Parker. Manual of Harmony

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MANUAL OF HARMONY AN BLEMENTARY TREATISE OP THE PRINCIPLES Od

THOROUGH

(J^plaaatifln of \\t

BASS,

Spttm

of ftotation;

TEXT-BOOK FOB THE USE OF SEMINABIES AND SCHOOLS, AS WELL AS FOR PRIVATE mSTRUCTION.

By J. O.

D.

PARKER,

A. M.

BOSTON:

PUBLISHED BY HENRY TOLMAN (Successors to George P.

291

& CO.

Reed & Nathan Richardson,)

Washington Steeet. 1862.

ntnvd,

aocording to Act of Congress, In the year 1866, by

NATHAN RICHARDSON, % the Clerk's

Office of the District

Court for the District of Ma«achxu«tts. '

fCBKBOTTPSD BT A.

B.

EIPDER, 6 SCHOOL STftSB.

P REFA.O E

In

this little

work, the object has been to prepare an elemen

tarJ

Text-book

once

brief, simple,

exist

upon the

and

diffuse,

pose,

for the

and

study of Harmony, which should be at concise.

is

excellent works already

voluminous

consequently often too obscure, for such a pur-

and by no means adapted

farther

Many

subject, which, however, appear too

for the

use of beginners. Nothing

here attempted than to impart a knowledge of sim-

A

ple chnral-writing in four parts.

encroach upon

the

of other

limits

step

beyond

this

would

branches of the science,

which, unfortunately, but few seem desirous of investigating in this country.

The author pretends simply studied

to

intelligible form.

to

have laid down nothing new

he has

;

present the rudiments of music' in a perfectly

No

musical knowledge whatever

posed on the part of the student

;

presup-

is

simply, a musical ear.

If

any deviation has been made from the usual method of presenting the subject, it was only when additional clearness would seem

to

be the

result.

In preparing these pages,

work ter,

free use has

that has recently appeared in

a

Professor

of the

been made of

a little

Germany, by E. F. Eich-

Conservatory^ at Leipzig.

Musical

Theory, as at present taught in that institution, though

differ-

;

PREFACE.

IV ing, perhaps, in

schools,

seems

some irimor points from the method of othei

to bear the

palm over

all

others for simplicity

and we have therefore given the preference

upon those

The method

discipline

doctrines

its

of Questions and Exercises pursued here, may-

Beside the common one of instruct-

have a double advantage. ing in this

to

points.

way

is

the former

classes of

younger pupils, or

necessary, they

may

in

any case where

also assist the private student,

by pointing out the more important matters con-

tained in the text, and the

latter

by exemplifying

the usual

With regard to the Exercises, the instructor should by no means confine himself to The few that are given will fall far short of those in the book. method of writing

for four voices.

perfecting the student in the contents of the several chapters,

be varied and multi-

and are merely intended as samples,

to

plied at the discretion of the teacher.

Neither

the end to be considered in

all

cases decisive

;

the same bass can evidently be harmonized in

ways.

is

the

Key

at

on the contrary,

many

Here again the Exercises serve merely

different

as a guide to

the student.

In conclusion, the author trusts he has met a decided want that has long been felt ple harmony.

Boston, August, 1855.

among

the teachejs and students of sim-

IjN'D

EX.

PAKT

I.

NOTATION.

CHAP.

HI,

THE DIATONIC SCALE OF C... THE CHROMATIC AND ENHARMONIC SCALES THE DIATONIC SCALES, MAJOR AND MINOR

CHAP.

IV.

RHYTHM

CHAP.

1.

CHAP,

n

1

6 9 14

PART

II.

HARMONY. INTRODUCTION INTERVALS CHAP. L CHAP. IL CHAP. m. CHAP. IV. CHAP. V. CHAP. VI.

23

24

PRINCIPAL CHORDS OF THE MAJOR SCALE .. PROGRESSION REMAINING CHORDS OF THE MAJOR SCALE DIMINISHED TRIAD TRIADS OF THE MINOR SCALE..... .

29

35

42 46

49

n

INDEX. FAGB.

CHAP. VII. CHAP. VIII. CHAP. IX. CHAP. X. CHAP. XL CHAP. XIL

INVERSION

MODULATION CHORD OF THE DOMINANT-SEVENTH INVERSION OF THE DOMINANT-SEVENTH.... OTHER CHORDS OF THE SEVENTH CHROMATIC ALTERATION OF CHORDS

53

60 64 69

74 81

CHAP.'xm. SUSPENSION

86

CHAP. XIV. ORGAN-NOTE CHAP. XV. PASSING-NOTES AND APPOGGIATURAS....... CHAP. XVI. GENERAL RULES FOR PROGRESSIONS IN

95

WRITING HARMONY CHORAL FROM " ST. PAUL" GENERAL EXERCISES SSY

93

97

99 102 Ill

PART

1.

NOTATION,

A MANUAL OF HARMONY AND THOROUGH

BASS,

N"OTA.TIOISr. CHAPTER

I.

THE DIATONIC SCALE OF C Notation is the system of naming musical sounds, and representing tbem by written characters, just as the speaking sounds of the voice are named and represented by the letters of the alphabet. The characters

Kotatioi».

which represent sounds are

Notea.

called Notes.

As these musical sounds may vary either in quahty or duration, the subject of notation naturally divides itself into two divisions. The

method of representing the this

former,

called Fitch,

and the two following chapters the ;

we

latter, called

shall explain in Pitch,

Bhythm^

will

form

the subject of the fourth.

There are but twelve musical sounds sufficiently distinct from each other to receive different names, and be represented by different characAll which lie between these twelve, are so faintly distinguishablcr from them as to be considered the same sounds; and all which Lie be^ yond them are but repetitions of the same, though more or less acute

ters.

in their quality.

Kliythm,

MANUAL OF HARMONY Tines and auui tones.

Key.

Groundworh of a Melody

These twelve sounds, with reference to their distance from earth and Whole Tones.* From each sound to the next above or below is but a semitone, and to the next but one a whole tone. According as a melody or piece of music begins and terminates upon one or other of these sounds, it is said to be in such or such a Key. There are consequently but twelve different keys in vj-hich a melody can be sung or played. other, are divided into Seviitones

But not

all

of the twelve sounds are required to

the contrary, let the student take his head,

and he

will find

it

make

On

a melody.

any simple melody he may have

in

contains throughout but seven different

Neither must all these seven necessarily be though he will seldom find more than that number. When others do occur, they form an exception, to be explained upon principles that enes, generally speaking.

used,

will be understood hereafter.

Key-Note.

DiaiSnic

There are but seven fundamental sounds, then, required for the ground-work of every piece of music. That which finishes the piece, (and the same generally begins it,) is called the Key-NoU; it is the principal one of the seven, it gives the name to the key in which the melody is performed, and upon it all the other six depend.

Now it is

evident that any one of the twelve semitones

may

be taken

Scale.

The seven tones of a melody, beginning with the keyand sung or written in order, form what is called the Diatonic

as the key-note.

note,

There are therefore twelve different diatonic

Scale of that key.

The seven sounds of one of these twelve

diatonic scales are

scales.

named by C has

seven letters of the alphabet, A, B, C, D, E, F, G; and been fixed upon to represent the key-note or first of the seven. the

Scale of C.

first

scale is called therefore the Diatonic Scale of

have been found

sufficient,

This

C

These seven letters with the aid of certain other signs which we

shall presently explain, to represent all the twelve semitones. Staff.

fejfer-Lines

Notes are written upon five parallel lines, called the Staff, and in the spaces between them; with the aid of additional short lines, as occasion requires, called Leger-Lines.

** The word tone^

It will

te seen,

may have two

significations.

The one, as

dis-

tinguished from a semitone, according to the text the other, meaning any sound, when considered independently by itself. A semitone is a tone, when 80unde(i ;

alone,

and having no reference

to the

sound next aboTc ov below

it

AND THOROUGH FIG.

BASS.

1.

There are two signs called beginning of every

Clefs^

One,

staff.

one of which

is

always found at the

y^ called the G clef^

(or violin clef,) is

used in writing notes for higher voices and instruments. It is always placed on the second line, (reckon always from below,) and a note upon that line always represents the sound above fixed upon as G; that is, the fifth sound in the diatonic scale of C.

FIG.

The other

clef

2i>

and instruments.

2.

called the

or bass

clef, is

put upon the fourth

It is

line represents F, or

F

used for lower voices

line,

and a note on that

the fourth sound of the scale of C.

FIG.

3.

i^=i^ Let us

now

FIG.

C

vrrite

down

the diatonic scale of C, using the

G

clef.

4.

D

fc ^

KoTE. There is still a third clef, -iH, called the C clef, used mostly for voices and instruments of middle register, which we are soiTy to find is gi'owing obsolete in this country, and which we have therefore unwillingly determined to dispense with in the present work.

Clefs,

:

MANUAL OF HARMONY

4

be seen here, that after writing down the seven sounds of the we have added an eighth, and called it C again. Tu prove that the scale still consists of but seven sounds, that this second C was not a new one, and that consequently no new letter was required, the student has but to sing or play through the seven sounds in A?rder, and he will find that, having finished them, he will amve next at a sound It will

scale of C,

but a repetition of the first C, though of an increased acuteness According, or, technically speaking, of a higher pitch. therefore, to what we stated on page 1, with regard to the twelve

which

is

in quality,

sounds of which the ear is capable, it is evident that the other lie somewhere between these two C's.

five

must

Their position and notation aSToTE

the

first

sounds in

Note

we

shall explain in the next chapter.

In singing, playing, or writing the scale, we always repeat tone, C, and finish with it, as indicated in Fig. 4, making eight 1.

all.

2.

Fig. 4 both

evident that if we had continued the series of notes in from above and below, we should have arrived at several

It is

repetitions of C, (as well as of the other sounds,) each of a different still the same sound, C. No human voice, and but few instruments, can produce more than three at the farthest. The piano-forte can produce seven; but it is clear that if carried beyond this, sounds could not be easily identified and distingished from each

quality as regards pitch, but

_

other.

The same C is

that

written on the

FIG.

is

first

written on the

first leger-line

above in the bass

clef.

below, in the

G

clef

Thus

CDEFGABC

5.

I

^ Se^

CDEFGABC QUESTIONS.

What is notation? What are the characters which What is meant by pitch ?

represent musical sounis called?

^

AND THOROUGH What

is

5

BASS.

rhythm ?

How many

musical sounds are there, sufficiently distinct for nota<

tion?

What What

is

meant by a semitone ?

is. a

whole tone? sounds form the groundwork of a melody or piece of

How many music?

_^

What is meant by the key-note? how many different keys can the same melody be performed What is the diatonic scale? In

How

?

m_any are there?

Which G?

What

is

diatonic scale

is

represented by the letters A, B, C, D, E, F,

'the staff?

'

" .

AVhat are leger-lines?

Of what use

How many On which On which

are the clefs?

are there in general use ?

line is the is

the

"Where does the

G

clef placed?

F or bass clef placed? same C fall in the G and F

clefs, respectively ?

EXERCISES. Ex.

1.

Write the notes C, F,

G

and A,

in the

G

clef,

without leger-

iines. 2. 3.

Write the notes C, E, B, D and G, on leger-lines, in the G clef. Write the notes A, F, B, C and E, in the bass clef, without leger-

lines.

4

Write the notes D, B,

G

and C, only upon

leger-lines, in the

bass

clef 5.

6.

Write the diatonic scale of C, in the bass clef, including three C*8. Write the diatonic scale of C, in the G clef, incladlng three C'g.

:

MANUAL OF HARMONY

CHAPTER

II.

THE CHROMATIC AND ENHARMONIC SCALES. By

sounding the different notes of the diatonic scale of C, a musica.

ear will easily perceive that they are not at a uniform distance from each other throughout. Between C and D, for instance, a semitone can

be inserted, which shall be readily distinguished from either of those two sounds. This, then, must be one of the twelve semitones, or one of the five Avhich were not included in the scale of C. In like manner, between D and E a semitone can intervene. But between E and F the ear can supply none. If we carry the investigation further, we shall find that the other three semitones will come between F and G, G and A, and A and B respectively. These five semitones are represented as follows. Sharps,

This sign, ^, called a sharp, the sound, represented cnen,

we wish

when

by that

placed before a note serves to raise

next semitone above. If, between C and D, we express iv

note, to the

to represent the semitone

thus

FIG.

6.

I and the note

The

is

called

'¥

C sharp.

five semitones, then,

not included in the scale of C, are wn'iteu

thus:

FIG.

^—

I Chromatic aroending.

7.

^-

The whole twelve semitones, written or played "^^^^ scaler

is

^ in order, constitute

called the chromatic scale, in centra-distinction to the diatonic

AND THOROUGH

BASS.

CHROMATIC SCALE, ASCENDING. FIG.

8.

j^^l^Eg;:^ Observe that we have styled is,

when

upper C.

this the ascending

chromatic

scale,

that

the twelve semitones are played through from a lower to an

When

played from an upper to a lower C they are written

different.y.

As a sharp

\), called a fiat, next semitone below. Thus, if we wish to pass to the semitone between it and A, we write it thus

raises a note a semitone, so this sign,

serves to lower

from

B

it

FIG.

^ ana the note

called

is

iescendin scale descending

is

B fiat.

9.

m So with the others.

The chromatic

therefore written thus

^ZI2^=^^-

Cbromatie descendinz

FIG. 10

By comparing

Flat

to the

-m-

-J?=5-Z^

the ascending and descending chromatic scales,

it

will

be seen that the same semitone can be written in two different ways. For instance, the semitone between F and G Avas written in the one case

F sharp, and in the other as G fiat. We shall see hereafter that theory requires a sound to be written sometimes in one way and sometimes in another, because, according as it is a sharp or a flat, it has a as

meaning. For instance, F sharp is theoretically quite from G fiat, though practically the sound is the same, and produced by the same kc}^ upon the piano-forte or organ.

totally different

different

Note. There are also signs called double sharps and double flats, X, bb> though less frequently used, and which serve to raise or depress a note two semitones. Thus the tone B might be written as A double iharp, and C as X> double fiat.

MANUAL OP HARMONY Enh&rmome Scale.

When we write the twelve semitones in order, representing each one, both as the semitone above lowered, and as the one below raised or if one of the seven sounds of the diatonic scale of C, also in its natural This brings us to the explace this is called the Enharmonic Scale. planation of a third sign, ls|, called a Natural, which serves to restore a note to its natural place, after it has been raised or lowered by means of a sharp or flat.

—

—

ENHARMONIC SCALE. FIG.

11.

:|^szp^

The Enharmonic and Chromatic Scales the

same in keys.

all

notes braced together,

it

will be seen, express the

Either of the three kinds of scales above described as the key-note

— or, in

it

may commence

any one may be taken other words, the scales can be played in any of is evident that the chromatic and enharmonic

upon any one of the twelve semitones the twelve keys. 'But

— that

same sound.

is,

produce the same succession of sounds in all keys, as each includes the whole twelve semitones. These two can therefore convey no idea of key or tonality, that is, the ear will not identify any particulai key when the passage occurs, excepting so far as they terminate upon scales will

the key-note.

The enharmonic

scale exists only in theory, but will never occur in

practice.

The chromatic

scale

is

frequently

met with

character, especially for the piano-forte,

cuted.

is

in

music of a brilliant most easily exe-

it is

however, appear under different forms, that is, requirsharps or flats, depending on the key in which the written. This will be better understood hereafter. It will,

ing more or piece

where

less

But with the diatonic scale the case is widely different. According as commences upon either of the twelve semitones, it differs with each one of them. As there are twelve, it is important that the student be familiar with the contents and structure of each one of them, before it

AND THOROUGH BASS. cammencing the study of harmony.

9

We shall therefore examine them

tt the next chapter.

QUESTIONS. Between -which sounds of the diatonic

scale of

C do

the other five

semitones intervene?

Of what

use

What

the chromatic scale?

is

Of what use

How

is

is

the sharp ? the flat

?

do the ascending and descending chromatic scales

differ in

writing?

What What

is

a natural?

is

the enharmonic scale?

Which kinds of scales are the same in Which kind occurs only in theory? How many diatonic scales are there?

all

keys?

EXERCISES. 7.

Write the ascending chromatic

scale, in the

key of C,

in the

G

clef.

8.

Wi-ite the descending chromatic scale of C, in the bass clef in-

clurling three C's. 9.

10. 11.

Write the enharmonic scale, in the bass clef, descending. Write the note A in three different ways. Write the note G in three different ways.

CHAPTER m. DIATONIC SCALES, MAJOR AND MINOR. The

diatonic scale

is

the

groundwork of all

the whole system of harmonic combinations.

amine

it

more

iifferent keys.

d.osely, with a

view

harmony, at*^ of must therefore exconstruction in aU the

rules of

We

to learn its

MANUAL OF HARMONY

10 Construction ic

Scj£?.*°^'

Let us take the diatonic scale of C. "We hare seen in the last chapter ^ ^^ ^^^^ ^ semitone removed from E, and also C from B; but that the other sounds are a whole tone from each other. The diatonic scale can therefore he divided into two parts, each consisting of two tones and a semitone; and the two parts are removed a whole tone fi-om each other; as is represented in the following figure. ^^^*

FIG.

12.

Tonic and Dominant,

The sound which commences the first half is called the Tonic, that which commences the second half the Dominant.

Degrees of the Scale.

The successive sounds are also called degrees of the scale,* and are numbered and named accordingly. Thus, C is the ^rsi degree of the scale of C, E the third degree, A the sixth, and so on. The dominant is

therefore the fifth of the scale. Fig. 12 represents the construction of every diatonic scale, whichever

of the twelve semitones the

same

principle

we

take as the key-note.

form the other eleven

We

can therefore on

scales.

For instance suppose we wish to form the diatonic scale of G. The half will begin upon G, the second half upon D, the fifth degree, or dominant. We must take care that each half shall consist of two tones and a semitone; and, if it becomes necessary, a sharp or flat must be introduced to produce this result. first

FIG.

13.

SCALE OF

C. ONE.

o^^;.

half.

one. half.

one.

m

i SCALE OF

G.

ONE. HALF.

ONE. OKE. HALF.

ONE.

^

I * Hereafter, -when scale.

we speak simply

of the scale,

we mean of course the

dza'.tikC

AND THOROUGH Here

it

will be seen that the degrees of the scale of

actly -with those of the scale of C, until

which ought

F,

11

BASS.

to be a

we come

G correspond

ex-

to its seventh degree,

whole tone from the sixth degree, E; whereas

F is but a half-tone from E. F must therefore be raised a half-tone by means of a sharp, and this will also produce the required distance from the seventh to the eighth degrees.

To take one more FIG.

instance, suppose

are

tofoimthe

scale o{ AJiat.

^

£^ B

we

14.

We shall find here that four flats will have to be used. is a tone and a half from A flat, and must therefore make

semitone to gree,

is

tone. will

it

but one tone.

For instance, be lowered a

In like manner, D, the fourth dewe require but a half-

a whole tone from C, the third, whereas

This must also be lowered accordingly; and so on. This matter clear by consulting the keys of the piano-forte.

become

When we stance,

wish to write down a melody in any key, in not write a flat before every A, B, D and

we do

but to simplify the notation, the beginning of each

FIG.

which means that all A's, or sung A flat, B flat, &c.

The

requisite

we

place the requisite

staff, in their

flat for in-

E

that occurs,

number

of

flats at

proper position, thus

15.

B's, D's

number of

A

flats

and E^s that occur, are

to be played

or sharps for each particular key are Signatures, It is important that the student

called the Signatures of that key.

should naake himself familiar with the signatures of every key.*

A piece

sometimes written partly in one key and partly in another Moduls^n, permitted to leave the original key for a while, though it must afterwards return to it. This is called BIcduJation. There will

— that

is

is,

occur, in this case, notes foreign to the

*

The order

in

wMch

key denoted by the signatures,

the signatures are usually arranged upon the staff will be

{earned by obserration and experience.

MANUAL OP HAKMONY

12 Aocidentala.

which, will have to be represented accordingly

or naturals, as the case

They

may

be.

They

by additional flats,

are placed, however, not at the coramenceraent of the

the signatui-es, bu: with each note as

it

eharps,

are then called Acciientals. stuflF,

like

So with the chromatic

occurs.

icale.

Kiadred

•

^^^'

Thofie keys

which have the most tones and semitones

are called kindred keys.

F, lii»org£aJ^*

Thus, the kindred keys of

G

in

common,

are those of G,

and so on.

which we have treated thus far is called the major But every major scale has its so-called para?ZeZ mirmr scale.

Tjie diatonic scale scale.

It will often be found that a melody contains all the seven sounds of major key, but the key-note, that is, the first and last of the melody, Observe, is the siocth degree of the major scale, instead of the tonic. then, that in this case the sixth degree becomes the tonic, and the melody must finish with it. As this minor scale contains the same tones as the parallel major scale, it must have thtsame signatures. For instance, take the scale of C. Its sixth degree, A, becomes the tonic of the parallel minor scale, which, like the major scale of C, will require no

a

signatures.

FIG.

16.

SCALE OF A MINOB.

I Of course the relative position of the whole tones and half-tones becomes altered in the minor scale. The half-tones here occur between the second and third degrees, and between the fifth and sixth, as ^vill be seen in the above figure.

To flats,

take another instance: the major scale of

B

flat,

E

of the parallel

FIG.

and A flat. minor scale. flat,

Its

flat

-

17.

^

9- \>

We shall find,

E

in Part II, that the rules of

gree of the minor scale to be altered

requires three

sixth degree, C, becomes the tonic

-

g harmony

o

^^=

require one do

:

AND THOROUGH

18

BASS.

Other tones are also sometimes altered for the purposes of melody. But the essential elements of the minor scale, and of its parallel major scale, are the

same.

QUESTIONS.

How may the diatonic major What is the tonic? What is the dominant?

scale

be divided?

Which is the first degree of the scale of C? Which is the seventh degree? Which is the third degree ? Which degree is the dominant? What is the order of tones and semitones scale

,

in every diatonic

major

?

What is meant by the signatures of a key? What is modulation V What are accidentals? What is meant by the term kindred keys ?

How is the parallel minor scale formed from How many diatonic minor scales are there?

" •

.

the major scale?

Where do the semitones occur in the minor scale? Which degree of the major scale is the tonic of

the parallel minor

scale ?

What is

the tonic of the parallel minor scale of

Of E major ?

major?

Which degree

of the

Of G major? minor scale is the

F major? Of A

tonic of the parallel

flat

major

scale?

What minor?

is

major scale »f minor? Of F sharp minor? the dominant of E major? the dominant of C minor? the dominant of G minor? the tonic of the parallel

OfB

What is What is What is

B

flat

EXERCISES.

E

12.

Write the diatonic major scale of

13.

"

14.

Write the major scale of D, with the signatures, Write the minor scale of D, with the signatures. Write the signatures of G minor. " " " E major.

15. 16.

17.

"

[2]

''

flat.

F.

minor?

Of C

—

P

MANUAL OF HARMONY

14

Write the si,?natures of B flat major. " " " D minor, in the bass clef. Write the s(;ale of G major, witli tlie signatures, in the bass clef, " " " r sharp minor, in tlie bass clef, with signatures. " " " " " E minor, " " " " " " " A major, Write the ascending chromatic scale, in D major, with the sig.^

18.

19

20 21. 22.

23. 24.

natures.

Write the descending chromatic

25.

tures in the bass

scale, in

G

minor, with signa-

clef.

Write the lescending chromatic scale, in C minor, in the G clef. Write the ascending chromatic scale, in B flat major, in the bass

26.

27. clef.

Write the signatures of B major, in the bass clef. " " " F minor, in the G clef. Write the scale of D flat major, in the G clef, with the signatures,

28. 29.

30.

including three tonics.

CHAPTER

lY.

RHYTHM.

Ws have

said that sounds

pitch or position. V»hie of Xotes.

may

vary in length or duration, as well as in

This can also be denoted by notation.

The note, ^, which we have hitherto used, is called a whole note. Each whole note may be divided into two halves, each half into two quarters, quarters mto eighths, and so on. FIG.

18.

V\Tiole Note.

Half Note.

Quarter Note.

:1^ Sixteenthjs.

d

—ia—

^

Thirty-seconds.

tzizilj

—1^=:

Eighths.

t^^=i*

WHEN TWO —

-OR MORH

-OCCCRIK

11-

-SUCCEBSION.JSixty-fourths.

AND THOROUGH Each of these has a corresponding

when a pause FIG.

•

10

BASS.

sign, called a Jlesi^

to

be used

Eesl.

occurs in a melody.

19.

Wliole

Half

Quarter

Eighth

Eest.

B-est.

Rest.

Kest.

Sixte^jnth Thirty-second Sixty-fourth Eest. Eest. Rest.

Music is divided into Bars or Pleasures, separated from each other by Bar a perpendicular line, each of which bars must be of the same value in notes and rests. FIG.

A

20.

dot after a note or rest adds to

FIG.

it

half

its

Dotted Notes anf

value.

Rests.

22.

^*-;^i

*--

When there is a pause of a whole bar to be observed, the wJioIe rest is always used to denote it, whatever be the value of notes required in each bar. FIG.

24.

^mi As may be seen from

the foregoing examples,

we may assume any

wtote

16

MANUAL OF HARMONY

length or value

we

please for each bar, taking care that

it

be t^nifonn

throughout. Oouiits.

In order to ensure this unifonnity, and make it more perceptible to is counted by regular beats, like the strokes of a pendu lum. Each count may represent any kind of note we please, and thfe number of counts in each bar is also optional. But this must always be denoted at the beginning of every piece by two figures, placed immediately after the signatures, the upper figure denoting the number of the ear, music

How indicar

counts in each bar, and the lower the kind of note which each count represents.

FIG.

25.

gi:^li^i:S^ FIG.

26.

12

3

12

In 25, the figure 2 indicates the

number

of counts in each bar, and 4

the kind of note represented by them.

In 26, the figures indicate that three eighth-notes are to be counted in each bar.

Common Time.

The rhythm, where four quarter-notes are counted in each bar, is the most common of all, and is hence called Common Time. It is, however, always represented by this character, (^, instead of by the figures

Alia Breve,

In like manner, the same character is used with a line drawn through instead of the figures §, and called Alia Breve.

|_ it

-P^^SePE It will

and not

be observed that these

diflFer

in the value of each bar.

only in the method of countiTig

AND THOROUGH Now

Note

that

we have learned the use of bars, we would mention that acci- Accidentala are good throughout one bar, and no fur- good

dentals, (explained in the last chapter, ther.

They must

)

therefore be repeated in each bar

tinued, or corrected

17

BASS.

by a natural if the note

i5

if

the altered note

to be restored in the

is

to

be con-

the upper figure is an even number, that is, when there are an number of counts in each bar, the rhythm is said to be direct ; and when odd, indirect. Of the latter, only the numbers 3 and 9 will ever be met vrith.

When

even

A primary accent always first

count.

When

the

occurs at the beghining of each bar, on the in which a piece is played is moder-

rhythm be

(In indirect

direct.

Direct

and

^^^^ Accent.

movement

ately quick, a secoridary accent falls

the

^^^ ^"^^

same bar.

on the middle of the bar, provided rhythm there can evidently be no

secondary accent.) If the movement be very slow, these accents may be again sub-divided. Or, if it be very quick, a primary accent can only fall upon every other bar, and a secondary accent upon the alternate bars. This, however, is a matter which the musical feeling of the student will make more intelligible to him than can be done by explanation.

A piece may begin

with a half, or any fraction of a bar; that

is,

with

an accented or unaccented note.

The sign /t\, called a Hold, over a note or rest, held indefinitely, without any regard to time.

means that

to

be

The following are the kinds of rhythm most usually occurring

in

it is

practice.

FIG.

28.

Cases often occur where a note the next lower order of notes.

[2»]

is

divided into

A quarter-note,

three,

instead of two, of

for example, can be di-

Triplet*,

MANUAL OF HARMONY

18

Tided into three eighths. They are then called Triplets, and the figure J is generally placed Dver the group.

Thus, a bar of

ccmmon

effect as 1^2 time, or 3

time

may

time that of

be

filled

out so as to hare the same

^.

These, however, are exceptions, and their use will only be learned by experience.

Svspo

"We have alluded above to the movement in which a piece is performed. This can only be partially indicated, that is, whether the piece shall be played more or less rapidly or slowly; the rest is left to the performer's It is done by means of the Italian words, Andante, taste and discretion. Adagio, Allegro, Presto, &c., &c., which, together with other terms, having reference to the style and expression to be observed, are written at The tenns the commencement of every piece. It is called Tempo. most in use, as well as their efi'ect, will be learned best by experience-

We

shall therefore dispense with

an enumerated

list

of them, referring

the student to his musical vocabulary.

QUESTIONS.

How are notes

divided ?

Of what use

the rest ?

What

is

is

the bar used for?

How does a dot affect a note or rest? How is a pause of a whole bar denoted ? How is the time, or method of counting a Where

are the figures placed

on the

What is common time ? How many half-notes in a bar How many quarter-notes ?

How

long

What is What is

is

an accidental

to

piece, indicated?

staff?

in aila oreve

rhythm?

be obsen^ed?

rhythm ? indirect rhythm?

direct

Where do3s the primary accent Where in rapid movements ?

fall in

moderate movements ?

AND THOKOUaH Which kind

of

19

BASS.

rhythm has no secondary accent?

What are triplets ? What effect may be given to a bar of common What is meant by the tempo of a piece ?

time ?

EXERCISES.

35.

Write a bar of sixteenths in § rhythm, with the counts. " " " alia breve rhythm, with the counti. eighths " " " " half-notes " common time, " " " " thirty-seconds in | time, " " " " time, using triplets,

36.

"

"

37.

"

"

38.

"

"

*'

"

"

••

31.

32. 33.

34.

39.

40.

I

I

"

in sixteenths,

" *'

"

in quarter-notes,

"

in half-notes,

O

"

in alternate quarter-notes

2

««

§

I

"

and

"

" .

rests.

sixteenth-notes and rests.

Note. We have now finished the subject of notation, and the student is "warned not to commence the subject of harmony until he is perfectly familiar with the

matter contained in the foregoing chapters. To his special attention we would re» commend familiarity with the clefs, and the twelre diatonic major and minor scales, with their proper signatures, and the position of the semitones in each. It is true that some keys are much more common than others yot he who aims at a thorough ;

mujsical

knowledge should be able readily to transpose from one key into

We shall make

But the student must be careful not to and remember that what and that when we speak simply of the scak^,

being the simplest as regards notation. identify the rules of is

true of one scale

vre

all others.

use of the scale of C for the most part in our future examples, aa

is

Harmony

too closely with that key,

true of another

;

aitaa the diatonic seal? of every key, without reference to tonality.

PART

n.

H^RM:o]srir

MANUAL OF HARMONY.

28

HA-RMOISTY. INTRODUCTION. The question is often asked ))y persons unskilled in music, bow one can learn to write it by rule. This confusion of ideas arises from their not making a proper distinction between melody and harmony. The former consists of a succession of single musical tones, of greater or less duration, following each other in a certain metrical regularity, and expressive of the thoughts of the composer.

It is evident that such a cannot be subjected to any law, any more than the author of a literary work is accountable to rules for the production

train of musical ideas

of his brain. They are the result of inspiration only. The /eu; points connected with the subject of melody, which arc in the slightest degree capable of being systematized, are rather more matters of innate musi-

than arbitrary rules; and, such as they are, constitute a tobranch of musical science, (that of Blusical Fo/v/z,) with have nothing to do in the present work.

cal feeling,

tally different

which we

It will be found, however, by listening to any musical composition whatever, that the ear is not taking in merely this succession of single musical sounds which form the melody, but that other tones are heard together with each individual tone of the melody, produced by one or more human voices, or by accompanying instruments. It is this com-

bination of sounds which constitutes harmony. is

performed alone by

itself,

Even when a melody

a musical ear naturally supplies these com-

which are heard in the imagination. So that every melody vmst be founded upon harmonic combinations, and the ear cannot avoid binations,

them.

Now it is clear that out of the various combinations that can be produced with aU the tones of which we have any knowledge, some will

:

24

MANUAL OP UARMONY

—

have an agreeable

eflfect upon the ear, and others not thtit the former be called legal, the latter illegal. Hence arise rules, by which these harmonic combinations must be governed. What these rales are, it is the object of the remainder of this little work to investigate. And, in the first place, we shall proceed to inquire what the tones are which we

may

have

at

our

command for forming harmonic

CHAPTER

combinations.

I.

INTERVALS. Intel

The

ml

distance between two degi-ees of the scale

is

called an

Interval. B.oyf

An

named.

interval receives

its

name hy reckoning

number

the

of

degrees from the lower to the upper of the two wl ich contain it,

and counting the FIG.

first

30.

Third.

The 3

as one.

intervals of the

major

Fourth.

Seventh.

i^

scale complete are therefore

denominated

follows

FIG.

31.

Prime or

Unison. Second,

m

Third. Fourth. Fifth. Sixth. Seventh. Octave. Ninth.*

Ijlgl^^ii -^ )-

* The repetition of the second, for harmonic purposes, ninth, as will be seen hereafter.

is

usually treated as a

AND THOROUGH BASS. The Unison, Fourth,

Fifth,

25

and Octave, are called Perfect

mtervals.

Perfect

and

The Second, Third, Major intervals.

When we

wish

to

Sixth, Seventh,

Major

modulate, and thereby alter the degrees of

by means of

the major scale

and Ninth, are called

receive modified names, and

accidentals,

become

the altered intervals

either

Minor, Augmented,

or Diminished.

A

minor

interval

is

fbrmed only from a major, by lowering ^^**'^

the upper degree a half-tone. FIG.

32.

Minor

Minor

Minor

Minor

Minor

Second.

Third.

Sixth.

Seventh.

Ninth.

S Or

in the

FIG.

key of

D

r^fer

=^

major,

33.

:^

^^s^

ii=:

'^

An augmented mterval is formed both from the major and .. . , ^ 11/. 1 perfect mtervals, by raismg the upper degree a half-tone.

,,

But augmented FIG.

thirds

and sevenths never occur.

34.

Augm.

Augm.

Augm.

Augm.

Augm.

Second.

Fourth.

Fifth.

Sixth.

Octave.

^«^

fe [2]

Augmooted Interrea.

:

MANUAL OF HARMONY

26 The same FIG.

in the

A

E

=

flat.

35.

fej Diminished

key of

f=ti|

diminished interval

lutcrrals.

terval,

^

^EfeEE^ is

formed from a minor or perfect

by lowering the wjoper degree a

in-

half-tone.

Diminished seconds and sixths do not occur. FIG.

36.

Dim.

Dim.

Dim.

Third.

Fourth.

Fifth.

I*

Jo:

:fe=:

Dim.

Dim.

Serenth.

Octare.

S

:lSE=

In accordance with the above, the student must be careful to make a between changing a tone by means of an accidental, and

distinction

changing

it

by moving FIG.

in a, the interval

is

to the

next degree of the

a minor sixth

tween

differ-

;

in h,

it is

an augmented fifth.

same sound upon the

theoretically they are different.

•nt degrees Of the Scale,

For instance

37.

the two intervals produce the

Intervals be-

scale.

(See Part

I,

Though

piano-forte, yet

Chap. 2.)

In reckoning the kind of interval between any two degrees of the g^ale other than the tonic,' we must regard as a new the lower degree ^ ° tonic, and reckon as if the upper were a degree of the new scale. For

we wish to know the interval between the fourth and seventh degrees of the scale of C, that is, between F and B, regard F as a new

instance, if

tonic,

and

Ave shall find that

B

is

an augmented fourth, B flat being tha may be seen in the following ex

perfect fourth in the scale of F, as

ample.

AND THOROUGH FIG.

27

BASS.

38.

Augm. Fourth

i S it will be found that in a major scale, from the third to the octave a minor sixth. In C, for instance, taking E as a tonic, C sharp and not C is the sixth degree of its scale, C must therefore be at a minor in-

So

is

terval

from E.

It is

important that the student be familiar with the different relations

v^hich the degrees of the scale bear to each other, as well as to the tonic.

An

mteryal

is

when the upper degree

said to be inverted,

ii

transferred an octave lower.

FIG.

— -i— 39.

Fifth

Seventh

Sixth

-^

'-

inverted.

^ s

S

L

1

inverted.

invertod.

It will be seen that a prime inverted becomes an octave, a second a seventh, and so on, as in the following table:

12

3

4

5

6

7

8

7

6

5

4

3

2

1

8

Note

1.

The same method can be used here for reckoning the inverted interval, from one degree to another that is, regard the lower note

as above in reckoning

a

new

u

;

tonic.

Note

2.

An

haverted ninth

is

but a second again.

But it will be found that the character of some intervals becomes altered by inversion, as, for instance, a viajor third becomes a minor Bixth.

In this respect the following rule will hold good

By

inversion, major intervals

minor

"

become minor, "

major.

inverted

MANUAL OF HARMONY

28

By

inversion,

augmented

intervals

diminished

augmented.

**

remain

*'

perfect

Hence arose the name perfect

become diminished,

*'

perfect.

intervals.

The fourth degree of the scale is called the Suh-Dominunt^ when inverted it is a fifth below the tonic, as the domi-

8ub-Domi-

because

nant Coojonance

Mflsonanoe

'

is

The

a fifth above. perfect intervals are called Perfect Consonances,

Thirds and Sixths, both major and minor, are called Imperfect Consonances.

All other intervals are Dissona^ices. (The meaning of these terms will be better understood hereafter.)

QUESTIONS. What

is

an interval?

Hew is an interval reckoned ? How many kinds of intervals are Which Which

the major intervals

How is

a minor interval formed ?

there?

are the perfect intervals in the

major scale?

?

What kind of intervals may become augmented ? and how ? What augmented interv^als are met with in practice ? From what hind of intervals may diminished intervals be formed? and how? What

the interval between the second and

is

fifth

degrees of the

scale?

Between the second and seventh ? Is the inten'al major or minor between the fourth and sixth degree* of the scale

Which

What

?

between the second and fourth degrees? an inverted interval?

is it

is

HoAV does inversion

What

affect the different intervals ?

does a perfect fourth become by inversion?

AND THOROUGH BASS. What " " "

does a minor third become by inversion? " " " an octave

" "

Why What

29

are the perfect intervals so called is

i

the sub-dominant?

Why is it so called? How aie consonances Which Which

'<

f'

"

a diminished seventh major seventh "

divided?

are the perfect consonances? the imperfect?

EXERCISES. 41. 42.

4a 44 45. 46.

Write the perfect intervals of the scale of B flat major. (( " " " major D u diminished " " Eflat " u augmented " " " C " minor " G " major " A '

'

" perfect

47.

"

"

.

ir1

F major, and

invert

them

"

" major augmented " " minor

D E g

U

((

Q.

U

it

« U

52.

diminished " " minor "

r<

u

n

(1

63.

" imperfect consonaiices of the key of A.

54.

" perfect « u

48.

((

49.

((

50.

(1

51.

55

flat

" n

CHAPTER

" "

"

G.

"

A flat.

n.

PRINCIPAL CHORDS OF THE MAJOR SCALE.

A

chord

is

a combinatioii of three

or

more

tones,

sounded Cbwl

together.

Every chord must be conceived of

as built

upon a

certain

MANUAL OF HARAIONY

80 Boot

tone, called the base,

by adding The base

to

is

it

fundamental

tone, or root of

chord,

>.he

certain others.

of course the lowest tone, and the chord

is

built

upward

from below.

The

Triad or

simplest chord of

Commoi Chord.

This all

all is

formed from a tone by adding to

third and ffth.

it its

is

called the Triad, or

Common

Chord, and from

it

other chords are derived.

FIG.

40.

Root.

of Chorda.

is named from its root. These, therefore, are the i!om chords or triads of C, F, A, and D, respectively.

Every chord

Names

mon

The above chords will, however, be found to differ in one respeo^. Those of C and F have major thirds, while those of A and D have nixnof thirds.

Major aad

A triad with a major third

is

called a

Minor Triad.

A

is

called a m,inor triad.

triad with a

Of all

minor third

major

triad.

the chords of the diatonic scale, there are three which refiuira

and we shall adduce several reasons most important of all.

special attention,

are the Chords of the Tonic, Dominant, and

Sub-Domi*^^*

Their intimate •oanwtion.

The

to

show

that they

principal chords of the scale are those of the to7iic,

dom"

r j j mant and3 suo-dommant. •

.

'

These, then, in the key of C, will be the chords of C,

FiESTLT. other.

They have a

G

and F.

natural connection, being built one

upon tht

AND TnOROUQH ilU.

81

BASS.

41.

m F

G

C

C, the root of the tonic chord,

becomes the

fifth of

that of the sub-

dominant, and G, the fifth of the tonic chord, becomes the root of that of the dominant. Thus it will be seen that these chords are intimately connected.

Secondly. These three chords contain all They form, therefore, its groundwork, and

the degrees of the scale. most frequently

are the

Groundwork of the Scale.

used, because they serve so perfectly to represent the key of a piece of

music, and fix in the mind the idea of tonality.

Thirdly. sic

A

proof of their importance

lies in their

Mu-

simplicity.

of the simplest kind, and of a light character, (such as dance-music,)

Tbeirsiraplioity.

its nature does not require complicated harmony, will be be grounded almost exclusively upon the harmony of these

•which from

found

to

three chords.

Fourthly. we

If

we

build chords

upon each degree of the major scale, The only MajorTriads major triads. All the rest are minor. of the Major

shall find that these are the only

Fifthly.

They

Scale.

are used in

making

cadences, of

which

hereafter.

Harmony is usually conceived of and written mfour One interval of the triad must therefore be doubled. The

tone most usually doubled *'

is

parts.

four parts.

the root, makinoj an octave. .

The

fifth is less

FIG.

often doubled, and the third less often

,

is

Oneinterrrf doubled

still.

42.

In theory we usually consider harmony as written for four voices, each voice singing one tone of the chord. Each part has a distinct name. Of the two extreme or outer parts, the lowest, that which takes the root of the chord, is called Bass. The higher, that which performs the melody, is called Soprano. Of the two middle parts, that next to

the bass

Cadences.

Harmony in

called Tenor,

and that next the soprano,

Alto.

Names

of the four voices or

parts.

:

MANUAL OP HARMONY

82 ThTMpofti^

Writing in Score.

:

Either tone of the chord may be tdken as the melody, that is, for the soprano voice; and according as the octave, third ox fifth is so taken, the chord is said to be in the 1st, 2d or 3d position respectively. The distribution of the alto and tenor parts Is also optional.

Usually a

diflFerent

staff is

taken for each voice, which

is

called

Thus

writing in score.

FIG. 43. a.

1st Pos.

6.

2d Pos.

3d Pos.

SOFBAKO.

Alto.

1^

Tenor.

Bass.

NoTB, It must be remembered that the tenor voice sings an octaTe lower than where it is written. For instance, in a in the above figure, the tenor lies apparently above the soprano but it is in reality the same E which, in letter c, lies in the alto ;

part.

We shall hereafter, for convenience, written for the piano-forte.

riG.

use only two staves, as music

44.

i^^^^N but the student must be able Distribution vf ihe chord-

is

Thus

to write all the

mz^: examples in

score.

was optional how the tones of a chord were distri ^^^^^ among the three upper parts. But they must lie within the ordi "We have said

it

AND THOROUGH

83

BASS.

nary compass of those voices, as indicsated in the following table, avoiding too frequent use of the extreme tones. FIG. 45. Soprano.

Tenor.

Alto.

Bass.

^^m^^^ liJot

more than an

octave should intervene

between any two parts, ex-

(

cepting between tenor and bass.

When

all

tave, the

three of the upper parts

harmony

is

an open or dispersed

lie

within the compass of one oc-

said to be in a dose position; position.

when

not,

it is

called

In a succession of chords, (of vfhich

hereafter,) a rrimgling of both kinds has the better effect.

The following example shows some of the more common

positions of

a chord, both open and dose.

FIG.

46. Close.

Open.

Open.

Close.

Open.

Open,

Close.

i^ili^il

i

ie^lllE^iHiiif In closing this chapter,

we cannot urge

He

inant.

upon the student dominant and sub-dom-

too strongly

the importance of the three chords of the tonic,

should be able to recognize them at once in

all tix; different

keys, before going on to the next chapter.

QUESTIONS. What What

How

a chord?

is

the root of a chord? a chord formed?

is

is

Of what

How

intervals

are chords

is

the

common

chord or triad composed?

named ?

What is the meaning of major and minor triads? Which are the three principal chords of the scale?

Close

and

^^^ ^°^

84

MANUAL OP HARMONY

What facts give them their importance? In how many parts is harmony usually written? Which

interval

is

most frequently doubled?

What are the names of the Which takes the melody ? Which Which

four voices?

the root?

tone lies in the melody when the chord Which, when it is in the 1st? What is meant by writing in score?

What alteration is made in writing the tenor What rules can be given for the distribution What is meant by a close position V

When

is

a chord

in the

is

in the

3d position?

part ?

of the tones of a chord?

open position?

EXERCISES. 56.

Write the simple triads of the tonic, dominant and sub-dominant

of the scale of C, without doubling.

E

57.

The same

58.

61.

Write the chord of the sub-dominant in the key of F. " " " dominant in A. " " " sub-dominant in B flat. " " " tonic in D.

62.

Write the chord of C

59. 60.

two

in

flat.

in four parts, in three close positions, ujing

staves.

63.

The same with the dominant of G.

64.

Write the chord of

65.

The same with the sub-dominant of E

Write melody. 67. Write melody. 68. Write melody. 69. Write melody. 70. Write melody. 71. Write 66.

A

in three

open positions. flat.

the chord of

F

in score, (open pos.) with the 5th in the

the chord of

E

in score,

(open pos.) with the 5th in the

the chord of

G

in score,

the chord of

C

in score, (open

the chord of

D

in score, (close pos.) with the

(open pos.) with the 3d in the

pos) with the 3d in the 3d in the

chords to the following bass, with the names of each chord according to the key denoted by the signatures. Use two sta res and

put the octave in the soprano voice.

:

AND THOROUGH BASS.

35

Close Position.

^JSg^^^H^ if^^&g^^^ ^m Open

Position.

-Jr^.

CHAPTEE m. PROGRESSION. The laws of harmony require that every chord bo considered not merely by itself, but also as connected with the chords that precede and follow

it.

In a succession of harmonies, the chords mast move smoothly and Prtgrerton. easily from one to another, and each part perform a smooth and flowing melody by itself, as well as blend well with the other three. Hence arise rules.

This movement of one chord to another

We have shown

is

called Progression.

preceding chapter that either tone of a chord may be taken for the melody. A pleasing variety is therefore obtained by taking sometimes the third, sometimes the fifth, and so on; but never (or very rarely) the same interval twice in succession.

KuLE.i'

mon,

it

may be

in the

When

two successive chords have

must be retained well connected.

in the

The

same voice

other parts

a tone in

com-

in both, that they

move

to the nearest

tone.

For instance, suppose we wish the chord of the dominant that of the tonic, or in other words to write

harmony

to follow

to the bass

Cotnfttion

:

F

:

^

T

^

MANUAL OP HARMONY FIG. 47.

9: We find according to to both chords.

then,

must

FIG.

retain

The it

Fig. 41, (chap. II.) that the tone

voice which takes G, or the

in the second chord,

where

fifth, in

G

comirion

becomes the octave.

it

48.

IS

ii be seen that the observance of

It will

is

the first chord,

—r—gs:

not only serves to con-

this rule

nect the chords, but gives variety to the harmony, by causing each voice to take different intervals in each chord. For instance, in the first

chord in Fig. 48, the tenor takes the third and the soprano the octave; and the soprano the third; while the alto voice has the connecting tone, which is in the 1st chord the fifth, in the second the octave. »

in the second, the tenor the fifth

Again,

if

we have

FIG.

the bass

49.

we

find in Fig. 41 that

ny

thus, then

FIG.

belongs to both chords.

50.

Si at

C

1

^0 —rzrr—

-f^^— g=4 —

We write the harmO'

—

r

^^g5^

mm

37

AND THOROUGH

vj. When Rule. ^^ two successive chords have «o tone in comtlie voices must move in such a way that parallel (or ^

_

mon,

S?j??^'***f* Fifths and Octaves.

eonsecuiive) fifths and octaves shall not occur. TyfO voices

m&v

raoYe in parallel {or

direct), in contrary, or in oblique

motion to each other. Parallel motion occurs

when both ascend

or descend at the

same

time.

Contrary motion, Oblique motion,

when one

ascends and the other descends.

when one moves and

the other remains stationary.

For example FIG.

51.

Parallel Motion.

ObUque.

Contrary.

pi^P^^ Parallel or consecutive fifths

and octaves, mentioned in the above

rtilc,

are such as these

FIG.

52.

-^

These are

r^-^

^

!^_^ -^-^ strictly

1

-^-^^ ^-^^— and invariably

to

;£S

1*1,

«^-^-

f

t^-^

be avoided.

Suppose now we have the bass FIG.

that

is,

other.

53.

the chords of the dominant and sub-dominant shall follow each

We have

seen that they have no tones in

common, and

therefore increased danger of consecutive fifths and octaves.

Jowing and similar progressions are consequently erroneous^

[4]

Parallel,

an"SoT/qu«

there

The

is

fol

°

°"*

MANUAL OF HARMONY

88

In a, consecutive

fifths

occur between soprano and tenor, and conseand bass; in &, fifths occur between tenor

cutive octaves between tenor

and bass, and octaves between

alto

and bass; and so on.

This error can always be avoided by making use of what we have contrary motion ; that is, let all the parts move in contrary Oc^eiTlujw described as avonied! motion to the bass. Besides the advantage of avoiding fifths, contrary CoDisectitiTe

motion has always an agreeable FIG.

NoTK.

effect

upon the

ear.

55.

The importance of the three chords we

great) the student •would

do well

to note in his

are at present treating being so

mind every

fact connected with Let him remember, then, that the tonic in the scale connects its chord with that of the sub-dominant while the dominant connects its chord with that of the

them.

;

same relation to the tonic chord, The more thorough his acquaintance with the relations of these chords to each other, the more skilftilly he will be able to manage harmonic changes and modulations, when further advanced tonic.

The dominant chord,

therefore, bears the

that the tonic chord does to the sub-dominant chord.

Leading Tone.

Rule. 3 The natural progression of the 7th degree of the when it appears as the third in the dominant chord, is to

scale,

the tonic. In accordance with this rule,

always be found, that the chord be one which shall contain the tonic of the scale, either as third, fifth or octave. This peculiar tendency of the 7th degree, of which every musical ear will sooner or later b&-^ it

will

which follows a dominant chord,

will

:

AND THOROUGH |ome senf Ibla, gives

it

39

BASS.

name

the

satisfactory termination, as

it

of the leading-tone. The feeling of were, which this progression gives to

every piece of music, is perhaps a sufficient explanation of leads us to the subject of Cadences.

A cadence may be

it;

and

this

simply defined as the conclusion of a piece, or of a Cadenw.

section of a piece,

< ^

,

;•

»

'

,

As 05?rery- simple melody finish# with the harmony should be the chord of the tonic.

tonic,* so the concluding

The last chord but one must generally be that of the dominant; preceded by that of the sub-dominant. The following is the most common form of a cadence. FIG.

'''^,]

56.

^1

^ This

is

called the authentic cadence.

AuthenUe Cadence.

Though

must invariably be that of the tonic, yet the melody is sometimes allowed to finish upon some other interval. The cadence is then called imperfect. Thus FIG.

the last chord

57.

9i=-==*

We have number

'=^

stated in the

begins upon the tonic the

Imperfer* Cadence,

commencement

also.

of exceptions

The student

of this -work that a

will,

perhaps, upon

he will find to this law

;

so

many, in

melody generally

trial,

fact,

be surprised at as apparently

to destroy the law altogether.

Without denying the existence of these, we still and certain it is, that, however it may be with tone of the melody itself, the harmony upon which it is grounded is almost

maintain that the law holds good the

first

*7xva,iat>li) t.V%t

^

;

of the tonic.

ay.

//J.|

^

^

/

u

*~^

S^t

^.^.

1^ ir\,.^

{„r\,^^)r

I

*dence.

f

w

MANUAL OF HARMONT

40 fH^gad

y^

Another form of cadence ^^^^

where the dominant chord is omitted, and by the sub-dominawt. This is It is, however, much less frequently used

is

tonic chord immediately preceded

ro"oa the plagal cadence. ^' it-* than tbp n" *;hGntic. ^IZ-

**

«

t* '

^

\^,-|

^w*

i*^-^

58. Jt^lagal

Cadence.

1=^

)ii

te

p

JThere are also other

ns5:

forms of cadences, which we shall leam iWr©-

QUESTIONS. iVhat

is

meant by progression ?

How must chords move from one to another/ How niay variety be produced in chords? ^hat

is

the rule for connecting chords together?

W>'ot \Vhat

is

parallel

is

oblique motion

motion? ?

What is contrary motion / What is meant by consecutive fifths and octaves f How may they be avoided? What rule is to be observed when chords have no tone In common? Which of the three principal chords have no tone in common? What tone connects the chords of the tonic and dominant' What tone connects the chords of the tonic and sub-dominant? Which is the leading-tone of the scale? What is its natural progression? What is meant by the terra cadence ? What is the most common sort of cadence called? Of what chords is it composed? When is the authentic cadence said to be imperfect? the last chord but one in the authentic cadence ?

Wb.afc

is

What

in the plagal cadence?

With what chord must a

piece terminate in eyery kind of cadeace?

,

^

,^

^

TO.

Make an

73.

" "

74.

^^

AND THOROUGH

4j,

EXERCISES.

y.

y

auffienticcacfence inTEe'tey of G.

" "

"

"A.

"

"

76.

Make a plagal cadence in D. Make an imperfect cadence in

77.

"

75.

BASS.

"

"

B

flat.

F.

G.

TTrite chords to the following bass, in close positior^*

'/Xi

two

Btares.

78.

^miii^ 79.

i^

i^:

80.

iiipE^; 81.

With an imperfect cadence.

§Lfe Write the following in open

positions, in score.

82.

^^-Write the bass

to the following chords.

83.

^^

-—5

84.

S^S [4»]

s

1^ s^

.

MANUAL OF HARMONY

42

CHAPTER

IV.

REMAINING CHORDS OF THE MAJOR SCALE.

We "will

now form

and examine FIG.

triads

upon

all

the degrees of the scaliv

their character.

59.

^=1^1

I I

II

The chords

of the

1st,

4th and 5th degrees have majoi

and have already been discussed.

thirds, It will

Minor Triads

IV

III

we denote them by

be seen

large numerals.

Those of the 2d, 3d, 6th and 7th degrees have minor third?

of the Scale.

/ ./

,

.

;

/

,

/,

.\

,

-

'„

•

-^

..

These we denote by small numerals. DimuoLshei Triad.

The chord of the 7th degree, however, from fifth

all others, ;

in having a diminished,

which gives

it

This chord we shall count of its peculiarity. Note.

shown in melody.

the

name

make

will

be found to

diffei

instead of a perfect

of the diminished triad.

the subject of a separate chapter, on ac-

We shall in future frequently make use of the method of indicating chord* Fig. 69

;

that

ia, l»y

placing Etuneralfl under the basfl-tone, or

otw

tto

:

AND THOROUGH

m

BASS.

In writing harmony upon these minor chords, the

rules

which we have given in the foregoing chapter, with regard

to

the connecting tone, and the avoiding of consecutive fifths and octaves, are strictly to be observed. It will be found on examination that when the bass moves more than Connecting one degree, there will always be one, sometimes two, connecting tones Tones In different Pro between the chords. "When it moves but one degree, there can be none gressionsV

whatever.

This

may

be seen in the following

table.

l^glt^l The progressions of a fourth and

fifth,

as in c

descend,) are peculiarly bass-progressions, as

and

when they

Bass-Pro»

seen in the last

gressions.

d, (also

we have

chapter.

In

c, e

and/, we find progressions which do not violate any of the Concealed

contain what are called concealed fifths and octaves; which occur

They when

two parts move

inter-

foregoing rules, but which, nevertheless, are considered faulty.

vals

h

a

fifth

in parallel motion,

and the second only of the two

Qctarefi^^

or an octave >*

FoT example FIG. 6L _.

a.

Th(i

•

--

"

" '

-

.

h.

efi'ect

of concealed fifths and octaves

is

in

some

cases less disa

greeable than in others; as in/, in Fig. 61, where the upper part moves but a semitone, and the lower takes a regular bass-progression. In

The consecutiTe fifths and oetaves, which we hare Kcil contra-distinction called open fifths, &o.

treated in ths former ch^p-

Whan allowftbla.

MANUAL OF HARMONY

44 that and

some other

cases,

which can only be learned bj

practice, they

are toleriied; but are in general less admissible in the extreme voices

(sopranc and bass,) than in the middle ones, (tenor and alto). In most be avoided, which can almost always be

cases, they are, if possible, to

done by contrary motion, even

at the

expense of the rule for connecting

chords.

In a concealed octave* ^ccur between the tenor and bass, which it is by contrary motion, as in J, though we do not retain the connecting tone D in ihe soprano in the second chord, but transfer it to

better to avoid

the tenor. In c we may retain it, the octave effect not being so bad here on account of the half-tone from F sharp to G, though it would have been better if the bass had descended.

Vubling the

"^d-

In/, of Fig. 60, it would have been better to double the third in the second chord, in order to avoid the concealed fifths in the soprano and tenor.

Thus: FIG.

63.

^ When, however,

the third

is

the leading-tone^

it

should not be doubled.

Thus it -will be seen there arc sevefal points always to be considered in •writing harmony and a skilful management of the four voices with reference to these points, especially when limited to a fixed meloily, can only be acquired by experience and long practice, and by listening to the Afferent effects when played or sung. The only plain direction that can be given, is a general observance of the di« rect rules already laid down, and an evasion of them oq.t n cases of necessity, where a better eflfect can be produced thereby, and a greater^! »-^oided, or for the sake Note.

;

of melodf. .'^l:'

J

:

AND THOROUGH

46

BASS.

is frequently employed, ^here the chord of Cadence used instead of the sub-dominant chord, in the last chordof tbt For example 2d degree

Another form of cadence the 2d degree

is

chord but two. .

FIG.

64.

QUESTIONS. Which

How

degrees of the scale have minor triads?

does the triad of the 7th degree differ from others?

What

is

this triad called ?

Under what condition

will there

always be found connecting tones

between two chords?

Which

What

progressions are called bass-progressions?

is

meant by

concealed fifths

and octaves?

In what cases are they more admissible than in others ? How may they always be avoided?

When must

the third not be doubled ?

What

may

chord cadence?

What

is

be used for that of the sub-dominant In forming a

the difference between concealed

and open

fifths ?

EXERCISES. Write chords

to the following bass.

*

86.

m

87.

§i^: liife

ii: -j:^

"^

MANUAL OF HARMONY

46

:z^^z^

ifej

Write the harmony indicated by the numerals to the following melody.

V

I

90.

VI

III

V

II

I

^^^=1^=1 The foUowin g 91.

IV

^^—

-^''

V

II

»£^- _s_. — {{])

open position.

in score,

I

III

VI

c^

V

II

~^~ _?=2_. ITSZI

I

ZS5Z -?^j: -

|-

i/' 92.

Make a cadence with

the chord of the 2d degree, in the key vf G.

CHAPTER

V.

DIMINISHED TRIAD. This chord, founded upon the 7th degree of the contains a diminished

fifth,

which

scale, or leading-tone,

interval, according to

page

28, is a

jMflSonance.

dissonance.

lis resolu-

This word we may more particularly define here as an interval which has an unsatisfactory effect upon the ear, unless followed by a conso'

tion.

nance,

which progression

Rule.

.

is

technically called

its resoluticn.

Every dissonance must be followed by a consonance.

The Diminished Triad indepen-

less

dent than

The diminished ,

^"^

.^

^^^

.

progression

triad

more

is

therefore less independent than the others,

,...-,

limited,

others.

Root cannot be doubled.

In the

first

place, the root of the chord, being the leading-tone,

stili

AND THOROUGH ha.5

47

BASS.

but one natural progression, (namely, to the tonic,) and cannot

therefore be doubled, otherwise consecutive octaves

now

Let us

In

a,

it is

;

is

what the consequence

will

be

if

arise.

we double

the third.

consecutive fifths must inevitably arise between soprano and b, the effect is the same as if there were only three parts, as in therefore no longer four-part harmony. The progression in d,

In

bass. c

see

would

the only practicable one.

Let us

now

double the

FIG.

fifth

66.

I ^—

9^ ftere, again,

From

consecutive fifths cannot be avoided.

the difficulty of

•)arative inutility,

appear,

we

it

managing

,

^

^

.

and hence from its comform. In what form it does

this chord,

seldom appears in this subsequent chapter.

shall learn in a

In certain cases, however, the root

may

be doubled,

as, for instance,

in a sequence.

A

Sequence

is

a succession of similar harmonies,

from a symmetrical progression in the

resulting

bass.

The following is an example of a sequence, with the allowed case of a doubled leading-tone.

§««„«,'? e

MANUAL OF HARMONY

48 FIG.

^mm^m

67.

be seen that the bass' makes a similar progression in each to the cadence. Such progressions in the bass geneFor this rally require equally regular progressions in the other parts. reason, the D is not retained in the tenor in the third chord of the above figure; and, for the same reason, the leading-tone is doubled in the

Here

bar,

it s^ill

till

we come

sixth chord.

QUESTIONS.

How does the diminished triad differ from others? "What is a dissonance? What rule is to be observed with regard to it? What is the progression of a dissonance to a consonance called? What renders this chord more dependent than others? In what case may the root of the diminished triad be doubled? What is meant by a sequence ? How must a sequence in the bass generally be treated? EXERCISES. 93.

Write chords

to the following bass.

Begin with the 5th in the melody.

Pte 94.

mm

:£ rE:

:t=:

Write the harmony I

-fcF=S

V

to the following

VI

II

m^f=ff^^.

III

Tii"

melody. I

I

lY

V

m I

31

i^:

\ r^fi

//.

-^ ^

,y

E t:

A

I

:

:

AND THOROUGH

CHAPTER

49

BASS.

VI.

TRIADS OF THE MINOR SCALE. It will

be recollected that the minor scale has in general the same

tones and semitones with

FIG.

its

parallel

major

Thus

scale.

68.

Scale of A minor.

I FIG.

69.

Scale of D minor.

But we mentioned

in Part

I.

that the rules of

harmony

required one

This is the 7th degree, which, as it now stands, is a whole tone from the octave or 8th degree. It is, however, generally raised a semitone,* in order to give it the character of a leading-tone, tone to be altered.

which the law of cadences requires

as well in the

minor

scale as in the

major.

The minor scale, then, considered win stand thus FIG.

as the basis of

harmonic structure,

70.

This alteration is not, however, denoted by the signatures, which stUl remain the-aame with those of the parallel major scale but by an accidental, so often as ;

that degre* occurs.

[5]

Alteratio« of the 7th degree of the Mino» Scale.

MANUAL

50 "We IfiterFals of

The

will first

examine

fourth, fifth

its

HARMONY

OF

intervals.

and octave are

still

perfect, as in the

major

scale.

the Minor

The second and seventh

Scale.

are also major, as in the

The minor scale differs from and minor sixth.

the major,

major

scale.

in having a mi:i

third Triads of the

Minor

Let us

now

see the character of

its

chords.

Scale.

FIG.

71.

no

I

&

VI

nv

S^-

As the numerals indicate, it will be seen that the 5th and 6th degree? have major triads, the 1st and 4th have minor triads, and the 2d and 7th diminished triads. Atlgmented triad.

But the 3d degree has a chord entirely new in its form, having a major third and an augmented fifth. It is hence called the augmented triad.

From

the difficulty of management, and the harshness which this

combinations, it seldom appears; nor is fundamental harmony of the 3d degree of which almost always appears with a perfect fifth.

chord presents in almost

all

this in general considered the

the minor scale,

In the chord of the 3d degree, therefore, in the scale of A minor for inG is generally retained, but in those of the 5th and 7th de-

stance, the

r

grees

it is

invariably

made

sharp.

Let the following fact be remembered.

The dominant has a major

The chords

triad in both major

and

mmop

of the tonic and sub-dominant are major in majoi

keys, and minor in minor keys. Progression

^*"

The same minor

rules are to be observed In connecting the chords of the

scale as in those of the major.

The only suggestion we would

——

:

AND THOROUGH

;

51

BASS.

make is to avoid the progression of an augmented second, e\ en at the ex- Augmented pense of the rule for connecting, as in the follomng example aToided. FIG.

72.

Uli Better.

=i=U=

i^i^f^^^lli^

^~ When,

in writing

chords to a given bass, we wish an interval to be al- FiguPta BaM. by the signatures, (as will always be the case

tered from that indicated

with the third of the dominant chord in the minor key,) this must always he denoted by placing an accidental over the bass note, with the figure expressing the interval to be altered. For instance, if we wished the chord of the 3d degree with the augmented fifth, we denote it thus:

FIG.

73.

65

i^5

^^• M. -y

I-.

(^

\7

,

b U 1?

~

Cf

'

?

When the third in the chord is to be altered, the figure 3 is generally omitted, and the accidental alone written over the bass. Thus FIG.

74.

^ ^ —^

h^ ^-—n-\^

It 1>

—^—

F 1-

QUESTIONS. Which degree

of the minor scale

For what purpose

Which Which

ig it

is

intervals are perfect in the

are

generally altered?

altered?

minor scale?

major?

* With regard to the progression of the tenor voice in c, in Fig. 72, we would mark that, in general, harmonic effects are bett«r when chords in close and op positions follor each other promiscuously.

MANUAL OF HARMONY

52 Which

are

How do

minor?

the major and minor scales differ in respect to

Which degrees have major Which have minor triads? Which diminished?

How does What

is

triads in the

tlieir

intervals ?

minor scale?

the triad of the 3d degree (minor) differ from

generally considered the fundamental

all

harmony

others?

of the 3d le-

gree of the minor scale? How does the dominant chord differ in major and minor keys? How does the tonic chord differ?

How with What

How is What

the sub-dominant chord?

progression

is

to be avoided in the

minor key?

the alteration of an interval indicated in a figured bass?

does a simple accidental over a bass note denote?

EXERCISES. 95.

^

^^m^^ ^

Third in the melody.

96.

^^^m

iS 97.

i

9%=p= —.^

^_ l_

—

^—

tr^

U

\

J

—

\

\—

!=^

^#=1^h

98.

s

99.

i5

^

X=rA

i.^ In score.

^^

-&

=-^

a

=1

AND THOROUGH BASS.

53

In score.

100.

^^^^m Write harmony 101.

melody.

to this

V

I

VI

^

^

YI

I

V

IV

$^^ 102.

^=^: -H:

ii

J

I

— — fe^l

?—?—

IV

III

V

IV

I

=-^

ii^r^-

V

11°

IT

i^i^

'B

CHAPTER

VII.

IXVERSION.

We

come now

to certain modifications of the triad,

where

it is

used

under different forms. Hitherto the root of the chord has always been put in the bass voice,

which,

we

stated in the outset,

was the general

rule.

Greater variety in harmony, however, is attained, if we modify this j^ and suffer the bass voice to take another interval of

rule occasionally,

the chord, as the third or

When

fifth.

This

is

called Inversion.

the bass takes the third, the triad

is

said to

be in the

1st inversion.

When

it

takes the ffth,

[5*]

it is

called the

Id

inversion,

MANUAL OF HARMONY

&4 FIG.

75.

2d Inversion.

1st Inversion,

m=^=f Observe that these are still the chords of C, though the bass note one case E, in the other G. figuring of Inversions,

*

k 'm

evident that in a given bass these changes must be denoted, in manner as the accidental was denoted in the last chapter. For instance, if upon the bass note E, we wish the chord of C, anduDtthe chord of E, we must signify it. This is done by reckoning the int. jrvals of the required chord from the actual bass note, (not from the root ) and It is

jike

placing the figures over

it.

FIG.

76.

^zzzz^: Thus we obtain the

figures §, but for brevity's sake the 3

Is

genDrally-

omitted.

Chord of

tiie

When,

therefore,

a bass note appears with a 6 over

it,

it

in*

dicates that that note is not the root of the required chord, }iat

ihat

we must

This

is

look for

called the

it

a third below.

Chord of the

Sixth.

1! we take the fifth for the bass voice,

FIG.

we

obtain the figures f.

77.

Pi^-l^

—

—

AND THOROUGH

When

:

'

u

BASS.

a bass note appears with the figures |,

wi must look

for the root a fifth below.

This

called the

is

ciMwdofihi Sixth and Fourth.

Chord of the Sixth and Fourth.

Obserre that according to the method we employ in denoting chords, nubajss note indicate the root of the chord, dmi. figures

Note.

merals and letters below a above,

(or,

Intervals

as

it is

commonly

called, ilxe figuring of the chord,) denote the requii^ed

Thus

from the actual bass note.

FIG.

:

78.

^ g ^

^ ^

1

1

6

S^ ^—^

—^-v

CI

ff -ff L

CI

o—

S

1

—

an

GI

CI

V

F

^

1

_-4

DV

Observe also that we indicate major triads by large numerals below,

and minor by small. "Wlien note,

we wish two

the

the figures |

chords to follow each other upon the same bass and the other not,

of which shall be an inversion,

first

must follow the

FIG.

others, in order to indicate this.

Thus

79.

I

^ When

a chord

is

I

not mverted,

it is

t

said to be in the fundamental posi-

rundam«iital Position

tion.

Of course, when an interval is to be chromatically altered, (as the 7th degree of the minor scale,) the accidental must be placed before the H'gure, as in the last chapter.

Sometimes, instead of a

drawn through

it.

sJiar^f)

before the figure, a diagonal line

is

:

MAMITAL OF HABMON;

66 HG.

80.

^^^^^

E6^j ig^ Si In the cbord of the

fwhichinter-

Sbkd in

sixth the

fundamental tone

one usually douhled, as in Chap. II.

;

is

still

sometimes also the

the fif^n.

[inversions.

The following are the usual forms FIG.

in

which

this inversion appears.

81.

w.

if===:^

Sometimes also the third is doubled, when a smooth progression is better, however, when it lies in the soprano voice, produced thereby more frequently also in minor than than in either of the middle parts in major triads.

—

FIG.

—

82.

i^^ip^fe In the chord of is

the sixth

and fourth, the

almost invariably doubled.

The following

are

its

usual forma

fifth

(bass-tone)

^ -^OoJiv

v^s^

i^A^^iX

AND THOROUGH FIG.

La.^^

/cri^

ii,_^

'^a^Cc^tCC

57

BASS.

83.

i S

IPiimiiliili^

P^EpgE^E is in cadences, where the dominant chord and that of the 2d or 4th degrees (consequently the last but two.) Thus

The

almost exclusive use of this inversion

tonic chord, so inverted, appears between the

FIG.

TJse of

the

'^nOadences"

S4.

EipEJIgEggiS^ggEiigE^ 6

n

m^mmm^mf^mi As was remarked

Chap. V., the diminished triad seldom appears Inversions It is generally used in the 1st inversion Kminished (as in the second chord in Fig. 84.) The root, being the leading-tone, Triad, is not doubled, but most generally the bass-tone or third sometimes in

iu the fundamental position.

—

also the fifth.

The common progression of

this chord,

when

inverted,

fundamental position, or The following are examples of its usual progression tonic chord, either to

its

is still

to the

to its 1st inversion,

:

FIG.

85. d.

gl^^i^^

ill^il The progression marked/, secutire

fiftt.a

in this figure, leads us to

are somet jnes allowed,

when

the

first is

remark that cona perfect, and the

ita

Progre»

s^oii'-

:

MANUAL OP HARMONY

68 second a diminished is

h

erHK^

i

,

,

but not vice versa. J..*^

-' i-

FIG. 86

The diminished

.

H ij

fifth,

therefore faulty

it

r^^

t-^

The

NOTS.

/

2d degree of the minor scale allows th« not being the leading-tone.

87.

i^^

m^ C

i^^^CZ-

C^^i,.^^

''"-^ ----*'W^«v

triad of the

root to be doubled,

FIG.

The foUowiu^ prcgress^a

yC^K^-^'^^

rule for connecting chords applies to inrersions also.

QUESTIONS.

When

is

a chord said to be inverted ?

What is the 1st inversion V What the second ?

How is

the

first

inversion figured ?

The second ? Where is the root to be sought Where in the second?

in the 1st inversiv^n'i

What is the 1st inversion called ? What the second? What do figures above a bass note indicate? What do numerals below it denote? What is meant by the fundamental position of a chord ? How else may a sharp be denoted in the figuring? What is the rule for doubling tones in the first inversion ? Which

interval

is

-

generally doubled in the chord of the sixth ssi

fourth?

How

is

Where

this inversion is its

commonly used?

place in an authentic cadence

In which inversion

ia

the diminished triad

?

commonly used ?

AND THOROUGH Which "What

Interval

is its

When

may be doubled ? common progression when

59

BASS.

^

inverted ?

are consecutive fifths allowed?

In what diminished triad

may

the root be doubled? and

why?

EXERCISES. 103.

Close position.

Write the

6

letters

and numerals below. I

6

6

teiiS[i 104.

The same. 6

6

i_teiii=| IP'3.

Transpose

lOo.

Open and i

this last (104) into

E

flat,

ana write the numerals, &c.

close positions, with numerals.

^8

6

2

J -251;

tr

^^m

J

07.

Figure the bass of the following chords.

=l==t

tz^=JE±ie=zfe

l^l^iiil 108.

^l^iii^^Jipp i^lii

-^

MANUAL OJ HARMONY

60

CHAPTER

YIII.

MODULATION. Before going on to learn new cliords, we will say a word about moda* we may make use of it in our exercises, to give them variety.

lation, that

Modulation.

We have remarlied previously, (see Part I., Chap. 3,) that a melody, (and of course the harmony that accompanies it,) is sometimes written partly in one key and partly in another, leaving the original key for a while, and afterwards returning to it; and it is evident that a piece must be incomplete, unless it terminates in the key in which it began. This passing from one key to another is termed modulation. So soon is used foi-eign to the original key, a modulation takes place; so soon as that tone is restored by au accidental, the piece returns to tho as a tone

original key. Passing

Modulation

Modulations

may

be more or

Sometimes only one is termed

less protracted.

foreign chord occurs, and the piece returns immediately. This

a passing modulation.

and has a cadence

Sometimes

it

remains a while in the new key, one half, or a smaller sec-

in that key, thus closing

tion of the piece.

Modulation into the

Dominant.

The simplest modulations

and of these, the So soon as the 4th degree is raised a semitone, the piece has modulated so soon as it is lowered again, the piece returns to its former key. For example: most common

is the

are into the kindred keys;

modulation into the dominant.

;

FIG. S8.

C. CI

HOM

The

GV

Cia.GI

DV

GIC.CI 6vn°CI CI

letters in the largest type denote

a change of key.

GV

CI

AND THOROUGH

A modulation

into the

61

BASS.

dominant key

is

sometimes called a

half-cadsnce, though not through the chord of the

sixth

and

fourth.

When

the 7th degi-ee

is

semitone, a modulation Into the

lowered

The chord of the

nant.

sixth and fourth

dences, that whenever

it

occurs

Into the

Sub-Domi-

sub-dominant takes place.

we

is

so rarely used, excepting in ca-

anticipate a cadence at once;

and

if

be founded upon any other than the tonic chord, it presupposes a modulation; or, (to use a familiar phrase,) we feel it coming, even before the foreign tone or harmony is introduced. As in the preceding it

Chord of the Sixth

and Fourth as a meansi

of Modulo tion.

founded not upon the tonic C of the origiit gives the idea at once of a cadence in the key of G, though the foreign tone, F sharp, has not yet occurred. figure: the 4th chord, being

upon the dominant G,

nal key, but

The following is an instance of a modulation into the sub-dominant; a mere passing one, however, there being no cadence. FIG.

89.

-0-

ilisf*^^

^fejZ:

b6

—

CI

C.

FIVF. BblV

FIC.GI

GV

CI

minor key (and vice versa) is also Modulation shows an additional proof of the necessity of i^**^ ^he paraising the 7th degree of the minor scale, for otherwise the modulation would not be perceptible.

The modulation

quite frequent.

into the parallel

And

this

*

Passing modulation into the parallel minor key.

FIG.

90.

ms^ -s-

0.

CI

CI A. [6]

E^ti^^

-^-

EV

al

C

GV

CI

;

MANUAL OP HARMONY

62

As one chord can belong

to several different keys,

it is not altogether a modulation, nntil one or two chords have followed that Avhich introduces the foreign cone,, or till a chord of the sixth and fourth has occurred. The chord of D major, for instance, is the tonic chord of the key of D major, the dominant chord of both G major and G minor, and the sub-dominant of A major. The

certain at 5rst

what key

is

aimed

at in

progression

FIG.

91.

i might therefore anticipate Mod. from C major

to

:m: either of the

above keys.

Thus

G major.

mi

t=mimi

iS:iiig To

1

I,

G minor;

^m

^Slp^ To D major.

^m

t«a

:

AND THOROUGH BASS. To A

63

major.

giigigi * The last modulation, however, is rather too abrupt. Modulations should always be gradual, and through the kindred keys. A better method would have been through A minor, which is closely allied to C major. Thus FIG. To

A

92.

major, through

A

minor.

^^^^

^^.

fe^

mE^^.

m^m

:-i

But the readiest and most useful means of modulation is through fhat is called the chord of the seventh, which we shall proceed to treat in the next chapter.

QUESTIONS. What is a modulation ? What determines it ? What is meant by a passing modulation? What are the simplest modulations? Which is the most common of all? What degree of the scale must be altered, -

-

'

^

•

to modulate into the sttbdominant? Which, into the dominant? Which, into the parallel minor? What chord is of eminent use in modulating? Why is it often doubtful into what key the piece is going to modti-

late?

How

should you modulate from the dominant to the sub-dominant?

i

MANUAL OF HARMONY

64

EXERCISES. 109.

Choral.

Close position.

Mel. Oct.

3(1.

n

^^: gigF¥!5^g -^-+

110.

1

6

Hi

—

-^

^

-C-l

Choral

iiS^^P^i^^"

111. 112.

113. 114.

ModiUate from C to G through A minor, finishing with a cadence. " " C to A minor, " ** " " E minor to A minor, " " " " GtoC,

CHAPTER

IX.

CHORD OF THE DOMDTANT SEVENTH. Formation of the Chord of

The chord of the

seventh

is

formed from the

triad, '

.

the s«Tenth. to it

,

«

by J adding &

,

the seventh of the root.

Chords of the seventh may be formed upon every triad of the scale.

—

:

AND THOROUGH

The

principal chord

This

A

is

of the seventh

Jx^ionC'

seventh.

G5

BASS.

is

that of the

-

'

dominant

'^^^^^^.

lH^^

•

of especial use in forming cadences.

chord of the seventh

differs

from the simple triad in not

DiseonMce.

being an independent chord. a dissonance, (the seventh J wKich must therefore be

It contains

re-

wived.

This resolution takes place according to a fixed rule, namely

The seventh must descend to

Rule.

The dominant seventh

almost-inv^ably followed by the and

is

"

tonic chord.

Let us sion of

now make

its

FIG.

intervals.

Its resolution,

the next degree below.

"^

"

Progressioi >

a cadence with this chord, and examine the progresAs it contains four tones, none need be doubled. :.*

-

93.

I

:

:•:

:^-

^

§!^ The seventh

(F, in the alto voice)

must descend

to

E; the leading-

tone (in the soprano) ascends to C; the root must ascend a fourth or descend a fifth and the tenor must take either the octave in the follow;

fifth. In the former case, the tonic chord must dispense with the fifth, as in the above figure; the latter progresoion can only take place when the root ascends a fourth, otherwise consecutive

ing chord, or the

^fths would result.

FIG.

For instance

:

94. Cons,

i^i [6»]

fifths.

Good.

-^

1

:

MANUAL OF HAK.vONT

66 This, then,

seventh,

is

when

the natural progression of the intervals of the dominant

followed by the tonic chord.

It

may, however, be

varied. First: the fifth in the dominant chord may be omitted, and the root doubled; and if we wish the tonic chord to be complete, it can be made 80 by this means. Thus

FIG.

95.

In this way, too,

it

will be seen, the additional

advantage

is

gained of

connecting the two chords.

may make

both chords complete in another way. The sometimes allovred to descend to the fifth of the resolution-chord. This is, however, an exception to the general rule, and is never when in the soprano voice, and permitted only in certain cases

Again: we

leading-tone

is

—

only

when FIG.

the root ascends.

__

96.

m

i^Siil?i^i In this case, the third, as in

jui^ti

fifths, as in c.

fifth

may

descend to the octave, or ascend to the

But if the root descends a fifth, we have concealed The example d is never allowable.

a and

6.

These then are the usual methods of resolving a seventh-chord, and must be evident in rendering a cadence much more complete and decisive.

its efi"ect

FalM

OwknM

Instead of the tonic chord, that of the 6th degree

low the dominant seventh.

may

sometin es

fol-

^

AND THOROUGH FIG.

:

67

BASft

97.

~n

•/-

fm

'

o^. — ^^ " ^-^ --^2^5

(O*^ *^-S5 cd:^" s

Here,

will

it

^CLL^^

«=s

C\'

*-i.

be seen, the seventh descends, and the leading-tone This progression is sometimes called the falst

ascends, as before. cadence.

Another method of resolving the seventh-chord is where the seventh varied remains fixed, instead of descending, and the other voices alone move; ResoluHoa. In which case the resolving chord must of course be one that shall contain the seventh as some other interval. Thus FIG.

96.

I P Here

it

will

^ be observed, the leading-tone

follows

its

natural pro*

seen above,

i»

fimply tb6

still

gression.

The

figuring of the seventh-chord,

as

figure 7.

QUESTIONS.

How is What

the chord of the seventh formed ?

triads

Which

is

may have

a seventh added?

the principal seventh-chord?

Of what

especial use

How do

seventh-chords differ from simple triads ?

Which

is

it?

interval contains the dissonance in this

chord?

What is the rule for its resolution ? What is the usual progression of the dominant seventh chord? What progression is sometimes allowed to the leading*tono? Under wh at conditions ?

m How

MANUAL else

may we make

OF

HARMONY

the resolving chord complete?

has this chord in an authentic cadence? "What is meant by the false cadence ? In what case may the seventh not descend? What is the figuring of this chord?

What

effect

EXERCISES.

6

8"

6

^s^^^^iB

g:-S 116.

6

i,

8*6

Htl

^iS^S^i^^g 7

6

m^rzgit 117.

In score. 3

6

^

,

mE^E^ I.

i

_t

^.

1

• Observe that in

all

I

t—H:

future exercises we place over

Indicating the interval with which the

melndv

is

to

tlie first

commence.

bass note the .

AND THOROUGH

BASS.

6

8

^S^§i=§:EE^^§ife^^§

CHiiPTER X. INVERSION OF IHE DOMINANT SEVENTH. 'The chord of the seventh

may

be inverted, like the

triad.

It

-

has three

inversions, according as the bass voice takes the third, fifth or seventh,

?vhich are called the 1st, 2d

and 3d inversions respectively.

•

FIG. 99. Fundi. Position.

Let us see

1st Inversion.

now how

2d Inversion.

Numbering

^

3d Inversion.

these inversions are figured and named.

the intervals from the bass note, 6. g.

The

therefore the CTicrd of the Sixth

first

and

we

Fir9t,b»w

obtain the figures

invers inversion of the seventh Fifth.

g^^y^, Chrtid.

FIG. 100.

generally eneraUy abbreviated

Iimnkm

is

g^

called

=

:

MANUAL OP HARMONY

TO

FIG.

101.

2d Inyersion.

9^=^^S— ••eoDd,

The second inversion

-

gives the figures |, abbreviated |,

and

is

called

the Chord of the :^ourih and Third. Note. Bcale,

Observe that in the 2d inversion of the dominant seventh in the minor must be ex is raised a semitone, and the figure

the third in the chord

pressed.

So with

all

usually omitted figures.

FIG.

102.

3d Inversion.

and

This gives the figures | f

2,

and

is

called the

Chord of the Second.

Third NoT£. Bais note not

lobe doubled.

The student must

fix

the figuring of these mversions firmly in his mind.

In the inversions of the triad

we showed

FIG.

might be

103.

I

^

bnt in those of the seventh-chord must be omitted in the other parts. Progreseion of the Seventh-

that the bass note

doubled, thus

The

this

can never be.

The bass tone

rules for progressions in inversions of the seventh are in general

chord when

the same as when in the fundamental position, founded upon the cadence-pr agression. That is, the 7th and 5th descend, and the third

inverted.

ascends

:

:

AND THOROUGH BASS. ft

must be remarked, however,

71

that the voice which takes the root of

it in the resolving-chord, instead of ascending a fourth or descending a fifth, as in the preceding chapter. For this latter progression belongs exclusively to the bass voice, and must never be used in any of the others. The following examples are

the seventh-chord inverted, retains

therefore incorrect:

FIG.

104.

i== 105.

m:

Correct.

The progression of the 2d inversion would be

as follows

FIG. 106.

i=1=^z:Es^IHS I And of the

3d

FIG. lOT.

g^gjgiijg^pgi^

~mm.

i/i.

oil

:

f-

MANUAL OF HARMONY

72 Rwolutlon of the Chord of the Becona.

tZtc/tJZ?

Observe that in the Sd inversion the bass takes the seventh, which j^^gj descend:'

it

will therefore receive the third of the tonic chord; so

that

The

natural resolution

chord of the ;5(:taTe

and

Seventh in the same voice.

chord of the second

of the

is

the

sixth.

As the seventh forms a dissonance with the root, there is a common method of letting the voice which talies that interval sing first the octave and then the seventh, performing two notes, while the other parts perform but one. This renders the effect of the dissonance much smoother. The voice must, however, lie in a different octave from that which contains the root in both chords. The bass note is figured 8 7, or, in an iuA-ersion, with the corresponding figures. Thus

FIG.

108.

iiaiiiei 4

8

7

ij^li^^iili^i^^iiS?! How figured.

In the 1st inversion, the second 6

Note.

is

generally omitted.

In the 2d,

this

variation rarely occurs, on account of the untimely effect of the chord of the sixth

and only

fourth. is

In the 3d inversion, the figure 8 merely

wanted, and the line after

it,

that

it is

indicate.? that the simple triad

to be retained in the other parts,

while the bass moves.

QUESTIONS.

How many inversions has the chord of the How is the first inversion figured? How the second?

seventh?

The third?

What What The

is

the

first

inversion of the seventh called?

the second?

third?

What

is

Whatis

the progression of the third in the inverted seventh-chord i? that of the fifth?

AND THOROUGH

73

BASS.

Of the seventh?

What chord forms the natural resolution How may the effect of the dissonance in

of the chord of the second? the seventh-chord he

made

smoother?

How is

the bass figured in this case?

*j

EXERCISES. 119.

I

6

#

^^ 3

-

6

i

ff

5

87

120.

-4

^

a3:3 ^-?s=

itEli^

Open. 121.

6

2

6.

3

-Sv."«

-t "Write

122.

harmony

to this

melody according

to the

numerals, using

inversions. I

V7

I

V7

I

V7

I

IV

vii°

I

IV

I

V7

I

^iS^^ieO 123.

,

Write the figured bass of the following chords.

^*-

m

gli^a^iEiEEl^ [7]

;

:

MANUAL OF HARMONY

74

CHAPTER

XI.

OTHER CHORDS OF THE SEVENTH. As we have said, chords of the seventh can be formed ujon any triad. Ifwe form them upon all the different triads of the major and minor scales,

FIG.

Tariety of SeTenthchords.

109.

we

shall obtain a great variety of seventh-chords, differing greatly from each other. Some have minor thirds and minor sevenths, (as the 2d degree, major, and 4th degree, minor scale;) some major thirds and

minor sevenths, some minor

thirds

and major sevenths,

be seen on examination of the above

Some

&c., &c., as

may

figure.

of these will be found less practicable than others, on account

of the harsh progressions that result from them.

The general

rules,

however, that we have already given for the dominant seventh, remain the same for these. Let us take this opportunity to review them

Progressions re Tie wed.

—

v^

The root moves to the fourth above, or fifth below """' The third to the next degree above, or to the third belowf The fifth to the next above or below, sometimes to the fifth below The seventh to the next degree below.

^

The rules are, however, subject to the exceptions we have already mentioned, and to others which we will now examine. Seventh-

rlrdegree^^

Two

verj'

important seventh-chords are those built upon the 7th de-

^^^® °^ ^^^ ^^^^®' ^^^^^ ^^^ minor.

They

differ

from others in having

diminished fifths, and their progressions differ, because the root, being the leading-tone, must move to the next, instead of to the fourth degree above. Thus :

AND THOROUGH FIG

76

BASS,

110.

I The

latter

has also a diminished seventh, and the chord

is

always

dis-

tinguished by that name.

S^'enth^'"^

be seen by the above figure, that the addition of the seventh to the diminished triad does not alter its close relation to the tonic chord, but that with or without the seventh its progression remains the same. It will

Care must be taken to avoid consecutive fifths, as the figure will show.' tonic chord necessarily has the third doubled.

The

The seventh-chord of the 7th degree major has this peculiarity also, must always be in the soprano voice. The following are the usual fonns in which it appears that the seventh

:

FIG.

111.

I P=i5>«

-S^*5s^

but never in these fonns:

FIG.

112.

iii^

S:

The chord of the diminished # r inversion. Thus

lition

Chordoftidt

•

seventh,

however,

may

be used in any po-

:

MANUAL OP HARMONY

76 FIG.

113.

IpEiiEESSl :E^?^=d^ PREPARATION" OF THE SEVENTH. Pr?paraldon B««fenth-

"We have thus far spoken only of the chord Avhich shall follow the seventh -chord, or its resolution; but not of that which should precede it.

As

the seventh

as

it is

it

as

when

is

called; that

some other it lies

a dissonance, the effect is smoother if it he prepared, let the preceding chord be one that shall contain

is,

interval.

(In general, a tone

in the preceding

had instances of it

in

Chap.

chord in

II.,

the

where the

is

said to be prepared,

same pai-t.

"W"e

have

connection of chords

already-

was

dis-

cussed.)

The following

are instances of the preparation of the seventh

FIG. 114.

We therefore lay it down as Rule. of the

a

The seventh must be prepared.

There are two exceptions. One is the chord of the dominant seventht which is prepared not by the seventh, but by the fundamental tx)ne.

AND THOROUGH FIG.

77

BASS.

115.

The other exception is the chord of the diminished seventh, which needs no preparation whatever. FIG.

i

PimiDished need°not be prepared.

116.

* _

^~

^^

t

_

,,7

-^--

^—t

_IZf_

'^

\

'^-^

-^

t

4

#

=

"

3

I

^

—

6

1~~^

I

may

follow one another. In fact, we often Sequence where the voices follow respectively a regu- of ^eventha. lar progression. In this case, in alternate chords, the fifth must be omitted, as in the following example*

Several seventh-chords

find a sequence of sevenths,

FIG.

IV.

::p:^=^=«._:t_g^^^i±_g__^j±: '^--4=^-

Such

is

the general progression of

Some, as we have used, and others have a slons.

said,

all

^

seventh-chords, with their inver- Unmeaning-> ness. and their harshness, are never consequent

on account of

totally

unmeaning

effect.

(As an instance of

the student play the seventh-chord of the ad degree of the major scale in the 2d inversion, and his ear will convince him of its flat and this, let

insipid chai-acter.) Some v/ill require great care in their management, on account of the increased danger of concealed and open fifths and octanes, as some of these chords have major sevenths, forming perfect

[7*]

inutilitj- of

many seventhchorda.

MANUAL

7S

OF

HARMONY

with the thirds in the chord. The most useful and frequent of the chords of the seventh and their inversions can be learned only by pracThey are generally those with minor sevenths. tice and observation. fifths

MODULATION BY MEANS OF THE SEVENTH-CHORD. Modulation with the Iiominant Sorentb.

We mentioned at the close of Chap. VHI., that the seventh-chord was a useful means of modulation. The dominant seventh is particularly so. As an instance of this, we will merely show, in the following table, into how many keys we can modulate from the key of C, through the dominant seventh-chord of the new key; the seventh in these cases, exceptionally to the rule, need not always be prepared though some one tone in the seventh-chord must connect with the preceding. ;

i^^iiii

^ifisil^ *='^*li^-^=^^feH: As the dominant chord is major in both major and minor keyg, the above modulations answer as well for one as the other. Thus it will be seen, we can modulate directly by means of the dominant seventh-chord.

into eight different keys

Modulations into the remaining keys can easily be effected by the E flat or K*

sertion of one simple triad; as for instance, into

in-

AND THOROUGH FIG

BASS.

,P

1-C

Into

E

IntoE.

flat.

-^'-

W'

QUESTIONS. State all the varieties of intervals found in different seventh-chords of

the major and minor scales. State again the usual progressions of the four voices in seventh-

chords.

How

do the seventh-chords of the 7th degree differ from others ? is the chord of the diminished seventh? "What is its progression ? Which interval has to be doubled in the chord which follows it? What peculiarity exists with regard to the seventh-chord of the 7th degree major? What is meant by the preparation of an interval ? Why must the seventh always be prepared?

What

What are the exceptions to this rule ? how many keys can we modulate

Into

directly

by means of the domi

nant seventh-chord ?

EXERCISES. 124.

7

mmmm Open.

6

#

i^

MANUAL 01 HAEMONT

80

i 'TjL

126.

1

i

t

e.

Write the bass in the key of F, and figure

2

r

m

it.

^ziS;Eg:

^^ ^^m^m

;3

:=]:

(i^l^?^liiii^: 127.

Write 5

this choral in score. 6

_

6

7

Open.

6

fe-

l2=t=:::r[:

b7

^^11^

p^a

-^-,-A.

gg^EpgjgpiEBiEg ^i

I i,.

7^_

6.

AND THOROUGH

81

BASS.

CHAPTER Xn. CHROMATIC ALTEPwATIOX OF CHORDS.

We lave now gone Note.

Many

through

all

the chords to be

met with

in practice.

and maintain the existence of chords of the But wherever these interxals occur, we think they can he explained on principles which will be explained hereafter, (see chapters on suspensions, organ-note, &c., &c.) For simplicity's sake, therefore, and because simplest theories are the best, we prefer to treat them as variations of the seventhchord, rather than render the system more intricate by the creation of new chords, and thereby confuse the mind of the student. theorists go still farther,

ninth, elsventh, and thirteenth.

from the chords we have already learned, some of their intervals. These chords are, nevertheless, to be considered as still the same in respect to their fundamental tone and construction upon the same. Varieties can be produced

by the chromatic

alteration of

Altered Chords.

There are, however, hnt four principal chords of this sort to be met with in practice.

The Augmented Triad;

1st.

Augmented Triad.

where the

fifth in

the

common major

responds to that which

minor

we gave

is

raised a semitone.

It cor-

as the triad of the 3d degree in the

scale.

FIG.

Whenever 4th, or

triad

.5th

it

occurs,

it

120.

is

usually considered as formed

upon the

1st,

degrees of the major scale, than as the proper triad of the 3d

"degree minor.

and the root

Its

descends to the at pleasure.

uniform; the fifth ascends a semitone, (often through an inversion,) or The seventh may be taken with it or not,

progression

is

to the fourth above, lifth

below.

Its progre« sion.

:

MANUAL OF HARMONY FIG. 121.

It

may

be used in the 2d inversion with a particularly good

raising of the fifth destroying the usual carfence-irapression.

FIG.

effect,

the

Thus

122.

I

isiEfElia^

It is often found in connection with the progression 8 7, described in Chap. X.; the perfect fifth appears with the octave, and the augmented Two voices will then move, and two remain stafifth with the seventh. tionary. The third of the following chord necessarily becomes doubled.

FIG. 123.

^^^^^^^^Elii^i^=

mmm t.

Ohorloftho

6

Chord of the Augmented Sixth.

2d.

4cu(uetited

Stxtb

This

is

formed from the minor triad

in the \st inversion,

by augmenting

the root of the chord.

In this case the fifth only can be doubled, because the augmented octave or root, becoming a sort of leading-tone,

can have but one progression, and cannot therefore

itself

be doubled.

:

:

AND rnOROUGH BASS, FIG. 124.

^^m^^^^M

gHES^IEjEEpg^EJ^jj; The chord will sometimes, though rarely, be met with in the fundamental position; although there can only be three parts, in that caseFor instance: FIG.

125.

I Sometimes

also in the

zii

^^1

2d inversion, where the

fifth

has very

much

the

character of a seventh, and the chord and progression those of a chord Of the second. Thus

FIG. 126.

ill 9

m ^1^

"=sdi The chord of the augmented

sixth forms a useful

method of modulat-

ing into a minor key, of which the second chord in the progression the dominant chord. Thus

FIG. 127.

13

;

MANUAL OF HARMONY

84 Of the Augmented

Chord of the Augynented Sixth, Fourth and Tldrd,

3d.

Sixth,

Fourth and Third.

This bears a close resemblance to the preceding.

It is

chord, having a major third and diminished fifth; and as plies, is

used only in the 2d inversion.

name im-

formed on the 2d and followed by the

It is generallj^

degree of the minor scale by raising the third, chord of the dominant. Thus:

FIG.

a seventL-

its

^^^^

128.

^

-i-

^ Its

Of the Augmentei Sixth and Fifth.

progression must evidently be always the same.

Chord of the Augmented Sixth and Fifth,

4th.

This

is

the seventh-chord on the

1st inversion, the root of the

gression

is

to the

pare a cadence.

The

4tli degree of the minor scale, in the chord being raised a semitone. Its pro-

2d inversion of the

tonic,

and therefore serves

to pre-

Thus

principal use of these altered chords, as they are called, is in

modulating.

QUESTIONS. What is the meaning of an altered chord ? How many principal ones are there?

AND THOROUGH What

How

85

BASS.

...

are they?

is

the

augmented

triad

formed?

On what degrees of the scale is it constructed? What is the progression of its intervals ? '"

In what combination is it frequently used? How is the chord of the augmented sixth formed? "Which interval is doubled V What modulation can be made with it? How is the chord of the augmented sixth, fourth and third formed? On which degree of the scale is it usually found? What chord follows it? How is the chord of the augmented sixth and fifth formed? On which degree of the scale? What is its invariable progression? -

-

-

What

is

the general use of altered chords

?

EXERCISES. 128. 4.

5^5

_5_^5 _5_6

7_3_

6_S

6

%\_

^_6_

129. 8

7

\

i

^

#

131.

ps

M

6

f-r^

6

F-p

pytT^-r

[8]

^

3 ^

6

,

^

_

^

^

t=^

J_

MANUAL OF HAKMONT

S§ In score.

132,

^i«.

^^Mfe Open.

4

5

'-^

5

if

;g^^gg&^^ r^

'

^^Af ^^l^^il

CHAPTER

XIII.

SUSPENSION. Another method of connecting chords together, and one which serves

monotony of a succession of simultaneous progresby means of what is called Suspension.

greatly to relieve the sions,

on.

A

is

suspension takes place, wlien a tone in a chord, whose

progression

is

to

he

to the

next degree helow,

the other intervals of that chord have the next.

For instance, in

this succession

of cnords

moved

is

retained, after

to their

phces

iu

;

87

'AND THOROUGH BASS FIG.

^

130.

i'

ii; the following suspension

FIG.

take place

131.

Here the

C of the

other voices have

An

may

soprano, in the first chord, to the next; and the

essential feature of a

suspension

tone shall form a dissonance with some

analogy to the seventh,

is

is,

retained after the said to be suspended.

tbat the

retained

other interval, (as

C

of Fig. 131.)

and

like

This gives

the seventh,

it

it

some

must be pre-

pared, as well as followed by a resolution. retained tone must be foreioTi to the resolution-chord.

The

Therefore

when a seventh

X., at the end,)

octa/e,

it is

FIG.

^

No

good.

is

in reality

it is

suspended by a per/ed octave, (see Chap. suspension; but when by a diminished

yio

For instance:

132. suspension.

Djsscnane* nere'sary to a

Suspension

D in the second bar

and

is

B

moved

Good.

il^liPiPi^

m

;te^^

1

T

MANUAL OF HARMON

88 Suspension of either Interval.

Snspeaded tone not to be double 1.

Either interval in the triad third or the fifth

it

may

the bass; otherwise the

eflFect

But when it is the any other part, excepting

be suspended.

must not be doubled

in

of the suspension

is,

evidently, completely

destroyed. If

it be the fundamental tone, that may be doubled, probe in a different octave from that in which the suspension

however

vided

it

talies place.

FIG.

133.

Incorrect.

liiilij^ijiPg

i^^ii^li^i FIG.

134.

Correct.

3

^1^^

o

-^

::^=s

m Suspension In the Bass

When

the suspension

in the bass voice, the suspended note mtist These generally occur before the chord of

lies

by no means be doubled. the sixth.

FIG.

135. 1

©-^ 2

Rr v^

^ H

^

^

--

t

—

.

f^

==

4

S

F

^ =i-h — ^^ —^ 1

AND THOROUGH

89

BASS.

Suspensions by no means remove or cover consecutive

fifths

and octaves. FIG.

136. Incorrect.

I^SPgagpj^jEg^ Suspensions

even

may be

double,

or in two parts at once

;

or

FIG.

Double and Triple Sus. pensionf.

triple.

137.

It will be found in practice that the furnishing a new connecting-tone Change of between chords by means of suspension, gives greater freedom to the Harmony during a other voices, and the strictness of the rules we have laid down for pro- Suspension, gressions in the former part of this work, becomes somewhat relaxed. For this reason, the harmony may change sometimes during the suspension from the originally intended chord to some other; proyj'rfed,

however, the suspended tone belong to the new harmony, words, that the resolution be the same.

The following

are instances of this

or,

m other

^

MANUAL

90 Example

6.

Di^^^^MK*

OF

HARMONY

shows the dose analogy between a suspension and the

seventh-chord. Snfpension

:

*

Sometimes a retained note gives a chord the character of a snspen For instance ^^°"' though no dissonance is produced. FIG.

139.

9^

—

Here the retained note forms with the other intervals a chord of the which contains no dissonance. Yet, from its unusual appearance in this progression, the effect of a suspension is certainly the prominent sixth,

one. BoflpensioTj from beloif

A

suspension

may sometimes

be from helow^ that

is,

when

the pro-

gression of the retained note is to the next degree above; though these are much less common than the other kind. It

generally takes place

when

the progression

especially in altered chords, (see last Chapter,)

is

to be

and

but a half-tone,

in the leading-note.

FIG. 140.

Here

also, the

suspended note must be doubled in no part but the bass.

Suspensions, like other chords, are figured

from the bass

note, as in Figs. 131

and

by reckoning the intervals

135.

QUESTIONS.

What is suspension ? What must the progression of a retained note in general be? What is the essential element of a suspension? What analogy can be traced between a suspension and a chord BOrenth?

of the

AND THOROUGH In which part

91

BASS.

may

a suspended third or fifth be doubled! is suspended? What effect has suspension upon consecutive fifths or octaves f How may the effect of a suspension be produced, without being on©

How is it when the root

in reality

What

?

other form of suspension exists

?

In what progressions does it generally occur? What is the rule for doubling in suspensions from below?

EXERCISES. 134.

i

'-

MANUAL OF HARMONY

92

56

^ee .

h

7.

^

7

3

g

I

f

8

_

,

4|3

|i:

j

^

138.

S.

I ^1

«

i^^ I

«

iE 7,

b7

6

8,

— — 76

te^^--

^.

8

i. --^

g

t

?

I'

^ ---^

li

-

^ ll^pS^^^^ 4 3

139.

^g^B

^

6.

t

I

~ ::

t

I,

S3,

t=l ^ ^

~'

^6

t,

1^

57

B5

?

Lztzdr^zz^zfct

67

i__ii.

1

1

:^£:

M-

J

i

AND THOROUGH

CHAPTER

98

BASS.

XrV.

ORGAN-NOTE. Another instance of tones being used that are foreign to the harmony, where one voice retains a tone, while the other three go through a succession of chords, to some of which that tone does not belong. When this single tone lies in the bass voice, it is called an Organ-note Organ Is

or Pedal-not..

or Pedal-note.

The following may FIG.

serve as an example.

-

.

141.

i^iig

first chord must be one that shall contain must be interspersed, and fall generally upon the accented part of the bar; and also the last must contain it.

Observe that not only the

the organ-note, but others

This prolonged note stance, the sopi »no

may

also

lie

in

some other

voice; as, for in-

Position of {]|inint^the

Organ-note.

Prolonged o°tii?r'^oic«

:

MANUAL OP HARMON*

94 FIG.

Or

142.

in the Alto

FIG.

143.

.d^^..

w

The bass however Figuring

Or^-note.

is

most frequently used

In the ease of the organ-note, the ^^ ^^^ intervals as before.

in this

way.

harmony must be

The example

in Fig. 141

figured according

would be figured

thus:

FIG.

144.

-

7 6

1^

Care must be taken that the intervals of the moving chords lie in diffrom the prolonged note, for if they interfere with it, its

ferent octaves

effect is greatly injured.

QUESTIONS. What other instance occurs in music, of tones foreign to the harmony ? What is a prolonged note in the bass voice called? Which chords in an organ-note passage must contain that note? Which

How

voice

is

most frequently used

for this purpose?

are chords figured in these cases?

What

precaution

is

to be

observed in organ-note passages?

AND THOROUGH

95

BASS.

EXERCISES. 140. 8

141.

7 4b3

6

42 2 In

8 7

1%

98

t §2

I

I

1^ 7^-

.A-

m

69

k^^^-^L-^-

77

It

i

'I

u

^

CHAPTER XV. PASSING NOTES AND APPOGGIATURAS. There are but one or two more cases which we have to mention, Yrhere the student will meet with tones that do not belong to the fundamental harmony of a passage.

These are either Passing

notes or appoggiaturas.

Passing notes occur where a voice, in moving from

chord

tones on in the

its

interval in one

to its interval in the next, takes the intermediate tones its

mean

way, the other voices holding their tones while.

The following

is

an instance

•

or semi-

in the first

chord

Pa-'Mn^

—

MANUAL OP HAEMONT

96 FIG. 145.

jLi}"

3^^-J=^ 1

^itp

S^

=2'

Here the soprano

in

— idH

passing from

C

—

!

r=5E

1

^-

to

the bass the intermediate tone between

E

A

z^i^zj^i

takes the

and

C.

D on

its way; so The smooth and

flowing effect which passing notes create, will be evident to Appogg»ntuta.

An

all.

Appoggiatura occurs, where the foreign note comes

first,

and

afterwards the harmonic interval of the chord.

For example

:

D and B in the following chords.

FIG. 14G.

J:

^^.

»

m

In appoggiaturas, as in the case of suspensions, the hannonic inter had better be omitted in the other

val which follows the foreign tone, voices.

Difference

between thrm.

Let it be observed that the difference between a passing note and an appoggiatura is, that one falls upon an accented note, the other upon an unaccented one.

The following

is

an instance of both passing notes and appoggiaturas

intermingled in the vai'ious parts; so that a succession of simple chordf in half-notes,

is

cut up, as

it

were, into a

movement of quarter notes.

AND THOROUGH

Fia

n

BASS.

147.

—i^ Here I

Bb V cvi /ii dni"

^=iiii,

i^ii^?El^lllpiiSi§ Et)I

BbV Ebl

CVI

/ii

/II

Ebl

Bbv

Ebl

AND THOROUGH Ex.

123

BASS.

106.

I a

Ex.

I

EV

aisffrvii"^'—

ai

ai

107.

I

ife^is=ii Ex.

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ai

6ii»

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6.

—

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I

—

i

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1

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—

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.

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Choral.

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MANUAL OP HARMONY

124 :id=::

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MANUAL OP HARMONY

126

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130 Ex.

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