naention that

{hh,)

it

in

a double na-

required to neutralize the efiect of either.

If the intermediate tones of

which we have spoken, can

occur in the course of a composition, they can also occur in

a scale.

Here

* The word measure signifies a musical division marked by perpendicular " bars." More of thi» in the chapter on Rhythm.

lines, called

35

22.

^^^^^^^^p^^m is

the scale of C, with all

its

intermediate tones.

We have

written the ascending scale with sharps, and the descending scale with flats, in order to avoid the introduction of natu-

A better

rals.

reason for

it,

however, will be given in the

" Theory of Music."

A

scale, in

which the intermediate tones are introduced,

called a

is

Chromatic Scale. In contradistinction to

it

the original scale

is

called the

Diatonic Scale.

Tones which c

l"

,

ct

and d

differ in

b ,

cI

name but not

Enharmomc, More

in sound, like 6

and/, &c., are called

cf this hereafter.

and

CHAPTBE

V.

THE MEASUEING OP TONE-EELATIOKS. Since Music

know

is

a combination of tones,

it is

necessary to

the relations of these tones to each other.

We

can designate

one tone

is

it

superficially,

higher than another, for instance,

higher than the d of the same octave.

above each tone there are statement

is

by merely stating that

But

many lower and

^

or a

since under

is

and

higher ones, this

by no means as exact as we should

desire

it.

Counting the degrees would be already much more exact. Beginning from any one which we call the

next above

it

call the first degree,

the Latin numerals are used for this purpose

and English names.

Frequently

the second, third, &c.

they will occur even in our work,

we

will give

we

;

and since

both the Latin

There are then

The first degree, or First, or Prima. " Second, or Secunda. The second " Third, The third, or Tertia. " Fourth, or Qunrta. The fourth, " Fifth, The fifth, or Quinta. " Sixth, The sixth, or Sexta. " Seventh, op Septima. The seventh,

— — — — — —

And

in

some .instances

Thus we have

it is

necessary to go even further.

37

The eighth The ninth The tenth

degree,

" Ninth,

or

degree,

" Tenth,

or Decima.

The

degree,

" Eleventh,

or Undecima.

degree,

" Twelfth,

or Duodecima.

degree,

" Thirteenth, or

degree,

" Fourteenth, or Decima quarta.

degree, or Octave,

eleventh

The twelfth The thirteenth The fourteenth

We perceive

Nona.

Decima

tertia.

at once that Octave, Nintli, Tenth, &c., are

nothing but the

second, third, and fourth degree, in a

first,

higher octave. that there

or Octava.

Yet, at a later period^ we shall discover

a difference, sometimes, between these degrees.

is

When we now spective pitch,

This relation

compare two tones

we place them

is

in regard to their re-

in a relation to each other.

called

INTERVAL.

We

G

and

But even

know

^X,

this designation is not sufficiently exact, for

we

that each of our degrees embraces j/?De different tones.

Which mand,

C and D form together the interval of D the interval of a fifth, &c.

say, therefore,

a second,

of those five

is

now

in reality intended ?

for instance, the fifth of C, it

or ^1"

,

or g^^.

They

all

from C, and consequently are

If

may be g,ov

stand upon the

fifth

we deg'i

,

or

degree

all fifths.

We require, therefore, a more exact tone-measure, and for it

we take

the smallest measures of our tone-system, the

HALF-STEP, and the

STEP.

We

are

now enabled

tone-relations of

the steps and

to give

any possible

an exact statement of the

interval,

by merely counting

half-steps therein contained.

Thus the second

38 d, for instance, contains

c

d and

or c c

b

(i b

—

d and d

and

dit

But

— it

e,

—

d"

.

two half-steps,

The

third c

— —

e

or four half-steps, c

c

—

cS

and

c4

—

d,

contains two steps,

cS

,

cI

—

d,

rf

d

it

e.

would be too troublesome always to give the exact

measure of an interval in so many steps and half-steps, and have been distinguished four classes of

for this reason there intervals,

which in themselves at once express the exact

measure of the

Each

relation.

interval can be

Major, or Minor, or Diminished, or Superfluous.

Each minor

interval arises

jor one, or in other words,

same major

it is

a half-step smaller than the

interval.

Each diminished minor

from the diminution of a ma-

interval, or

interval is a half-step smaller than the

two half-steps smaller than the same ma-

jor interval.

Each superfluous

interval is a half-step larger than the

major interval.

When we

once know, therefore,

tervals are, it will be easy to

ished, or superfluous intervals. tion of the

major intervals

how

make

of

And

large the major in-

them minor, diminthe best representa-

is

ouK SCALE itself; for each tone in interval.

it

forms with the fundamental tone a major

Consequently

39 c

d

is

a major second,

c

e

"

a major

c—f c g c

a " a major sixth,

c

b "

c

a major seTenth,

— " —d "

c

an

c

The major second

— — — — — — — — —

it will

be easy

octave,

a major ninth;*

When we remember now

— — — — —

that

contains 1 step,

— — — — — — —

third fourth, fifth,

sixth,

seventh, octave,

ninth,

2

steps,

2

steps,

of

it

4

steps,

5 stops,

5 steps, and 2 half-steps,

6

the major fifth c

many

i. e.,

interval, it will be easy to

g

The minor

c

d

b,

e

i,

b

b, b, b, b,

g

to

from

intervals

c

for instance,

we wish

to change

a minor one, we must subtract a

change the

c

g^

.

C—g^

is

a minor

c are therefore

the minor second,

— — — — —

— — — — —

third,

fourth, fifth,

sixth,

seventh.

We must bear in mind that these intervals are merely major, as

to the fundamental tone of the scale

selves form various intervals is

half-steps,

half-steps (by depression or ele-

If,

into

c—f c—g c—a

*

and 2

steps,

a minor, diminished, or superfluous one, by add-

vation) as are requisite.

fifth.

1 half-step,

and 1 half-step, and 1 half-step, and 1 half-step,

measure the other intervals.

to

ing or subtracting as

half-step,

and

3 steps,

Having once obtained a major

make

third,

« a major fourth, " a major fifth,

no*

a major

fourth, &c.

;

thus

(c)

.

The

related

other degrees amongst them-

d—f and e—g are

not major thirds

;

f—b

40 In order to change c

must be elevated a jor seventh c

I

—

6

g

S

a minor seventh,

ct

—

the

of the

g

ma-

must be depressed

In order to make of the

.

h a diminished seventh, b must be de-

pressed an additional half-step

In this manner

venth.

"

b i

fifth,

make

In order to

a half-step, and must become 6

minor seventh

a superfluous

into

half-step.

it is

;

c

It

—

b

^

is

a diminished se-

very easy to represent any mi-

nor, diminished, or superfluous interval.

In the last chapter we

we

now

find

intervals,

made mention of enharmonic

tones

which though of equal height in re-

gard to the tones constituting them, have different names,

and which, therefore, are called

Enharmonic

Intervals.

Thus, for instance, the minor third with the superfluous second c c

g

S is

di

;

c

e

^

is

enharmonic

the superfluous fifth

enharmonic with the minor sixth

c

a

t ,

&c.

CHAPTER THE TONE

SPECIES, SEXES,

We have seen that grees,

VI.

Music has at

its

OE MODES. command seven

de-

upon which, however, can be constructed a great num-

ber of tones and tone-relations.

It

is

possible that

these tones and relations can occur in one composition.

work of art has certain

since every

tendency, since sensations,

it

is

it

limits of

all

But

design and

expresses a certain round of ideas and

natural that the tones and tone-relations

should be limited in the same manner

;

that for each composi-

tion there should be a certain circle of tones and relations,

within which the composition should exclusively or principally

move. This circumstance

facilitates the task of

intr^ucing the

student into the empire of tone-formations, without the risk of his losing himself in the infinity of manifold forms.

The seven

degrees, so lately mentioned, form the basis' of

every composition. five

But each degree can be represented

in

different manners, and thus there are innumerable pos-

sibilities

of combination.

But of

all

these possibilities, the system of

modern Music

has selected two as the only essential ones. called

Tone Species, or Modes, and are either major or minor.

They

are

42 distinguished In both are the seven degrees, and they are to each other from each other by the relation of the degrees degree iorms -with and by the size of the interval which each

the

first tone.

THE MAJOR MODE has exclusively major intervals.

we formed

Consequently all the scales

in the fourth chapter are major scales,

to the major

and belong

mode.

THE MINOR MODE contains also major intervals, with the exception of the

Third and Sixth, which are mmor. change major intervals into minor,

Since

We

the third and

to

be easy for us to

it will

change a major mode into a minor.

we know how

have but to depress

sixth to change C-major,

—e—f—g—a— — 6

d

c

c,

for instance, into C-minor,

—

d

c

Thus we

t

find that the

—f—g—

b

fit

—— b

e

1

i

c.

minor scale has the following steps

d— —f—g— a — b —

c

The most

e

^

I"

1"

1

n

i

conspicuous step in this scale,

to 6, a step of a superfluous second.

c.

i

is

Like

the one from a all

•>

other super-

fluous intervals, this progression in the course of the scale, afiects

us disagreeably.

,aa. -S^

^^^^

43 This, however,

is

not the case in every tone-succession

for instance, not in the following

23.

P

±>

>!.

:

V. !fe

w

•where the superfluous second has been avoided,

n and

it is

not

our object to obtain a mild tone-succession, but a firm basis for our compositions.

CHAPTEE Vn. THE KEYS. In the fourth chapter we have been taught the number of the

major

and how they can be formed.

scales or keys,

now form as many minor we hare

also learned

scales or keys.

what signature

scale or key.

The

different law.

Their signature

it,

We can

In the same chapter

to give to each

major

signatures of the minor keys follow a is

not as the scale demands

but each minor key has the signature of that major key

which

lies

The

a minor third above

signature of .^-minor

it.

is

npt, as one

would expect,

a sharp before g, nor does that of D-minor consist of a

and h

l"

; but ./2-minor has the signature of C-major,

ct

and

D-minor has the signature of 2^-major.

Here

D, G,

C,

y,

Bb,

Eb.

are the signatures of the most usual minor keys.

Two

keys, (a major and a minor key,) which have the

same signature, are

called

PARALLEL KEYS, Or PARALLEL TONES.

The

parallel-tone of a minor key, as

we have

seen, lies a

45 minor third above a major key

We

lies

it,

and, vice versa, the parallel-tone of

a minor third below

it.

can now more fully understand the object of the

nature.

It tells us

elevated

—

1,

what degrees are

2, it serves us as the

;

to be depressed or

token of the key in which

But we know

the composition has been written.

such signature can belong to two different keys der to ascertain exactly in what key a piece

must turn point,

we

to its

will

But

harmony.

if it

until

we

is

;

also that

and

in or-

we

written,

arrive

at that

remember that generally

THE LAST TONE and

sig-

of a picCe,

ends with a chord,

THE LOWEST TONE

of that chord,

in connection with the signature, will be a sure indicator of

the key.

If,

for instance, the signature consisted of

sharps, and the lowest tone of the last chord were p,

would know at once that the piece

is

composed

two

we

in B-minor,

the parallel tone of D-major.

But what of those degrees signature

is

not suitable 1

in the minor keys for which the

The

t

or

i"

belonging to them

is

placed before the respective notes as often as they occur, thus making these elevations or depressions almost accidental.

CHAPTER Vni. RELATION OP KEYS.

When

we compare the

find that each deviates

different

keys with each other, we

from the other to a greater or

Thus C-major and G-major

degree.

tonej/and/S

.

deviate but in one

Comparing, however, the scale of C-major

with U-major, we find that the two scales tones from each other has_/lt,

Two

c'i

,

less

;

C-major has

_/",

c,

differ

in four

g, d j J5J-major

gi, di

keys which have several tones in common are said to

be

RELATED.

We

have just now seen that this relationship can take

place in a greater or less degree, according to the tones which the two have in

common.

There

number of

are, conse-

quently, different

DEGREES OF RELATIONSHIP. Finally, tion

we have

between

in the

already seen several manners of connec-

different

keys

;

the major keys were connected

form of the Quint-circle

;

the minor keys, with the

parallel major keys, and with their own major keys. are, therefore, three kinds of relationship.

There

47 Relation of

1.

Here the Quint-Sircle

The keys

degrees.

Major Keys.

indicates the relationship with its

lying close together in the Quint-circle,

deviate from each other in but one tone, and stand in the f,rst

degree of relationship to each other.

the Quint-circle before us thus 4

6

spread

:

310133466 b

6

When we

3

»

Q^^Dh—A\,—E\>—B\,—F—C—G—D-~A—E-'B—F!i we

key has

find that each

bors to the right

and

its

two nearest relations as neigh-

to the left.

Relatives of the second degree are those which differ in

Thus X>-major on one

two tones.

side,

and

B

!>

-major on the

other, stand in the second degree of relationship to C-major. 2. Relationship

The

of Parallel Keys.

parallel keys are related to each other in the first

degree, for they differ

C-major and

from each other in but one tone.

./2-minor,

C-minor and

E

b

Thus

-major, are relatives

of the first degree.

When we we

combine

this

new kind

perceive a

kind of relationship with the other, of relationship between the keys.

We have found that each major key stands in relationship of

—

degree

the

first

its

Parallel

1, with its neighboring

key,

—

^for

JP-major, and .;2-minor.

instance,

major keys

;

2,

with

C-major with G-major,

But now the major keys

G

and

F

stand again in the first degree of relationship with their Paral lei tones,

E-minor and D-minor.

Consequently we can con

sider these minor tones as relatives of the second degree to

the first major key (C-major.) hibits to us

The

following diagram ex-

43 0-major, Ji'-major,

»

A-miaoi, G-major, as relatives of the

first

degree.

jK-minor, as relatives of the second degree.

l)-ininor,

We might pursue ther, but this Tvould

these degrees of relationship

much

far-

be but an unnecessary waste of time and

paper. 3.

Relationship of

Minor Keys with

Major Keys,

their

and amongst themselves.

We know grees from

we should

already that each minor key deviates in two de-

its

major key, in Third and Sixth.

consider

them as

Consequently

relatives of the second degree.

But a singular coincidence draws

this

bond of union closer

together.

The

fifth tone,)

and the Sub-dominant, (the fourth

Tonic, (the

scale are its principal

first tone,)

the Dominant, (the tone,) of each

moments, and these three moments be-

long to the major scale as well as to the minor

communism

of tones

later period,) that

is

we can

tone as relatives of the

And

finally

so influential, (as

we

;

and

consider the two modes of the

first

we consider

this

a

shall see at

same

degree.

those minor tones which stand in

the relation of Tonic, Dominant, and Sub-dominant to each other, as relatives of the first degree.

£-minor and D-minor as

D—e—f—g—a—bh—4—d—e—f c

d

to

two and three points

:

—

g —e—f—gl —aa— — —d h

e—fi—g

When we

consider

relatives of the first degree

.>3-minor, though their scales deviate in

a—h

Thus we

c

e

a~-b—c—di—e

combine these relationships with those found

49

under 2, we can form a similar diagram of relationships of first

and second degree. ^-minoi, iJ-minor, C-major, E-nunor.

F-major, It

Gr-inajor.

remains now for the student to form similar diagrams

«f other major and minor keys.

FIRST BOOK. ELEMENTS OF MUSICAL COMPOSITION.

First Part. Composition for Single Farts, {Monophonic Composition).

CHAPTER

I.

THE FIRST FORMATIONS. 1.

THE TONE-CHAIN, WITH

ITS SPECIES.

"i

A Musical composition consists

of one or

more

successions of

tones (tone-chains) which progress simultaneously, and which are

intended for one or more instruments

;

one or more voices

for

or for instruments and voices together.

Beginning with the most simple

have already to make a

—the

single tone-chain

Por a

distinction.

—we

tone-chain does not

contain merely sounds, which succeed each other, but that sue cession

is

hy

regulated

sound

is

(Rhythm), which indicate

certain laws

when one sound should succeed the

other,

and how long each

to continue.

But regardless of

all

rhythmical laws,

we

will, for

the present,

analyze the mere tonical contents of a tone-chain.

These tones can succeed each other in various manners.

They

can progress from low to high, from high to low, or these two

be mixed. We distinguish therefore ascending (a), and descending (b), tone-chains, and those, which both ascend and The repetidescend, and which we will designate as vague (c). tion of one and the same tone, too, might inappropriately be directions can

called a tone-chain (n)

other

by

;

and

finally the tones

regular degrees, as in a, b, and

c,

or

can succeed each

by irregular degrees

as in B.

A

^^ -•—#-

B

C

54 It is

effect

easily perceived that ascending tone-chains produce the

of exaltation, elevation, tension, while, on the contrary,

scending ones produce the effect of relaxation, or return

de-

to repose.

Vague tone-chains awalce neither the one nor the other sensation but with a certain indecision remain between the two

distinctly,

knd have a share of

either.

Yet with

all their

deviation in detail

they can, in general, belong to one of the two principal species,

-»^J^

^=='^iir'ir7Z i 3c:

i We have now only to is

more

restless,

add that the motion of " step by step' motion i»

quiet and even, while the skipping irregular

unsteady,

and nervous. But more of that anon.

Tone Eegulation. The vast resources which music has

command make

at its

it

absolutely necessary that, in our attempts to produce or invent

we should observe a certain order and limit, in ordei way amidst the enormous mass of tone-formations. We require foundation upon which we can construct our forma tions, and from which we can derive them. tone-chains,

to find our

s,

We will

select the diatonic scald- as our first foundation.

since even this scale has its different species,

them the

original

But

will select from

and most satisfactory one

The Major

The reasons

we

Scale.

for this choice will in a future chapter

become

ap-

parent of themselves.

The major

scale,

from

i Tonic,

its

Tonic to

its

octave, rests

-gs: =i=«=

moves thence through the remaining degrees {d to b), and upon the Tonic, or its octave. Al] perfectly agreeable to our feelings, and the more so -when

closes, satisfactorily, again

this is

upon the

we compare

it

to other tone-chains

;

for instance,

with

55

i

ir^r

or with imperfect tone-chains (not beginning, or not ending with

the Tonic).

m

-

w

.0.

We recognize The

the scale.

m

-

the Tonic, therefore, as the heginning and end of latter originates

from the Tonic and returns to

it.

—

moment of repose, the scale the moment of motion, Here we have discovered at is formed. last an antithesis which runs through the whole science of musi& Repose and Motion, Tonic and Scale. In juxtar-position to the Tonic

the

—

Analysis of the Scale.

When we that

it

examine the

scale in its

halves, exactly alike in steps

and one

;

i.

we

find

consists of

two

smgle progressions

contains Steps and half-steps, and that

it

each half containing two steps

e.

half-step.

E F

B

G one

one

A

G one

half

B one

C* half

* We suppose that every student of composition is familiar with tin major scales but in case of the student's not being able to represent to himself such a scale at once, we refer him to the above measurement of th« ;

scale for assistance.

We know that on

every tone of our tone-system we can construct a major they all progress like scales have like proportions

and that all major the above c major scale,

1 step,

1 step,

;

-J

step,

1 step,

1 step,

1 st«p,

-J

step.

In order then to construct a major Scale on any particular tone, we have but to write the seven degrees from it to the octave, and justify it afterwards, by means of flats or sharps, according to the above diagi-am. In constructing the scale on a, for instance, we first write the seven degrees

ABGDEFGA A

to b, a whole step, agrees with the diagram ought to be a whole step, and consequently will have to be enlarged by changing c into cj| c^io d is now a half-step, dto e a whole step both in accordance with our model eiof, however, is merely a half-step when consequently /has to be changed into/|, and, it ought to be a whole one for the same reason, g into g^.

and measure each

step.

6 to c

;

;

:

;

In constructing the scale oid\> major, thus:

Dh

we would

E F G A B

first

write the degrees

G Dh

and then regulate the distances from one degree sharps or flats, whichever is wanted.

to the other

by means

of

56

The one of these other leads to

tone-chains originates in

c,

the Tonic; the

the Tonic ; both find in c their centre and juno

c,

tional point.

G

£

A

O _^

B

C Even

we

in this formation of the scale

F

JS

find the

Tonic the

chief

point from which the other tones advance, to which they return,

and around which they move. ^Rhtthmioal Formation of the Tone-Chain.

2.

We have until now considered the tone-chain and scale, and

we have

another should resound.

after

happen

at equal

particularly, in a

ionical contents only of the

tacitly

and unequal intervals of time most infinitely varied manner.

fore begin again with the

;

and the

latter

We will there-

most simple, and imagine a regular

each tone of equal value;

cession,

admitted that one tone

This resounding, however, can

for instance,

suc-

the scale

in

crotchets (quarter-notes)

i? us,

because one tone like

the other passes by, without distinction.

The longer we would more fatiguing and

But

this

form does

not

satisfy

continue this chain of equi-long sounds, the confusing would

it

be to

us.

Our

feeling urges us to distinguish

and to regulate ; we must divide this chain to make Admitting the division by two as the conception.

would begin perhaps in «

and

ry

this r^

it

easier of

easiest,

we

manner A

f\

thus arrive at the simplest

regulation

of time.

Simple

Measure. This regulation, at present, exists only in our imagination, or

on paper ; but to make it reality we distinguish every first note of a measure (marked '^) by a stronger accentuation. This accent

makes every beginning of a measure

perceptible,

and by these

57

means we have introduced

into our scale a variety to -which de-

cided and absolute necessity has led us.

Our and

tone-chain appears

now

well regulated in regard to time,

been made perceptible by the alternate

this regulation has

change of strong and weak intonation rhythmical

A

in short, it has

;

been made

has received the Rhythm.

it

;

Rhythmical Tone-Chain

is called a Melody, and a melody is and simplest creation of art. Already in our first attempt we found it necessary to begin

the

first

and end with the Tonic as the most important pleteness and perfection

was

owing to

tone,

and

its

com-

and But now we have learned also to distiuguish rhythmically important and unimportant tones. If our melodies shall now be round and perfect, rhythmically as well as tonically, in fact

this beginning

ending thus.

we

have rhythmical chief

will find it desirable that they should

notes for the beginning and for the end.

We

experience an unsatisfactory feeling in the above melody,

because, though beginning on a principal part

portant one

;

and the melody

is lost,

as

it

ends on an unim-

were, because the end-

it

note has no weight.

We will therefore re-form

our scale in this manner

n 3.

The beginning has

lost its emphasis,

and the satisfactory end remunerate us

but the succeeding notes for

it.

But perhaps we prefer not being tied to this particular form of beginning it may be possible to have a beginning and ending ;

alike satisfactory.

And

here

is

all

appears to us imperfect in sible,

remember a

the time to

accompany us through

our labors. its

we should always retain

necessary

—

^let it

what

is

wanting."

we know,

Whenever a formation

parts, or not clear and comprehen-

of it whatever

be found wherever

In this instance

to supply

principle which should

"

that

it

it is

may

we have found good

—and

or

afterwards try

our object to place the be-

ginning and ending of our melody on an accented part of the also know, that the eight notes of our scale have measure.

We

58 to appear in four measures

part

it

—

at least

we know

at present

of no

Finally, if the last tone has to fall on an accented

other form.

either in the shape of a half-note, or a quarter-

must be

by a quarter-rest. down would give us a

note, succeeded

This noted

figure

something like the

fol-

lowing:

m

The

and we see at once clearly what has to be done.

three

wanting notes have to enter the vacant measure. The first of these can do so in the form of a quarter note; the other two have to

become eighth notes.

s

iw We have now arrived all

our demands. 1.

at a formation

which ccarresponds with

It is

In regard to tone-succession, beginning

and ending on

the Tonic. 2. It is

3. In

rhythmically well regulated,

regard to accentuation of beginning and end-note,

it is

and well closed off, and thus satisfactory. same time we have obtained But at the three species of notes half-notes, 4. A variety of rhythm and this variety proves quarter-notes, and eighth-notes distinct

—

itself at the 5.

same

;

—

titne-,

A means of promoting

our object:

for,

the end-note, the

aim of the whole, has the longest duration; and the eighth-notes,

immediately before

it,

serve to accelerate

movement towards it, and to make the end-note more characteristic. We have now a gradation of rhythm the

as well as of melody.

Thus

far

ascending.

we have inadvertently represented all our tone-chains as Nothing prevents us now from attempting a descending

one: 6.

P

s -&-

59 It

exhibits a steady and satisfactory return to repose

—the begin-

ning of all our tone movements.

But both formations have a very one-sided elevation

is all

;

the other

is

character.

exclusively relaxation.

The one Only the

combination of the two in a larger whole can in every respect satisfy us.

m

mm

^ m

We have now arrived at a tone

formation which, issuing from

rhythm to the Tonic of a higher octave, marks this point by a rhythmical pause, and then returns in We perthe same steady manner to the repose of the first tone. ceive also that this formation is composed of two halves (a and b) which, each by itself perfect, combine to make the perfect whole, a whole consisting of two subordinate wholes. But though each the Tonic, rises in pitch and

of these parts or phrases resembles the other in rhythmical formation and tone-contents, the direction in the tone succession of

each is exactly opposite ; the one forming the reversed counterpart of the other.

Such formation, consisting of two perfect phrases,

thesis

and

antithesis, is called a Period.

Formations which lack the satisfactory ending of a period or

8.

m

phrase are called passages. Retrospection.

We

have now conceived the first ideas of composition, and them in tones. They were

realized 1.

The

tone-chain,

with

its different

sions.

The

first

foundation of

all

directions

and progres-

—the

tone succession

diatonic

scale.

between repose and motion in the scale. and simplest rhythmical order, by the aid of which a mere tone-chain became a melody.

The The

distinction first

60 5.

The

fixed

division, 6.

and manifold valuation of sounds, mensural

and accent.

The melody strove

to acquire a rhythmical

marked point

of beginning and ending and became a phrase. 7.

This brought ns to a variety of rhythmical motion.

8.

The invented phrase (thesis) demanded a counterpart (antithesis), and the two together formed a Period.

9.

A

formation of a

new

—the

nature

passage

—

^was indi-

cated.

And

thus

we have

arrived at the three fundamental formations

of all musical constructions

Phrase

—Period—^Passage—

and have recognized the characteristics of their construction.

61

CHAPTER

II.

INTENTION OF MONOPHONIO PHRASES. THE DESIGN AND

1.

In order to arrive at

our

first

new

progressions

satisfactory phrase (No. 5).

different parts ; in the first

ITS EFFICACr.

we wiU

We

measures a

see

it

return

now

to

constructed of

series of quarter-notes

;

in

the latter quarter and eighth-notes, which lead to the final note.

Thus we can

distinguish various tone-groups

;

for instance,

a tone-

chain of quarter-notes.

'i w A group ending more satisfactorily is in the latter measures.

^

10. ».

If still

we

are willing to resign a satisfactory ending,

we

can select

more groups.

g

"•^w

Such forms which contain the germ and the impulse of longer Each junction of two or more notes

phrases are called designs.

can serve as a design. signs,

how

and

it is for

to apply them,

continually at

new

of these designs scale has given

Every composition

us to consider

how we

consists of such de-

are to nurse these germs,

and how to multiply them, in order to arrive

phrases, passages, and periods. is

us

already sufficiently prepared. six,

The invention The simple

and every new formation adds to that

number.

Every design can be applied by

itself

fi2

By

1.

repetition on the

By

repetition in a higher or lower range,

p^

i By

3.

repetition in opposite direction.

i By

4.

degrees,

^^^a

12.

2.

same

5

repetition in notes of longer or shorter duration (aug

mentation and diminution). Augmented.

Original design.

13.

DiminiBhcd.

^j-jS

5.

By

changing of i^esis (weak, unaccented part of a measure)

into arsis (accented part of a measure), or vice versa.

P^3

f By expanding

or contracting the design ; a smaller for a larger interval, or vice versa. '%6.

".^^^^^ 7.

By combining one

design with another, or

We need not mention

signs,

can already see is.

We

and leave

it

-&-

more to a phrase

that these different manners of applica^

tion can change with each other, or

formation

by changing

1^

iw We

i. e.,

how

combine to a greater whole.

inexhaustible the field of musical

need therefore only show a few of these deto the industry of the student to invent others.

^

63 But to

return again to our actual

task,

we

will begin

time with the most subordinate of our formations

We say most subordinUte, because

this

the passages.

they do not even end within

themselves.

2,

Each

FOKMATION OF PASSAGES.

repetition of a design produces a

repetition of the third design, in

No.

passage.

Thus the

11, gives us the following

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