A key to the exercises in Part II of A treatise on harmony

in Fart

FACULTY

,

Faculty of Music Library

Anne Bolger

UNIVERSITY
OF TORONTO

A KEY

TO THE EXERCISES IN

PART II

— OF —

A TREATISE ON

HARMONY

BY

J. HUMFREY ANGER

Late Professor of Harmony, etc., at the Toronto Conservatory of Music :

Hon. Mus. Doc., Trinity University, Toronto;

Mus. Bac., Oxon; F.R.C.O.

BOSTON, MASS.

THE BOSTON MUSIC COMPANY

(G. SCHIRMER, INC.)

Copyright, 1913, by THE BOSTON Music Co.

For all Countries
B. M. co. 3710

PREFACE

To the purpose, the double purpose, of a Key, and to the use,
the proper use, of the same, reference was made in the Preface to
the Key to Part I. Reference was also made to the fact that the
great majority of the exercises may be harmonized satisfactorily in
more ways than one; but, that the solution given is regarded by the
author as being the most desirable one in the interests of the
student.

In addition to the above, two other points arise in connection
with the exercises in Part II, to which a brief reference must be
made. In the first place, it has been thought well to symbolize only
the chord or chords under consideration in each chapter; for, the
student should be thoroughly familiar with the various chords which
have been previously considered. In the second place, in regard to
the figuring of auxiliary notes, and in accordance with a very gen-
eral law, the accented ornamentations alone are represented in the
figures.

To Miss N. R. Hearn, for indefatigable clerical work, the ac-
knowledgments and thanks of the author are due, and are herewith
cordially tendered.

Toronto, Canada
March 24th, 1913

CHAPTER XII

SECONDARY SEVENTHS

(Pages 198-204)

I

1. (»F, II7; Bb, VI7; Eb, III7. (b) D, IV; G, VI 7* ;
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* In Exercises 3 and 4, a different chord of preparation has been employed in each ex-
ample, in order that the student may become familiar with the various chords available for
introducing the discord ; it must not be supposed, however, that they are all equally effec-
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SECONDARY SEVENTHS

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17. («) The dominant seventh occurs upon the fifth de-
gree only of a scale; secondary sevenths occur on other degrees.

(b) The constituent intervals of a primary seventh are a
major third, a perfect fifth and a minor seventh; those of sec-
ondary sevenths vary, but are never the same as the former.

SECONDARY SEVENTHS

133

(<c) The term 'primary' is usually employed in reference
to a chromatic tetrad only, the dominant seventh being a pri-
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I?1 IV+ IV-6 1+

143

CHAPTER XIII

CHORDS OF THE NINTH

(Pages 216-221)

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CHORDS OF THE NINTH

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3. (fl) Bad ; the ninth must not be placed a second above
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2

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(/) Bad ; as V92 (third being omitted), but good as V72.

CHORDS OF THE NINTH

145

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13. (a) The dominant ninth occurs upon the fifth degree
only of a scale ; secondary ninths occur on other degrees, of
which the supertonic is the most important.

(b) The constituent intervals of a primary ninth are a major
third, a perfect fifth, a minor seventh and either a major or
minor ninth ; those of secondary ninths vary, but are never the
same as the former.

(c] The term ' primary ' is usually employed in reference to a
chromatic pentad ; only the dominant ninth being a primary
diatonic pentad.

150

CHORDS OF THE NINTH

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(1) (2)

(1) (3) (4) (5) (1) (1)

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Root Db.

" Ab.

" Gb.

<« Eb.

«« Ab.
•" Ab.

Natural resolution.

Bb.

Eb.

Natural resolution.

Natural resolution.

Ninth resolves while the other notes remain

stationary, and the chord becomes a V7, with

deceptive resolution.

Stationary resolution. The seventh and

ninth resolving naturally in the next chord.

Primary ninth (chromatic) on supertonic.
Ab.
Ab. The seventh introduced as a passing note in

the bass.
Ab. The second resolving, the chord becomes

V73, with natural resolution and ornamental

treatment of the fifth.
Eb. The third moves disjunctly to the ninth of

the succeeding chord.
Ab. The second resolving, the chord becomes V7.

15.

CHORDS OF THE NINTH
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157

1. (a)

CHAPTER XIV

THE DERIVATIVES OF V9

(Pages 236-243)

I

(*)

r

n A I ~a~\ I — z? — n — T™ ^ — n

466-
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P=p=t=f:

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J

D-
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3.

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THE DERIVATIVES OF V9

159

6. («)

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f i

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THE DERIVATIVES OF V9 161

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11.

467 7 66667 6 5 — 6

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18. (a) This is a chord of the diminished seventh and
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Generator
A

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Key

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167

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169

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29.

4

M

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171

31.

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* The more advanced student would regard this chord as xIV70 resolving upon V,
Chapters XVIII ( Part II ) and XX (Part III ).

172

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J |_

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THE DERIVATIVES OF V9

173

34.

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174

THE DERIVATIVES OF Vg

T

m

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r — r

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h46 446 #4 66687

3 b 3 b 4 5 # -

2

C+ F+ D- A-

CHAPTER XV

SIMPLE SUSPENSIONS
(Pages 259-264)

(0

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SIMPLE SUSPENSIONS

177

4.

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179

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SIMPLE SUSPENSIONS

8.

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5432

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181

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SIMPLE SUSPENSIONS

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183

13.

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184

SIMPLE SUSPENSIONS

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SIMPLE SUSPENSIONS

185

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186

SIMPLE SUSPENSIONS

i=±^Z*3

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CHAPTER XVII

AUXILIARY NOTES

(Pages 308-319)
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3. Measure i. (a) Consecutive fifths (treble and alto) at

third beat.
(I)) Consecutive fifths (alto and tenor) at

fourth beat.
Measure 2. (c) Consecutive fifths (alto and tenor) at

first beat.
(d) The use of the mediant chord (first beat)

not desirable.
(e) Similar motion to the struck fourth

(treble and alto — second beat).
(/) Consecutive fifths (treble and bass) at

fourth beat.
Measure 3. (g) Incorrect treatment of a dissonant note

(B in tenor) on first beat.
(Ji) Consecutive fifths ( treble and alto) at

second beat.
(/*) Incorrect treatment of a dissonant note

(F in bass) on second beat.
(/) Consecutive fifths (alto and tenor) at
fourth beat.

224 AUXILIARY NOTES

(k ) Consecutive ninths ( treble and bass ) at

fourth beat.
Measure 4. (/) Consecutive fifths (treble and tenor) at

first beat.
(m) Incorrect treatment of a dissonant note

(£ in alto ) on second beat.

6. At (a) each note is harmonized separately; there are
five distinct chords.

At (£) B and A are treated as free turning notes ; there are
now only three distinct chords.

At (c ) B and G are treated as changing notes ; and now
there are but two distinct chords.

* By the term " melodic " is understood a minor scale, in which the unmelodious in.
terval of an augmented second is not present.

AUXILIARY NOTES

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53. Ex. 28. Transposed a major second higher, may be re-
garded as a reply to this question.

54. Discords are divided into two classes, viz : —
I Essential and II unessential discords.

Essential discords comprise tetrads (chords of the seventh)
primary and secondary, diatonic and chromatic ; also, pentads
(chords of the ninth) major and minor, primary and secondary,
and diatonic and chromatic, including also, their derivatives,
and various modifications.

Unessential discords comprise suspensions, rising or falling,
and tied or struck, and their ornamental treatment ; also, aux-
iliary notes, accented and unaccented, diatonic and chromatic,
various chords (modifications) which arise from their use.

The Boston Music Company Books

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\ Treatise on Harmony, Part I J. H. Anger 1.25

\a Treatise on Harmony, Part II "1.25

\b Treatise on Harmony, Part III " 1.25

\c Key to Part I, Treatise on Harmony " 1.25

\d Key to Part II, Treatise on Harmony " 1.25

\e Key to Part III, Treatise on Harmony 1.25

2 The Modern Enharmonic Scale " .30

3 Elementary Theory of Music and Treatment of Chords R. Wuerst .50

4 Studies in Musical Graces E. Fowles L25
4# Key to the Exercises in "Studies in Musical Graces" E. Fowles .75

5 Gymnastique Vocale A. A. Giraudet 1.25

6 Exercises in Sight Singing (Solfeggio) S. W. Cole .60

7 Exercises for Training of the Boy's Voice E. Douglas .60

8 Position and Action in Singing Ed. J. Myer 1.25

9 Vocal Reinforcement " 1.50

10 The Renaissance of the Vocal Art "1.25

11 Elementary Violin Lessons E. Gruenberg 1.50

12 School of Trio Playing. (Two- voice inventions, with a third

voice added and arranged for Organ by Max Reger and

Karl Straube) /. S. Bach .75

13 The Organ Accompaniment of the Church Service H. W. Richards 1.25

14 The Plain-Song Service E. Douglas .60

15 Practical Harmony S. Macpherson 2.00
ISa Appendix to Practical Harmony 1.25
\5b Questions on Harmony .60

16 Form in Music, v/ith especial reference to the Designs

of Instrumental Music " 2,00

17 The Rudiments of Music " .75
\7a Questions and Exercises upon the Rudiments of Music .75

18 Practical Counterpoint " 2.25

19 Music and its Appreciation 1=50

20 The Technique of the Modern Orchestra Ck. M. Widor 5.00

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460
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49
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G. Farlane

Charles Trew

C. Schroeder

Henry Farmer

A. Eaglefield Hull

Tobias Matt hay
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Charles Tree

Herbert Antdiffe

Reading Exercises on Notes

Reading Exercises on Time

Reading Exercises on Phrasing

Elements of Music, Simply Explained

Handbook of Conducting

Catechism of the Rudiments of Music

Organ Playing: Its Technique and Expression

The Child's First Steps in Pianoforte Playing

The Forearm-Rotation Principle in Pianoforte Playing

Counterpoint: Strict and Free

How to Acquire Ease of Voice Production

Living Music

Rhymes on the Rules of Harmony. Founded on Dr. Prout's Harmony

C. H. C. Knowles

350 Exercises in Harmony, Counterpoint and Modulation S. Macpherson
Handbook of Violin and Viola Playing C. Schroeder

Handbook of Violoncello Playing "

Instrumentation. (Revised and Supplemented by Richard Strauss)

Hector Berlioz
Handbook for Singers
Beethoven's Pianoforte Sonatas. (Letters)
Beethoven, A Critical Biography (ill.)
Studies in Phrasing and Form
Advice to Young Musicians
Sidelights on Harmony
Harmonic Analysis
Time, Rhythm and Expression
The Pianist's Handbook :

Part I, A Theoretic Companion to Practice

Part II, A Handbook of Musical Form

Analysis of Bach's "48 Preludes and Fugues." 2 Books, H. Riemann ea.
Catechism of Musical Instruments. (Guide to Instrumentation) "
Catechism of Orchestration
Introduction to Playing from Score

51 ,The Voice and its Control Churchill Sibley

52 The Tenor Voice and its Training E. Davidson Palmer

53 The Boy's Voice at the Breaking Period "

N orris Croker

Carl Rcinecke

Vincent d'Indy

S. Macpherson

R. Schumann

Louis B. Front

Franklin Peterson

Net.
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54 Manual of Voice Training (with a complete course of exercises)

E. Davidson Palmer .75

55 A Short History of Music W. S. Rockstro i.oo

56 Life of Ethelbert Nevin (ill.) Vance Thompson 2.50

57 Studies in Musical Interpretation Tobias Matthay 1.50

58 A Concise Dictionary of Musical Terms F. Niecks i.oo

59 Introduction to the Elements of Music .50

60 Modern Instrumentation for String Orchestra, Military and Brass Bands

John Fitzgerald i.oo

6 1 Practical Instrumentation. Seven Parts, complete Richard Hofmann 10.00
620 Part I. The Strings 2.00
626 Part II. The Wood- Wind 2.00
62C Part III. Strings and Wood- Wind Combined 1.25
62d Part IV. The Horns " 1.25
626 Part V. The Combination of Strings, Wood- Wind and Horns " 1.25
62/ Part VI. The Trumpets, Cornets, Trombones, Tubas and Instru-
ments of Percussion 2.25

62g Part VII. Harp, Mandolin, Zither, Guitar, Piano, (Cembalo),

Organ and Harmonium 2.00

63 The Rightly-produced Voice E. Davidson Palmer i.oo

64 Pianist's Manual M. Arnold .50

65 Catechism of Pianoforte Playing H. Riemann i.oo

66 An Introduction to the Study of Theory. (A Sequel to the "Elements

of Music") Franklin Peterson .75

67 The Student's Handbook of Musical Knowledge .75

68 Catechism of Music i.oo

69 The Appreciative Aspect of Music Study S. Macpherson .50

70 Harmony, its Theory and Practice Ebenezer Prout 2.00

71 Double Counterpoint and Canon 2.00

72 Harmony Simplified (also published in German and French) H. Riemann 2.00

73 Dictionary of Music 4.50

74 Catechism of Musical Aesthetics i.oo

75 Musical Biographies of Composers, Classified in Centennial Periods

A. M. Browne .50

76 A Practical Guide to Violin Playing H. Wessely 1.25

77 Summary of the Principal Rules of Strict Counterpoint S. Macpherson .50

78 Common Sense and Singing John Kennedy .50

79 Practical Elements of Thorough-Bass W.A.Mozart .75

80 Wagner and the Reform of the Opera E. Dannreuther 2.00