Harmony simplified: or, The theory of the tonal functions of chords

Citation preview

CORNELL UNIVERSITY LIBRARY

BOUGHT WITH THE INCOME OF THE SAGE ENDOWMENT FUND GIVEN IN 189I BY HENRY WILLIAMS SAGE

MUSIC

MT

rn

n Ver8i,y

50.R55 i896

'

"**"

3 1924 022 305 357

Cornell University Library

The

original of this

book

is in

the Cornell University Library.

There are no known copyright

restrictions in

the United States on the use of the text.

http://www.archive.org/details/cu31924022305357

ATJGENER'S EDITION No.

HARMONY

9198

SIMPLIFIED OR

THE THEORY OF THE

TONAL FUNCTIONS OF CHORDS.

BV

DR.

HUGO RIEMANN,

Professor of Musical Science at

Leipzig University

TRANSLATED FROM THE GERMAN.

THIRD IMPRESSION

AUGENER

LTD. LONDON

Printed in England

by

AUGENER

Ltd.,

287 Acton Lane, London,

W.

4.

©e&tcatefc TO

PROFESSOR

EBENEZER PROUT.

Professor of Music in the University of Dublin,

B.A.,

etc.

THE DISTINGUISHED PIONEER OF MUSICAL PROGRESS.

THE AUTHOR

——

—

$

CONTENTS. Introduction (Harmony

page

i.

— Melody — Tone relationship — Overtones — Undertones — Majoi —The three functions — Modulation.)

chord and minor chord

CHAPTER

Writing Confined to Pure Principal Harmonies

I.

(Tonic and Dominants) §

I.

page

Overclangs and Underclangs.

§2. Four-part writing

(T—D

—The

10.

writing of

°T—

° S)— The conand Chords of six-four (-Z?Jand S\i)°D)— Complete (bi-lateral) and §4. Contra-fifth step cadences. and °D °S) Consecu§ 5. The whole-tone step (S "J? and tive fifths The tritone— Score. § 6. The turn of harmony ( + + + +S Contra-fifth change {°S—Z> ) and fifth-change (°S + -D) Diminished and augmented and "D part-progressions False

single chords.

§3. Plain-fifth step nection of chords Consecutive octaves

—

—

(T—S

"T—

— — —

—D

T

—

°T— D)—

—

relation

CHAPTER

—

—Modulation.

II.

Characteristic Dissonances

— Parallel-Clangs

—Leading-Tone-Change Clangs § 7.

The

{D

characteristic dissonances

dissonant tones

— Alto

—

—

page 55.

S vn S6

1 ,

,

D —Treatment vl

,

)

of

clef— Figuration with passing and auxiliary notes.

—

1 § 8. Chords of seven-three (IP "Sp ; °Tp, °Sp, °Dp, + -Dp)

vu

)

and

parallel clangs

— Treatment

—

(Tp, Sp,

Dp,

of feigning consonances

—

Doubling of the third allowed Third change Leading-tone change Minor-third change Whole-tone change Tritone change Tenor clef Third step Minor-third step Leading-tone step. §9. Dorian sixth,

—

—

—

—

—

Mixolydian seventh, Neapolitan sixth, Phrygian second, Lydian fourth Revival of these as means of expression Close Contra-whole-tone change Tritone step Half-close Deceptive-close change Double-third Chromatic-semitone change Augmented-sixth

The church modes

—

change

—

— —

— Chromatic-semitone

step.

— —

—

—

Contents.

vi

CHAPTER

III.— The

Theory of

Dissonance

— Sequences-

Intermediate Cadences § 10.

page 107.

—

—

Completion of the Theory of Dissonance Passing dissonances Prepared Altered chords Syncopated Unprepared dissonances figuration. The sequence as melodic imitation of har§ II. Sequences

dissonances

—

—

—

— — Five-part writing, § Intermediate cadences (Inserted) and [omitted] harmonies — The notation transposing instru-

mony

formations

12.

for

ments.

CHAPTER IV.—The Change

of Tonal Functions (Modulapage

tion) § 13.

141.

—

meaning of the simplest harmony steps Characteristic Modulating power of harmony steps. § 15. Modulations by means of chords of seven-three and of minor nine-three Enharmonic Change. § 16. Modulations by means of the third-change clangs. § 17. Modulations by means of bolder harmonic progressions (leading-tone steps, third steps, etc.). § 18. Modulation by means of the most far-reaching harmony steps (tritone step, etc.). § 19. Independent creation of musical sentences Period formation. § 20. Pedal-point and

Change

of

figuration.

§ 14.

—

modulating sequence.

Exercises

:

pages 11,

16,

20, 21,

82-83, 85-87, 104-106,

1

23, 25-28, 30-34,

18-120, 126-127,

Explanation of the Terminology in Alphabetical Order

Alphabetical Index

...

._

I

and

39-43. 5°-54. 64-69, 33 -, 4°> 180-187.

the

Chord ...

Signs page 191

page 196,

HARMONY

SIMPLIFIED.

INTRODUCTION. The Theory of Harmony

is that of the logically rational and of chords (the simultaneous sounding of several notes of different pitch). The natural laws for such connection can be indicated with certainty only if the notes of single chords be regarded not as isolated phenomena, but rather as resulting from the motions of the parts ; chord successions arise from simultaneous melodic motion of severalparts. The history of music teaches us that simultaneous melodic progression in several

technically correct connection

was practised and more and more perfected for centuries before the idea of harmony in the modern sense (chord) was even Thus harmony, in so far as it may be defined as conceived. composition in several parts (polyphony), takes root in melody. Melody is the logically rational and aesthetically satisfactory parts

With regard to motion of a part through notes of different pitch. the aesthetic laws for melody formation, we refer the student to the philosophy of music (cf the author's " Catechism of Musical f As the foundation of .-Esthetics " [ Wie horen wir Musik "]). rational motion in melody common to all ages and all races, the history of music suggests the diatonic scale, the simple step succession of the natural notes of our present note system '

:

with

its

regular insertion of a semitone step {b c, e /), alternately

two and three whole-tone steps. The age of tbisfundamental counting by thousands of years, and the respect in which it has been held, are a sufficient guarantee that it is a demand of nature, that it is logical and necessary; indeed, even irregular constructions of melody may be traced back to this foundation. The notes of this fundamental scale stand in such relation to one another as the ear can apprehend with certainty, and as are expressed in acoustics and mathematics by certain simple These ratios, are the same as those which numerical ratios. exist between the numbers of vibrations of elastic bodies that after

scale,

Introduction.

2

produce the notes, and of the

conveys them to our ear. columns of air enclosed in tubes, or if we put aside reasoning on physical grounds and only take into consideration perception by hearing such relations of notes to one another (recognised by the ear) as allow of their appearing musically intelligible and rational when sounded in succession, are called harmonic (from the Greek apfiofaiv = to join), and, indeed, these are after all the same relations which have to be regarded as standard in viewing the combinations of several parts, harmonies in the sense recognised nowadays. Just as harmony, then, (as chord succession) has referred us to the melody

Such simple

air that

ratios of vibrating strings or

—

—

of single voices, so melody (as a succession of notes standing in harmonic relation to one another) refers us again to the original laws of harmony, so that we must say Every note of a melody owes its cBsthetic effect in great measure (viz., abstracting from the effect produced by its absolute pitch, or by the fact that it represents a rising or falling of the melody-line) to its harmonic meaning. And by the harmonic meaning of a note we understand its relation, as accurately perceived by the ear, to other notes of the same melody or in composition in several parts to notes of other accompanying melodies. :

—

—

One note compared with other notes (we shall speak now only of notes whose relation is recognised by the ear as harmonic and ratio,

intelligible) is

starting

either itself the

from which

fixed point, the prima

are considered, or, conversely, it is in its turn cofisidered in its relation to some other note ; in the former case it is, therefore, the starting point of reference for other notes the prime ; in the latter, a note to be referred to the prime, and whose distance from it is expressed by the ordinal number corresponding to the degree in the fundamental scale which the note occupies, counting from the prime. So, e.g., if we compare c with g, either c is the prime and then g the fifth step measured from c upwards ; or g is the prime, and then c is the fifth step measured downwards from g (underfifth). The general name for the distance of notes from each other, measured by the degrees of the fundamental scale, is the

others

—

Interval.

The

verdict of the ear declares those intervals simplest

—

i.e.,

understands them with the greatest certainty, and requires pure intonation for them most inexorably which mathematics and physics reduce to the simplest numerical ratios, either by measuring the duration of vibrations in time or the extent of sound-waves in space, or by dividing a tightly stretched string Starting with the latter as more convenient and in various ways.

—

easily intelligible, we shall find that the simplest division of the string is into two halves ; each half of the string then gives the octave of the note sounded by the whole string, and both halves yield one and the same note. But it is evident that the ratio of

more

—

Introduction.

3

the unison, 1 1, will be more easily understood than that of the whole to the half, 1 '/,. Next to these two comes the ratio of the whole to the third part (1 '/ )> to which the musical interval 3 of the twelfth (fifth of the octave) corresponds; then follow 1 double octave, 1 1 (major) third of the double octave, 74 /5 1 '/e fifth of the double octave, or octave of the twelfth ; in notes, if we take c for the whole string :

:

:

=

:

:

:

:

If,

conversely, 3

and

we

start with

a higher note,

e.g.,

thrice-accented

understood notes which lie below e\ then doubling the length of the string will have to take

e

(