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14 5 6
HARMONY
ON TB8
Inductive Method.
BY HUGH A» CLARKE,
Professor of Music, University of Pennsylvania.
•--■;' ■'%'
PHUiADSU'HIA :
L E I-: c*(; W A T . Iv E R,
No. 1113 Chestnut Street.
Coprrighl, 1880. bj Lu * WilKlm.
It
:
^•r.^'ffv--- jc^---
(A
^^
«A
^
t
INTRODUCTION.
This book makes no claim to be a new theory of
Imrmviny; but merely a new eystcm of teaeliiii-j;
harmony, by what in universally recognized as the
best method of teaching, viz., the inductive.
The theory of harmony is the province of the
acoustician, not of the musician. It is often asserted
that music has gained largely by the labors of the
acousticians; but this is not so evident, when we
remember that all the best music was written before
the science of acoustics was born. The instinct of
genius discovered, afcer many trials and mistakes,
what combinations and successions of sound were
agreeable and expressive, without asking or caring
why. And the science of sound has made but little
advance in explaining this "why;" and has not
added one chord or progression that was not known
to Bach.
Science can analyze sounds, but not music. It
can say to what the various qualities of sound are
to be attributed; but can give no explanation of
their effect on the emotions. Indeed, the best
authorities on acoustics, viz., Ilelmholtz, Pole, Parry,
are agreed that it is useless for tlie musician to
theorize as to the origin of chords. It is enough
for him to know what combinations and progressions
if
iMHIKi'-'
r-^
4 INTIlOlit CTION.
praclit't' iiiul t'X]K .it'iiCf li:ivi' proved fr'xxl. >'o
lictlcr proof is icciuirctl of tlin nscU'ssiicss of this
tlicorizing iibout Iho orifriii of cliords, tluiu tlic
divprsily of views witli n'giird to tlio origin of the
minor clionl ; o\ving,to the fiiot,th!it its thinl rannot
bo an ovi'rt(«io of its fiindamental.
Tho object of the writer on harmony and compo-
Hition ought to be, to reduce, to some Hystem, the
mass of facts (for want of a better name) of v.liioii
our modern miisie is tlie outgrowtii. These facts
are:
Ist. A te?npered scale.
2(1 (and resulting from tlie llrst). A number of
keys related in many ways.
3d. The possilile combinations of sounds, called
chords.
4th. The seeming rules tliat govern the successions
of these combined sounds. Rules, be it remembered,
that are not the i-xpression of some natural fact ;
but are merely the residt of a consensus of tlie best
taste in the art.
Tliese foui' facts make up tlie substance of har-
mon;/, and form tho groundwork of composition,
which deals chiefly with melody and form.
Many departures will be found in this work from
the usual methods of teaciiing, notably the following :
..
1st. With regard to the formation of the minor
scale.
}.'00(|. >'o
■iiH'ss of tliiw
lIs, tlinii tilt'
origin of tlio
( tliir<l raniiot
: mikI fonipo-
i" H\'Kt0in, tllf
me) of v.iiicii
Th.'sc facts
A iminl)or of
ounds, called
10 successions
renicmbcred,
natural fact ;
IS of the best
tance of har-
eomposition,
rm.
lis work from
the followin;^ :
of the minor
II
INTHODI I'TloV. n
2d. Till' 11 ferrinn of nil (lis:<()iiiint chords to two
roots.
3d. The disoardiiij,' of Mh' time-honored ligured
bass.
4tli. The formuhitinjj of simple rules for modula-
tion.
My reason for the ilrst departure is, that the rela-
tionship and signature of the minor scale is thereby
n.xed at once in the nienuuy of the pupil.
For the second.— That it reduces the confiisiii-r
multiplicity of rules for the use of elioids with the
seventh, to four that have no exceptions.
l"'or the third.— That it is a hindrance, rather than
a helj), to the pupil. The author has had numbers
of i)upil3 who could write or play a fij,nired bass ;
but Avho were quite in the dark as to the reasons
why they used such successions of chords. Many
of these pupils Irul spent one or two years studying
with good masters. And have themselves acknowl-
edged that they have learned more in a month, on
the itlan pursued in this work, than in all their
previous studies. It has always been to the author
a mystery, why figured basses were used for teaching
harmony. They were, originally, a sort of musical
shorthand; and, in these days of cheap music, are
only a, survival of— not by any means— tlu; fittest.
The iiiithor is often met with the argument that ''all
the great nuif.ieiau. learned thi.^ way."' Well, the
Ml
INTKOKIlTlON.
pity is, they had not a better and ciisicr way. It it*
no nrgunu'nt, that liocausc a man is a great poet,
therefore the system pursued in teaching him hiH
IctterH waH the best i)OHBible.
With regard to tin- fourth de).arture from usual
prnetice.—Tlie author feels a pardonable pride in
having reduced the art of modulation to four simple,
easily' understood and comprehensive rules. Hitherto
the plan followed in teaching modulation, has heen
to give th>> pu|)il various examples, wliich were to
be transposed to all (he keys, until they were II xed
— parrot fashion — in his memory. When ho wisiied
to make a modulation, he m\ist remember one of his
" patterns." Hy mastering the rules her« given, the
pupil can make his own modulations in endless
variet}-, iind make them understandingly.
It is well to bear in mind that music is an art,
not a science ; although the 8tud.v of harmony is
often wrongly called the science of music. The
rules of musical construction are not the result of
scientilic investigation; l)ut are deductions from
the practice of those distinguished by their artistic
eminence. Many musicians think these rules are
the expressions of some natural law. Many, not
musicians, think they are tlie arbitrary and often
unreasonable dicta of musicians. IJnt botii are
wrong. Good taste is the only arbiter in matters of
art. And since the standards of tnste vary with
every period of the world's history, it is not possible
p way. It is
great poet,
ling liitn his
! from usual
ble |iri^lt! in
four Himplu,
OS. Hitherto
on, lias i)cen
liieii were to
ly wore fixed
3n he wished
er one of his
r« given, the
i in endlcHS
nc i8 nn art,
harmony is
music. The
till' result of
ictions from
their artistic
se rules are
Many, not
y and often
ut ixitii are
in matters of
to vary witli
not possible
}
INTBOIU'CTION. T
to give to any of itH decisions the nt^imp of perma-
nency, and say : ThlH is ft rule that can never be
broken.
In conclusion, the author would express h.s tlmnks
to his numerous pupils, both present and p.st, for
the warm interest they huve iMken in the progress
of this work, and for their kind wislu's and iu<iuirie»
from all parts of the country.
IT. A. CT.AIIKK,
Profriior of Mutic al the VnivertUy of Pe . tylvania.
Philadelphia, Novemher 15, 1880.
I
W
PRELIMINARY DEFINITIONS.
1 _A degree means from one letter to the next, whether a
whole or half tone.
2.— Chords and intervals are always counted up from tho
lowest Ltter. In counting the number of letters in an inter-
val, both letters are included, thus : C— D, is a second, two
letters being included ; C— F, is a fourth, four letters being
included, and so on.
3.— A chromatic change retains the letter, but alters the
pitch, thus : C— C#, is chromatic. A diatonic change changes
both the letter m1 the pitch, thus : C— D, or E-F, are diatonic,
although on 's a whole tone, the other a half tone. An enhar-
monic change retains the pitch, but changes the letter, thus:
C#— Dl», F— E#, G— FX, «tc.
4. The word base is used to indicate the lowest note of a
chord, without regard to its pitch. The word bass (trota the
Italian ba»io\ uieans a low or deep sound.
5.— A diatonic scale is one that includes all the seven letters,
without omission or repetition. (There are various kinds of
diatonic scales, viz. : The Greek, the Gregorian and the modern.
They differ in the arrangement of the tones and semitones.
The modern resemble two of the ancient scales, in their arrange-
ment of tones and semitones ; but differ, in being tempered
(i. e., a little out of tune). For explanation of tempered scales
see Helmholtz, or Stainer's, or Groves' Dictionary).
I
(8)
\
ONS.
? next, whether a
iteJ up from tho
Iters in an inter-
is a second, two
our letters being
r, but alters the
10 change changes
1— F, are diatonic,
tone. An enhar-
the letter, thus :
I lowest note of a
rJ bats (tram, the
the seven letters,
3 various kinds of
a and the modern.
33 and semitones.
!, in their arrange-
1 being tempered
)f tempered scales
)nary).
>
CHAPTER I.
1. An Inters-al is the difTerenee in pitch between
two sounds.
2. The name of an interval depends upon the
number of letters it includes ; the kind of interval
upon the number of semitones it includes.
3. There are five HHr7s of intervals, viz.: Major,
minor, augmented, diminislied and perfect.
The following table contains all the kinds of seconds, thirds
and fourths.
Thirdt. Fourlhi.
Seconds.
^^^^^^^E^l^-I^^^
Semitones \ 2
MIn. Moj.
3
Aujt.
a 3 4 5 4 6 6
Dim. MIn. Mnj. Aug. Dim. Per. Aug.
4. By inverting these intervals we get all the
kinds of sevenths, sixtlis and fiftlis.
Sevenlhi.
-^ — -o — o-
Sixths.
-fil — s-
:=g^liE|B^^^^^^^
Fifth:
-O — r« — r»-
Semil<>B<-i 11 10 U
MaJ. MIn. Dim.
10 9 8 7
Aug. Maj. MIn. Dim.
8 7
Aug. Per. Dim.
f. On examination it will be found that the inver-
sion of a second produces a seventh; of a third, a
sixth; of a fourth, a fifth. Also, tiiat an interval
and its inversion together make an octave— and, as
(9)
n
!
ii.^^
10
ci.abke's harmony.
the octave contains twelve semitones, an inttTval
and its inversion must make twelve semitones. Thus
the major second contains two semitones, conse-
quently its inversion must contain ten, etc. We
also find tliat the inversion of a major interval pro-
duces a minor, and the reverse ; of an augmented, a
diminished ; of a perfect, a perfect. Removing one
of the sounds of an interval an octave does not
chiingo its name, except in the cases to be pointed
out hereafter, thus :
Third.
Third.
I
W^^
i
Both these intervals are thirds, or the second example is a
third plus an octave.
6. Intervals are also divided into consonant and
dissonant. The consonant intervals are : The major
and minor thirds, and their inversions, the minor
and major sixths. The perfect fourth and its inver-
sion, the perfect fifth ; and the octave. A conso-
nant interval is One that gives repose to the ear ; a
dissonant interval does not ; but it must be resolved,
a term that will be explained in its proper place.
Before going any further the student must become thor-
oughly familiar with all these intervals. This is best done
by writing them out, •ommencing with every ti, # *nd t> in
the scale.
*l. A tetrachord is a series of four sounds, ar-
ranged as follows : From first to second, and second
I
an inttTval
tones. Thus
ones, conse-
n, etc. We
interval pro-
lUgmonted, a
emovlng one
,ve does not
o be pointed
d example ia a
msonnnt and
: The major
;, the minor
nd its inver-
!. A conso-
;o the ear ; a
be resolved,
)er place.
become thor-
B is best done
fl, # and \> in
sounds, ar-
, and second
CliARlCE'S HARMONY.
11
to third, are major seconds ; from third to fourth, a
minor second, thus : G, A, Bi^C.
8. A major scale consists of two ti-trachords sepa-
rated by a major second, tiius •.
Tetrachord. Tetrachord.
^ I
==.l^^=:±E~?r::
:A:
-«-
m
Separating whole tone.
9. Every tetrachord' may be found in two scales,
viz. : The scales of its first and of its last note.
Thus C, 1), E^F belongs to the scales of C and F;
F, G, A, Bj^ to the scales of F ami B.^.
10. Scales having tetrachords in common are
called related scales. Thus the scales of F and G
are related to C, because they eacli h ive a tetracliord
that also belongs to C ; therefore every major scale
has two major relations, because C is the model for
all major scales.
Scale of G.
{
Scale of D.
Scale of C.
i|^
i
Scale of Bh.
Write tetrachords, commencing with every J. t and b, and
mark the scales to which they belong. No letter must be
repeated or omUted in any scale.
I
Kfr
CHAPTER II.
1. A common (^horrt (or perfect chord) consists
of three sounds. The lowest is the root; tlie re-
maining sounds are the third and fifth over that
root. The tiiird may he major or minor ; the fifth
muKt be perfect. A chord with a major third is
called a major chord ; with a minor third, a minor
chord. Since there are only seven letters used in
music, it follows that seven groups will make all the
common chords tliat are possible, thus :
Fifths. — E, F, G, A, H, C, T).
Thirds.— C, D, E, F, 0, A. B.
Roots. — A, ?>, C, D, E, F, G.
These groups may be modified by ift, 1», elc. For example,
the first group, A, C, E, may be
etc. ; but the lettert never change.
2. Six common chords may lie written in every
scale. Three will be major; three, minor. The
seventh note of the scale, called the Icaxliini note,
cannot be used as the root of a chord, because the
fifth over it is diminished.
(12)
W !' " " I' B
hord) consists
root; the re-
Ifth over that
liiior ; the fifth
major third i-;
third, a minor
letters used in
ill make all the
s :
C, D.
A. B.
F, G.
ic. For example,
^
ritten in every
I, minor. The
? leadincf note,
rd, because the
Cr-AUKK'S IIAIIMONY.
13
Example :
1
i=l-E
3 15 8 Dim, fifth.
H
Tonh.
Subdom. Dom. I.cacling
note.
The major chords are on the first, fourth and fifth notes of
the scale. Those notes are called the tonic, siibdo.ni.iant and
dominnnt, and the chorda written on them are called by the
same names.
The minor chords are on the second, third and Mxih notes
of the scale. These notes are called the super! onic, n.ediant
and submcdiant, and the chords written on them are called
by the same names.
3. It is easier to -write Buccessioirs of chorda in
four parts (or for four voices) ; but as tlie chord
consists of only tlirc., sounds, it is necessary to
double one of tlie members of the chord to make a
fourtli part.
We will commence by doubling the root, thus:
1
i
C is the root; it is at the base and doubled by the highest
voice or part.
4. A chord with its root at the base and doubled
in one of the upper parts may be written in t'.iree
positions, called : Octave, tierce and quint.
I
mm
sJ m
I
14
ni.AUKR'S HARMONY.
Octave {He). Tierce (3). Quin/ (5t).
::ff±
m
-«-
zs^
SJS^
i
8e.
ZJSr.
5t.
is:
m
Cloit Harmony.
Diiperied Uarmomj.
In all its posilions apd doubling this chord is etill tlie
chord C, E, O.
This doubling might be carried to any extent; but it can-
not niter the name of the chord.
5. In writing a succession of common chords
with their roots at the base, the following rule must
be observed : Never write two chords in succession
in the same position. If it be desired to malie the
succession as smooth as possible, retain all notes
common to two or more chords in the same part
(voice), thus:
St. se.
The following examples are to be written according to these
-nles, Tiz. :
Ist. The base note is the root.
2d. The root only is to be doubled.
3d. Two i-hordg in the same position must never be written
in succession.
4th. Make the chords as oonneoted as possible.
■'
m I'OiinMiirnrairmi -
At.
lil
m
Harmony.
■d is gtill the
t; but it can-
mon chords
ig rule must
11 succession
to make the
in all notes
e same pail
3. 5t. 8e.
1
ording to these
iver be written
CI.ARKE'rt HARMONY.
15
I
fi. The knowledge gained must now be applied to
the harmonizing of a melody. The following re-
marks will point out the way to accomplish this :
(1 ) Every note in the melody may be the root, tiiird
or fiftli, of some one of the chords in the scale. If it
be treated as a root, tlic chord will be in the octave
position; if as a third, the chord will be in the
tierce position ; if as a fifth, the chord will be in
the quint position.
Example:
6 8 8
^^^^^
-9'
N. B. — Two' chords may be written in the 8 position in suc-
cession when the extreme parts move opposite ways.
In this example, C is treated as the root of the chord of C,
consequently it is in the octave position ; D as the fifth in the
chord of G, consequently it is in the quint position ; C as the
I
utitr"
10
(!IiARKE'8 HARMONY.
third in tlio oliortl of A, conaetjuently it ia in the lierc.^ pubi-
lion, etc.
(2) Begin and end with tlic tonie ciiord.
(3) After deciding on the chord any givon note is
to liave, write first of all the root in the bass.
Ilarmonizo llio folla^^ing plirase of melody in as many ways
as possible :
-e) — g-
^
-1 — ®-
i
Three chords aro possible for the first note, two for the
B«c-ind, three for the fourth.
1 \e following melodies must be harmonized according to
fhcao rules ; they should oil bo transposed to all the keys and
harmonized over and over.
Note. — The bass must never proceed by long skips, it is
best not to exceed u sixtli.
i
^SM5i-|- V ^« T f g, l /a » f. "°^
m
E ^;^n^^^m ^^
The bass should never ascend or descend two fourths or
fifths in succession.
the tieroj pubi-
)ld.
givi'U iioto is
le bass.
in ts many ways
m
jlo, two for the
ed according to
all tho keys and
long skips, it is
two fourths or
^mt
claeke'h harmony.
IT
It cannot bo too often repeated that common chnrdu onli/, with
tho rootM at the base and not doubled, are to be used ill those
exerciscH
Examine each chord as you write it, to see if it conforms
to these rules This is the only way to suooooc a the absence
of a leiichcr.
1 Tho progression of common cliords is perfectly
free, tliat is, any two common cliords may bo written
in Hiicecssion, but some successions tlo not sound us
well as others. They arc not to be understood as
forbidden, because the effect of a progression dc-
peiids altogether on the design of the composer and
tho context
The following rules might be given for such successions :
Two /nnjor chords whose roots are a whole tone apart do
not sound well, except in the following positions : At No. 1 —
two and three are sometimes used; four is hardly tolerable;
five is intolerable.
•i 3 4 6
Two minor chords whose roots are a whole or half tone
apart are bad in any position, except in the passage ot No. 2.
M^:^^^^
J:: I,
18
CLARKR H HARMONY.
A minor chord followed by a mnjor whuno root in u minor
third higher, is bad unless in the following positions:
(1^
::*:
P
m
jBt
m
Oood.
Better.
A mi^or chord, followed by a minor or the revorHc, wlioso
roots are a half tone apart, except in the following pogitions :
:t
i^^fEiE^^
(^
m
^
^
zgiz
m
Nos. 1 and 2 are best.
8. It is not always necessary to use the root of a
/jhonl for a base note. Tlie third or fifth may be so
nsed. When the third is used for a base note the ,
chord is said to l)e in Its Jirst inversion i when tlie
fifth is used for a base note the chord is said to l)e
in its second inversion. It is important to remem-
ber that tlie name of the chord is unchanged, iio
matter what the inversion of the letters composing
it m&y be, thus :
s root in II minor
isiliona:
fa
1
reverHc, wlioso
wing positiuuB :
-Ol-
m
the root of a
fth may be bo
base note the ,
oiii when tlie
is said to be
nt to rcmem-
nchanged, iio
rs composing
CI.ARKR'et HAKMONV.
19
i
EE^:
-•-
i
In thift oiample the Ittliri »re C, E, ; it la therefore the
chord of (.',
To And Iho mot of a chord it is only neoensary to arrange
the lelturs composing it, ao aa to read: 1, A, 6. The loweat
will be the root.
Example :
1
i
3
5 «
EE^lEllEl^iEi^:
1 a 6
No. 1 is the chord of A, Ist inversion, the letters read A, C, E,
41 2 " " Q, 2d " with root doubled, 0, D, D,
•■ 8 " •' C, Ist " with fifth doubled, C, E, G,
<i 4 1. n F. 2d " " " " F. A, C,
••• 6 " " D, Ist " * I>i fi A,
>f C " " K, Ist " with fifth doubled, E, 0, B.
The pupil should write all the common chords in all the
keys; in nil their positions and inversions. Remember that
position applies to the hightst note of a chord with its root at
the base ; and invenion applies t a chord with any member
but the root at the base, and has no regard to whiit may be at
the lop of the chord.
9, Hitherto we have doubled the root of the chord
only ; but it in not the only member of the chord
that can be doubled, but is the 6e.s< when the root
is at the b.ase. But when the first inversion of the
chord is used, the fifth is just as good a monibei to
double as the root. (For the present the third must
not be doubled).
I
II >
J
20
clahkk'h iiaumuny.
In llie fnllnwinn OKtimplc, tlio first inversion of iomo of tli«
ehonU w.ll lio foiinil— Honiu with root, nome with flftli doubled.
N. D.— The doubliiiK of a membor of a chonl nt uniaon in
exprrsHcd )iy*writing llio nolo ns above. It is hm (hough two
of the gingers in a qiinrtetto hud the game note to sing.
1, Chord of (', Ho position, lloot doubled. Tonlo chord.
" 0, IbI invcTHion, " Doiii.
C, Ho position, " Tonic "
" (", iHlinvcrtdon, " " "
" F, 8e position, " Subdoin. "
" D, 1st invoTHion, •' Sup. tonlo "
" G, 8o position, " Dom. "
<< (;_ Ho " " Tonic "
" F, 1st inversion, " Subdoin. "
" 0, 1st " " Dom. "
" r, 3c position, " Tonic "
" 0, 1st invcrHion, Fifth doubled, '• "
'< 1), Ist " Root doubled Sup. Icmic "
" l», 3« position, " " "
C, 6t " " Dom. "
•< C, 3e " " Tonic "
In writing the following exercises, it is optional to molto the
notes cither roots or thirds of chords. Try both and let (he
ear decide. The f .Unvini; example will point out llio way :
No.
1.
(1
2.
II
n,
11
4,
11
r.,
(1
c>.
11
">,
11
8.
11
0.
*i
10,
11
11,
11
12,
11
lil,
11
14,
11
15,
11
16,
1
it
■i
--o —
i
;i of iomo of tli«
til flflli (loubUd.
'tot ^< \ — ^
I IS 14 1A in
oril at uniHon in
U an tliough two
e lo Hing.
Bil, Tonic chord.
Doni. "
Tonic "
Siibdoni. "
Sup. tonic "
Uom.
Tonic "
Subdoin. "
Dom. "
Tonic
\ed, ••
led Sup. Ionic "
Uoni. "
Tonlo "
ional to malco the
botli iind let the
t out tlio way :
ci.aukk'h iiahmonv.
81
Thin i^ I'videnlly in ilie key "f «' ; it """"t Hicreloro liogin nnd
•nd witli ilie loniu cliord
Tlio neti.nd notn miiy 1>« root of the chord of K. or the third
of the cliord of V. (Try liolh).
No. ;i cniiiiot l.o a root, heing llio leading nolo; II must
therefore ho iv third in chord of tl.
No 4 may be root of C, or third of .V (Again try both)
No. 5 root of A. or thirl of F. (Again try both).
No. root of F, or third of U. (Again try both).
No. 7 root of 0, or iliiid of E (Sou dinngreoable progren.
kloni, piige 17).
10. The following rtiUi muHt bi- Htrictl.v observdJ :
Never let two \mrU or voices proceed in octavt-s
or imiis with each other. (Any two parts mny bo
an octavo or llftii iipart ; but not twice in succession;.
P^
^
^1^^
P=^--'3F^3=
i^^^^^
In the first bar, the bans and tenor are a fifth apart in the
fl-st chord, f}' and also in the second, ^ \ making two fifths In
succession between the same two yoices. Abo the bass and
alto are on octavo apart in both chords.
Consecutive fifths and octayes, lilto this example, only occur
when two chords are written in succession in the same posi-
tion ; hence the rule forbidding it.
In the second bar, fifths occur twice in succession between
the alto and soprano.
In the third bar. fifths occur twice in succession between the
tenor and alto.
(Consecutive or parallel fifths will be treated farther on).
I
Clarke's harmony.
15
i=^
^
t=f::rt
f-
t=r«=t
-«--p
£s
i
S
ra #, ^ -
x^
^
STK
= :g=»p:>-c p
tS>5^
i
w^^
^m
=^^
B
3^^i^ ^y
^
:^
i.^
r<S>-
1
igE
p
iSM
ep
f=
Transpose these exercises into all the keys.
11. The next step is to use this first inversion
when harmonizing a melody. The following re-
marks will make it easy :
Every note in the melody may be the root, third
or fifth of some chord ; but if it be treated as the
third of a chord, the first inversion cannot be used,
because it is forbidden as yet to double the third.
If the note in the melody be treated as a root or a
fifth, either the root or the third may be used for a
base note.
1 23 4& 87 8
±
W:
No9. 1 and 8 must have the tonic chord, which will be in the
octave position.
No. 2 may be treated as root in the chord ot' D, and mw^-
have the root or third at the base ; or it may be treated ns the
^
m
:^^
m
iipSi
first inversion
B following re-
! the root, third
I treated as the
jannot be used,
ouble the third,
d as a root or a
ly be used for a
hich will be in the
)rd ot" D, and ma.*--
y be treated os the
clabkk's harmony. 23
fifth in the chord of O, and may have the root or third at the
base.
No. 3 may bo root of E, third of C, or fifth of A ; if treated
as third of C, the root must be at the base ; with the other
two chords, either root or third may be at the base.
No. 4 may be root of F, or third of D.
No. 5 may bo root of D, or fifth of Q.
No. same as No. 3.
No. 7 sara ' as Nos. 2 and 6.
(Try all these varieties itiid observe which sounds best j if
several sound equally well, observe the different effects they
give).
The pupil should now be able to harmonize the following
examples.
It will be well to bear in mind the following remark :
It generally gives a better effect to make the extreme parts,
bass and soprano, move in opposite directions ; ». «., when the
bass descends, let the soprano ascend, and t'ic« vena. This is
not a rule, but only a remark.
^
^^
-^^
L^^lr r r r 1 ^
Note. These examples, even if well harmonized, sound un-
satisfactory ; owing to the wan* of the perfect cadence, treated
in the following chapter.
I
!T
fc^
IT
24
CliABKK'S HARMONY.
12. We proceed now to the use of the secciid in-
version of the common cl ord, i. p., with the lifth for
a base note. A chord with its fifth at the l«vse, is
nhcaijs (witli two exceptions whicli we will ignore
for the present) a tonic chord. Therefore, in tlie
key of C, with ths chords so far at our disposal, the
only chord that can be used in its second inversion,
is the chord C, E, G. The following rules must be
observed when it is thus used :
Ist. It (the second inversion of the tonic) must
be preceded by some chord belonging to the scale.
(This seems superfluous at present, Init its impor-
tance will soon be seen.)
2d. It must be followed by its dominant (excep-
tions will be pointed out in time.
-&■
^^
in
In this example at X ^'^ second inyersions of the tonio
chord, (ho first example is preceded by th^ gubdominant
chord, the second by the supertonic. (These are the most
agreeable to use before this second inyersion, but any other
can be used ; as was remarked before, it depends on the de-
sign of tlie composer and the context.)
The close of this example is wbat is termed a full or perfect
cadence It is the way the great majority of compositions
end, viz.: with second inversion of tonic, followed by domi-
nant with root at the bass, followed by tonio in octave position.
,
11
the aecc iid in-
;h the fifth for
it the base, is
ve will ignore
jrefore, in the
r disposal, the
ond inversion,
rules must be
le tonic) must
g to the scale.
l)ut its impor-
ninant (excep-
X
f^
m
ions of the tonic
th^ Bubdominant
ese are the most
on, but any other
epends on the de-
1 a full or perfect
r of compositions
ollowed by domi-
Q octave position.
,
CLARKE'S HARMONY.
25
We found that the best note to double, when the root was at
the base, is the root; when the third is at the base, either
root or fifth ; but wlien the fifth is at the base, the best note
to double is the fifih ; next, the root.
Every change in the position or inversion of a
chord gives a new effect to the chord. The octave
position is grave, massive and full of repose ; the
tierce is graceful and inclined to melancholy, p-.ir-
ticularly when used as a final ; the quint is bright
and eager, always indicating something to como.
With regard to the use of the different members
as base note : A chord with root at the base, is like
a cone in a state of stable equilibrium ; witii its
third in the base, in a state of neutral equilibrium ;
with its fifth in the base, in a state of unstable equi-
librium.
A careful study of the following example will enable tl e
pupil to write the exercises that are appended.
=^
■»^
*
1
•-©-
zst
■-^^
s^
4::
i
*
*
Where these marks if: are, the second inversion of the tonic
chord may be used ; because No. 1 , the F preceding, may be
harmonized by the chord of F, or by the first inversion, chord
of D ; No. 2, the A preceding, by the chord of A, or first in-
version of F ; No. 3, by the same as No. 2. And in each case
the note following may be harmonized by the dominant chord.
After 1 and 3 the root of the dominant is at the base ; No. 2
the third of the dominant at the base. The remaining notes
are to be treated according to the rules already given.
2
r-ji'
d6
Clarke's harmony.
:
The marks X >■> ^^^ ^'^^ exercise indicate the places where
the second inyersion of the tonic may be used.
m
^e
?^
:fc^
-4— L.
-9-
X
X
^^^^^^^W
^^^^iTF
-1 — 1-
«-•-■
:p^
1:::?:=^
1
jgg^P^^JF^lpg^Pllif
13. We now give an example to illustiatc how
this second inversion may be used wlien harmonizing
a melody.
After writing the exercises that follow, tho pupil should
carefully go over again from the beginning, and should trans,
pose all the basses and melodies given into all the major keys
and harmonize them. This is absolutely essential to tbo cou)>
plete mastery of the subject.
I
--»=is:
m
p
gg ff
-»
1
*
3
8
At No. 1 w» have a note belonging to the tonic chord, pre-
ceded by a note that may belong to chord of D or G ; it is fol-
lowed by a note belonging to the dominant chord. No. 2
belongs to the tonic chord, etc. No. 3 belongs to tho tonic, etc.
) the places where
id.
tp::
1^
X
'^m
EfJE^
£EF
illustiatc how
en harmonizing
tho pupil should
and should trans-
all the major keys
lential to tbo com-
m
*
3
Jonic chord, pre-
D or G ; it is fol-
iDt chord. No. 2
[8 to tho tonic, etc.
clabke's harmony.
ST
In short, whenever we find C, E or followed by 0, B or D,
the C, E or O moy have the second inversion of the tonic, and
tho Q, D or D the dominant chord.
The use of this second inversion of tho tonic is tlio only
thing met with so far that is at all difficult, and a, little study
and perseverance will soon overcome it.
I
W
^? l f ff CLn[ I?^'5^^S5
k
T^f^' l ^ricJir^- g^
14. The third of a chord may be doubled under
the following circumstances :
1st. When the parts or voices doubling it are
moving in opposite directions.
2d. When two chords are written in succession in
the tierce position.
3. The doubling that results from slriking full
chords on the piano, organ or orchc-stra.
I!
'JL-'
.
S8
CLARKB'8 iiahmony.
No. 1. The E is doubled by the bass and soprano, the bnsi
ascending, the soprano deBcendiDg; in the second bar the
motion is reversed.
No 2. In the first bar the C is dpublcd by the soprano and
tenor ; in the second bar tlie A is doubled by the same voices ;
but in this cose they proceed in the some direction. This is
the only woy an exception to the rule about writing two
chords in the tierce position in succession can occur. The
third is doubled to avoid tho oonseotftivo fifths and eighths
that would result from doubling the root.
No. 8. The harmony reduced to its simplest form is only
the chord of C, tierce; G, quint; D, tiercj; A, quint. The
doublings in this case are merely for the s ke of fuller effeot,
and the harmony is to be judged as to its correctness by re-
ducing it to its simplest form, viz. :
:g=
E
i
m
m
The same remark applies to Ibo pvrolKl Cflhs and octaves
in this last example.
Two chords in succession in tho octave ^nd quint
position sometimes occur, when the extreme parts
move in opposite directions.
I
goprano, tlie bnsi
) second bar tho
f the Boprano and
' tho same voices ;
lircotion. This is
30ut writing two
, can occur. The
fiftlis and eiglitlis
jlest form is only
i; A, quint. The
ke of fuller effect,
correctness by ro-
l fifths and octaves
ctavciind quint
extreunc parts ,
clabke's harmony.
99
^^^^
$^
i
No. 1 is common in terminations.
No. 2 is an example of consecutive fifths, from the slow
movement of Beetho'cn's "First Symphooy."
The second inversion of the dominant chord may be used
M follows:
i^^^H^^
X
X
SI
^
m^
It must be preceded and followed by the tonic
chord.' It must never occur on the accented part of
the bar. If the tonic before it have the root at the
base, it must after it have the third at the base, and
vice versa.
This example has two notes in tho bar, therefore only one
accent; if there were four notes in the bar, the third would
be an accented note.
A subdominant chord maj' be used in its second
inversion, provided it is preceded and followed bj'
the toaic, with tlie root at the base.
80
CLARKE'S HARMONY
*
^mm^m
*
^
■.T-
1
At H: the Beoond inversion of the subilominant occurs; in
each case it is preceded and fgllowed by the tonio, with its
root at the base.
inant occurs ; in
te tonio, with its
CHAPTER III.
1, The minor scale is formed from the major, by
reananginy the notes, commencing witli tlie sixth.
It is called the relative minor of the major scale,
from which it is formed, and has the same signatnro.
2. The most important chords in the scale are the
tonic, siibdominant and dominant. In the major
scale these are all major chords. It was found
(p^ge 12) that six chords might be written in every
scale, three major and three minor. By rearranging
the scale in this way, the three minor chords will
occupy the position formerly occupied by the three
major chords ; i. e., the first, fourth and fifth notes
of the scale, or tonic, subdominant and dominant.
C maior.
I
m
Sr-^S-
:«=
k
O major.
m
HBMft
s
A minor.
E miner.
^
- ^f « " " '■tl ,
^^a^^
A is the sixth note in C major. The chord, A, C, E, is the
tonic of A minor and the sixth or submediant chord in C.
D, P, A, is the subdominant of A or supertonio of C.
£, G, B, is the dominant of A or mediant of C.
(81)
I
JJ'
J9
OliABKE'rt IIARMONV.
Thin in Jho oldest foi'm of tlie minor ncnlc, nnJ ooncRpondii
to tlio Qrecli llypo-Dorian (or, according to Qlarvanua,
iColinn) ; the major loalu being tlie Lydian (or Ionian, accord-
ing to UlareanuH). This form of tlic minor scale in very Hide
used now, because it does not admit of any liarmony but com-
mon ohordc.
3. Two forms of minor scales are used at present,
called the melodic and the harmonic. In the melodic
the sixth and seventh are raised in ascending. In
the harmonic the seventh only is raised, both ascend-
ing and descending. This is the only form with
which we have to do at present ; hence whenc^ver a
minor scale is mentioned, until further notice, it is
always understood to have the seventh raised.
No. 1 is the melodic scale of A minor.
No. 2 io the harmonio scale of A minor.
4. We have found (page 11) that every major
scale had two major relations. It follows, since the
minor is formed from the major, that the relative
minors of these major scales must also be related
to the given scale, thus :
C major has for major relatives, F and G.
The relative minor of C is A.
The relative minor of F is D.
The relative minor of O is E.
Consequently we have in every scale a group of six
U
, nnd oorreitpoiidH
ig to Qlar«anu8,
or Ionian, acoord-
Huulo in very 111 lie
liarmony but ooui-
ised at present,
In the melodic
aacending. In
id, both ascend-
jnly form with
nee whenever n,
ler notice, It is
raised.
it every major
Hows, isincc tlio
lat tlie relative
also be related
F and G.
a group of six
("I.arkk'h harmony.
m
keys, Ko clowly interwoven tliat llioy cannot be iUh-
nnitfd, and we can paHH from any one to any ollu-r,
without niakinj? a permanent change of key ; or, in
other words, any chord belonging to A minor, F and
I) niinor, (1 and K minor, can be nsed in the key of C.
In all of these minor keys the seventh must bo
raised to make a leading note. Therefore in A minor
we will find O^; in D mim)r, C^f; in K minor, D^.
Tliereforc every raised note in any given scale
Avill be a leading note to some related scale. And
no note in tlie scale (with one exception, to be men-
tioned later) can be raised unless it leads to a re-
lated scale.
i
^pr-^^
dfp-^-'^
Zo=a^
4(0 T 8 W 10 11 13
1. Tonic.
2. Leading note to D minor.
8. Supertonio.
4. Leading note to E minor.
6. Lending note to F mnjor.
7. Leading note to mnjor.
0. Leading note to A minor.
We SCO from this example that a cbromntic scale may be
written in any key without using a sound foreign to its rela-
tions, except in one place, viz., the Clh.
5. Four common chords may bo written in the
minor scale.
8*
.<u
Ot.ARKK rt riARMnW.
ri:
^M.
=?:^fe-^-iS-ll?_-:!i
m
1 'i 3 4 6 « T I
The lat ii lonio.
The firth on (he 2<1 of the icnie In diminiRhed.
The flflli on the !1J of the Roalo i« kugmented, owing to the
raiving of the lOTentb.
The 4th is the lubdunilnant.
The 5th is the dominant. This chord ba« become miijor,
owing to the raising of the leading note. This is the only
chord that contains this railed note. Therefore we get this
exteusion to the former rule, yi*. : Ererjr raised note In any
given scale will be a lending note to aoroe related scale, and it
tHiml be harmon zed by the dominant chord of Iht nenle to which it
leads. The mixed note or loading note is the third in the
dominant chord.
The fitli chord is nii^jor.
The fifih on the 7:h of the scale is diminished.
(Rules will bo given in the proper place for the use of chords
with diminiiihcd flrths/
Ti. It will at once l)c seen that tlic easiest notes to
harinotiizo in any given base or nielodj-, must Ik- the
notch raised by accidentals ; 1)i juiisc tliere is onl}'
one wa}' of liarinoni/.ing eacli one.
1 2^S 4,.^IV 8_7 9^9 lU 11 12 18 14 1ft
m
, owing to the
1)eonme miijor,
lis ia the only
re we got tbii
ed note in any
?d Bcair, and it
»e<il« to which it
third in the
d.
oufle of chord!
iest notes to
nuiHt 1h> tlio
1 10 re iH only
i-\ <5>
rr
'^=9-
m
•i IS 14 1ft
ci.arke'h harmony.
86
No. 1. Tonic.
No. .'. Uoininanl of D minor.
No. n. Tonlo of D minor.
No. 4. Dominant of ('.
No. Ti, Tonio of C, flmt inveriion.
No. (1. Dniiiiimnt of A minor
No. 7. Tonio of A minor.
No. 8. Dominant of major.
No. 0. Tonio of mnjor.
No. 10. Tonio of major, first inrergion.
No. 11. Dominant of B minor. The F mimt be »harp, be-
oange E minor is the relative of 0, ond Q has an F<f,
No. 12. Tonlo of E minor.
' Nob. 18, 14 and 15. Chords in the scale.
It will be observed that eyery one of these uomlnant chords
Is followed by its tonio. This is called the first progression
(or resolution) of the dominant chord, and must bo for the
present strictly adhered to.
Before proceeding to harmoniie the following exercises, It
would be well to construct a few tables like the accompanying,
which will show at a glance the relations and the possible
accidentals in the given key.
rrinoipal key, Bl>
Minor relations.
••••G (leading note Fi().
D (leading note C#).
Major relations.
F (leading note Et]).
C (leading note Bt)).
Et> (leading npl^t D).
1
3C
OLAItKE'S HARMONY.
An eaE>y wny to remember the notes that may be raised, is :
They are the first, second, fourth and fifth of the scale.
In the exercises that follow, will be found both basses and
melodies, to be harmonized. There are no neir rules as yet to
be observed ; but we have made a gain of four chords, viz. :
The chords that contain the accidentals, which chords are the
dominants of the related scales. These exercises mutt be
transposed to all the keys.
iS^^ ^^ ^^^^I^
S^^g^ ^gE^^^^ ^ iL flZpg
^•-^k=W=^z
^^^
1
gff| --= 77=q^ '^=^"=fe=|^^
Sp^
pz^^—
m
9!Ee
3fc==:^
a ys T --»
:pz
t=T=±
:p=±=^
-®-
"ZZ — — ^
i
^^^^irf i ^^ ^^m
X
may bn raised, is ;
of the scale.
nd both basses and
new rule? as yet to
r four chords, viz. :
hich chords are the
exercises mutt be
^^1^8
i^
*^
• — *-
^^
r
'ZZ — — ^
i
^^S
■^V;-
clauke's harmony.
37
PlS^^^l^^felpi
1. In addition to the related scales there is another
scale from which we cin borrow some chords, viz.,
the parallel minor. By parallel minor is meant the
minor scale beginning with the same ke5-note. Thus
the parallel minor of C major is C minor; it has
three flats for signature, being the relative minor
of El,.
Rule. In any given major scale the chords be-
longing to its parallel minor may be used. These
chords are three in number (one being the same,
whether the key is major or mi.i0r, viz., the dominant).
C Major,'
w^-
m
4 6
6 5 6
*^
i|E(6|):4ae^l
minor, parallel minor of C major, and relative minor of Ey
I ,
1j#
I
II
38
CLARKE'S HARMONY.
We now have a means to hnrmoniie E'c or Al> in a malody
in the key of C, viz. : By C, E^ ; F, A>, C; or A', C, E^ ;
which laal chord includes botii these notes.
C, Eb, 0.— Is generally used as follows, t. «., preceded by the
major tonic or dominant, and followed by the dominant or
chord on the sixth of parallel minor.
^ (
^=±
t fc^Ofa : ^
^=Tfi=
F, Al>, C. — Preceded by the tonic, or major subdominant, or
submediant, and followed by the tonic.
Al» C, E'?. Preceded by the tonic or dominant, and followed
by the tonic or dominant.
^Sg^^^
n
yi
it
E
Bl
n
b
' Al> in a malody
1; or A', C, E^!
preceded by the
lie dominant or
subdominant, or
ifeft
ant, and followed
fe
M
m
CLARKE'S IIAEMON'-'. 39
All these chords are frequently used in succession, as follows:
'^P-
-»-
ffi
in
W-
1
8. The last common chord is the chord of the
lowered supertonic, which is formed as follows :
Rule The supertonic of any scale, major or
minor, may be lowered, and a major chord may be
written on it. Thus the supertonic of C is D ; lowered,
it becomes D^. The major chord written on it is
Dj,, F, A^.
This chord should be preceded by the tonic or
subdominant, or by one of the chords of the parallel
minor, and should be followed by the dominant, or
by the second inversion of the tonic.
This chord is more frequently used in its first inversion than
in any other way ; and in this form is called the Neapolitan
sixth — for some unknown reason ; and has a strange account
gifcn of its derivation. (See Grovt't Diet., Neapolitan tixth).
I
40
CLARKE'S HARMON',.
^
->-
7(S>
f
-W
^^^^^
-»■ a g—
:t=a:
i
1, 2 and 8. First inrerBion of lowered aupertonic : preceded
by tonic, major and minor; followed by dominant, or tonio
second inversion.
4. The chord is preceded by the chord on sixth of parallel
minor, and has the root in the base.
6. Preceded by subdominant of parallel minor.
In the following example from Weber (Der Freiscliulz), the
second inveri-ion of this chord is used, followed by the dominant.
^HM L t-rrt ^;^
^
m
^-f^
7±Z±
^.
'?^
'^.
m
^^ag^^^ss
liiiii
f
:f=l
m
apei'tonic : preceded
dominant, or tonio
on 8islh of parallel
minor,
Der FreiNcliuIz), the
Ted by the dominant.
^
^M
irtSi^ig
P
^SS
CtARKE's HARMONY.
41
^^{^^j^I^}^
9. We return now to the rule (on page 24) that
the second inversion of the tonic must be preceded
by 8om,i chord belonging to its own scale. This
must be now understood to include all the chords
thus far mentioned, viz., the chords from the parallel
minor, the lowered supertonic chord, and even some
of the dominant chords of the related keys ; but the
rule still holds good that this second inversion must
be followed by the dominant chord.
I
X
-1-
r
^
-o — ^
X
1^
i
a
^^^pr^^
I
X
^^^^
No8 4, 5 and 6 are not commonly msS. with, but can be rery
effective. These three examples (4, 6 and C) areacon-radiction
I
42
clabke'h harmont.
or exception to the rule (page 86), that the dominant must be
followed by (he tonic. (The progresgions of the dominant will
be more fully treated in the next chivplor).
Another rule must now be given, viz. : When a note is altered
by an accidental it mast remsin in the same part or voice that
it had before alteration, thus :
Bad.
Oood.
^mm^
O'
B
n
d
No. 1 is bad, because the C is natural at the one extreme of the
firt chord, and sharp at the other extreme of the following
cliord.
No. 2 is good, because the CIK occurs in the same part or
voice, vi7., the bass, that has the Ct].
A passage like example 1 is called a cross or false relation.
It cnn occur sometimes without a bad effect, as will be pointed
out in the proper place.
Inminant must be
Ihe dominant will
n a note is altered
part or voice that
ine extreme of the
of the following
the same part or
or false relation.
w will be pointed
CHAPTER IV.
•
1. The dominant cliord may have the seventh
over the root added to it. This seventh is minor.
Being a dissonant interval, it must resolve ; i. c,
move always in one direction, viz., downwards one
degree.
^-
-^^<:^=S''-^
i
:^g^^^
In this example we haTe the dominant chord of C with the
seventh, F, added. The voice or part that has the F, mutt
afterward have E. J'he note to which the seventh descends,
is the third of the tonic chord ; hence the rule, that the domi-
nant must be followed by the tonic. But there are other
chords in the scale that contain this resolution note, that may
be struck after the dominant. This gives us three progres-
sions for the dominant with seventh :
1st. To the tonic chord.
2d. To the chord on the sixth of the scale.
3d. To the dominant of the relative minor.
The first progression can take place no matter what the poii-
lion or invTiion of the two chords may be. In this progres-
sion the third of the chord must ascend one degree.
(43)
If
.44
CLARKE'S IIARMONT.
The second progreesion can only take place when the roof
of both ohordB are at «he base. In this progression the tliird
may descend when (he fifth of the chord is at the top.
The third progression may talie place no matter what the
position or inversion of the *wo chords. In this progression
the third does not moTC, because it is the fifth of the following
cl ord. The root mast be raised chromatically to the third of
the following chord.
It is of the greatest Importance that the pupil should fix in
his memory these three progressions of the dominant chord
with sevenths. The following examples mutt be worked out in
every key.
^gjj g4— ^ "^^
i^^^^^^
aoe when tha root*
'ogresBion the third
at the top.
10 matter what the
n this progrcsBion
flh of the following
sally to the third of
pupil should fli in
lie dominant chord
tit be worked out in
»^3?L
1
clabke'h harmony.
45
'^E^M^^^^^-
In the above examples we h»Te CTery rariety of the first
progression of the dominant with seTcnths.
No. 1. AVith roots of both chords at the base, and seTenth,
fifth and third of the dominant chord at Iho top. It will bo
seen from this example that when the roots of both chords are
nt the base, the fifth of the tonic must be omitted, owing to
f-e progression of the sercnth and third of the dominant. (It
is common in terminations to let the third of the dominant
descend to the fifth of the tonic, but it is in questionable taste.)
No. 2. We have the first inversion of the dominant with
setenth in all positions.
No. 3. We have the second inversion of the dominant with
seventh in all posiiions. This second inversion of the domi-
nant is under no restrictions as to its use ot any time, owing
to the presence of the seventh. The small notes in the bars
indicate that the D ntiy go to C or E ; if it takes the E, the
third is doubled ; but it occurs in contrary motion, and is very
effective, particularly when it occurs as at X-
No. 4 is the third inversion of this chord, viz , with the seventh
for ft base note. The small note in the first bnr of this example
shows how Iho third of the tonio may bo doubled in contrary
motion.
From these examples we get the following rules for iho first
progression of the dcaiinant with seventh :
Ist. When the root of the dominant is at the base, the tonic
must hove its root or fifth at the base ; never the third.
2d. When the third of the dominant is at the base, the tonio
mutt hove the root at the base.
IT
46
CLAHKRH IIAUMUNY.
8d. When (be flfib of the dominknt is at tb« baio, tho tonic
muat have ib« root or third (somctimei tbo flftb, but it ia not
good).
4(b. When the BeTcnlh of the dominant is at Ike base, the
tonio mutt hare the third.
Second progrciaion of dominant with seventh ;
No. 1. TbeeeTcnth iaat the top. The third of tlie dominant
muat ascend. The third of the chord on the sixth niu.H bo
doubled, to avoid the conaeoutive fifths, which would occur if
the D were to take the E.
No, 2. The dominant has the i. ih at the top. , The third in
this case can either ascend or descend.
No. 8. The dominant has the third at the top, oonspquently
the third of the following chord must be du ibled. (See rule
for writing two chcrud in tieroe position). The sniall notes
at the end of each bar signify that the chord on tho sixth of
the parallel minor is included in this second progression.
Example 3 ia sometimes followed by the chord on the sixth
in tho octave position, but rarely
:i^
in
':g^
-9-
i
t tb« baio, tho tonic
no flftb, but it ia not
', is at Ibo base, the
Tentli ;
^
bird of tlio dominant
1 the sixth niu.U bo
rhich would occur if
e top. , The third in
he top, oonspquently
do ibled. (See rule
i). Tlie sniall notes
liord on the sixth of
ad progression.
le chord on (be sixth
OLARKE'H HARMONY.
Third progression of dominant with sevcntht
(^tei^^^J
(^^^^^^^
(
:=li5^5|j>
'n
--sQ>
2! — u — 9- — \--~^ — 9-^ —6
(
-» 9-
-9 !»-
J 1 ^-
^m
(P^i^#^#.
m^^^m
n
Iq thoM esftmples are %\\ tho vurielios of which Ihij. pro-
groosion ia oapkbte.
I
l^;i%.
48
ChARKBH IIAH>U»NY.
n will bo »ccn llmt ilie root of the first chord alwnyH ho-
conici the third of the .ccond (by the ohromatio alicratlon,
effected by the #). Thli !• In Moordftnce with the rule on
page 42, Ihnt wheneter a note Ir altered chromaUcnlly It niu»t
remain in the Bame part or Toice that it hiid previous lo alter-
alinn. It will also be accn that the aetenth alwaya descends
one degree.
It is evident that this third jirogression of the dominant
(I. c, lo the dominant of the relative minor) con only liiko
place in a mnjor key. This leuvea but two progressions for
Iho dominant wilh seventh in a minor key, tIi., lo (he tonlo
and to the chord on the siilh.
(The author cannot insist too strongly on the neocusity of
becoming thoroughly f iniilin.r with these three i-.ogrcssions in
every form and in every key, before proceeding any further.
Their Importance will become more -ad more manifest as we
proceed).
The exercises that follow should be writtoT repeatedly and
transposed to all the keys. A careful study of this example
will indicate how this new chord may be used vthen harmon-
ising A boss or melody.
It must first bo remarked that all the dominants of the re-
lated keys may also have the seventh added, and henceforth
must not be used without the seventh. We have already
found that every nolo in the soaie may be either a root, third
or fifih (except the loading note, which cannot bo a root; the
supcrlonic, which cannot be a third ; the subdominant, which
cannot be a fifth). We now find thr.t they may nearly all be
sevenths.
b* :*
-f^ —
m
No. 1 is the seventh iu the dominant of the related key,
obord nlwayH ho-
romatlo allcrntion,
) with tba riilo on
omallcnlly it muMt
I proviouH lo alter-
h always d«*oends
n of the dominant
lor) cnn only liiUo
vo progrcinions for
', Til., lo (he tonio
on the neocusHy of
reo )>i'ogroi8ion8 in
leding ony further.
Dore nianifeijt as we
ito-1 repeatedly and
idy of this eiample
used i^hen harmon«
ominants of the re-
Icd, and henceforth
We have already
I either a root, third
nnot bo a root ; (ho
8ubdominan(, which
ey may nearly all be
1
f (ho related key,
(;i..vHKi': H ii.vu.Mu.xr.
40
No. 2 is the Hcventh in (he dominant of the relative minor, A.
No, 4 in the sevonlh in the dominant of the key.
No. 5 is (he seTenth in (he dominant of D minor, (ho rela-
tive minor of F.
No. is (he seventh in the dominant of K minor, the rela-
tive minor of 0,
No, 7 lins (o be lowered to Ui', because C is the dominant of
P, and ll.> is (he minor sevenlh over C; .ilso, 11 \n tliit in (lie
key of F. (This gives us a means to harmonize D^ if it should
occur in a melody in (ho key of C).
Since (he sevondi always descends, it is necessary before
(readng a note oh n sovenlh, to observe that it must be followed
by a note one degree lower than itself.
Bar 1. Tonic, domionnt of key, with seventh, followed by
Bar 2. Chord on sixth, followed by dominant of F, seventh
added, second inversion.
Bar S. Tonic of F, followed by dominant of 0, seventh added,
first inversion.
Bar 4. Tonio of 0, followed by dominant of A minor, sevonth
added, first inversion.
I
CliARKE'S IIABMONY.
Bar 6. Tonio of A minor, followed by dominant of D minor,
Beventh added, third inversion.
Bar 6. Tonio of D minor, first inversion, followed by same,
tierce position.
Bar 7. Second inversion, tonio, followed by dominant, with
seventh added.
Bar 8. Tonio of C, with fifth omitted.
The same melody, with another harmony :
(I
Z=^^- '^
^s^:e
m
W^^^
-9 9-
-9 — ^
m
The pupil should analyze this without difficulty.
Try to find opportunities for all the resolutions of the domi-
nant.
5iES^^
^ ._f__>_^b^
r
;^^*i
g
L,|,
linant of D minor,
followed by Bame,
by dominant, with
^
m
BBculty.
lutions of the domi-
.-T-^-J-W-
4-
m
Clarke's harmony.
51
^^9 »-q*=g
?=^:8F=^
-i—r-^r
S
pi ^ ^jgfiigEg j ^ ^^pg ii
p^^gi
XT ' * ' ^
^^
^z=pig=f=ii?ririff _{ > _H*->-
^fe r^^
±-T-f^
m^^^ ^mm^ m:
f>~0
■tE^EIE^tS
F^
It:
m
-#-i-
1^
^^^H^^il^
I
52
clyhke's harmony.
Note.— It is not necesaary to write a separate chord to JTery
note. If two or more notes in ruooession are members of the
eame chord, the chord need not be written with all of them.
Thus : Not ;
mm
I !
2. When the root of a dominant chord with seventh
's omitted, the remaining notes form what is called
the chord of diminished fifth on the leading note.
It must follow the rules for the progression of the
dominant, as though the root were present, except
when it is used in its first inversion (which is the
best way to use it), when the seventh may ascend
or descend.
^=txa^-^«;^^=:«^
1 a 8 4
No. 1. Dominant of D, with serenth.
No. 2. Same, with root omitted.
Nos. 3 and 4 are the inversions.
No. 5 is llie first inversion, with the Herenth ascending.
There are two exceptions to the rule that ibe seventh must
descend :
BT—J:
m^
chord to dvery
lembers of the
all of them.
with seventh
rhat is called
eading note,
ession of the
;sent, except
(which is the
may ascend
^
m
ascending.
be seventh must
m
^
CLARKE'S HARMONY.
68
No. 1. The dominant, second inversion, with the scTenth at
the top, is preceded by the tonic, tierce position, and followed
by the tonic, first inversion. This is the only way this pro-
gression can take place.
Nos. 2 and B. The seventh is doubled, and one resolves and
tb<> other ascends.
3. Any number of dominant chords with sevenths
may be written in succession, whose roots are a fourth
apart, ascending, or (what is the same thing) a fifth
apart, descending. The easiest rule to remember
this progression by, is : Lower the third of each
chord chromaticall}-, and it will be the seventh in
the following chord.
Jtoo/(.— B E A D Q C
In this example the six dominant chords that may be used
in the Icey of C are written in succession.
Other progressions of the dominant chord with
seventh may be met with that cannot be brought
under any rule. They are not common, and can Imj
better learned by studying the works of good writers
than bj' attempting to give rules for them.
5lE
^^^^^s
5i:-^^^^Sfe^
64
CLAEKE'S HARMONY.
ig^^^}^^^^^^
55^^^
5S
:f=3t
s
^^^
jg^^
p
g^=?=
=*=F
^ f^^^f=r=g
^1 I
m
%^^ =^^2£ i ^ j ^ "'"S^ ^
^
-f^Vr f^
^^
je|F
S
^^,.ai-i;i
?
^
i
^^
^^
^m
CHAPTER V.
1. The ninth over the root may be added to the
dominant chord. The ninth is minor (t. e., an octave
and a semitone) in minor keys. In major keys it
may be major or minor, but is naturally major.
2. The ninth resolves like the seventh, by descend-
ing one degree. The first progression of the domi-
nant only is possible when the ninth is added, viz.,
to the tonic chord.
3. The ninth cannot be used for a base note ; nor
can it be written close to or below the root.
4. There are therefore only three inversions of
this chord.
56
CLARKE'S HARMONY.
In (his example are all the dominant chorda Ihnt can occur
in C, with the ninth added.
No. 1. Dominant of C, with m^or and minor ninth.
No. 2. Dominant of its relaiite minor, A.
No. 8. Dominant of F, with major and minor ninth.
No. 4. Dominant of its relative minor, D.
No. f. Dominant of 0, with major and minor ninth.
No. C. Dominant of its relative minor, E.
The small notes indicate Ibe resolution of the seventh, ninth
and third.
When writing in four parts, it is necessary to omit
one of the notes of this chord. The best one to
omit is tlie fifth, or the third or sevcntii may be
omitted.
The following example oonUlns all the inversions and posi-
tions of the dominant of C, with seventh and ninth.
The pupil should write all the dominant chords in the same
way, with mnjor and minor ninth.
2 3 4
5
^IJBZ.
7~g^'f =s
TB^'^ 6
^^^^
-®^-
-«x'-
Ep^
i
'^^^^
^
9 10
m
^-!.»i»:t;i
Is Ihnt ci»n o«cur
or ninth,
lor ninth,
lor ninth.
Ihe geventb, ninth
cessary to omit
le best one to
eventh may be
rersions and posi-
1 ninth.
ihords in the same
-jPv.-
i
i
i
CLARKE'H UARMONY.
6t
Nor. 1, 2, 3 and 4 are the yarioua inversions of the cliord,
with all the members present.
Nob. 5, 0, 7 and 8 .ire ezamplea with the fifth or third omitted.
Nos. and 10. Same, with minor ninth.
The pupil should try to find more than are here giren.
5. Although the seventh may be added to the
dominant at any time, the ninth cannot. Observa-
tion of the way it is used by good composers is the
only way to learn. One rule might be given, viz. :
The ninth should not be added when making a per-
fect cadence, unless it is done as follows :
i
3-
^ — ^
I^IE
^m^ m^
The ninth is resolved before the seventh, by deseendinK to
the root of the chord.
J,ij=i
J i
1 — T—^-
r
:4i4
8»
68
claukk'h harmony.
!
p
^:^
:a.
SSTl
II
m^^^m
TT
An analysis of this example will guide to the best manner
of using the ninth with the dominant.
6. This chord of dominant with ninth is mere
nscd without tl.un with the root. When the root is
omitted, the cliofd may have the three progressions
of the dominant.
Example:
It^ii
«■
'^-
\il prog. 'id.
ad. Sd, bol!t ciordt vUh
ninth, root omitted.
:.m
When the root is omitted, the remaining notes
may be inverted in any way ; but the major ninth is
rarely used as a base note.
1. 1 he succession of dominant chords, mentioned
in the last chapter (page 47), c n talte place, with
the ninth added. It is celdom written with the voois
r)rcscnt ; but if* common without the root.
m
1
le best manner
inth is mere
n the root is
progressions
I, bol!) ciordt viUh
root omilled.
lainin^ notes
major ninth is
ds, mentioned
te place, with
with the '\ioi3
Dot.
clabke'b harmony.
{)»
Slii^El^ES^Tft
Rooln—B K
f^^mi
■szrz:
mt
I
No. 1 is a succession of dominants with minor ninllis, root
omitted. This is known as the diminished seventh cliord.
No. 2 is tlie same siicceBsion ; but the alternate chords have
only the seventh. The chord of B!> major is the lowered super-
tonio of A, hence it can be followed by the dominant of A, na
above. «
The pupil should write all these chords in aV the keys and
in all their inversions.
When harmonixing the following exeTciscs, it U po8i>ible,
whenever a dominant chord is used, to omit the root and add
the niRlh. It will be seen that the lowered notes in the Bcale
may all be treated ns minor ninths. We find so far that it ia
poss'ble to have four raised notes in ft scale; that they are
leading notes to related scales ; also, we may have four lowered
notes in a Fcale which will be ninths in the dominant chords
of the scale and ita relations (although there are other ways
to harmonize the lowered notes). So the accidentals, that can
be harmonixed in a scale, tlways occur in dominant ohords,
or the parallel minor, or lowtred surertonic.
\n\
1
60
CI.AHKR'ri HARMONY.
Tho dominant wltli minor ninth mny have tlie root
nnd third omitted. Tho result is ivdiminiHlied tliord
on tho Bccond de|?rce of b minor scale, Tho same
remarks, as to invcrrtion and progresHion, apply to
this chord as to tho diminished chord on tho leading
note in tho minor key. It takes the place of a super-
tonic chord, and is generally followed by tho second
Inversion of the tonic.
^^^f^^P^
A minor.
C major.
•• i
pr^^rrr m W^ ^
-I — h
f=bp
f TV i f^ r ^ ^^
^^^^^^^
'i-a;
have the root
tiniHliod thonl
lu. Tho same
iHion, apply to
on tlio luading
Inco of ft Bupcr-
I'V tho second
^^
^^
^^
i^^
]
ms
IXABKK'm IIAIIMONV.
61
i
"PT
ite
n^-:^
^^ mtmm^ m^m
m^mm^^^^^i
n
'
' 1
I !
aJ^
CHAPTER VI.
1 The eleventh may be added to the dominant.
It is perfect; being the perfect fourth, removed hu
octave. The third mi.Ht l)e omitted when the eh'venth
is added. It resolves, by descending to tlie third of
tiie chord. If the ninth be present, it generally
descends to the root at the same time that the
eleventh descends to the third. This chord may be
inverted in any way (except the ninth, whicli eam.ot
he a base note or close to tlio root). In four-part
writin{,s the fifth, seventh or ninth may bo omitted.
^^^m^^^^
\
s^m^s^^m
The above con.ainH examples of the way this chord i» gen-
erally used when (he root !• present.
2. Tliis chord is more often used without the root.
The root being omitted, tlie • lord has tlie three
progressions of the dominant, and it may be in-
verted in any way. The following rules must be
observed : ^^^^
II
> tho (lomiimnt.
rth, ri'inovi'd an
hon tlie t'U'Voiith
g to the third of
nt, it gi'iicriiUy
3 time tliat the
\n clionl nmy ho
th, whicli I'tiiniot
t). In four-part
may bo omitted.
^^m
f this chord in gen-
without the root.
rd has tlie three
id it may be in-
ig rules must be
n.ARKK's HARMONY
«8
iHt. IftluM'h'veiith dfK<t!nds,th4" llftli miiHt n-main
Htiifioniirv or awcond.
2<1. It' llu' I'hvi'iiUi rcmaiiiH Htati<niary, tlie llflh
miiMt tisceiul one degroe.
3d. Tiio root an<l tliird being absent, tho seventh
and ninth are free to move in any direction.
Rkmabk — It iH liolter, in K«nerat, that the eleventh ihoulJ
bo he«ril In the preoetling chord ; but it ia not neociMry.
3dE^
-31]:
7.
f
-»--
^^^^^11
No 1. DominaDt of C, eleTenth added, root and third omitted.
The elevenih desoenda; the ninth also ; the fifth remains.
No. 2. Same, with minor ninth.
No. 8. Same, toUowed by tonio. Eleyenth remaina ; fifth
Mcends.
No. 4. Same, with minor ninth.
No. 5. Same, followed by dominant of relative minor.
No. 6. Same, followed by chord on sixth.
64
clarkk's harmony.
No. 7. First invergion of game chord, followed by tonic. The
seventh, F, may go to 0, E or C.
No. 8. Same progression, with minor ninth.
No. 9. First inversion, followed by chord on sixth.
No. 10. First inversion, followed by dominant of relative
minor.
No. 11. Second inversion, followed by tonic.
No. 19,. Second inversion, with minor ninth.
No. 13. Second inversion, followed by dominant of relative
minor.
No. 14. Second inversion followed by dominant of relative '
miror.
No. 15. Third inverHion, eleventh and ninth resolving on
third and root of the chord.
No. 16. Third inversion, followed by dominant of relative
minor.
No. 17. Third inversion, with minor ninth, followed by
dominant of relative minor, with enharmonic change of Al?
toG#.
It will be seen from these exampleei, that the only chords
that can follow this one are the three that may follow the domi-
nant chord with iko seventh ; hence this group is considered
to oome from ^he dominant, as its root.
(Harmoni;<) the melodies already given over again, and try
to introduce this new chord.)
Uecapitulation of the harmonies of the dominant :
i
'^
p
^-
m
lit. 'id. 3d. ith. 6tk.
Tli'i 1st group consists of major third, perfect fifth and minor
seventh, and is a dominant with tihe seventh added.
'oUowed by tonic. The
ninth.
ord on sixth,
dominant of relative
tonic,
ninth.
7 dominant of relative
J dominant of relative '
d ninth resolving on
dominant of relative
r ninth, followed by
Tmonic change of Al>
that the only cliords
it may follow the domi-
lis group ia considered
n over again, and try
le dominant :
Wi
\th. 6lh.
perfect fifth and minor
enth added.
CliARKE'S HARMONY.
65
The 2d group consists of minor third, diminished fifth and
minor seventh, and is a dominant with major ninth rdded ;
root omitted.
The 3d group consists of minor third, diminished fifth nnd
diminished seventh, and is a dominant with minor ninth added ;
root omitted.
The 4th group consists of minor third, perfect fifth and
minor seventh, nnd is a dominant with major ninth and
eleventh nddcil ; root nnd third omitted.
The 61 h group is the same as the 2d ; consequently it may
be eitlier dominant with major ninth added, root omitted, or
dominant with minor nintL and eleventh added, root and tliird
omitted.
Consequently the 2d group in the above example may come
from either G, the dominant of C, or E, the dominant of its
relative minor. The 5th group may come from Bb, dominant
of E!>, or G, the dominantof C, its relative minor. Therefore
there are four notes In common between the dominant harmony
of a major key and the dominant harmony of its relative minor.
By the enharmonic change of the minor ninth there arc five
notes in common, thus :
1. Dominant of C, with major ninth.
2. Dominant of A, with minor ninth and eleventh.
1^
1. Dominant of C, with minor ninth.
2. Dominant of A, with minor ninth ; the A!* becoming 0».
'■■■ 't
it
66
OI<ABKi:'S HABMONT.
3. It is owing to this fact of there being so many
notes in common between the two chords, that any
group, derived from one, may be followed by any
group, derived from the other.
lii
Every group in this example, except tliose marked X. be-
longs to eitlier the dominant harmony of C or of A minor.
(It is sometimes objected to this way of treating these
chords— That to be consistent, such groups as the following
should be treated as coming from the dominant, vii. : D, F, A,
which would bo the fifth, seventh and ninth; or F. A, 0, which
would bo the seventh, ninth and eleventh. This objection is
easily met as follows : There must be a dissonant interval in a
chord or it cinnot be a dominant harmony. In all the c
groups there is either a minor or diminished •geventli, «>r a
diminished fifth. I would Bgaiu say that i*, is only for llio
sake of simplicity and system thnt the domimmt is treated ..s
the root of the«e chords ; not from a belief that it ia so.)
i
4. The succession of dominant chords (see page
53) is also p:)ssil>le wliou the eleventh i^ added, al-
though the third is not present.
ere being so many
3 chords, that any
! followed by any
, those marked X> ^**
if C or of A minor
i»ay of treating these
roups as the following
ominant, vii. : D, F, A,
inth; or F, A, 0, which
enth. This objection is
dissonant interval in a
armony. In all the e
tninished •seventh, or a
that i', is only for tlu
) dominint is treated iis
elii'f that ills so.)
lit chords (see page
[eventh i^ added, al-
olarkk'b harmony.
6t
^^^^
2. Dominant of C.
8. Dominant of F. Bb is the lowered third of the preceding
chord.
5. Dominant of G.
6. Dominant of C, with elerenth.
7. Dominant of F, with eleventh.
8. Same, with minor uinth.
CHAPTER VII.
1. The supertonic of any key, major or minor,
may be treated ae the root of a harmony similar to
the dominant harmony. The four groups that may
be derived from this harmony are always followed
by the tonic chord, which sounds bjst in its second
inversion. The dissonant notes in a supertonic har-
mony do not require resolution, as in the dominant
harmonies by descending: they generall}'^ remain
stationary (because the seventh, ninth and eleventh
over the supertonic make this tonic chord).
If the second inversion of the tonic is to follow
the supertonic harmony, the latter should have the
root, third or fifth for a base note. If the first in-
version of the tonic is to follow, the supertonic har-
mony should have the ninth (minor is best) for a
base note. If the tonic, with root for a base, is to
follow, the seventh of the supertonic harmony should
be in the base and the root omitted.
V a w 8 4
I
the
1
ad(
1
(he
]
ad(
]
adi
ba
ad
ad
fo
lo
is
a<
P'
II.
major or minor,
irraony similar to
groups that may
always followed
i)jst in its second
a supertonic bar-
in the dominant
generall}'^ remain
nth and eleventh
! chord).
onic is to follow
should have the
. If the first in-
le supertonic liar-
or is best) for a
for a base, is to
; harmony should
^^
\r
clabkk's harmony.
60
No. 1. Supertonic harmony of C, seventh added, root at
the base.
No. 2. Supertonio harmony of C, seventh and major ninth
added, root at the base.
No. 3. Supertonio harmony of C, seventh added, third at
the base.
No. 4. Supertonio harmony of C, seventh and major ninth
added, third at the base.
No. 5. Supertonio harmony of C, seventh and minor ninth
added, third at the base.
No. 6. Supertonio harmony of C, seventh added, fitlh at the
base.
No. 7. Supertonio harmony of C, seventh and major ninth
added, fifth at the base.
No. 8. Supertonio harmony of C, seventh and minor ninth
added, fitth at the base.
^^m
,r
No. 1. Supertonio harmony of C, minor ninth at the base,
followed by first inversion, tonic.
No. 2. Supertonic harmony of C, seventh at the base, fol-
lowed by toni> . root at the base. (In this progression the E'?
is almost universally wriiten Djf.)
No. 3. This is the only way this harmony, with the eleventh
added, can be used, viz., with the minor ninth and in this
position.
No. 4. This sometimes ooouis, the third falling to the root
of tbe tonic.
S :!
i '
TO
CLARKK's IIABMONY.
The Bupertonio harmony may bo written after tho lowered
supertonio chord, as follows:
15
s=^
-9 9-
i
liil
NY.
(ten after tho lowered
i
CHAPTER VIII.
1. The chord of augmented sixth is a dominant
or supertonic harmony from root to seventh, or from
third to minor ninth, with the fifth lowered chro-
matically. The easiest way to remember it, is : the
so-called root is the minor sixth or minor second of
the scale. This so-called root is the fifth of the
original chord lowered, and is, strictly speaking,
only a passing note between the fifth of the chord
and the note below, to which it descends. This
chord must be followed by the tonic or dominant.
^fej^^^
Ist example. First chord in the dominant of G, or super-
tonic harmony of C. Second chord is the augmented sixth on
lowered sixth of C, or lowered second of G. The third chord
is tonic of G, or dominant of C. Fourth chord is tonic of C.
In this example the root is present.
2d exaipple. The root is absent, the minor ninth present;
D being the root. A is the fifth, which is lowered to Al», and
is called the root of the augmented sixth. The augmented
sixth lies between the Ab and F#. This chord may be in-
Terted in three ways. It is not often used in inTcrsions how-
cTer.
(71)
! S
ii
CI^ARKE H UAKMUNY.
^f
Z^SCZ
ifsr
-5?
t^i;^
-Ml
\n N:.i 1 the lowered flTth, Ai>, skips to the root.
iu )S" ; bo lowered fifth aaccndg to the natural fifth.
The Hixtli degree in a minor scale does not require
to be lowered when writing an augmented sixth over
it ; or, in other words, the dominant chord in which
this note is the fifth, requires an accidental.
Root: B. F^ is the fifth ; but F is natural in A minor.
2. The angirentcd sixth on the sixth degree of a
minor scale may be followed by the tonic of the
relative major. This progression is best with the
roots of both chords in the base.
Augmente)} sixth oa sixth of A minor, followed by tonic of C,
the relative major.
This progre^ion can be explained by our theory of the three
progressions of « dominant chord. The root of the first chord
is D, therefore it is only the dominant chord of £, followed by
the chord on the sixth of itc scale.
(The flntiot, illustration I know of Ih-.s progression is in the
introduction to " Faust" — Gouucd.)
Y.
m
the root,
le natural fifth.
edocs not require
mentod sixth over
n.t chord in which
ccidental.
.lural in A minor.
! sixth degree of a
the tonic of the
1 is best with tlie
followed by tonic of C,
tar theory of the three
root of the first chord
lord of £, followed by
9 progreaaion is in the
CLABKK's IIAHMONY.
n
i^m^
1 1 ; — -<- ^__
P"^^
¥
1 1
i
H--^
^^M^M
•«»
^^ri^^s
\nr\ :d~T
No. 1. Augmented sixth on sixtbdegreeofD minor, followed
by dominant.
* ^ 2. Augmented sixth on sixth degree of F, or supertonio
of C.
No. o Augmented sixth on sixth degree of C.
No. 4. Augmented sixth on sixth degree of G.
No. '^■. Augmented sixth on sixth degree of A minor.
No. o. Augmented sixth on sixth degree of C. This is the
only way this inversion can be used smoothly.
No 7. Augmented sixth, lowered supertonic of C, followed
by dominant ; or dominant of C, with lowered fifth, followed by
dominant.
4
\)
/
74
oi.arke'u iiahmony.
The Augmented lizth oompletei the liit of chorda; what
fbllow »re either (uepenaiona or retardation!. Introduce the
•uginented sixth as often ae poieible in the fullowing example;
also the supertonio harmony.
^^^^^^^
:rt?Bc:t}ff=j
^^ggtg-£^^35g
-^^^^^^^
I .
lilt of chords; what
tioni. Introduo« the
i« fallowing eiample;
s^^ai
it£^^F=f^
CHAPTER IX.
1. When paHsing from one chord to nnotlicr, one
or more of the meml)crs of the first chord may Iw
prok)ngcd into the second chord; provided, they
afterward ascend or descend one degree to a member
of the stoomi chord. This is jailed retardation.
111 ' II '
In the lit example the U is prolonged from the first chord
(with or without a tie), in which it is a member, into the second,
in which it is not a member. It then resolves, by descending
onp degree, to C, the root of the second chord. The prolonged
D is the retardation. The note C, on which it resolves, is the
retarded note. This is therefore a retardation of the root from
above.
The 2J example is a retardation of the root from below.
f
7 ftrr:
Ill
■-V.
w
CLARKE 8 IIAkMONY.
No. 1. Retardation of root from Bb)Te anU b«low.
No. 2. notardaliun of third rrom above.
No. B. Rolardation of third from bslow.
No. 4. Retardation of third from above and below.
No. 0. Retardation of third from above and root from below.
Nu. 0. Retardation of root and third from above.
No. 7. Retardation of third from above and root from abov«
and below.
No. 8. Retardation of (Ifth from above.
No. 0. Retardation of fifth from below.
No. 10. Rclardtlion of third from above, root from above
•nd below and fifth from above.
Tho following rules must be observccl :
Ist. A retardation that renolvos upward, must
ascend a semitone, except when the noto on which
it resolves is tho third of a chord ; in which case it
may ascend a whole tone ; or, !n other words, tho
root, third and fifth ra. be retarded from ?ibove by
a whole or half tone. Th'i third may bo retarded
from below by a whole or half tono. Tho root and
fifth by a half tono only.
2d. The noto on which the retardation resolves,
must never Iw sounded dose to or above the retarda-
tion (the root >nay be sounded above).
V.
lU
and b«low.
».
B and below,
I and root from b«low.
rom tboT*.
• and root from nbovo
ovo, root from above
served :
V09 upward, must
the noto on which
1 ; in which case it
1 other words, the
d?d from iftbovo by
I raa}' bo retarded
)no. The root anc^.
tardation resolves,
r above the retarda-
ove).
1 r
CLAWtB'H HARMONV.
77
'dM^k
♦ ' -"~"-|© 4|»
No. 1. The C and D are Bounded together.
No. '1 li pouible.
No !) it bad.
3d. The note of resolution may be sounded at the
octave below.
I I
' — i J
^i^^
4th. All t^ese retardations may occur in any of
the parts but the base. The only one that can occur
in this is the retardation of the third from above.
^^&=f^
I.I
fTF
n
I
1
r^
78 CLARKE'S HARMONY.
The following example can be easily aaalyied :
^S0?^-t
W-
J;^!
P -:jsr\
W^-
z&
■I--
9
--»--
«-- ■
i
^
J~6
-&-
t==!!^!_t.-;
ssr
1
=g=Tf;^
:<sr
i
2. A retardation that resolves by descending, may
skip to tlie note below its resolution.
f^^^m
f f
■^
I
A retardation that resolves by ascending, may skip
to tlie note above its resolution.
'T
ES=itFS=ii^
^
:±=i:
~o — ©
J-
1
Y.
laljried :
*
-«»■
H]
_t-
231
1
£ — e *
—I 1
rl ^-
II
— ' — 1 _
"tt
4
— o — — 1
^ II
)y descending, may
on.
scending, may skip
iiii
CLARKE S HARMONY.
19
Either may skip to some other member of the chord
in which they resolve, before going to their note of
resolution.
^ VT^^
1
I—
^
IL
r
-^
1 r"
SE?E*i
rii:^
i:-:^
^
I
Or tliey maj' skip to some other member of the
chord and return to the retardation.
r —
^uJJ
"1 r-
I- I
"1^
S
"Ur
5E^
zitg.
aLz^^
^
i
Or they ma.v skip to some other member of the
chord, and then, if a descending retardation, to the
note below, and if an ascending retardation, to the
note above the resolution.
Sitt*
Hi
f
80
"3^-.
CLARKE'S HABMUXV.
—1
h© —
s
*^r
E-i
Ei3E
i
•#+•-
1
<s--#-
i
ft^
The notes joined by the lines are the retardation itnd its
resohiiion.
Harmonize the following melodies — Firot in the sopruno,
then in the slto, then in the tenor part; so as to become
familiar with retardation in all the parts. In (he first example
(he re(ardations are all marked wi(h a (io. This is not always
necessary, because a note may bo turned into a rctardadon
by having two chords 'vrKten to it, thus :
Soprano. Alto. Tenor.
i
_?£::--■:
::fzif~
:?=p4--P=^
y-i y - -J
-^:^^-
::r-
:^f=T
Jfliii
retardation itnd its
r^t in the supruno,
t; so ag to become
In (he flrst example
This is not always
into a retardation
Torior.
^^£,
--•q f—s~
fc
c'labke'8 harmony.
With the retanliilions i-kipping:
81
-•-
-®-T#-
;^^^£qr=5^=?r-c==:ff
i^
^3g=f — g— #- :
tE^EE^.
r»-— #•
^^^
Without ties:
t>=:-
;pil!i§ig
g^S?s3!^SiE5
g^pp^^^gj?^^
4*
1
;Pi
15*
t « " 7.j;
I li
CHAPTER X.
li
1. An appoggiatura or changing note is a note
struck with a chord ; one degree above or below one
of the members of the chord. Its only difference
from the retardation is, that it need not.be a member
of the chord preceding the one !in which it is struck.
All the remarks applying to the retardation, apply
to the appoggiatura, viz. :
If above the root, third or fifth, they may be a
whole tone ; if below, a half tone, except below the
third, when it may be a whole tone. They may skip
in the same way that the retardation does. They
maj' occur before two members of a chord, provided
they are a third or sixth apart.
■)f I ^ ii M. I
n
^
-9-
r *f
s
B
iii
(«2)
note is a note
'e or below one
only difference
ot.be a member
ich it is struck,
ardatiou, apply
they may be a
:cept below the
Thej may skip
)n does. They
chord, provided
U
■f^dL-:^
-«-
-1 —
HS-
s
=*^
*^
is:
H —
-«s>-
olarke'b iia»,:.ionv,
83
-o-
f^^i^tep
Ai the * we have 'ngle appoggiaturns, from A to B ; at B
are double appoggiaturas ; at C tbey skip to '.be note above or
to the note below their resolution.
2. Appoggiaturas always occur ou the accented
beat of the measure or on the first member of a
beat.
3. When these dissonant notes occur on tlie un-
accented beats or on the second member of a beat,
they are called passing notes. There aro five varie-
ties of passing notes.
1st. Those that enter by degrees, either diatonic
or chromatic.
-^-J-
:iU:
^-=f
^^^
f
M
84
CLABKK'8 habmqny.
I^^^^^l
No. 1. The pabjing notes are on the unaccented beats.
No. 2. The passing notes are on the unaccented members of
the beats. , -^
No. 8. The passing notes are chromatic.
The diatonic passing notes generally occur between
two harmonized notes, as in the above examples;
bv't sometimes two diatonic notes in succession are
passing notes. This can only occur as follows, viz.,
the first note is the root of a chord, the last its fifth,
or the reverse.
K^^*
Sometimes a passing note and changing note occur
in succession, as follows :
-Tt— '^ — ^ - <
^1
scented beats,
icented members of
ly occur between
ibovc exainples;
in succession are
p as follows, viz.,
the last it& Afth,
■m
Clarke's harmony.
85
The remarks with regard to retardations and
changing notes apply equally to passing notes, viz, :
An ascending passing note may skip to the note
above its resolution ; a descending passing note to
tlie note below its resolution. Also, the note of
resolution and the passing note should not be
sounded together; but the note of resolution may
be sounded at the octave above or octave below.
Also, passing notes may be doubled in thirds or
sixths. They may also l)c doubled at the octave by
parts moving in opposite directions. Lastly, both
ascending and descending passing notes may skip
to another member of the chord before resolving.
nging note occur
m
r
««»!
8e
CLARKB'H HABMONY.
^^Jri#|l
a-
;^
^^^^^^mM
No. 1. PaSBiBg note, skipping to note above.
No. 2. Passiog note, sklppiog to note below.
No 3. Passing note, dounlcd in thir.ls an'l sixths.
No. 4. Passing note, doubled in thirds and octaves, three
^"no! 6. Passing note, doubled in thirds and octaves, three
^'no. C. Passing note, douDled in thirds and octaves, fo ir
parts.
Appoggiaturas :
±: 1
r-f=^-^q
^t^=f=
jd=dr-i-f-:
|^^fe=:3
.- K \
9^^—0 :
■# — ^
::p^=sr:
:?=*:
^
1
Same, skipping:
^gi^^^^^
#-#-
e;
^^^^^^^
y
*=F*^
1
w.
1 sixths.
ind octaves, three
aud ooloves, three
and octaves, fo ir
-M
m
>=*
^e
^^a
^ I
clarkb'h harmony.
Pnssing nfites. first specie' ;
87
bS?^^^^J^
^^m^m^^^M
>Samo ;
EE^
ji^i^fe^^gi^
The second variety of passing, notes consii-ts, in
striking after a harmonized note, the degree above
or below, and returning to the harmonized note.
i
k^ E^^A^
*
gg clabkb's harmony.
All the remarkB concerning the pvovioJiH variety,
apply to this one.
N. B.
m
No. 1. Both the note. »bow .nd b«low the harmoni«ed note
are struck.
No. 2 Both the notes below »nd abore.
No. 3- Doubled in thirds.
No 4, Doubled in sixths.
No. 5. Doubled in thirds, not«i abote and below.the Sarmon-
ized note.
The third variety of lABsing notes enter by skips ;
but are subject to the same rules.
nh
4-
1 a » *
V.B.
(viojiB variety,
(_^ — i
m
t barmonized note
below.the Sarmon-
enter by skips ;
1,1:1
olakkg'h harmony.
89
No. 1. B ia a ptiaiag note, onterinK by ikip. It ih one
dcgrcu below the note to which it puHses. It is a Henillone;
because all notea of this lorl, whether pawing, chanKing or
retardations, niu.'t be, if below the root or fifth of the chord,
a Hcniilonc.
No. 2. Same, skipping to note aboTe.
No. .S. Same, skipping downwards.
No. 4. Notes below and above.
No. C. Notes above and below.
No. 0. Notes below, doubled in thirds.
No. 7. Notes below, doubled in sixths.
No. K. Delow and above, in thirds.
No. 0. Same, in sixths. '
Although, when these notes are above a harmonized note,
(hey may be a whole or half tone. Yet if naturally a hiilf
tone, they cannot be changed to a whole tone: although, if a
wliule tone, they may be changed to a half tone. It is fur this
reason that, at the places marked N. D., the first F is made
sharp and the second natural. This first F# is a passing note
to 0; the Ft] is a passing note above E. If this passage
occurred in the key of Q, then both the F's would be sharp.
Before treating of the two remaining rarieties of
passing notes, we will give the following general
rule for all the preceding varieties (including retar-
dations) :
The notes that lie one degree on either side of a
harmonized note, may be struck Jwfore it, either by
prolongation from a preceding chord, or by entering
diatonically, chromatically or by skip; provided,
always, that the dissonant note, be it a retarding,
changing or passing note, is followed by a liarmon-
ized note ; which harmonized note may either follow
90
clarkk'm harmony.
immi'dlately or may bo delayed by the dissonant
note if below, skipping to the note above, and vire
versa, or skipping first to some otlicr menber of tl»e
c'liord,
TIjo fourtli variety ia a variation or ornamentation
of tlie first.
Tlio following example! will explain their uie:
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Wi"^"
CliARKE'a HARMONY.
91
These examples might be multiplied indefinitely ; but enough
are given to explain the formation of passages of this kind.
One of the best places to study their yarieties, is in the -works
of Handel. This variety can be doubled in thirds and sixths.
The fifth variety is called the anticipatory note.
Its use will be easily seen from the following
examples :
■n
^^^t^jg
r— ^
*=*
i
f
^
r -fi
(- «J ^ p;^
r ^6
The last is the almost universal termination of all
of Ilanrlel's solos, airs, songs, etc.
Second variety :
m
^
i» # i»-
|,i." t \ ^ rgtr I' gtf-^to^'^
Third variety :
^^tefegg
^r
92
CLAKKl'a HAEMONY.
V- \J ^ I ' t I J ■'! i I * l^^^i' I I * ^^^^Bl ■■■• — I
P
IgE^E^^E^
^^
^i^gi^i^
Fourth yar'.e(y :
P**-
^.^1 iUtit^ ^t^^^sm
N. B
All varietieB :
^^^SS^^^
If.
It^E^M
*-liM-»-
^r--^-
1^
^^P
jE^S^
m
.fe^-?^?^
p.
-PlTF
Jf=«:
CliARKC's HARMON r. 98
^3E
-ta^-
^ii
^^ g ^^g^ag ^-^^g
S£=JZ=?=PZ^
?^
^
At N. B. is the melodio miaor scale, first ascending, then
descending. This is the only way it can be used, viz., as pass-
ing notes.
or
^m^
i
^^^^mm
i
94
clahke'h harmony.
(^^^^g^i^^t
l^^^pt
The foregoing are exampleB of the use of U 2 melodic and
harmonic minor scales, with the diUirent harmonies.
No. 1. Ascending, with tonic. First is best.
ho. 2. Ascending, with dominant. Both are good.
No. 8. Ascending, with subdominant.
No. 4. Descending, with tonic. First is best.
No. 5. Descending, with dominant.
No. 6. Descending, with subdominant.
N08. 7 and 8 are used at the base. The skips of augmented
leooBds in passagM Uke the »boTe in the base, being very dis-
agreeable.
!■ :i
^fe^pl
lae of \1 3 melodic and
It harmonies.
is best.
oth are good.
; is best.
rhe skips of augmented
le has*, being very dis-
CHAPTER XI.
We have now acquired all the means of harmony,
except a few irregular or rare progressions and some
other matters that would not come in well under any
of the headings so far. This chapter will be devoted
to all these matters.
1. Pedal Point — The tonic or dominant, or botli,
may be held for an indefinite time, and any succcs-
sion of harmonies belonging to the key, may be
written with them ; provided, the prolonged note is
a member of the first and last chord in the series.
This prolonged note may have a place in any of the
parts ; but is more often used as a base note. The
harmonies written with a pedal note should progress
as though the pedal note were absent. (It is better,
as a general rule, that no harmonies more remote
than the dominant harmonies of the related keys be
used.)
I
'1 I
96
CLARKE'8 HARMONY.
^-^_-J— ._
^mi
\ , — .« — -I
The pcd«l point is often of very short duration, as in tlie
following example!:
-r
^^
^^
^IHE
I I
yiAA
iwF^E^m.
j-^
»_z-i
^^
2. Exceptional progressions of the dominant with
seventh.
m
frrt
j^
rt duration, a8 in tho
^mm
«ai
r the dominant with
P
m
CI.AUKK h IIARMU.W.
97
In this example Ibo dominant ia followed by llicHutidominunl,
firHt in-crsion. The seventh does not resolve. This progros-
aion can occur both in major nnd minor keys.
(P^;
— e, a-
.iii^ss
1
In this example the dcmiuaut is followed by the beoond in-
version of the f upertonic. (Properly consider*.!, the whole
passage is dominant harmony ; the A— A being merely passing
notes, doubled at (he octave, by two parts prooefding in oppo-
site directions )
The following progressions of the dominant with seventh
will sometimes be found, but are rare :
^ 9
The following progroision of the seventh sometimes occurs
when the bass descends to (he third of the tonic. This is done
to avoid the doubling of the third in direct motion.
(P^pi
^^=^11
;;«'
<i-iai'~-r-y>i^:^f^irt?'^ i^-jp*Jtwr*r«^;*
■^
9e
ci.arkk's harmony.
8. The fifth of a major chord may be cimngcd to
an augmented fifth, provided the augmented fifth
ascends one degree. (This applies also to a domi-
nant with seventh.)
^^^^^^^m
^t= M.j:T^^ ^^ II 7^ £ ^
1^^
No. 1. The pecond chord is a combination of .pasBlag note E
and augmented fifth, C^.
1 A'-
This example is a combination of a doub'e retardation and a
changing note. Such combinations are only possible when the
dissonant notes, taken collectively, form part of the dominant
harmony of the key of which the chord on which they resoWe
ia the tonic. In this example, C#, E, Q, are part of the domi-
nant harmony of D. D, F, A, is the chord in which these
notes resolve.
lY.
nay be cimnged to
10 augmented fifth
ics also to a domi-
ition of .passiag note E
i
DuVe retardation and a
only possible when the
n part of the dominant
1 on which they resolve
, are part of the domi-
chord in which these
CLARKE'S IIAKMONY.
00
S. CImnpinf,' and pnHsinjr notoH may hv donhlcd
when they are ai» aiigmcutt'd fourth or diminiHiicd
fifth apart ; provided, the two sounds nlwnys move
in opposite directions to tlicir resolution.
11^
Passages like this may be explained on the theory of a
" harmony within a harmony ; " boonuso they always boar the
relation of either dominant or supertunio harmony to the chord
with which they occur.
6. Passages like the following can be used, con-
sisting of passing notes of various kinds. The
design of such pnssages seems to take possession of
the listener and cover the harshness of the numerous
dissonances.
100
CI.ABKE'a UABMONY.
i^^^idiBlfe
Tlu'y in^^*- «i'wayH begin and oml with ii cliord.
Vr.rlouH pnwageH of tliis kind can bo found ; but enough
has been taid to guide lo their underglanding.
7. False Relation.— Wlien a note, occurring ui
two Buccessivo chords, is chromatically changed,
without remaining in the Hamc voice, it is termed a
false or cross relation.
^^PU^
i
^^
hi
m^^mm^
No. 1 is always b«d.
No». 2, .S, 4 and "> are common.
Ii
IB I.
ir.
iU^
tl with a chord.
10 found ; but enough
iding.
note, occurring 141
natically changed,
oice, it is termed a
:^™ii
■*•.
r^
«f
CLARKE H HARMONY.
101
Tli« fullnwin^ niiglit l>e firiven ana rule fur tlioio progmidonit:
A fitUo relntion iiiunI iipvvr bo niailo with llio third of the chonl
(Exaiu|ilo 1) ; but it iiiuy ocnur with nny ollinr inoinbor. Kx-
tniple 2, It Ik the seventh ; thi' iinigrcNHion iit r^re. Einmplo
R and 4, It '\n the rooi thiit ir 'ored ; 8 ii Itetler than -1. Kx-
an.ple T), the fifth Ih altered : tKix is very coiiiinon and Ih alwayH
good.
8. Wlien liny two parts ascend or descend togetlier
to an octave, from some other interval, it is called a
concealed octave :
^
m
Iwcause, if tlie intervening notes are pnt in as in this
example, two ootavcH will rosnlt. The unpleasant
effect is supposed to be obliterated when the npper
part moves a semitone, as in this example.
A fifth, which enters in this way, is also called a
concealed fifth.
I
ES^
:±3=
t^
9. When the different notes forming a harmony
are struck successively, instead of simultaneously,
the chord is said to be broken or disj^ersed.
t\
r5»T
!|!
102 CliABKE's HARMONY.
The following are the commonest forms of d'spersion :
i"-> r f r > r r -^
No. 1 is called an arpeggio.
Nu 2 bus no distinctiTO name.
No. 3 is called an " Alberti bass," from lis reputed inTentor,
Dominico Albert!. Of conrse, this dispersion may be varied
'n many ways. It may also have passing notes interspersed
with the members of the chord.
I
X X
XXX
^^
^
■¥^
^
m
XX X
X X
^1^
-^
f f f\ tU
^
^
These and many other forms ore frequently met with, par-
ticularly in modern piano music.
Consecutive fifths and octaves may occur between
a part or voice and tlie dispor.5ed notes of the accom-
panying chord ; also, consecutive dissonances.
IS of d'spersion :
n"TT —
y^^^^
P
n Its reputed inventor,
persion may be varied
ing notes interspersed
X X
^^
^
m
quently met with, par-
may occur between
notes of the accora-
dissonances.
m
A
CLARKE S HARMONY.
B O
lOS
-• — I-
ISIJ
-'^
i
At A there are two fifths; at B, two octaves; at C, two
sevenths. But the ear does not recognize them, because it is
at once satisfied that the harmony is as follo'vs :
dispersed or broken, for the salce of variety.
10. Concerning Consecutive Fifths. — There is an
unfortun.ate prejudice against consecutive fifths in
the minds of the majority of musicians, in spite of
the fact that they are often used by the greatest
writers. The excuse given for this is, tb^t these
writers knew how to use them. If this is true, it
would seem to be the duty of any who attempts to
teach harmony- or composition, to find out and formu-
late the riilcb by wiiich these composers worked.
The following remarks are an attempt to supplj-
some sucu rules :
1st. Two perfect fifths, occurring between extreme
parts, arc alwajs disagreeable when the roots are
within one degree of each other. The disagreeable
104
oi.arke's harmony.
effect is ii little less when the root>( nre a third apart;
still loss, if a fourth apai-t; and least of all, when a
fifth apart. In the last two eases the softening of
tlie effect is owi-ig, probably, to tlic fnct that there
is a connecting sound, \'\/.. :
©-
-»-•
m
It will be seen that the connection in tlie second example is
still closer than in the first. These two cases are to be foond
in tlie works of many good writers. Of course, the effect is
still more softened by contrary motion between the extreme
parts. (Seo example on page 29.)
It is possible to have two perfect fifths, in succession, between
the extreme parts, when one of them occurs between any two
members of the chord but the root and fifth.
The first fifth is between the root and fifth of the chord ; the
second, between the fifth and seventh of the chord. (The absence
of unpleasant effect here may be owing to the fact that it is
the dominant of a minor key, followed by the dominant of its
relative major, and these two chords having so many sounds
in common.)
2d. Two perfect fifths, in succession, may occur
between the middle parts (tenor and alto), as follows:
nro !i third apart;
sast of all, when a
s the softening of
lie fiict that there
1
,he second esnmple in
CAses are to be found
r course, the effect is
between the extreme
in succession, between
curs between any two
ftli.
Rfth of the chord ; the
ic chord. (The absence
; to the fact that it is
iy the dominant of its
nvin;; so many sounds
session, may occur
1(1 alto), as follows:
clarke'8 harmony.
105
■without any unpleasant effect. Of course, if they
can occur at the distance of fourth or fifth between
the extremes, they can between the minor parts do
likewise. They may even occur a third apart, with-
out any serious unpleasantness.
T==^
1
3d. Perfect fifths, one degree apart, may occur
between the base and the tenor or alto, when they
result from the resolution of nn augmented sixth
chord, as follows :
(This can be found in Moiart and Beethoven.)
4th. Perfect fifths, a third apart,may occur between
the base and tenor or alto, as follows :
m
-»-
^ — S^ — If
5»
•rrr^
111
lOf)
OLARKErt HARMONY.
5th. Of course, they may be a fourth and fifth
apart.
Otij. A diminished can always follow a perfect
fifth, in a descending passage, as follows :
-»-
The perfect may follow the diminished, as follows :
S
:f:
iT
i
I do not put forth any of these remarks ns rules (except the
last, which is old) ; but merely to point out the way that con-
secutive fifths are often need by good writers. No satisfactory
reason has ever been given, why they should be unpleasant.
Indeed, thern is good ground for suspicion that it is merely
the result of education ; the learner being from the beginning
cautioned against tliem as the unpardonable sin' in writing.
(See Helmholz and Pole on this subject.)
If the deciphering of old manuscripts is ^o be trusted, there
was a time when the only intervals used were the perfect
fourth and fifth as follows :
P^^
This was known at diaphony. It may be that the forbidding
of consecutive fifths, altogether, was merely a reaction from
this unquestionably barbarous style of oompoaition.
ill|i «
J
rourth and fifth
bllow a perfect
lows :
shed, as follows :
118 rules (except the
t the way that con-
's. No satisfactory
uld be unpleasant,
n that it is merely
from the beginning
ible sin' in writing.
^0 be trusted, there
I were the perfect
that the forbidding
ly a reaction from
position.
CHAPTER XII.
Suspended Dissonances and Sequences. — Before
it was discovered that the seventh could at any time
be struck with the dominant chord, il; was used only
as a suspension and coutd be added to any chord ;
but it was and is necessary to prepare it ; i. e., it
must be heard as a member of the preceding chord.
The modern or harmonic system has retained this
rule from the old or contrapuntal system ; therefore
the seventh and the ninth may be added to any
chord, major or minor, by suspension. It must
always resolve like the seventh and ninth in the
dominant chord ; and a chord with seventh or ninth
added by suspension, has three progressions, just as
the dominant chord has, viz. : It can be followed by
a chord whose root is a fourth above (tonic) ; a
second above (chord on sixth), and a third below
(dominant of relative minor).
Preparation. Su$peniton. SeioluHon.
i
s
?
i
Si
^
X 1
(107)
,1 ■
108
oi.abkk'8 harmony.
Chord of £, with auspendeil seTentli ; tlio seTenih resoWes
on C ; and
The chord marked 1, in Rimilar to first progression of domi-
nant with Hcvcnth.
The chord marked 2, is Kimilar to second progression of
dominant with seventh.
The chord marked 3, is similar to third progression of domi-
nant with seventh.
Tlie seventh and the ninth are the onl}' suspensions
possihlc. Tliey can be inverted like the dominant
with Bcventii and ninth, in short fliords with a sus-
pended seventh or ninth, arc in every respect to be
treated just the mnie as dominant chords with
seventh or nintii.
It will be seen that a suspension differs materiallj'
from a retardation, because it always resolves down-
wanly and never w the same chord in which it
occurs. Suspensions may skip to the note below
their resolution, or to some other member of the
chord. They are also frequently ornamented by
passing notes.
•^M^
tlio seTenih resolves
progression of domi-
iieooni) progression of
i progression of domi-
ic onl}' suspensions
like the dominant
fhords with a sns-
v^ery respect to be
nant chords with
f
1 differs material!}'
ays resolves doicn-
■hord in which it
o the note below
er member of the
y ornamented by
- |»-^^^. =J
ci.arke's uarmony.
109
-.-=&=^-Jt^.
-'z^Er=is-.
»-
P=i::p=ft
z^
! I I
5^^^^
— -_:rfi:
m
This example is founded on the following suocossion of bus-
pended sevenths :
(i
3tf!^at;
5=^
-t — '— f
\^m\^^i^^m
(^^^^i^e^^
Sequences. — A molodic sequence consists of the
same phrase repeated at equidistant degrees, thus :
i^'^^Ee^
m=f^^^^=^f&?^^^
A harmonic sequence consists of a series of domi-
nant and tonic harmonies (general!}), or augment od
sixtli and tonic or dominant liarmonies ; tlio roots
of wliich proceed by similar step?!.
[iJI
110
CLAR»'B'8 HARMONY.
:i^¥3^:£f^
^1
|^^t^_^^3^^
,is=?=
EE^
-®-
^
i
(1^^
1
s^
^^^
No. 1 is a sequence of dominant and tonic chords ; the tooU
fall a fifth and rise a sixth alternately.
No. 2 is a sequence of augmented sixths and dominant chords.
the roots falling » semitone. ..-»»,», Ti,«
No. 3 contains both these examples in the first bar ine
second bar is a repetition of the whole phrase, one degree
higher.
It would be impossible to giye examples of all the harmonic
sequences that might be^made. The above examples are
enough to explain the manner of their construction.
11(1 ;
m
^
m
i^^^3E
m
tonic chords ; the toots
lis and dominant chords,
1 in the first bar. The
lole phrase, one degree
pies of all the hannonio
le above examples are
■ construction.
CLARK E'h HAHMONY.
Ill
Tlic contrapuntal Heqncncc consists of ii sucws-
sion of common chords, with roots moving in some
regular i)lan. Tho diminished chords cm be used,
with tlic h)we.st note of tiie group for a base note,
nltliouffli tliore is a rule the eontrary (see page 52).
Tliis permission is for the sake of preserving the
form of the sequence.
fpf^fp^m ^^
^^^^^r^^=Ffl£^^' _UJ'-iJt
No. 1 is one of the commonest. The roots rise a fourth and
fell a third.
No. 2. Roots rise a fifth and fall a fourth.
No. 8. Roots fall a fifth and rise a fourth.
112 OLARKR'H HARMONY.
No. 4 oon.i.t» of a phmHO of four chord., toreated a third
lower.
No.. 1, a and 4 can l.o changed into harmonic sequence.
easily 1 a* follows:
m^'ff
(^^^^^^^^^
n
Of course, it is not necessary in any sequence that
the roots of the chorda must always be at the base.
The following example, are contrapuntal sequences, with
seventh and ninth added.
:=tiUi^itT5Nfefe
I 1
E^S
i;M
wm.
4
ONV.
uhord*, rcjflaleil a third
nio liarmonio sequenco*
'^m^
^^^
^ •-
^^
y in any sequence t^iat
always be at the base.
Urapuntal sequences, with
«
-J-4
=F^
I 1
»
lI.AaKK's IIAR.MONV.
113
-i=^^rE^
e^^m^^
^E^^^^m
No. 1. Sequence of suspended seTentha ; roots fall a, fifth
and rise a fourth.
No. 2. Scijuenoe of suspended sevenths ; roots rise a senond
and fall a third.
No. 8..Sequenrc of suspended ninths; roots rise a fourth
and fall a fifth.
No. 4. Sequence of suspended ninths ; roots fall a third and
rise a second
No. 1 may be changed into tho harmonic sequence (described
on page 68), as a suooession of dominant chords.
il^i^^^^
TO
If
114 CLARKK'H IIAHMO.NV.
No. 2 may b« changed into » harmonic ••<|ueiioo in two wayi.
(^"^^^^I^
No. 1 is » Mquano* of dominant obordi raiolTing on tlie
iiitii (if ibeir toalo.
No. 2 ii a iiequenMof dominant aliorda with roots omitted,
reMolving on their tonio*.
! I
u
NV,
iiequeiioo in twowayi.
— — t
m
ordi rtsoWing on the
rdi with roots omitted,
CHAPTER XIII.
ModuIjATIon. — Moiliiliition \n tlio net of pnnRing
tVoin one koy to nnotlwr. Tliero in, imfortuimHtly,
no wiiy of ilistinguiHliinjj hetweon niodiiliitionH to
related nn»l nioduIntiouH to non-rolntcd kvya. The
term tranHition Ih sonietimea used to uignifv a sud-
den change to a remote key. It would, i)jrhat)H, bo
a good method to use the term modulation to signify
the change to a related key, and transition to signify
the ciiange to a non-related key. It is verj' unfor-
tunate, but true, nevertlielcss, that the musical
nomenclature of the English language is in a very
confused state.
I shall use the word modulation in its generally
accepted sense — to cover all possible changes of key.
All modulations may be reduced to four rules :
Ist. By taking advantage of the fact thnt the
dominant chord is the same, whether the key is
major or minor.
This will give six modulations from any given
key, because there are six dominant chords in every
key.
The following exiimples contain all the modulations that may
be made by this rule, from the key of C.
(116)
- - ■^.m^'^.^i^
li^T^
116
CI-AB1\.E S HABMONY.
*i#-
i^^f^p
In 1, 2 and 3 the msyor tonics of the key are changed to
minor.
No. 1 becomes C minor, relative minor of Eb.
No. 2 becomes O minor, relative minor of Bt>.
No. 3 becomes F minor, relative minor of Ab.
In 4, 5 and 6 ttie minor tonics of the scale are changed to
major.
These examples are, of course, mere skeletonb, being too
abrupt to have any musical effect as they stand ; in fact, it
might almost be laid down as a rule that no modulntion has
any intrinsic beauty; it depends altogether on the wny it is
usi'd. Some of the most beautiful examples in the works of
the grent masters are as simple as possible ; but the manner
of their use gives them all their exquisite effect.
ONY.
a
tP
^'r--''" y"r -
t the key are changed to
linor of Eb.
linor of Bt>.
inor of A\>.
' the Boale are changed to
mere skeletonb, being too
ia they stand ; in fact, it
lie that no modulntion has
[together on the wny it is
examples in tlio works of
possible ; but the manner
[uisile effect.
Clarke's harmony.
117
It will be seen that by extending this rulo to each
new key that is reached, that it is possible to pass
through all the keys. For example, the first modu-
lation changes the key to E^ ; then by applj'ing the
rule to tlie chords in E^, six new changes would be
obtained.
The following examples will show how effective a modula-
tion of this kind may be made.
C minor.
^
i-ld-
W^
^ J. ^
-^-
EE^
(i
s^gi^i
m=^ES^-=f--
*=«=«^
I I
±^i=^^ ^ ^^^iirl
r==J:J^
fcx=t=t=^
■X ' ' ' ■ ' : —
;■
'^
I'i
III
11
Hi
118
CliARKB'a HARMONY.
C major.
I
i
W--
g ?^=Ftf
m^^^
?=i=p=
i
The second means by which modulations may be
made, is hy taking advantage of the different places
in which a major or a minor chord may be found. .
A major chord may be found in six places, viz. :
As a tonic, subdominant, dominant, sixth of a minor
scale and lowered supertonic of a major or minor
scale.
gJ Z^ g Z^Z^^
.a « 0-.
1
ONY.
E3^
H
modulations may be
f the diiTerent places
)rd may be found.
I in six places, viz. :
ant, sixth of a minor
>f a major or minor
_« ffl-
1
CI<A.BK£'8 HARMONY.
119
•^ I ' or
iT^
is=^.
le^
(i?i
^=P=
i
-^
No. 1. C major as a subdominant. (When treating a chord
as a Bubdominant or lowered supertonic, the modulation is
more decided if it be followed by the second inversion of the
tonic.)
No. 2. C major as a dominant.
No. 3. C major as chord on sixth of E minor. (This modu-
lation may proceed to E major, in accordance with the rule
that any chord in a minor key may be. used in its parallel
major.)
No. 4. C mnjor as lowered supertonic of B major or minor.
The following harmonic sequence may be constructed from
this last example.
ig=£^r,^=j§:=»- g"
1
■iHi^.'«»>*^i^B**ii^'@*a-SSirt*^SSl«i^»-^
m
t
i
120
CLARKE'S llABMONY.
Each common chord bears the relation of tonio to the ilomi-
nant that precedes it, and lowered supertonic to the dominant
that follows it.
The following examples gite the modulations that may be
obtained from the two remaining major chords in the key of C.
^
m
■j^tzf^zzz.
5tZ«=
i
n
F us dominant.
F an isizth of A minor.
) I •' I 'or
m.
z^— ^
^
-9-
m
F IS lowered supertonic of K
(} ii>< ^ulidominant.
O iM si-xtli of n minor.
NY.
an of tonio to the (Jonii-
ertonio to iho dominant
>dulation8 that may he
r chords in the key of C.
J— H
fcs
^m
X
fcz«=
^
m
I Blxtli of A minor.
m
s^i
X
1
a iix Hlxth of R minor.
CLAUKE S HARMONY
191
'■o-p-
■■^~
X
l§::^
1r
^m^
a as loworod xuportonic of F$.
A minor chord niaj' be found in six pliicoH, viz. :
Tonic and snlHlominant in a minor koy, and t^nper-
tonic, mediant and subniediant in a major key.
l^^^lSif
X
ai;
p^ll^E^la
«t
H
A minor aa subdomiuant of E.
i=#i-^f=^4^i^
X
jE^p^^
A minor aa mediant of K (third degree).
^i^l=3-^!^gl
i
A minor as supcrtonic of G,
m
I
122 clabke'b uakmony.
(It would be superfluous to gire any more exMnplea. The
pupil ougbt to bo able to construct them himself.)
A major chord may have an augmented sixth
added to it.
No. 1. C major, changed to augmented Rizth on sixth degree
of E.
No. 2. C major, changed to augmented sixth on lowered
supertonio of B.
No. 3, G major, changed to augmented sixth on sixth of B.
No. 4. Q major, changed to augmented sikth on lowered
supertonio of F#.
A major and minor chord may bo treated as the
seventh, ninth and eleventh of a dominant harmon3-,
provided the fifth from the root is added. Thuf>
C, E, O may be the seventh, ninth and eleventh from
D, by adding A, the fifth from the root, D.
No. 1. F, changed to dominant of C.
No. 2. C, changed to dominant of 0.
>NY.
17 more exhmples. The
m liimself.)
n augmented sixth
ed Bizth on sixth degree
>nted Hizth on lowered
ted sixth on sixth of D.
ented eikth on lowered
ly bo treated as the
I. dominant liarmon3-,
>ot is added. Thus
h and eleventh from
he root, D.
clarke'8 iiakmony. 123
No. 3. E minor, changed to dominant of U.
No. 4. B minor, changed to dominant of F#.
The third of the major chord may bo changed,
thus :
p=i
i^^=ffi
because it becomes the ninth when treated as above.
Tiie minor chord may also become tiie fifth,
seventh and ninth of a dominant or supertoniu har-
mony, b}' adding the root or third to it.
^^^^^m
•«■ W W T5.
^te^
X
No. 1. A minor, changed to dominant of 0.
No. 2. D minor, changed to eupertonio harmony of F.
No. 8. E minor, changed to dominant of D.
The third means of modulation is by the chromatic
alteration of chords. Common chords may be chro-
matically altered, as follows :
(; major.
C minor.
to or i'i~ to or or" ;
i. €., the third alone or the third and fifth of a major
chord may be lowered, or the root may be raised.
124
CLARKE'8 Il.VftMONT.
The tliird alone of a minor chord or the third and
fifth may be raised, or the fifth may be lowered.
In the above example, C, E, Q is major; C, E>, 0, minor;
r, E\>, 0!», part of the dominant of D> or D!», or Biipertonio
harmony of G> or Eb ; CJ^, E, O is pm f dominant harmony
of D or B, or supertonio harmony ol' ,ir E.
i
1
m
No. 1. C, E!», 0, as coming from Ab, dominant of Db.
No. 2. C, Eb, O, as coming from F, dominant of Bb.
No. 3. C, Eb, G, as coming firom F, i.ipcrlonic of Eb.
No. 4. C, Eb, O, as coming from Db, supertonio of G^.
The most important modnlationa of this kind are
obtained from the chromatic alteration of groups of
four notes (see page 64).
1^
*
m^mm
l?t group.
Koot: a.
4tli.
C.
2.1i)r4lli.
EiorC.
3.1.
r.
Commencing with the first group, the third may
be lowered alone, or the third and fifth together, or
third, fifth and seventh together, or third alone, fol-
lowed by fif h and seventh together. This process
iaiMHa*
NT.
d or the third and
lay bo lowered.
lojor; C, E>, 0, minor;
•> or H\>, or Btipertonio
'{ dominant harmony
,.r E.
'-^&=S^-
1
4
dominant of D!>.
lominant of B':>.
jporlonic of E!>.
Bupertonic of 0?.
ons of this kind are
oration of groups of
1. 3<I.
r.
roup, tlie third maj'
id fifth together, or
, or third alone, fol-
ither. This process
clabkk's hak.monv. 125
maybe reversed by commencing with the last group
in the above example.
In the following examples aro gome more changes of this
kind. A little study will enable the pupil to oonstruol others.
The last means of modulating is by the enharmonic
change of chords. A common chord may be changed
as foUoM's :
g^g^^^
No. 1. D!", changed to CS, dominant of F^.
No. 2. F# minor, changed to Qb minor, the minor subdomi-
nant of Dt>.
1S6
Ct.ARKR H HARMONY.
All jincrmpntpd sixth chord rany bo changed to a
duinitmnt, and tho rcvcrMc.
^^P:^
.^m^-
l^l^^l^^pi
to to
Nob. 1 and ;!. Augmented bixth, changed to dominant by
enharraonio alteration of the sixth.
Nos. 8 and 4. Augmented sixth, changed to dominant by
cnhnrraonio alteration of the first, third and fi(Mi.
Nos. 5 ond 0. Dominant, changed to augmented sixth by
enharmonic alteration of tlie seventh.
Nos. 7 and 8. Dominant, changed to augmented sixth by
enharmonic oltcration of the flrst, third and fifth.
The most pioliflc source of enharmonic modula-
tion is to be found in the diminished seventli chord ;.
This chord, it will be remembered, results from
adding the minor ninth to a dominant or superton!c
harmony, and omitting tho root.
Three groups of sound} form all tho diminished
snvonth eliords. Since there are twelve m.ijor ehorla
to which the ninth may be added, it follows that
each group must bo obtained from f )ur rootn ; al-.o,
' ' it^ijwwiwuliiii
NV.
ny bo changed to a
8
e
to
tnged to dominant by
inged to dominant by
[ and fiftli.
> augmented Hixth by
augmented siztli by
1 and fifth.
nharmonic inodiil".-
led seventli chord ;.
ercd, results fro-.u
Inant or supcrtoivc
all the diminished
wclvo major ehor la
ed, it follows that
hi fr)ur rootn; nl o,
t'l.ABKE'rt KAKMUNY.
127
since there tiro six dominanta In every scale, it fol-
lows that each group must occur Iwio;' in every
8L-ale as a dominant harmony ; alio, there boing six
Hupcrtonio chords in every scale, each group mur.t
occur twice as a supertonic harmony in every scale.
P'or convcnicnca we will number the groui):^ as fol-
lows : Tiiat from dominant of C, first; from domi-
nant of F, second ; from dominant of O, third.
Hooti: a,
Unmtnant of C,
Suporton. harm'y of l",
E,
A,
(Db).
(O.-).
B, AS
(Ob).
r, D, D, A\
n;., o, E, iy,j.
Roots: I), II, Ats
(o«).
Domluantof O, E, »> B>.
(c;)
Suportonio harmony of C, A, Oi;, Ey
(F|).
No. 1 occurs in C, as dominant of C and dominant of its
relatiye minor.
No. 2 occurs in C, a') dominant of F and dominant of its
relative minor.
No. 3 occurs in C ns dominant of and dominant of lis
relative minor.
In the following examples are all tho roaolution? possib'o to
the first group. Tho pupil can easily wi-ito Ihouo of the re-
maining groups.
IJX
<'t,AKKK'"< IIAKMilNV.
f^fllYsrlT^-ffe^il
Hoot: (>
RtNit: r^i It,
No 1. Written as coming fVotii O ; renoWoil, flrnt, an iloml-
imnl or ('; Hooonil, iim Bupertuiiio Iinrmnny of F.
No. 'J. Written as coining from E; roKolvcil, first, uh domi-
nant of A ; RocontI, an luperloiiio harmony of I).
No. H. Written uh voniinK from C# ; renolveil, flrsi, nn domi-
nant of F# ; Hccond, iis Nupcrtoniu hnrmoiiy of U.
No. 4. Written a8«oin!ng from !)• ; ro^olvcd, flml, an domi-
nant of K'j; Hi'cond, nt Kiiportonic linnnony of A '.
Olio incinlM'r of a <i;r(Mi|i iiiav ho iuld mikI llio ip
inniiiiiiu; three mivv be niixod a seinitoiu'. 'I'ho result
is a (liimiiiaiit or siipertoiiic chord of which \\w licld
note is tlu! root.
11
"^"-1;
IS, .—I
^^Ei
>\\.
-jiar
renoWod, flMt, an ilomU
rioiiy of K.
rexolvpil, first, us doml-
noiiy of 1>.
renolveil, flrHi, i\« domU
■moiiy of U.
ro.iolvcil, flrHl, nx domU
inony of A >.
1)0 lulfl Mild lllO IP
'initoiii'. 'I'ho ri'Miilt
111 of whioli tlio lieltl
•r:!?5f— r«-
il
clarkkV iiakmunv.
1S9
No. 1. V held ; I lie chord li.'oomei, ftr»t, dominant of Hl», or
■econd, utiperlonio hi»riiioiiy of Ki'.
No '-'. A 'held; llu- «liord hocomeB, flrtl, dominftnl of Vf,
or necoiid, miixTl 'iiio hnrmoiiy of fl:*.
;>',). ;t. B hfld ; the chord hcooiiieM, flml, dominant of E, or
■econd, iuporfonio harmony of A.
No » l> hold ; Ihu chord hcoomen, flfit, dominant of 0, or
ieoon<l, dupertonio harmony of ('.
L-istly, one inomhcr may ).(• Iicl<l, tlio remaining
throe niiHi'd a Hi'initniio, iiml tlic nolo tlmt Ik-co??!*"*
the scventli, may l)e clmnged to an augmented nixth.
The pupil should write out all theiie Changs'* in nil the groups
repeatedly. This is the only wny to become familinr with them.
It would take too much space to write examples of all these
various modulations, and would, besides, be of very little real
UHO to the student. The bettor way is to try, from the rules
here given, to construct modulations. A littlo perseverance
will accomplish it. Of course, it is possible in a modulation
to mix any or all of these rules together.
The works of Wagner, Raff, Chopin, Qounod, Schumann, and
others among the modern writers, will furnish endless examples
of ingenious modulations that may be profitably studied. And
there is no posaible modulation that the rules here given will
not explain.
CHAPTER XIV.
Writing in Parts. — Music is said to be written
in parts, when eacli voice (or instrument) has an in-
dependent melody of its own. This kind of writing
belongs properly to the study of counterpoint ; but
the object of this chapter is to give some idea of the
process.
1st. In tivo parts. — The following intervals may
be used nt anj' time : Major and minor third, major
and minor sixth, augmented fourth, diminished fif:h,
perfect fifth and octave. The perfect fifth should
be avoided, being ineffective. The same remark
applies, but not with eqiuti force, to the octave or
unison. The octave and unison make the best end-
ing. The minor second ma}'' be used as a susp'^ nsion
(it results from the inversion of a suspended seventh,
see page 107), and must resolve according to the rules
for suspended dissonants (page 108).
^
1
Inversion of
i
^
•^ r
^
i
(ISO)
?; i
IV.
mid to be written
•ument) has an in-
lis kind of writing
Liounterpoint ; but
e some idea of tlie
ing intervals may
ninor tiiird, major
1, diminished fif:h,
irfect fifth should
'he same remark
to the octave or
ake the be<5t end-
kI as asusjynsion
ispended seventh,
irding to the rules
0.
CLARKE'S IIARMONV.
131
The mnjor second maj- be used .10 a suspension,
or it may bo used na part of a dominant chord ; but
in this case one of the notes nhould (not noeossnrily
the seventh, as in the preceding case) bu held from
the preceding chord.
Seventh held.
I
i
^m
i
B«ot hold,
The augmented second may be used as follows ;
It represents the third and ninth of the dominant
harmonj' — the ninth, followed by th root.
The dim. lished third can only occur as a passing
note.
i
I I
The augmented fouri;h may be used at any time,
but it '-ust resolve — being partof a dominant chord,
viz., third and seventh, or fifth and minor ninth.
m
132
CI.ARKK'8 iiabmo.vy.
z^<^—-n
Aujirmpiitoil foiirtli ns third nnd seventh in dominant of C.
i^^H
AuKitinntcd fourth ii8 iiah nnd minor ninth li, domlnnnt of A.
The diminished fourtli may occur as a retardation
(it is always the retardation of the fifth of a chord).
m
The root of the second chord is E. The remaining
intervals being inversions of those already given,
are, of ooiirse, sulyect to the same rides.
It is possible, in two parts, to represent the har-
mony very effectively, by allowing one or both parts
to proceed through the members of the chord.
^t^^ jife^
r
Bar 1 is all dominant of A.
Bar 2. First beat, (onio of A ; tho rest of the bar, Uominant
of P. It is important to remember that when the harmony
ehangei, the dissonant notes must resolve.
ONY.
ith in dominant of r.
i
ilnth Ir, dominant of A.
3cur as a retardation
;he fifth of a chord).
1 E. The remaining
hose already given,
ne rides.
o represent the har-
ig one or both parts
of the chord.
^
st of the bar, Uominant
hat when (he harmony
e.
MM
ri.ARKE's IIAIIMUNY.
l;i:j
The angmenle<l sixtii cliord may bu represented
as follows :
i
Or as follows :
^m
* These ar--^ the only ways it sounds well in two
parts.
The perfect fourth can only be used as follows :
^^m
viz., as retardation of third of a chord.
Or
^^
^^
viz., one or both parts proceeding through tiie meu.
lu-r ( of the chonl.
---^ L^tf^'V fe i i- »> i>r= " «'^
11
134 CLARKE'S HARMONY.
Or
in which it is a passing note on the chord of P.
All the dissonantcs and the perfect fourth may
be used as appoggiaturas or as passing notes.
The following rules must be observed for the pro-
gression of the parts :
Ist. Contrast them as much as possible.
2d. Use contrary motion in preference to any
other.
3d. Never use a cross or false relation.
4th. Never proceed by parallel motion to a perfect
fifth, except as follows :
i
^
^=^=t:
1
(called a horn passage). Of course, this does not
apply in a passage like the following, in which the
same chord is repeated in another position.
1^
■*4ll|i»«|
>NY.
the chord of F.
perfect fourth may
tassing notes.
•bserved for the pro-
s possible,
preference to any
relation.
1 motion to a perfect
ourse, this does not
Lowing, in which the
er position.
I
clarke'8 harmony.
185
.5th. Never proceed to an octave in parsilU'l motion,
unless the upper part rises a semitone.
Gth. Never write two major thirds in succession,
whose roots are less than a perfect fourth apart.
Bad. ""O*'-
Last of all and most important. The composition
must be so constructed as to express the harmonic
succession as definitely as if it were in four parts.
In three parts.— Ml the preceding remarks and
rules hold good ; but the following are relaxed, viz.,
the dominant with seventh, or any of the dominant
harmonies can be struck without any preparation ;
also, the supertonic harmonies. The following table
gives the best way of representing all the harmonies
in three parts.
i
j» -gt^ -g
186
olarkk's harmony.
Nc. 1. Common chord. (Of course, all may he inverted.)
No. 2. Dominant or supertonic harmonies.
No. 3. Aunmented sixth. First, when followed by dominant;
second, when followed by the tonic.
The perfect cadence may be made as follows in
three parts, viz., the tonic, with the root omitted and
tlie fifth doubled. (It is only the position tliat en-
ables us to recognize this as the chord of F.)
i
:f:
J*.^.
i
Px o
w
■» -^
The rules, with regard to proceeding by parallel
motion to perfect conconls, are relaxed, with rosranl
to the lower and middle or middle and upper parts ;
but are still binding on the lower and ujiper parts.
Also, two major thirds may ocr-ur (see above)
between the lower and middle or middle and upper
parts.
MONY.
3l
le, alt may he inverted.)
Tmonies.
hen followed by dominant ;
)o made as follows in
h the root omitted and
y the position that en-
he chord of F.)
proceeding by parallel
re relaxed, with roirard
iddle and upper parts ;
iwer and ujiper parts.
lay ocpiir (see above)
le or middle and upper
CLABKE's IIARMOW.
^^^m
ite.
W=f ^^zL^ ^
3^
f^
137
No. 1. Fifth in parallel motion between lower and middle
parts.
Mo. 2. Fifth in parallel motion between middle and upper
parts.
No. 3. Major third between lower and middle parts.
No. 4. Major third between middle and upper parts.
No. 3 is much better than No. 4.
With regard to fonr-part writing, nothing new
need be said. It is subject to the same rules a.s
three-part, and differs only in its greater variety and
copiousness.
138
Clarke's iiARMONr.
The following examples are intended principally
to show the manner of using passing notes and
'ipPoggittt'Tas. One of the best ways to study free
composition in two parts, is by examining the violin
(Inots of Spohr, Pleyel or Viotti. For three-part
writing, the string trios of Beethoven and Mozart.
Of course, in all these compositions there are fre-
quently four and even more parts produced by play-
in^^ double notes. Also, many parts are merely
f 1;>3 and accompaniments. Still there are plenty
cf I'xamples of pure two and three-part writings to
be found in them. Perhaps the finest specimen of
t-.vo-part writing in the world, is the concerto for
two violins, by Bach.
IM
lONir.
intended principnlly
J passing notes and
3t waj-s to study free
examining the violin
otti. For tlirce-part
tiioven and Mozart.
ositions tliere are fre-
rts produced by play-
ly parts are merely
Still there are plenty
;hree-part writings to
le finest specimen of
is the concerto for
CLARKE'S IIABMONY.
1S»
Tlio threi- following examples are founded on this
harmony.
5^-E^
.rSS^JSS^
TO ^ jT^
T^
i
In two parts :
^^^
MONA*.
?^-i^Lib
9
^m
T
TT
^^^^
f
=^-#'
:.-.r=f=3C
^^^
^^^
S=i:
8 r -T-
(*--
CI.ARKKS IIAIIMONY.
141
,i^^_^^[^P
zqir.
,p?:=^^
JTi=£.
;:^-
^
mi
■tr
.^
i^m
^5=25=
®-
iT=P;:^',J^
^^P^P
■^ ■•■
I H^ M # ^
|,g?pE='=»3g4-^^
^^slp.
CLARKK'H IIAllMONV.
i_J_,4_itiJj-^,-^
'^^fE^'^
=.:ip|tf=to:sl:
r
i
■^^'
I *. i J ! x^i.*J
lONV.
-J.
Uii:
1^^
L_J^_ ,
CLAKKEli IIARMUNY.
148
J i .
^ — #■
(
1^^^^
S
i-4i
; _b^ , iA..^_^i
s
a
§1^?^
\^^L_ y —
m^.
i
CONCLUSION.
The 8tudei.t, who has thoroughly mastered tliis
course, should be i)repared for the study of couuter-
point, fugue, canon, and the various forms of com-
position. It is difficult to study harmony without a
teacher, and almost impossible to study these higher
branches without a guide at first.
I have omitted any explanation of the figuring of
chords (thorough bass). Tliere are hundreds of
works Avherein all tlie information wished for may
be obtained on tliis subject.
For tlie study of strict counterpoint. Cherubim's
is perhaps the best work. For the study of form,
no work will suffice. Some good ideas on this -ib-
ject may be obtained from the works of Dr. Marx.
Finally, constant writing is the only way to learn to
write well. No amount of genius will make up for
the lack of hard.work.
(U4)
^-^iOnwi,
M
:oN.
ughl}' mastered tliis
the study of coiiuter-
rious forms of com-
y harmony without a
to study these higher
3t.
iion of the figuring of
ere are hundreds of
ition wished for may
nterpoint, Cherubini's
or the study of form,
ood ideas on this "'ib-
e works of Dr. Marx,
e only waj' to learn to
luius will make up for