A Treatise on Harmony. Key to the Exercises in Part 1_Joseph Humfrey

lOSTON MUSIC COMPANY EDITIOH 00 ID ;co

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J,

Humfrey Anger

A KEY to the Exercises in Part I of

A

Treatise

on Harmony

BOSTON MUSIC NEW YOKK:

G.

SCHIRMLR

CO.

Digitized by in

2010

tine

witii

Internet Arciiive

funding from

University of Toronto

littp://www.arcliive.org/details/treatiseonliarmoOOange

A KEY TO THE EXERCISES IN

PART

I

— OF A TREATISE ON

HARMONY J:-HUMFREY ANGER Harmony, etc., at the Toronto Conservatory Hon. Mus. Doc, Trinity University, Toronto; Mus. Bac, Oxon; F.R.C.O.

Professor of

of

Music;

'^a^

„«

-^

^"4'"

BOSTON, MASS.

'%

THK HDSTOX MUSIC COMPANY (G. SCUIRMER, I.NC.)

Copyright, igog, by

J.

Humfrey Anger

Copyright assigned, igio, to G. Schirmer, Boston

50

B. M. CO. 2108

PREFACE This Key has been prepared with a double purpose in view in place as an aid to the teacher, especially one whose energies are chiefly directed to practical music, and who, consequently, is unable to devote any great amount of time to theory and secondly, as an aid to the student, but more particularly one who, through the force of circumstances, is unable to place himself under the immediate direction of a fully qualified teacher. Many such teachers and students are scattered here and there throughout the length and breadth of the land, and it is hoped that the solutions to the exercises (284 in number) may lead to removing some of those difficulties which beset the paths of all who desire to be proficient in this important branch of music. ;

the

first

;

Although the great majority of the exercises may be harmonized more ways than one, especially in the case of melodies and blank rhythms, etc., where the choice of chords is left to satisfactorily in

the discretion of the student, yet the solution given, in every case, is regarded by the author as being the most desirable one under the circumstances, and tlie one considered as being in the best interests of the conscientious seeker after knowledge.

The student

is

earnestly advised to refer to the solution of an

work the same. If he is studying harmony with a view to being successful at an examination, it cannot be too seriously impressed upon him that to regard and treat the Key as a "crib" is little short of hopeless folly, and to do so would probably result in disaster when the critical moment arrived. Let him first work an exercise as carefully as possible and to the best of his ability, and then let him compare the result with the solution given in the Key, thoroughly examining every note and every chord by this plan he will obtain a valuable lesson, his interest will be awakened, his ambition aroused, and with steady perseverence he will be enabled to conquer every difficulty. exercise only after having endeavored to

;

J.

Toronto, Canada December, igo8

HuMFKEv Anger

—

CHAPTER

I

THE MAJOR DIATONIC SCALE (Pages 15-16)

1.

Pitch, force

and quality

—a Chromatic — a Enharmonic — a

2. Diatonic

scale in scale

a semitone apart

it

;

is,

(§1).

which tones and semitones occur. in which semitones only, occur. which the sounds are

scale in

therefore, not used in

The term 'enharmonic',

indicating change of

change of pitch, is employed for a found on page 37. 3.

The

principal use of the tetrachord

the formation of

Any

scale, reference to

new

major scale

is in

than

less

Harmony

(§2).

name without which

will

be

connection with

scales.

may be formed from

its

attendant scales

by taking the upper tetrachord of the preceding, and the lower For example, the scale of A tetrachord of the succeeding scale.

may be formed by

taking the upper tetrachord of the scale of D,

and the lower tetrachord of the scale of

E

flat

the scale of (§§4,

A

flat,

In like manner the

scale of E.

may be formed by

taking the upper tetrachord of

and the lower tetrachord

of the scale of

B

flat

5. ^)-

4. (a)

{[>)

-

--^3 g 6.

-

^ -!zre>-

sr^- -z?-^-

- glg g^ _.. rr^

-zg-g-

7Sr-^

Tonic

the tone-note of the key.

Mediant

— the middle

note,

/g

being midway between tonic

and dominant. Dominant portance to the

— the ruling

tonic.

note,

being the note next

in

im-

•

;

THE MAJOR DIATONIC SCALE

The submediant is so called because it is a third below the and hence midway between the tonic and the lower or

tonic

sub-dominant (§9).

F sharp

8. is its

is

the tonic of this scale

;

and the

scale of

G

flat

enharmonic equivalent.

te f=

»f

XT

leading-note, subdominant, dominant, medi-

Supertonic,

7.

and submediant.

ant,

-«>-«-,

-s?-^^iS^^sfeS ±:^^z;^=^:^

-Zgr-g--

-s^«'-

(a)

0)

^5^^^^;g!=p§g :|eM^ r-^

^b^"^ 0)

(a)

10.

{d)

(c)

{e)

{h)

(^)

11.

^ W^£^mA

stepj^i f 12.

B

(a)

flat

;

(/)

(/^)

E

;

:r=.

(r)

A

flat

;

(^/)

F

sharp

;

(e)

D

flat

(/) C sharp. 13.

Subdominants

{a) (/')

14.

m

— G,

E

III

I

I

V

A,

D

B, C

flat,

L

I

VI

The

V

V

VI

IV

P=i= -P—

J:

^4z=i

15.

flat.

flat.

Leading-notes — C sharp, A, D sharp, G, E sharp,

II

V

-^

!-

(S'-r-

:f:=±l

passage III

is

written in the key of

VI

I

fe-^^H

-

IV

II

III

d:

L

V

A

flat.

VI

L

1

F.

THE MAJOR DIATONIC SCALE

i^^

r=tiF

«5t

-6>-^

(.b)

dJc

S^feE^^S^

-kT4-M4

d»:

Si^^§

jcili

=f=tif:

Many

of the exercises in this

are of a suggestive character

;

may be

natures of other scales

able for students to write out

in

and the succeeding chapters No.

example, the sig-

4, for

given, in fact, all

it

is

often desir-

the major scales with their

correct signatures.

In order to avoid confusion which

may

possibly arise be-

tween symbols and Roman numerals when employed for other purposes, the former

T

may be w ritten

n

TH

IT

thus

T

:

7T

—

L

Further tests on this and the succeedinp; chapters, especially designed for the use of students who jiossess the Key, will be found in the

author's

'

Additional Exercises to Part

I.'

CHAPTER

II

INTERVALS (Pages 28-30) 1.

The terms

major

'

'

and

tonic scales, refer to the interval

and the

note or tonic

it is

a minor third

Name

2.

minor

'

(

§10

In a

).

of Interval

Symbol

Major third

3+

(p)

Perfect fourth

4

(c)

Major second

2+

{d) Minor third

3-

Perfect fifth

5

6-

(/) Minor sixth {g) Major sixth (//)

between the key-

a major third, and in the minor

is

{a)

{e)

as applied to the dia-

exists

third degree or mediant of the scale.

major scale this interval scale

'

which

6+ 2-

Minor second

(/) Perfect fourth

4

(y) Major ninth

9+

3.

^ -^5 ^ ^

{b)

{c)

{d)

{e)

{s)

(/)

(0

(.h)

e>

~G>—

6-

5

7-6+4 Name

4.

—'5'—^

of Interval

(a)

Minor sixth

{b)

Augmented

{c)

-^-

a z?

-

3-

3+

zL^^z: fy

7+

5

Symbol

Semitones

6-

8

5x

8

Minor seventh

7-

lO

{d) Perfect fourth

4 6+

9

(