CORNELL UNIVERSITY LIBRARY

m

it'*'^ "Z~,,

II

3'

CORNELL

UNIVERSITY

LIBRARY

The

original of

this

book

is

in

the Cornell

University

Library.

There

are

no

known

copyright

restrictions

in

the

United

States

on

the

use

of

the

text.

GRAMMAR

OF

MUSICAL

HARMONY

©Se

S>ub8tance of Hectureis DELIVERED IN

ST.

M

A R

T

I

N'S

HALL

THE

TEAINING

INSTITUTIONS

OF

THE NATIONAL

SOCIETY,

BY

JOHN

HULL

AH,

PR0FSS80R OF VOOAI, MUSIO IN KINO'SOOLLEOE, AND IN QUEEN'S COLLBOE, LONDON,

AND ORGANIST OF OHARTEEHOUSE.

NEW

EDITION.

LONDON:

LONGMANS,

GREEN, READER,

AND

DYER.

lOBDOH;

SAVILl, 1DWARD3 ASD CO.. PEIMTKES, OaAHDOS BTBEEt, COVENT QAKDBN.

PREFACE.

There

are

some

terms belongingto everyart or sciencewhiclij thougli convenient

or indispensable to adepts^ are a source of

embarrassment

tobeginners. In music,

melody, harmony,

and

counterpoint, are

among

these.

A

successionof individual sounds,

and

a succession of combinations of sounds, are obviously differentthings,

and

assuch theyrequire different designations,

—

the veryexistenceof

which

makes

itdifficult to appreciatethefactthatthe things designated,

though

different,

must

neverbe considered separately.

For,asuccession of sounds can hardly be recognised asmelody, unless it be

capable ofproof,

by

the addition of that

harmony

of

which

it is onlyone part/ whileasuccession of combinations of sounds will be

unworthy

of the

name

of

harmony,unless the various parts of

which

it is

composed

beindividually melodious. Certainit is that a musician never conceives

melody

without associating it with

harmony,

as he neverhears

harmony

without being able to trace out

more

orless

ofthe

melody which

it

must

of necessity contain.

The

line ofdemarcation

between

harmony

and

counterpoint beinglessstrongly

marked

than that

between

melody

and harmony,

their distinction

by

different

names

is attended with

much

greater inconvenience.

For

that distinction

would

seem

toimplythatthe arrangement of individual parts

was

something over

and

above, or even different from,

making

the chords in

which

they are contained

succeedone anotherproperly.

Now,

no

one could be considered as a harmonist

who

could not connect one consonant combination with another, prepare

and

resolve discords,

and

reconcile the frequentlyconflicting interests of combination

and

progression.

And

yet

by

the

term

counterpoint is understoodlittle

more

; for

thetreatment of

mere

passing notes can hardly be brought altogetherunderthose

strictrules to

which

a science isgenerally supposedto be amenable.

iV

PREFACE.

OF

Hakmony"

must

therefore be prepared to find that it contains

much

that

relatesto those parts of musical science

which

are

commonly

treated

under

the

separate heads of

Melody and

of Counterpoint;

and

that

many

things usually reservedforsubsequent explanation axe introduced, as it

may

seem, prematurely. Should

he

find, also,that

some

points

on which

musical theorists are not agreed, areputin adogmatic form,it

may

be

hoped he

will attributethis, nottoignorance of, or indifference to,the opinions of others, but to a conviction that beginners

shouldnot be distracted

by

the consideration of opposite theories,

and

that, as a consequence,alldiscussions

on

disputed points should be kept out of elementary books.*

The

student

who

is desirous of mastering the contents of the followingpages should

come

prepared for the task, not only

by

the possessionof

some

theoretical

knowledge, but also of

some

practical skill.

He

must

be familiar at least with

thetreble

and

bassstaves; with the construction of

major and minor

scales,

and

therelations of one scale to another; with the nature

and

names

of the various

musicalintervals; and, in short, with whatever

may

be classed

under

the

name

of the

"

accidence" of music. Moreover, he

must

have

some

ideaof, or

some means

of ascertaining,

"the

sound of

what he

sees;"

and

—

inversely

—

some power

of

expressing theeffectof

what

heimagines. Itis difiicultto conceive

any

means by

which

this

sympathy

of eye

and

ear can be attainedexceptingsinging or

playino-inconcertwithothers, orthe practice of an instrument like the pianoforte

from

which

many

differentsounds can be producedatthe

same

instant.

Considerableproficiency inthe artof

music

has beenoften attained

by

persons

who

have

had

littleor

no knowledge

ofthe science,- or,

more

properly speaking

to

whom

theneglect of study has

been

partially supplied

by

_{favourable organization}

or that indirect culture which,

bemg

unconsciously received

and

therefore never takenintoaccount, is often mistaken for it.

But

topursue the science of

music

withoutreference to the art

would

seem, if not altogetheraprofitless _occupation

certainlya verylaborious

and

uninteresting one.

The

musical student

must

begin

—as

he

shouldgo

on—

withthp considerationof

what

ispractical;

he

must

collect

hisfactsbefore

he

can theorize

upon

them.

Of

what

avail can it beto inquire

why

this combination or that progression is pleasing to the ear,unless

_{he have}

PREFACE.

V

ascertained, orcan ascertain, forhimselfthatitis,orthatit is not so?

—

Itis

from

the neglect ofthis preliminarytraining ofthe ear (hardly possiblewithouttraining ofthevoice orthe hand) that so

many,

especiallyofthose

who

beginitsstudylate

inlife, fail in acquiring

any

real acquaintance with, or living interestin, music.

Dealing with symbols of

whose

powers he

knows

nothing, the

mere

theorist in

musicisinapositionakinto thatof

an

artist painting

on

porcelain

—

^ignorant of thefactthathiscolours will

come

out of the furnace other than they

went

in.

Music

has a

body

as well as a soul;

and

we

shall

form

but animperfect

acquain-tancewith her

whole

being, if

we

studytheone withoutreference totheother, J.

H.

March, 1852.

The

reprint of this

work

has afforded an opportunityfor revising the text,

and

for

making

several alterations in the examples.

A

copious

Index

has also been

substitutedforthatappendedto the FirstEdition.

A

seriesof

"

Exercises to

accompany"

the foUowiag

Grammar

ispublished in

aseparatevolume.

J.

H.

August, 1853.

The

demand

for a Third Edition has presented a second opportunityfor

making

such emendations asthe experience of another five years has

shown

tobe needed.

In

the

body

of the

work

thesehave not proved

many

; but thelast three Chapters

—

embracing

a verydifficult

and

importantpart of the subject of the

work

—

have beenentirely remodelled.

J.

H.

CONTENTS.

OHlfTBB PAGH

I. The Harmonio Chord 1

II. Intervals

—

Consonant andDissonant 3

III.

The

Triadand

Common

Chord 4

IV. ArrangementoftheTriad . . . ^ 6

Y. Figured Basses 8

VI. MotionofParts 10 VII. ConnexionofChords 14

VIII. Sequences 17

IX. ResolutionofDissonances 18

X. DiscordsbySuspension 20

XI. Inversions ofthe Triad 23

XII. SuspensionsonInversions of the Triad ₂₇

XIII. FimdamentalDiscordoftheSeventh 30

XIV.

Eesolution oftheFundamentalDiscordofthe Seventh 33

XV.

SuspendedEesolution 37

XVI.

DiscordsbySuspensionon FundamentalDiscords ₄₀

XVII.

Inversions ofthe Discordof the Seventh 41

XVIII.

Licencesinthe Eesolutionofthe Seventh 47

XIX.

Interrupted ResolutionsoftheSeventh 51

VUl

CONTENTS.

CHAPTER rk»M

XXI.

FundamentalDiscordof theNinth 55

XXII.

ChromaticIntervals 57 XXIII. Discordofthe Diminished Ninth 59

XXIV.

Inversions of theDiscordof theNinth andSeventh 60

XXV.

ChromaticIntervals

66-XXVI.

Chromatic

Harmony

.68

"XXVII.

PedalPoints 71

XXVIII.*

Cadencesor Closes 72

XXIX.

Progression ofFundamental Basses 75

XXX.

Modulation 77

XXXI.

Rhythm

....,-

78

XXXII.

Harmonizing 80

*TheattentionoftheTeacherisespeciallydirected tothenotein p. 47, referringtothestudy of these

GRAMMAR

OF

MUSICAL

HARMONY.

CHAPTER

I.

The

Harmonic

Chord.

1.

All

soundresults

from

vibrations

communicated

totheair

by some

disturbing

force.

Sound

is_{musical or otherwise according to the regularity} with

which

such

disturbingforceis exercised.

2.

The modes by which

musical sounds are produced

and

controlled^

though

susceptible of infinite modification,

may

be classed under two heads:

—

_1st,

wind

instruments

—

pipesthrough

which

air is forced^

and

which produce grave or acute

sounds asthe pipes arelarge or small; 3ndly,instrumentsoi percussion, the gravity or acuteness of

whose

sounds depends onthe size,weight, or tension of the material of

which

theyare composed.

Thesinglelawof sound whichforour present purpose it is necessarytounderstand,is

bestexplainedbyreferencetoa,.stringfastenedatboth ends.

3.

A

simple,

unmixed

sound can never be maintainedfor

more

thananinstant.

Every

principal sound generates others which, though often inaudible,

and

never heard with the

same

force as theirgenerator,

no

less certainlyexist,

and

that in infinite

number.

Fig. 1.

4. Suppose a string of a certain length

and

thickness gives a

soundcalledDo.

For

aninstant afterit has been setin vibration,

it sounds that

Do

only; then, in addition, though

more

faintly,

the

8™

above; then the (perfect) 5^'^

tothat8™; thenthe double 8™; then the (major) 3'^,the S**",

and

the (minor) 7""tothat double 8™; thenthetriple8™; thenthe 9*^tothe double8™; thenthe3">

_and

4'"

tothetriple8™;

and

so on,

ad

infinitum.

^

Sothatwhenavioloncelloplayerdrawshis bowacrossthe loweststi-ingof his instrument,

he producesnot onlythesoundliterallyduetothatstring,butallthe soundsin fig. 1.

5. Subordinate sounds thus unconsciously produced, are called harmonics to

the prime, or lowest sound.

The

combination of a prime

and

its harmonics is called an harmonic chord.

6.

Now

it is found that sounds identical with those in an harmonic chord

may

be produced artificially,

by

dividing the string which gives the

same

prime

into aliquotparts.

For

ifa stringthirtyincheslong gives the lowest

Do

in fig. 1,

G. M. H. B

2

THE HAEMONIC

CHORD.

[Chap.I.

i

ofit (fifteeninches) will giveDo, the 8™;

f

ofit, Sol, the (octave) b*^; 4- Do, the double 8^«; J- _Me,the 3^";

^

/So^, another S"";

_f

Si\>, the

minor

7**;

_i

Do,

the

treble 8^«;

^

i?e, the 9*''j

-^V Afi, the 3rd; _{-jV -Fo,}the

4*

;

and

so on. {Compare

figs. 1anrf 2.)

/tff. 2.

Thenotesand fractions marked * arenotmathematicallyinstrict accordance; i.e.,the sounds recognised by uniyersal consent as the minor 7"" and perfect 4"" to Do, are not

producedbyprecisely ^,andprecisely-jlj-of thestring.

7. This artificial arrangement partiallyaccoimts for the

phenomenon

of har-monics. It is evident that while a string produces one sound (the prime), it

vibrates duringits wholelength,

and

that as soonasthe octave is heard, each half of the string vibrates separately; infact, thatdivisions like those indicatedabove

are

made

by

Nature,

ad

infinitum.

Fig.3.

+

Theruledline infig.3 representsastringat rest; thedotted lines indicate thedirections

whichthestringwould takewhensoundingthe prime, its8'°,and octave 5*.

Thepoints ofintersection (markedin fig. 3) arecalled nodes.

8. Harmonics,

up

to a certain point, areimitated in the construction of the organ, the peculiar fulness in the quality of

which

instrumentresults chiefly

from

this imitation; the

term

"full organ" being

apphed

tothe combination of various

harmonic "stops" with those producingprimary sounds.

The further consideration of this subject belongs rather to natural philosophythanto music; but the necessity for the foregoing explanations will be found in their practical application towhat immediatelyfollows.

CHAPTER

11.

Intervals

—

Consonant and

Dissonant.

9.

Sounds

are consonant (fit to be sounded together) with one another, according to the order in.

which

they aregenerated in an

harmonic

chord.

As

harmonics

become

more

remote

from

their prime, they

become

less perfectly

consonantwithit orwithone another; then, dissonant; and, finally,their relation ceasestobe appreciable in

any

musical system.

10.

The

relation of two different sounds onetoanother is called an interval.

As

musical soundsare consonantor dissonantwith oneanother, so aretheintervals

which they

form

said tobeconsonant or dissonant.

11.

The

consonantintervals aretheoctave,the _fifth, and the third; with the

inversionsofthe

two

last, the fourth

and

the sixth.

The

dissonantiatervalsarethe seventh

and

the ninth; withthe inversion of the former, the second.

13.

The

ninth doesnot admitofinversion.

13.

The

imperfectfifth

and

itsinversion the pluperfect fourth are anomalous,

being,

though

essentially dissonant, sometimestreatedlike consonant intervals. 14. Consonantintervals arefurther divided into perfect

and

imperfect.

15.

The

perfectconsonances arethosefoundbetweenthe sounisfirstgenerated

in the

harmonic

chord

—

viz.,theoctave,thefifth,

and

itsinversion, thefourth.

The

imperfect consonances are the third,

and

its inversionthe sixth.

16.

Examples

ofalltheseintervals arecontaiued in the

harmonic

chord, either

between

the prime

and

theharmonics orbetween one

harmonic

and

another. Fig.4.

Consonant. Dissonant. Anomalous.

33!

_feo:

-^-:§:

?^

?^

o o

-^--^

XX

T~T

xz

TT

xx

O

Maj.&Min. Maj.&Mm. Octave. Kfth. Tourth. Thirds. Sixths.

Perfect, Imperfect.

Seventh. Second.

Imperfect Pluperfect Ninth. Kfth. Fonrth.

17. In

an harmonic

chord consonances are generated before dissonances, and

CHAPTEE

III.

The

Triad

and

Common

Chord.

18.

From

the three notes ofdifferentnamesfirstgeneratedin a

harmonic

chord

is formed the simplest of musical combinations, the triad

—

a bass note with its

3"^*

_and

5*''.

When

_the

8™

isadded, the combinationis called a

common

chord.

By

thetermhasaisheremeantthelowestpart,whatever beitspitch,oron whateyerstave

it

may

be written.

Fig.5. Fig.6.

TT"

S

-^-19.

A

common

chord contains

none

but consonantintervals. Fig.T.

331

-^

"TT"

-^--^

:^

<j

-^

~o~

Octave. Fifth. Fourth.

Major. Minor.

Thirds.

o

Major. Minor.

Sixths.

20.

When

the 3"^ of a chordis separated

from

the bass

by

two tones (amajor

third) the chordis said tobe major.

_^^

Fig.8.

31.

The

tonic (1^*sound) of a majorscalebears amajor

chord, as does the dominant, (the B*"" above,)

and

the

sub-dominant, (the S***below.) (See_{fig. 8.)}

22.

But on no

other notes besidesthe tonic, dominant,

and subdominant

of a scale, cana major chordbe

formed

withoutnotesforeignto thatscale.

E.g., a major chord onBe (the 2"" of thescaleofDo) wouldrequire

Fa

to be made sharp.

A

majorchord on

Mi

(the3"")wouldrequire Sol^; and

onia

(the6"')_{Doi. While} aperfectmajor chord on Siwouldrequirenot onlyiee|,but

Fa

_|; since

Fa

^isanimperfect

fifthfromSi.

Fig.9.

m

1 3 n 4 6 6

Chap.III.]

THE

TRIAD

_{AND COMMON}

_CHORD.

23.

So

that in treating each note of the natural scale (or

any

scale of like

construction) as the bass of atriadcomposedonly of suchsoundsas are

found

in the scale itself,

we

producethree majorchords,

and

four

minor

chords; one of these

latterheingalso imperfect, i.e.,having animperfectfifth. Perfect Chords. Fig.10.

s

Major,

-XT

Minor.

32:

S

Minor. Major. Major. Minor,

Imperfect.

Minor. 24.

A

bassnote bearingatriadis called also aroot,or radicalbass.

Theterm

pWme

isrestricted to rootswhich bearharmonic chords; consequently, neither

the2°^3"*6*or7""_{sounds of a scalecanbeaprime; nor, indeed,} (as willbeshown here-after) can the1"or the

4""-25.

In

thetriadsofatonic, dominant^

and

subdominant, are comprisedall the notes of the scale to

which

theybelong.

Seefig. 11,where

Do

is in the tonic chord.

Re

inthedominant.

Mi

inthetonic.

Fa

in Bubdominant, Solinthetonicanddominant,

La

inthesubdominant,and Si inthedominant.

Fig. 11.

/^

-^

^

CT"

26.

From

threechords thusrelated, everyscaleissaid tobe derived;

and

one

or other of theirroots will serve also as a root to

any

note of the scale. {Compare

figs.11and12.)

CHAPTER

iV.

Arrangement

of the

Triad.

27.

The

sounds of a triad

—

still

more

of a

common

chord

—

admit of

much

variety intheirarrangement. Since, solongasa combination consists exclusively of

S^

S*"^ or 8^^ to a bass note, it is still a

common

chord, let those notes

stand in

what

relation they

may

to the bass or to each other, or be their

number

everso great.

-^

HE

-^

HE

JZi. Fig.13.

3ZZ

-^

O O

H

_-^

xx

TT

-^

SIE

HE

X3IIO:

HE

HE

-nr-c^

_HE

-^

s

TX

HE

S

HE

HX

HE

©

HZ

Of the chords in fig. 13 some consist of four notes, some of more, and someofless

;

moreover,some arewell arranged, some badly, some indifferently; but theyareall equally

common

chords,ortriads, ofDo.

Theprincipleswhichguide usin ourjudgment ofthesechords must be deducedfrom the

harmonicchord.

=P

m

28.

As

the eye passes up fig. 14, (the

harmonic

chord,) it , „ ^y-14.

will be perceived that the notes lie nearer together; that the

largest intervals are at the bottom of the chord

and

the smallest

at the top; moreover, that this diminution of the intervals is

gradual,

and

that there is

nowhere

any disproportionate hiatus.

We

have first

an

octave,then a fifth, then a fourth, thena major

third, then

two

minorthirdsinsuccession,thenthreemajorseconds,

and

then aminorsecond.

"

^

29. Inwriting chords, ofwhateverkind, the arrangementofthe

harmonic

chord should beimitated as far as possible.

The

lower notes should be separated

by

the

largest intervals,

and

the diminutionoftheintervals should begradual.

Infig.15this ruleismoreorlessstrictlyobserved;infig. 16it isaltogether disregarded.

Fig.15

91

-^

JOT

H3:

<~>

T-r

-^-~Ci

Hz:

-^

jCC

<ri

-^

H3:

HX

_Ci_ Fig. 16. "TT-

HX

s

s

HX

-^

HX

HX

IHT

HX

Chap. IV.]

ARRANGEMENT

_OP

THE

TRIAD.

s'lg. 17.

30. Again,a

common

ctord

must

containonly

8™

5**^

_and

_S'^

to a bass note.

In

arranging chords for

more

than four voices,

(and

from

other causes,)

we

must

of necessity double (i.e., write

more

than once) thisor thatnote orits 8™.

The

harmonic

chord

givesus alawin this case; sincewithin the limits of the

common

chord it contains

no

lessthan three

Dos

(theprime

and two

8'''^), two Sols (5"™ tothe prime),

and

onlyone

Mi

{S^ to the prime).

Whence we

derivethefollowing rule

:

-e-31.

Double

the

8™

(totheroot)ratherthan the 5*^,

and

the5**" _{ratherthan the}

3"*

; especially

when

the3"^is major.

Infig. 18this ruleisobserved; infig. 19 violated.

a b c a b c Fig. 18.

s

-e>- ~cr-

-^>-iB:

23:

S

-^

"ry

-^r

Fig. 19.

BE

122: "C7-~<rr ~C7-<:>

8

CHi PTER

V.

Figure

d

Basses.

34

Musicians use a kind of "short-hand," wherein the intervals

which

the notes of a chord

form

with its bass, are expressed

by

figures.

A

bass so accom-panied iscalleda figuredhass, orthoroughbass; i.e., a bass written throughout a

composition, in such a

way

as toindicate (partially) the general effect.

35.

Thus

a bass note

which

is to be accompanied

by

a

common

chord (its

8™

5^

and

3'*) is figured e or ^ oreven 3; the highest

number

usuallyat the top.

The

common

chordhowever (asits

name

would

imply) is so

much

more

oftenused than

any

other singlechord,that, saveto contradict otherfiguresbefore them,the

above are seldomwritten; itbeingunderstood, inthorough bass, thatabass note

withoutfiguresis tobeara

common

chord

—

of

any

number

of notes in

any

position.

Thusfig. 22, orany otherformof thechordofDo, isimplied byflg. 23,

fig. 24, orfig.25,andstillmore oftenby fig. 26. F'S- 22.

Fig. 23. T7' "TT" Fig. 24.

331

5 3 Fig.25. "g:r-Fig. 26. "TT^

Thefigures

may

be placedoverorunderthe bass notes,indiflferently.

36.

When

accidentals are to

be

introducedinto the chords, the figures

must

be preceded

by

accidentals (or otherwise modified) accordingly.

In

the case of a

common

chord, the intervaltobe alteredisoftenthe only one

marked

at alL

More-over, the3^'^_{requires so}

_much

_more

_{frequent alteration than}

_any

othernote of a

chord, thatthe accidentalis usuallyput without thefigure to

which

itrefers.

37.

Thus

I, or b,or ^,

under

or over a bass note,

means

jf3, or b3, or 113; that the

3^

(from the

bass note) is to be

made

sharp, orflat, or natural.

iFig. 27.)

No

interval but the 3"* is ever thus

implied

by an

isolatedaccidental

Fig. 27.

^^

^fe=@

^

~CS

—

C5"

QE

_-O

_—

^

O O

I' n

Chap. V.]

PIGUKED

BASSES.

Fig.28,

38.

A

short line

drawn

obliquely across the

right extremityof a figureindicates that the note

corresponding with it is to

be

raised a semitone.

Thus

g;isacontraction of 15, ify.28), or,

contra-dicting aflat, oftl5 ifig. 29.)

Fig. 29.

-^-C5~

:^

^

fcitt

( >

321

-^

& \>

Inoldfiguredbasses, the elevation of a note a semitone is often indicatedbyasharp, although the particularnote referredtoisreally to bemade natural

—

in contradistinction to a preceding_/?a«.

Fig. 30. Fig. 31.

39. Itisnot usualto express alterations inthe

8™,

which

must

be

made

perfect {fig. so), unless expressly

marked

otherwise Cfig. 3i.)

"t

I

fr J

-;^

S

ZQ_

#«

rrif( fi f f iiiiiifwirimnniwftu.*m.»\

CHAPTER

VI.

Motion

of

Parts.

40. Continuous

harmony

may

be produced either

by

thecombination of several

instruments capable ofsoundingbut one note at a time, (such as the

human

voice,

the oboe,

and

others,) or

from

one instrument capable of sounding

many

notes ata time, (suchastheorgan

and

thepianoforte.)

In

aseriesof chordsarrangedfor voices,

the particular notes sung successively

by

eachindividual voice are saidto

form

a

part;

and

although with equal propriety

we

might

speak of theindividual parts in

continuous

harmony

performed

on

the organ or pianoforte, such parts are less easily discriminated

by

the ear or the eye.

The

science of

harmony

is

most

con-venientlystudied,

by

supposing, atfirst, allsuccessionsofchordstobe intendedfor

performance

by

voices.

The exampleswhich immediatelyfolloware infour parts,which parts, forthepresent, willseverallybe spokenofas theSoprano, theAlto,theTenor, andtheBass.

41.

When

two or

more

voices sing the same notes in

two

or

more

following chords, they are said tosing in unison.

The

unison oftwoor

more

differentvoices is forbidden in music of anydefinite

number

of parts; since if

two

out of fotir voices singthe

same

notes in following chords,not onlyarethe (supposed)fourparts

reducedto three,but an undue prominenceis giventotheone partthus doubled.

Thus fig. 32beginsand ends in fourparts,but at ** _{there are onlythree; because the} BassandTenorsingthesamenotesintwofollowing chorda.

Fig. 32.

m

Fd=-J

|.l

o

ll

.f^

'r

-

_T^°

\ '

i^T^

J

2zr

?

3D

-^

J-n

33

23

:ni

-o-:x3i

<i

II

43.

The

motionof

any two

real parts in respectonetoanothermust

be

contrary,

obhque, or similar. •'

Chap.VI.]

MOTION

OP

PARTS.

11

otherfalls {fig.33); in oblique niotion,

when

onerises orfalls

and

the other stands

stiU{fig.34); in similarmotion,

when

bothpartsrise orfall, {fig. 35.) Fig. 33.

33

Fig. 34. Fig. 35.

^^

"Trf

f'l

'

°r|"

=^

^^d

Contrary, Oblique. Similar. Fig. 36.

^s^

-^-44

The mere

iteration of the

same

notes, {fig.36,)

sometimes

termed

"_{parallelmotion," is motion only}

as respects timp, not tune: consequently, the union

ofthe

Tenor and

Bass

on

the

same

notes {see ff, fig.32,)

does not violate the laws of motion or progression,

though

it should be usedsparingly, forthe reasons given in par. 41.

45. Contrarymotion, or oblique motion,

may

be

made

under almost

any

cir-cumstances,but similarmotionissubject to

many

restrictions

and

liable to

many

rules.

46.

The

first chordinfig.37 a (as has alreadybeen shown) isin agood, indeed, aperfect position.

The

position,of the second chord is of necessity equallygood,

since itis identicalwiththat ofthe first. Nevertheless, the secondchord, in its presentposition,

must

not followthe first; because the Bass

and

the Alto keep an

octave apart in similarmotion, thereby

making

consecutiveoctaves {fig.37b); while

the Bass

and

the

Tenor

keep afifth apart insimilar motion, thereby

making

con-secutivefifths{fig. 37c.)

Vjf.37a. Fig.38a.

^

TZ7

m

/\- < J

Q

3:±

^

^

47. Ifitberequiredto

make

the chordof

Re

followthe chordofDo, thelatter

beinginthe position offig.S7a, the parts

must

move

as in fig.38a, or at leastin

sucha

way

astoavoid consecutive fifths oroctaves.

48.

In

fig. 38 the Alto, instead ofrising

from

Do

toRe, in consecutiveoctaves,

withthe Bass (whichalso risesfrom

Do

toRe)fallsto

La

{fig.38S),thereby

making

contrarymotionwith the Bass;

and

the Tenor, instead ofrising

from

SoltoLa,in

consecutive fifths with the Bass, falls to

Fa

{fig.38c), thereby

making

contrary motion withthe Bass.

49. Itis true that in fig. 38,

La

and

Re

still remaininthe second chord; but

the

bad

effect ofconsecutivefifths isavoided

by

those notesbeingsung, not

by

the Alto

and Tenor

voices,(asinfig. 37,) but

by

the Soprano

and

Alto.

From

theabovewededucethe following importantrule

12

MOTION

OF

PARTS.

[Chap.TL

50.

Two

parts in unison, or separated

by an

octave or a perfect fi^^ i?

o^

chord,

must

notbein unison, or separated

by

an

octave or

by

aperfectfifth

m

the next; or,tousetheaccustomedformula, consecutive unisons, octaves,

and

perfect

fifths are forbidden,

and

miistbe avoided.

Fiy. 39.

51. Consecutivefifths,

when

not of the

same

kind, are allowed;

I.e.,

two

parts separated

by

a perfectfifthiuonechord,

may

be separated

by

aniTwperfectfifthinthe next,especiallyin descending,

{Seefig.39.) Thislicence should,however, be used sparingly.

< \

o

J

j=L

S

33

^

52. Consecutive octaves

and

fifths between notes

which

move by

sUps

{see

Jigs.40 and41)are equally to be avoided withthose

between

notes

which

move, asin fig. 33,

by

degrees.

Fig. 40. Fig. 41.

Chap. VI.]

MOTION

OP

PARTS.

13

55. Moreover,

two

parts

moving

for

any

lengthoftimein consecutiveintervals

of exactly the

same

kind,be they

what

they

may

exceptoctaves, give

an

impression

of,

and

often are intwo different scales.

Fig. 44.

O

< >

-^

123;

-^

33lfe

<~> "C5"

-O-

<>

Q

<rT -<^-

"TT

Fig. 45. -J-T

-S--^

_o

<->

TT"

o

<„>^_S_o

-33

_o

_Q

-

XT'

Fig.46.

Theupperpart of fig. 44isthescaleof Sol; thatoffig. 45, ofFa; that of fig. 46, of

Mi; while thelowerpart ofallthreeisthescaleofDo.

Moreconvincingthanargumentwill be any attempt to singorplay thesepassages, the effectofwhich(ofthelastespecially)isabominable

CHAPTEE

VII.

Connexion

of

Chords.

It willbe remarkedthatthetwo chordsinfig.37 hare nonotesincommon; notonenote in the first chordisrepeated in the second. Mi, Sol,and

Do

arethe3"" 5""_and8'""_to

_Do

;

Fa, La, andBe,toBe.

56.

The

chordswhichfollowone another with the

best efifect are generally those

which

contain one or

more

notes in

common;

such

common

notes being

said to connect together the combinations of

which

theyformpart. Thus, ia fig.

47

the

8*

of thefirst chordserves as the

5*

of the second; the

8* and

3"^

of thesecond chordas the3"^

_and

S*""of the next, &c.

The

common

notes are tied.

Fig.47.

p^

e

l^

-^

TT

P

57. Successions ofunconnected chords (as ofthe chordof

Do

by

that of

Re

in fig.37) areexceptional; beingpeculiarlysusceptibleofconsecutivefifths or octaves,

always

somewhat

harsh, even

when

free

from

positive error,

and

generally difficult to singin

some

oneor

more

progressions.

58.

When

two

notes ofthesame

name

and

pitchoccur in

two

following chords,

itis desirablethat they bein the samepart, (i.e., be

sung

by

the

same

voice,) in both chords.

Infig. 57nearlyeveryone of the chordsis connectedwith that nexttoit bya

common

note. Theconnexionineach caseisindicatedbyatye.

59.

Wben

two

notes of the

same

name

but of different pitch occur in

two

following chords, it is necessarythat theybeinthe

same

part

—

i.e.,

be

sung

by

the

same

voice iabothchords.

m

Fig.iS. znsi

-oi

—

^-35:

"f:^ not Fig. 49.

^

23:

60.

In

fig.

49

the

Mi

l> _{of the} Soprano_{part of the second chord}

is said to stand

in"falserelation" tothe

Mi

^ ofthe Alto part in thefirst.

False relations ofthiskindwere allowedbythe old masters; possiblyfrom the difficulty foundin singing the chromatic semitone. {Seefig.48.)

Chap.

Vn.]

CONNEXION

OF

CHORDS.

15

61.

Harmony

of

wMch

any

individual part contains

many

large intervals has always an effect

more

orlessdisjointed; large intervals, too, in rapid succession

are

more

difficultto singthan small ones.

As

a rule, therefore,

—

62.

In

continuous

harmony,

the parts should

move

mostly

by

small intervals

;

large intervals being introducedsparingly,

and

generally innot

more

than onepart

atatime.

63.

Kgs. 50 and

51 consist ofthe

same two

chords.

The

effect of the former,

though

consecutive octaves

and

fifths are avoided, is disjointed,

and

the parts

(especially the Alto) aredifficult to sing.

On

the contrary, theeffect ofthelattei isgood,

and

the progressions are easy; because eachpart

moves

to thenoteofthe

second chord

which

isnearestto thenote it has just quitted inthefirst.

Fig. 50. Fig. 51.

^^

"T

Fig. 52.

^-xx

-^

i i < •

16

CONNEXION

OF

CHORDS.

[Chap.

VIL

66. Parts are allowed to cross one another; i.e., the

Tenor

may

riseabovethe

Alto, or the Alto above the Soprano. {Seefig.56.-)

No

part, however,

must

faL belowthe Bass; unless,indeed, the part so fallingisqualified to taketheplace of

theBass

—

the lowest part.

Fig.56.

-©f

^i^^

2±

_-&

-^

> / ^

Q

|

xi

3ZI

-^-33

-Or

_-0|

XX

X3I

3Ii:

"TT-Infig. 57, the rariouBrules and recommendations giren in the foregoing chapter are generally observed.

u

Fig. 57.

d

-^

-tTTT-

^

Z2:

^^

-^

^

TV

l

_°l

' tt'

°

l

^^

'

iin

S3:

b5

67.

The

laws

which

regulate the influence of accidentals on the stave, apply

equallyto figuring. In bar5 offig. 57the

minor

S^

tothesecondbassnote {Do)

isnot expressed in thefiguring, becauseit has been alreadylowered a semitoneas

the

8*

tothefirstnote o/^Ae same bar

{Mi

b).

17

CHAPTER

VIII.

Sequences

68.

By

therepetition of the

same

succession of intervals

on

different notes, a sequenceisproduced.

In each part of fig.58eyeryalternatenoterisesorfalls bythesame interval; theBass

hjfourthsandfifths,the Tenorbyseconds,theAltobysecondsandthirds,andthe Soprano by thirds,sxidi.secpnds.

Fig. 58.

^

-&

^

321

-&

_^

^

_7^

_^B^

:^^

-^-69.

A

sequence

may

betonalorreal.

n

70. In a ^ona2sequencetheintervals are perfect or imperfect,majoror minor,

as theypresentthemselves in thescale.

Fig. 58 isatonalsequence; the progression of the Bass in the first complete bar is by animperfectfifth; inthe nextbarby aperfectfifth. The first interval in the Sopranopart

isa minorthird; the next butone, a majorthird,&c.

71.

In

a real sequence the respective intervals are exactly alike, involving generallyveryrapidmodulation.

^

By

making fig. 58 a realsequence (fig. 59),we shall modulate in four bars from

Do

into

Do

b. Fig. 59.

m

f^

I

J

b

J'

^^

m

_zzc?:

J2c^:

^P=t^^^

Tonalsequences are

much

morefrequentlyusedthanreal.

72.

When

a basspart, or

any

portion of a basspart,

moves

in sequence, every other partshould

move

insequencealso.

18

CHAPTER

IX.

Resolution

of

Dissonances.

"The dissonant intervals aretheseventhandtheninth; with the inrersion of the former, thesecond," {Par.11.)

"Theninthdoes notadmitofinversion." (_Par. 12.)

"_Theimperfect

fifthanditsinversionthepluperfectfourth" arealso"essentiallydissonant" intervals. {Par. 13.)

73.

By

a dissonant intervalis not

meant

anything of necessity harsh, or

dis-agreeabletothe ear; but,technically, a combination

on which

the ear cannot rest,

and which

therefore suggests another combination, to

foUow

it.

74.

The

progression of

two

parts separated

by

a consonant interval is, to a certain extent, amatter of taste or choice; in general they

may

make

contrary

motion, oblique motion, or similarmotion.

But

a dissonant interval

must be

resolved; the parts

between

which

it is found must

make

certain definite pro-gressions inrelationoneto another, in order that the ear

may

be

relieved

from

the

feelingof suspenseto

which

ituniformly givesrise.

75. Dissonantintervalsare mostlyresolved

by

contrary or oblique motion, one

ofthe notes invariably

moving

one degree.

76.

Of

two

parts separated

by

a seventh, the upper should fallone degree, while the lower

may

keep itsplace {fig-60),rise a fourth{fig- 6i),atfallafifth {fig-62>

Fig. 60. Fig. 61. Fig.62.

-^

—

^

—

—^

—

©-Asafifthistheinversionof afourth,figs. 61 and62aretheoreticallyidentical.

77.

Of

two

partsseparated

by

a second, thelowershould

/oW

one degree, while the upper

may

keep itsplace {fig-63),rise a fourth {fig-64), orfallafifth{fig.65<fc6).

Fig. 63. Fig- 64. Fig. 65.

-f-

=

<r>

-Q

_q

₈

_—^0—5—

Q

_q

^er

Chap. IX.]

RESOLUTION Or

DISSONANCES.

19

78.

Of

twoparts separated

by

aninth,theuj^er should/a//onedegree,whilethe lowernote

may

keepitsplace (,Jig.67), risea fourth ifig.68), ovfall afifth(Jig. 69).

Fig. 67. Fig. 68. Fig. 69.

221

O

^^

^

—

—

^—

—

^

79.

The mm^A

must

he carefully disthiguished

from

thesecond; since

though

found betweennotes of the

same name,

those intervals arenotinversionsofeach

other.

" The

ninthhas

no

inversion." (Pan 12.) Thiscautionisthe

more

necessary,

becausethe second, likeevery other interval, is sometimes

made

compound, (i.e., increased to

an

octave second,) (/?.66,) whileaninth can never with propriety

be

reducedto a second, since twodissonant notes cannot be resolvedbymeltinginto one.

Fig. 70.

Comparetheresolutionof thecompound(oroctave) second(fig. 66)

with that of the ninth {figs.68and69.) Also the resolution of the /[

ninth(Jig.67) withfig. 70, thefirstinterval in which is not a ninth, vj)

'^Qcp^-buta secondimproperlyresolved.

^

80.

A

second can always be

made

compound,

{i.e., increased to

an

octave

secondj) but aninth

must

neverbe reducedto a

second-81.

A

dissonance shouldalways

be

resolved; it

must

sometimes, also,

be

pre-pared; i.e., the note

which

causes it

must

appear in the combination

immc

diatelypreceding.

82.

A

dissonant interval is therefore liable to three processes

—

preparation percussion,

and

resolution.

Inthe following examples, the dissonances are prepared,aswell as sounded andresolved

Fa,the dissonantnote,appearsintheJirstaswellas thesecond combinationofeach.

Fig. 71. Fig. 72. _{Fig. 73.}

cT^

..

.Ci_

my

_o

_{^e_}

_^j

_<>o

_^—

t >

o

Q

-Fig. 75. Fig. 76.

£3_

^^^

_-^>

20

CHAPTER

X.

Discords

by

Suspension.

83.

A

combinationinwhichiscontained a dissonant intervaliscalleda discord;

as one

composed

onlyof consonantintervalsis calleda concord.

84.

By

prolonging a note not

common

to

two

following chords

from

the first

into the second,

we

producea discord

by

suspension.

A

discord

by

suspension (as its

name

might

imply) must be prepared(.par.81), aswell assounded

and

resolved.

85.

In

fig. 77,the chord of

Fa

isfollowed

by

the

chordof Sol; butin the

Tenor

partthe note

Do

(not

common

tothe

two

chords) is maintained during, half of thetime duetothechordof£10/.

Thus

a dissonant

interval (asecond) is produced between

Do

and

Re

;

whereby

the bass note Solis

made

tobear a discord

by

suspension; the dissonant note(Do) being preparedin

the chordofFa, soundedin thefirsthalf ofthe chord

ofSol,

and

resolved inthesecond half.

86. Again,infig. 78, thechordof

Fa

isfollowed

by

the chord ofSol; butinthe Sopranopartthe note

La

is maintained duringhalfofthetime dueto thechord

ofSol.

Thus

a dissonantinterval (aninth) isproduced betweenthis

La

and

theBassnote (Sol),which,

there-fore, bears a discord

by

suspension; the dissonant

note (La) being preparedin the chordFa,soundedin the first

haK

of thechord ofSol,

and

resolved in the

secondhalf.

87.

A

double discord

by

suspensionisproduced

by

yvolonging two notes not

common

to

two

following chords,fromthefirstinto the second. Thus,infig._79, the

two

suspensions in figs. 77

and

78 are combined.

Fig.77.

^

-^>-

T-y

FS=S

|

J-^-^A

_"<-> Fig. 78.

J-X2

-^

m

-^

<_>

±±

Fig. 79.

r^

-ri-

_-^

~C5"

S3I

-ci

4 3 88.

A

discord

by

suspension is distinguished from

any

other species of discord

by

its place in a bar; being sounded

on an

accented beat,

and

resolved

on an

unaccentedbeat.

89.

The

resolution of a discord

by

suspension isusually

made

by

the dissonant note takingthe

same

progressionit

would

have taken

had

therebeen

no

suspension.

Thus, in fig. 77 the progression of

Do

is only delayed, not altered. This rule,

however, explainsnothing: forthe

Do

does notfallto Si,becauseit

would

probably have done so

had

there been

no

suspension, but because theear requiresrelieffrom

Chap. X.]

DISCORDS

BY

SUSPENSION,

21

90.

The

agreeable eflfiect of a discord

by

suspension results

from

the delay of

the dissonant note in

making

the progression expected of it.

A

dissonant note,

having

been

prepared,

must

be

sounded and

then resolved. Suspense

and

certainty

cannot be simidtaneous: it is manifestly absurd that percussion

and

resolution

should takeplace at thesameinstant.

91.

A

dissonantnote

and

the note

by which

it istoberesolved

must

neverbe soundedtogether.

92.

Prom

adiscord

by

suspension, omit the note

by

which

the dissonance is ta heresolved; and, except in the case of the ninth, even the

8™

to that note.

In fig. 80, the combination at * is intolerably harsh from the percussion of Do, the dissonant note, with Si, the 8" of the note on which

Do

is afterwards resolvedj while the

combinationatfcontainstwoSi's

—

major

3^

tothebass.

Infig. 8l,thedissonanceat*isnotaninth,butasecondimproperlyresolred. (_Seepar. 79.)

Fig. 80. Fig. 81.

-^>-gL=iJ

4 3 9 8

Comparefigs. 77 and78with the abore.

93.

A

dissonance shouldbeprepared, sounded

and

resolvedin the

same

part,

—

the dissonantnote

and

the notes

which

prepare

and foUow

it should be sung

by

the

same

voice.

Infig. 82, the dissonantnote. Do, is prepared in the Temor part and sovmded in the Soprano. Infig.83, the dissonantnote,La, ispreparedintheAltopart,and soundedinthe Soprano. Fig. 82.

^

Fig. 83. "C5~ *• T

d

J-^s

"nrr-

_-^

-a

4 3

Comparefigs. 77 and 78with the abore.

94.

In

order toprepare a discord

by

suspension (aswellasfromother causes)

it

becomes

necessarysometimes to alter the position of the chord immediately precedingit. This

may

be done

by

writing

two

chordstoasinglebassnote,instead

ofone(.seeJig.84),but

more

elegantly

by

writing

two

notesinstead of onein asingle part(.seefig.85),

which

is

made

to cross theother. (Par.66.)

22

DISCORDS BY SUSPENSION

[Chap.X.

Fig. 84. Fig. 85.

^m

^

fi:

The relations of theupperpartsof amusicalcomhinationto theirbass are expressed by figuresplacedunderor overthat bass. (Chap. F.)

95.

A

straight line afterafigure indicates that the note due to that

figureis tobecontinued,whatever changes

may

be

made

inthe other parts oreven

inthe bass of thecombination in

which

it first appeared.

Thepassagesin figs. 77, 78,and79a.refullyand exactlyexpressed as follows.

23

CHAPTER

XI.

Inversions of the Triad.

97.

The

different arrangements of wliicli the upper notes of a chord are susceptibleare generally describedaschanges ofposition. Thesechanges,as

we

have

seen, arenumerous,

and

afford

much

varietyofeffecttothe combinationsin

which

they are made. Thisvariety is greatlyincreased

by

inversion; wherein one or

other of theuppernotes ofa chord beingsubstituted fortheroot,

becomes

the bass.

Thus,of a combinationcontaining no sounds but those foundinthe triadofDo,

Mi

or Sol

may

bethelowest. (^CompareJigs.90, 91,and92.)

Via.90. Mg.91. Pin. 92.

^^

-^>-

-<^-m

_TT-

T~y

"TT"

-^

98.

The

primeor root of a chordistherefore not, ofnecessity, the bass.

Thebass offig. 91isMi, offig. 92, Sol; therootofbothchordsisDo. Offig.90,

Do

is

both bassand root.

99.

When

the 3'^'^

_from

_{the root of a chord}

_becomes

the bass (asinfig. 91), the

firstinversionis said to beused.

100. Itis " understoodthat a bass note withoutfigures '-^'^' ®^' ^^-^^• is to bear a

common

chord." (.Par. 35.)

Were

the bass

offig.93 presentedalone,the

common

chord of

Mi

would

be due to it.

Some

indication, therefore, is

wanted

to

show

that the chordin fig. 93is tobewritten or played,

and

not the chord of

Mi.

On

comparing fig.93 with

fig.

94

(the triad of Mi), it willbe foundthatthe differ-ence between

them

liesin onenote; thatin fig. 93 there is Do, asixthtothebass,

and

infig. 94, Si, a fifth.

101

.

Thisdifference is expressedunder fig. 93; § implyingthatinstead of the

5*^

_and

3^^ toDo, the 6*''

_and

3'"*_{are tobewritten.}

103.

As

thechord of the Sixthdiffers

from

thetriad onlyin oneinterval, it is

generallysufficient to express thatinterval only, inthe figuring.

The

3"^ to the

bass,being

common

toboth chords, is seldommarked.

103.

Thus

when we

finda 6

under

a bass note,

we know

atonce that thebass isnot the root; and, in the presentinstance, thatitisthe third to theroot.

"cr

c^

24

INVERSIONS

OF

THE

TKIA.D. [Chap. XT.

104.

For

thearrangement ofchords with the root in the bass,

two

rules have

been given:

—

"Doublethe8"ratherthanthe 5* andthe S*ratherthan the 3'S especiallywhen the 3"*ipmajor." {Par. 31.)

«Omitthe8"ratherthanthe

5%

and the5"^ratherthanthe3'"." {Par.33.)

105. These rules, "apparently contradictory," {par. 32,) are based

on

the

same

principle

:—

that the notes of a chord

may

bemultiplied or omittedin pro-portion totheirimportanceor effectiveness.

106.

The 8™

istheleast effectivenoteinachord,

and

therefore

when

doubled

is less obtrusive,

and

when

omitted more easily spared than

any

other note.

Whereas

the 3"^ (especially

when

major) is the most effectivenoteinachord,

and

therefore

when

doubled is more obtrusive,

and

when

omitted is less easily spared

than

any

other note.

107.

Of

thechordofthe Sixth, the bassis itselfthe

S^

from

the root;

and

the

S'*

and

6**

from

theformerare5*''

_and

_{S"- to thelatter.}

I^.95. See fig. 95,where Mi, the bass, is the3'^_{fromthe root}

Do

(indicated

by a dot). While Sol, the 3'S and Do,the 6""fromthebass,arethe 5"" and S'"fromtheroot.

Therules inpar31 and33,therefore, slightlymodified,

may

beappliedto thefirstinversion of thetriad,thus:

—

S

T7~

108.

In

writing the chord of the Sixth, omit the

8™

tothe bass, (especiallyif

the bassbe a major

3^

fromthe root,)

and

doubletheG"*ratherthan the 3^.

Ofthe threefollowing,fig.98ispreferabletofig.97,and fig.97 tofig.96.

Fig. 96. Pig.J7. Fig- 98.

-TT

Fig. 97.

~r-T--^

-©-

-^

m

~r-r

XX

nzn

6 6 6

Infig. 102,severalchords of the Sixth areintroduced; the 8"to the bassisomittedfrom allof them,and the6"" isgenerallydoubledratherthanthe3'*.

J

, I

rJ

Fig 99.

3ii:

CT^

jz^a^

-^

IZL

-^1^

3Zf

^W

^fA

_T^T^

-^

-^

m

-Or

zx

_^

"T

HE

t i

Chap. XI.]

INVERSIONS OF

THE

TRIAD.

25

109.

When

the

5*

from

the root of a triadis thehass,the secondinversion is

saidtobeused. Fig.

100

is

an

example of thesecondinversion of thechordofDo.

Fig.100.

m

jCSI

Fig. 101.

^e^

"TT-110.

Were

the bass of fig.

100

presented without

figuring, the chordofSol

woidd

be dueto it.

On

com-paring fig.

100

withthe triadofSol{fg. loi),adifference

of two noteswill befound.

In

the latter thereare Re,

aZ^,

and

Si,a3"* tothebass; in the former,Mi, a6"",

and

Do

a4"'_{to thebass.}

111. This difference is expressed

under

fig. 100;

4

implyiagthat instead ofthe 5*^"

_and

3"^,_the

&^

_and

4«'

toUiebass aretobe written. *

112.

Thus

when

we

see %

under

a bass note,

we know

that thebaas is not the

root, but the 5"* to theroot.

Fig.102. 113.

Of

the chordof the Sixth

and

Fourth, the bassis itself the

5**

_from

the root;

and

the 4"*

and

&^

from

theformer are the S"*

and

3"*to the former.

Seefig.102,whereSol, thehats, isthe S*fromthe root

Do

(indicatedby

adot). While Do,the 4'\and Mi,the6'" _{from the hass,arethe 8*and} 3"" fromtheroot

^

331

The rules repeated from pars. 31 and 33

may

therefore be applied to the second

in-versionof thetriadthus:—

114.

In

writingthechord of the Sixth

and

Fourth, omit the

8™

to the bass rather than any other note,

and

doublethe

4*

ratherthan the 6*''.

Ofthe three following chords,fig. 105ispreferabletofig. 104, andfig. 104to fig. 103.

Fig. 103. Fig. 104.

X3I

Fig. 105.

"n--et-

-^

m

TT- -e>-<r^>

zm

115.

The

omission ofthe

8™

to the bass iu the chord of the Sixth

and

Fourthis recommended, not, asin the case of thechordof the Sixth, enjoined.

Fig.106.

116. _I is oftenfollowed on the

same

bass

by

|.

When

two

sets of figures are placed

under

thesamebassnote, half the time

of thatnote

would

be giventoonechord, halftotheother.

More-over,it isgenerallyunderstoodthat the 5*''istofollowthe6*'',

_and

the3'''' _tofollowthe 4"^, in the

same

parts.

In

thisprogression,

too, the

8™

to the bass, beingthe only note

common

to the

two

chords, is generally added. {Seefig-.106.)

G. M. H.

J=^

-e>-J

ffi

X2

CL

26

INVERSIONS

OP

THE

TRIAD.

[Chap.XI.

Infig.107, severalchords of theiSixth and Fourth areintroduced; the 8"to the bass

isomittedfrom moatofthem.

"ig. 107.

A^-U-^^

hh^

-^

^

3Zi:

Or

3

<:±.:^

m

_zx:

-©r

33

xn

_-©r

2=?

"T~r

HE

4 4

117.

In

passing to or

from

inversionsofthetriad,orof

any

other combination, the

"fundamental

progression," i.e.,the progression

which

the root

wovld

take

were itin thebass, isoften

made

in oneof theupperparts.

Seefig. 99,bars 1

—

_2,wherethe

Fa

in the SopranopartfallstoDo,which

Do

again

risestoSol; allthree notesbeingoctaves to theroots. Seealsofig. 107,bars1

—

^2,where

27

CHAPTER

XII.

Suspensions

on

Inversions

of the Triad.

118.

"

By

prolonging anote not

common

to

two

following chords

from

the firstintothe second,

we

producea discord

by

suspension." (^ow. 84.)

A

note

may

be thus prolongedorsuspended not only

when

theroot isthebass,but

when

any

ofthe inversions of achordareused; the suspension itself occasionally appearing

in thebass'.

119. Fig.

108

is the suspension (4 3)

on

a root {Sol), explained in Chap.

X.

Fig.

109

is the

same

suspension on, or ratherof, thefirst inversion of Sol; the suspended note

and

that

by which

itisresolved appearingin the bass. Fig.

110

contains the

same

suspension

on

the secondinversionof the

same

chord.

Fig. 108.

rTn—

5

J.

Fig. 109. <•>

-^

J.

Fig.110. <'>

1^=^

-r-> I < >

=ni

—

r

^

-^>-^

«P.

_Q

-&-

-&-

(~i

-©r

-^-7 6

4

—

120. Inverted suspensions are subject to the

same

rules as suspensions in a

direct

form

; the dissonantintervals they produce being equallyliableto

prepara-tion, percussion,

and

resolution. (,Par. 82.)

Observe, thatinfig.109 thereisbutonechordtotwo bassnotes,eachofwhichisfigured, sincethe noteswhicharethe5""_{and2°^ to}

_Do

arelikewisethe6""_andS""to Si.

Fig. Ill contains examples of the suspensions explained above. Thesuspensionon the second inversion of thetriad(fig.110) isnot

much

used.

28

SUSPENSIONS

ON

INVERSIONS

OP

THE

TRIAD.

[Chat.

XH.

121. Fig.112isthe suspension (98)

on

a root {Sol), explainedalso inChap.

X.

Fig. 113 is the

same

suspension

on

thefirst

iMWmore

(of/So?); fig. 114,

on

the

secondinversion. Fig.115isthe

same

suspension of the root {Sol),the suspension

appearinginthebass.

Fig.112.

E

_^

J

Ei

^

^^

"TCT" <r> t > 9 8 Fig. 113.

3

<=* <_> -€3-7 6 ii-i^Sr. 114.

CHAP.Xn.]

SUSPENSIONS

ON

INVERSIONS

OF

THE

TRIAD.

29

134. Fig.

117

isthe double suspension _{(2 §)}

ou

a root (Sol), explainedalso iii Ghap,

X.

Allitsinversions are

shown

in figs. 118, 119,

and

120.

Pig.117.

'60

CHAPTER

Xm.

Fundamental

Discord

of the Seventh.

125.

In

the

harmonic

chord of

Do

(Jig.i), immediately above the second

5*

(Sol), isfoundtheminor

7*

(Si\,).

136.

The

seventh is a dissonant interval. (.Par.ii.)

"A

comhinationin

which

is contained a dissonant interval is called a discord." (Par.83.)

A

discord

com-posed onlyofsounds foundin the

harmonic

chordiscalledaJundamental discord

;

that underconsiderationis calledthe discord oftheSeventh.

Fig.122.

^

137.

In

fig. 133 are

combined

,Siib

and

Mi^.

The

former of these notes

indicates a scale ofatleast oneflat; the latterproves ascale of not

more

than one flat; i.e.,the scale ofFa.

138.

The

root of theharmonic chord (of

which

thefundamental discord ofthe Seventhisbutan extract) istherefore n^t thetonicof the scaleto

which

the notes

composing it belong.

A

major

common

chord, iudeed,

may

be

formed

on

the

domiaant

or

on

the subdomiuantofa majorscale,,as

weU

as

on

the tonicj butthe

minorseventhcan onlybe

combiaed

with the

common

chord

on

one of these notes

—

^the dominant.

139.

In

treatingeachnote of the natural scale (or

any

scaleoflikeconstruction)

asthe bass ofadiscordofthe Seventh composedonly of such sounds as are

found

in

the scaleitself,

we

shall produce but one chordexactly likefig. 133, i.e.,

combining

a major

S^

with a minor 7*^. _Thisone chordwillbe formed

on

thedominant.

i^.123 Perfect Chords. 3 4

:S:

Imperfect. 7

#

Major3'* MinorS"" Minor3"^ MajorS'* Major3** Minor3"i

„ 7"^ _„ 7"^ _„ 7«^ _„ 7"" Minor71^ _„ 7»^

Minor3""

„ 7tt

130. In fig. 133are exhibited

no

less

thau/oMr

different kinds of discord:

—

On

the 1°'

_and

4"' _{a perfectmajoi shord with a major} 7"" 2"^3"^

_and

6'"

_„

_minor

_{„ „}

_{minor 7*}

7"' _{an iwperfect „ „}

_„

_„

_7*

»

Chap.XIII.]

_FUNDAMENTAL

_{DISCORD OP}

_THE

_SEVENTH.

₃₁

131. This last combinatioii governs, or decides th6 scale;

which none

of the

others are competent to do. Since offig. 123

—

32

iTTNDAMENTAL DISCORD OF

THE

SEVENTH.

[Chap.Xllii

136.

The

epithet "

fundamental"

is not confined to discords of the dominant

Seventh, butis applied alsotothose

quasi-harmomc

chords

which

consist of a bass note with its 3"*

5*

and

7^, even

though

the 3"* _{be minor, the}

_7*

_{major, or the}

5*

imperfect.

Thediscords infig. 123areall"fundamental."

137.

A

bass note bearing a

7*

in addition to a

common

chord, is Jiillff

8 . g

figured

l-

But

it has

been

shown

that the figures s are seldom used save to

3 .

*

contradict others.

A

single figure 7, therefore, is in general suflScent indication

ofthe discord ofthe Seventh

138. Inwriting

common

chords, the studenthas

been

recommended

(where the

progressions admit) to double

and

omitcertainnotes ratherthan others. (Chap. /F.)

The same

rules,

drawn

from Nature, aregenerally applicable to the discord of the

Seventh; save that inthelatter the3"*tothe root isnot ofsuchvital importance

as in the former; since if the 3"*_tothe rootbe omitted

from

the

common

chord, it then contains

no

imperfect consonance, whereas if the 3"" _{be omitted}

_from

the discord oftheSeventh, therestillremains

an

imperfect consonancebetween the

5*

and

7^

sounds, whatever be their relative positions.

^

"TT-Fig.128. Fig.129.

-€^

-Gf-

^

TT"

_33:

7ig.130. r-»

33

CHAPTER

XIV.

Resolution

of

the

Fundamental

Discord

of

the

Seventh.

"

A

dissonantintervalmust be resolved; the parts between which it is found must mate

certain definiteprogressionsinrelationoneto another,inorder that the ear

may

berelieved

fromthefeelingofsuspense towhichituniformlygivesrise. {Par.74.)

140.

The

fandamentaldiscord of the Seventhinits complete form includesat least two dissonantintervals

—

the seventh or its

inversion the second (sometimesboth),

and

the wwperfectfifth or

itsinversion the/^^wperfectfourth (seldomboth.) {Seefig. 131.)

,Fig.131.

-^-

-Qcy-ei

:S-"Of twoparts separatedbyaseventh,the upper shouldfaU one degree, while the lower

may

keepitsplace,riseafourth,orfallafifth." {Par.76.)

"Of two parts separatedbya second,the lower should fall one degree, while the upper

may

keepitsplace,riseafourth,orfallafifth." {Par.77.)

141.

Of

two

parts separated

by

an imperfectfifth,theupper shouldfall

and

the lowerrise,each onedegree. {Fig. 132.)

While

of

two

partsseparated

by

a pluperfect

fourth, the lowershouldya^/

and

the upperrise, each onedegree. {Fig. 133.) Fig. 132.

—

^

Fig.133.

-e>-

S

-^>- "i-T ~r~r

-e>-143.

When

a bassnote bearing a discord ofthe Seventh rises afourth ox falls

a.fifth, allthe dissonantintervals contained in it can beproperly resolved

on

the following chord. Fig. 134.

-^

3Ze:

-e^

-f^-

xx

Fig.