Presented to the
LIBRARY of the UNIVERSITY OF TORONTO from the
ARTHUR PLETTNER ISAMcILWRATTH
COLLECTION
SCHMIDTS EMOTIONAL SERIES
KEYBOARD TRAINING IN
HARMONY 725 Exercises Graded and Designed to Lead from the Easiest First Year Key-Board Harmony Up to the Difficult Sight-
Playing Tests Set for Advanced Students.
By
ARTHUR
E.
HEACOX
Professor of Theory, Oberlin Conservatory of Music. " in Harmony," Ear Training," "Choral Studies."
Author of "Lessons
PART
PART
I.
II.
Price, eaehi $1.125 net
The
ARTHUR
P.
SCHMIDT
Co.
NEW YORK
BOSTON
8 West 40th
120 Boylston St. Copyright 1917, by
Tk Artkmr P. Sc*m
ImrrmatiomJ Copyright
uatnd
Co.
St.
Preface The object of
book
furnish a graded series of exercises for practice in harmonizing melodies and figured basses at the key-board, so arranged that the pupil is led gradually from the easiest first-year work up to the difficult sight playing tests set for advanced students. this
is to
The material was prepared and arranged in the course of several years of harmony teaching, where pupils are required to "realize" each problem at the key-board, and pass annual sight-playing examinations before a committee of Theory teachers. Through this training alone, many students have been enabled to pass the harmony sight-playing tests required for membership in the American Guild of Organists.
The arrangement
handy manual for systematic daily practice at the key-board (preferably in short periods). The subjects are taken up in the usual order, and the key-board work may parallel any standard work in harmony. The figuring, in the figured bass, is that familiar to most American and European musicians. In order to include some representative French examinations, a short chapter of the material is that of a
devoted to the peculiarities of the French system. The sources of the exercises are various. The greater part of the first 680 were written expressly for this book. Those from examination papers are so indicated. Nearly is
one hundred (from 642 on) are typical examination questions from the sight-playing tests and paper work of many of the finest music schools and universities in both America and Europe, together with an important list of the problems set by the American Guild of Organists, covering the years 'O7 to '16. The Author's request for these materials, with permission to print them, was met with a most generous response, and he wishes here to express the keenest appreciation of the beautiful examples and the courtesy which accords their use.
Full credit is indicated with each exercise. Especial mention should be
of the cooperation of Mr. Warren R. Hedden of the American Guild of Organists, of Mr. Frank E. Ward's, contribution to the subject of "Sevenths", and of M.Vincent D'Indy's
made
beautiful
MS
Oberlin, Ohio,
given in facsimile at the end of the book. 1917.
Figured-bass
is
the whole foundation
of the music^and
is
flayed
with both hands in such a manner that the left hand plays the notes written down, while the right adds in consonances or dissonances the ,
result being an agreeable harmony to the glory of God and justifia/ble gratification of the senses; for the sole end and aim of generalbass, like that ff all music, should be nothing else than God's glory and pleasant recreations. Where this object is not kept in view there can be no true music, but an infernal scraping and bawling.
Johann Sebastian Bach.
Table of Contents (N.B.
The numbers
refer in every instance to the paragraphs)
PART Chap.
I.
I
Page 4
Triads
triads in Fundamental Position, to harmonize a bass, I. To harmonize a soprano, 2- The soprano Change of chord, 4, Bass repeats, 6- Rule for no common tone, _ Cadences,?. Rule for common tone, 8- Harmonizing first six tones of scale, 9- Tendency of scale steps, 10. Review primary triads, it- First inversion, 12- Successive Chords of the Sixth, 18- Second inversion, 14- Secondary triads in major, 15- Thirds of sec. triads, doubling, 10- Rule for n-V, 17- Rule for n-l|, 18- Secondary triads in minor, 19. Augmented in-
The Primary leaps, 8-
Inversions of secondary triads, 21- Triad on Leading Tone, 22- Permitterval, Special rules for minor key, 20ted Consecutive Fifths,28- Three successive chords of the sixth, 24- Doubled third in successive chords of the sixth, 26- Similar motion of all the voices, 26- The Sequence, 27- Sequence design, 28, 29, Sequence in mior,
80-
Phrygian cadence, 31.
The figuring
(5
),
32-
General review, 33-
II. Chords of the Seventh Page 36 Chords of seventh formed, 34- Dominant Seventh, 35. Triad (vu) not independent, 38. Introduction of Dom. The Dom. th, 417th, 37. Resolution of Dom. 7th, 38- Inversion of Dom. 7th, 39. Licenses in resolution, 40Table of all the primary dissonant chords 42- Use of Dom. 9th, 43- Leading-Tone seventh, 44- Diminished seventh, 45- Secondary sevenths, 46. Cadencing progression, 47- Double function of Leading-Tone seventh, 48Cadencing sevenths in fundamental position, 49- Significance of the Cad. res., 50- Tendency of IV, 51- Other resolution*, 62- Introduction of sevenths, 63. Resolution, 5V Supertonic seventh, 55Supertonic ninth, 5658of Various resolutions, of the secondary sevenths, 67- Freer use the sevenths, Mastery of conservative
Chap.
usage, 69-
PARTII Chap.
III.
Page 3
Alterations
Alteration presented, 60- Rules for, 61- Application and exceptions, cross-relation, 2- Special alterations in major, 63Dim. 7ths by alteration, 64- Augmented Sixth, 5_ Aug. sixth chords in harmonizing a melody,66Progressions compared, 67- Augmented sixth chords "not of the key", 68- No limit to resolution, 69-
Modulation
Page 12 a for and 71means of 70Half Modulation by choral, 72harmonizing Suggestions triads, deceptive cadence, The tendency chords of a key, 78- Modulation through the Dom. 7th, 74- Removes in the key-circle, 75- Mod. Passing by the Dom. 7th to next-related keys,7. Modulatory inflection, 77- Reaching a new tonic, 78-
Chap.
IV.
from key to key, deceptive resolutions of the Dom 7th, 79,80- Modulation by the Dim. 7th, 81- Modulation by the Aug. six-five chord, 82- Sequences, and use of any form of the Aug. sixth chords, 83- Modulation by the Din. 7th on the raised fourth degree, 84. Sequences by way of the dim. 7th on raised fourth, 85- Modulation by the Neapolitan chord, 86- Special intervals, enharmonic notation, pivot chords, (Ex.65).
Chap. V. Non-harmonic Tones The Suspension, 87- The Preparation, 88. The Suspension embellishments, 91-
Appoggiatura,92-
Page 28
itself, 89- The Resolution, 90- Passing-tone and 93Anticipation, Comparing the unornamented harmony, 94-
Chap. VI. The French System of Figured oass Examinations by eminent Frenchmen, 95-
Chap.VII.
Significance of special figures and signs, 96-
Examination Papers from Various Sources
(In this list the
A
Page 41
numbers refer
Page 44
to the exercises, not to pages)
bass from Bach's "Thorough Bass" made "for his scholars1 841. Eight different basses on one choral, Kitte] (Bach's last pupil), 64S American Guild of Organists, sight-playing examinations from 1907 to 1816, fig.
644-677.
',
Knox Conservatory of Music, 678-79- Cornell Conservatory of Music, 680-81. Oberlin Conservatory
of Music, 682-841. Harvard University, 687-90. Columbia University, 681-98. New England Conservatory of Music, 694-90. Royal Conservatory of Music, Moscow, Russia, 697 -99. Trinity College of Music, London, 700703- Royal College of Music, London, 704-14- Oxford University, 715-16Cambridge University, 717-18Paris, The National Conservatory of Music, Chapuis,719-tt. Lavignac,7tt. Gabriel Faure, 7-Guilmant,724Vincent D'lndy, (Tbfc Schola Cantorum), 725-t7, Facsimile of M. D'lndyt solution of No.7t6, Page 62.
in Harmony Keyboard Training PARTI ARTHUR E.HEACOX
Chap. I. Triads Primary Triads in Fundamental Position 1.
To harmonize
these basses (at the key-board) observe the following rules: (a) The bass must be the root of I, IV, orV. (b) The common tone is always kept, the other voices progressing to the nearest chord-tones. bass note. (c) The soprano will begin on the root, third, or fifth, according to the figure over the first (d) The alto and tenor, with the soprano, will form a complete triad in close position. (In review,
solutions in open position are recommended.)
Ex.1
C 1.
5
I
IV
I
V
I
F
I
V
I
IV
I
e
i
I
iv
8
16.
18.
17.
J J
|
J0J
|
ii
r
s
p
V 3.
If the
soprano leaps from one note to another of
trie
same chord, the
inner parts
may
follow
above a stationary bass as in Ex.2. Here the upper 'three parts must always present the complete triad. This kind of movement adds much to the very limited resources. it
the
the
4. The change from one chord to another is most- frequent at the bar. In chord repetition above same bass note, the first appearance of the chord should be on an accent if possible^ except at first accent of a phrase which brains on a weak beat (Ex.2).
Transpose the model to other keys, and then harmonize the following sopranos
Model
Ex.2
(a)
19.
A.
f*
of a chord-skip melody with chord repetition
F
IF
6
5. This
When
is
the converse of
The leap
to 24.
a given bass repeats a nole the chord will, remain the ty
3,
and
is illustrated in
Ex.2,
if
same but change
its position.
the bass be considered the given part.
of an octave is equivalent to a repeated note, Ex.2, (a).
Harmonize the following basses taking advantage of repeated bass notes make the soprano more interesting
7.
A
closing Formula, or Cadence,
is
formed by arranging the primary triads as
Cadences are Perfect or Imperfect according to the last two chords are V-I, and Plagal when IV-I.
The progression V-I
is
note
in
the soprano; Authentic
in
Ex.4.
when
the
the typical so-called Cadencing Resolution or Progression.
Play the following Cadences Perfect
Ex.4
last
f\
in every key, then Imperfect
^>
harmonize the basses Imperf-rt
A
Perfect
.
,
__
P
V
ffj
43
-o-5-
PHI 44.
fe
t
8 a
r r
^
}
gj
8.
\
adherence to the rule of keeping a common tonefll) has been justified cause of the importance of establishing, in both mind and fingers, the habit of observing this prin-
8. Thus far
ciple.
It
strict
will, however,
now expanded
conduce to greater flexibility
in
Jhe movement of the voices
if
the rule
is
to read as follows-
RULE FOR THK COMMON TONE
A
tone
common
to
two successive chords
usually kept in the same voice, but
is
if
not kept, the
upper three voices progress In contrary motion to the bass, to the nearest chord-toneh. 9. The
first six
tones of the diatonic scale
may new be harmonized with
1, IV,
and
V, in fun-
damental position as before, in both major and minor, asr ending or descending (Ex.5). The unme'lodic character of the bass, occasioned by leaping from root to root, may be excused until inversion is
introduced.
Transpose
to other
keys
Ex.5
10. Not rule in
f
positions of the chords arc equally good for the contrary motion allowed under the
For example, the strong tendency of the Leading-tone
8.
key-note,
all
in
the progression V-I, prohibits Ex. 6
(a).
In like
ward tendency of the Subdominant (four in the scale) in below if it is to ascend. Flay and compare (b), (c), (d). (a)
7*r
Ex.6
si
(b)
(c)
in
the soprano to progress to the
manner, but to a less degree, the down-
the soprano,
makes
it
(d)
best to reach
it
from
10 55.
g 56.
A.
Mr
[rir~r
i
11
73. I
V
I
IV
I
V
I
V
I-
Primary Triads in their .
The vocabulary
is
now
I,
I 6 , IV,
essentially all the typical progressions:
Ex.8
Ex.9
86. *>:ft
First Inversion.- Chords of the Sixth IV,
V,
and
V 6 The -
following examples contain
91.
3
6
r
vin
92.
94.
*}
93.
|
r
i
r
u
if
*
..6
if
14
13.
In successive chords of the sixth in close position,with a stepwise bass, it is correct to in one of the chords to avoid consecutive fifths and octaves. Certain positions
double the third
permit doubling the root and fifth alternately, but for this some experience is necessary. In genearal, have the roots progress in parallel sixths with the bass, and if in doubt double the third in one of the chords, but never the third of V 6 , which is the Leading- tone. For exceptions, 27,28.
A
B (
+
.
<-
(b)
i
Ex.10
i 6
(a) (b)
(c) (d)
The The
6
third doubled in
6
IV,
6
(5
Ve in V 6
the root in
6
.
doubled in IV.e, the root, Consecutive fifths, and octaves corrected at (a). The fifth doubled in IV, Leading-tone doubled fifth
m
.
in
V
(poor).
tendency to the Tonic, consecutive octaves with the bass would result; furthermore, the leap downward in the soprano, when its strong tendency upward is so evident, produces a disappointing effect. Test at the Piano.
if
Leading-tone in the soprano followed
(e)
If the
(f)
Successive chords of the sixth without a stepwise bass, no need of a doubled third.
its
(g) All the voices progressing in similar motion while the chord remains the same, permissible consecutives are avoided.
Transpose Ex.10 (A) to other major keys, then harmonize the following figured basses and sopranos along; the same lines 104.
366
105.
6
-Jt
ft
106.
5
6
yy
J
f
~f*
'
6
6
6
10
Primary Triads in
their
Second Inversion.- The Six-four Chord
k The most important Six-four Chord is the Tonic Six-four in the authentic cadence. It must be on an accented part of the measure, or the accented fraction of a beat, and the V which
must be relatively unaccented. The bass-note of the six-four must be doubled, i.e. the So strong is this formula that any six-four chord on an accent tends' to declare itself a tonic chord and promise a closing cadence which, if admitted at an unsuitable place in the phrase, gives it a weak and halting character. Since this accented tonic six-four chord resolves so emphatically to the V (and in fact is a V with its third and fifth delayed), it should be preceded by some form of the subdominant or
follows
it
fifth of the chord.
tonic harmony, for if preceded by V, virtual chord repetition a poor progression, par. 4.
From
the above,
it
is
from weak
to strong
beats results-
evident that the introduction of a six-four chord demands more than
may spoil the phrase which contains it. In Ex.12, the six-four chord is shown on unaccented beats, introduced in special ways. Under these restrictions the six-four
ordinary care, or
chord
it
largely shorn of its power to promise a full close, and in this subordinate relation becomes a medium through which the voices pass, rather than an independent harmony. is
Closing Formulas,- The Authentic Cadence with
m (a)
Ex.11
I!i
on an accent. (f)
ff>
HE l
A I
An eight-measure sentence
Ex.12
or Period
*
3
11
8
a i
7dT First I
By cadence, _ (a)
(b)
(0
4-meas. phrase.
Partial Close [[Second 4-meas. phrase
far the most important six-four chord
is
the Ij on an accent,
in
Full Close
the authentic
a full or complete close.
The close
is
partial
when
the phrase ends with a
V
preceded by an accented
I|.
Test these phrases at the piano. (c)
Secondary value_the
root prepared, the bass progressing stepwise in one
direction, seldom or never accented.
till
(d)
The bass
the second of three repeated notes. (Weak)
(e)
The bass
the second of three notes belonging to the
same chord.
(Little value
the bass is treated somewhat contrapuntally.
(f) The figures (J,) or (\^) over one bass note, require first a six-four chord, then a chord in fundamental position _ usually the progression IJ-V.
Transpose Exs. 11 and 12 to other keys, studying them thoroughly through the medium of both eye and ear; then harmonize the following exercises with vocabulary: MtfciUM*
I,
I8 ,
1,
IV,
IV, IV,
V,
Ve
,
VJ.
16
6
112.
S
4
4_
6
113.
4
3
TTT
114.
8,
5
fi
6
^ 116L
TT
^
..
E.
4
8
3 117.
Oi
IT'
^ 6
8, /rJ
g
4
17
126.
n?
Yl
IV
is !
)
<
u
IS
.1
TT. 127.
I"
128.
IS
'*
Vt
UnfitTUrcd *
129
Seek
to use suitable inversions in the following
'
130.
j
r
r
ir
131.
P
r r ir
132.
J
M
J
-
r r
Use a % correctly at each+, otht-rwisp treat as N.B. In meas.K thesis on the second brat.
Secondary Triads in Fundamental Position 15. The triads on (a)
(b)
A
Ex.13
The
Roots ascending
As independent
/ (c)
n substitute for
PPP (IV)
IV:
leaps of a third
weak.
chords.
m m mm
m
nV nV
in thirds are
the vi for lithe in for i.
(IV)
Major keys
vi, are subordinate chords used in the following three ways:
As substitutes for the primary triads (u for IV etc.). As connecting chords, preferably with the bass descending by
to successive^rpots.
(a)
u, in,
and
in
(b) ^
Strong
(P)
(I)
ImlV
Vvi
*=$
T in
VI
II!
(C)
m in
vi
(IV)
II
m
m
i
18
16 The
thirds of the secondary triads are the principal tones of the key and may be doubled rather freely for the sake of a better melodic outline. The upward tendency of the leading tone and the downward tendency of the fourth and sixth degrees of the scale, especially when in the soprano,
must more or
less determine the
chojd
to
be used and the tone to be doubled.
the introduction of the secondary triads and the resulting increase in the number of possible progressions ranging in value from good, to fair, or poor; the student must depend largely on
With
the study of models compared and tested by ear at the keyboard. Here dependence on rules, or eye memory, will not at all suffice.
i
(e)
Ex.14
^-^
(f>
(g)
,
(h)
(i>
(j)
Bad.
In Ex.14, study the various progressions (a)(b)
motion
The n an
an ascending
to
from u to V.
excellent substitute for IV, and with the same treatment,
GENERAL RULE FuR common
Give up the
apply
i.e.,
contrary
tftiss.
n^
tone and lead the upper three voices contrary to an ascending bass. (Does not
in inversions) (c)
Improved
The common tone
kept. Possible here for the
sake of the melody. Not recommended.
at, (d).
(e)
Bad on account
of the objectionable Covered Octaves.
These
especially bad because the soprano tone (F) has a downward tendenrv ($
compelled
in the outer ie)
and
is,
voices are
nevertheless,
to ascend.
(f) Good. The inversion of V and the ultimate downward resolution of the (F) in the soprano are excellent. Here the commpn tone is best kept. (g) (h) Freer treatment of the voices, but good. (i)(j) The n after V. Use seldom. If used these are among the few fair progressions.
Ex.15
ii
18.
In Ex.15, study the various progressions from u to I|. (a) (b) An excellent substitute for IV-If in the closing cadence. (c)
Impossible on account of the consecutive
fifths.
GENERAL RULE FOR Lead the upper three voices contrary
(Compare with Ex. ll)
n-l|
to^an ascending bass, and avoid having the fifths of the
chords above the roots. (d)
The common tone
is
given up between IV- H, in order to keep the rule for n-I|,
immediately following. (e)
VI as a substitute for
I
(Tonic function). This is the best position of VI. Its third, is called a deceptive cadence because the I is ex-
the key-note (root of I), is best doubled. This pected instead of the VI. (f)
Complete descending scale
in major,
harmonized by the use of in-FV beneath
seventh and sixth degrees.
Transpose
(f)
to every
major key.
its
T9
Harmonize (he following exercises (The 11, m, and vi in major keys) 133.
8 4
134.
III
135.
146. vi
* r r 148. AL.
IV
V * J
I
II
r
IV
6
IV
V
147. I
II
f
-O-
ir vi
II
In
s
Secondary Triads in Fundamental Position in Minor keys 19. The subordinate in major, but
triads in minor (n*,
with far less freedom.
The
u^>
VI) are used in the same three
III',
and
III'
ways as those sometimes apthe Harmonic mi-
are both dissonant chords,
proached, or left, with difficulty on account of the augmented interval (fi-7) in nor scale. The most used progressions are shown in the following example which should be stu-
died and transposed to other keys. (b)
-tv
&
t
ii AUK.
Ex.16
2.
& n (a)
(b) (c)
V
m'vr
VI
as
F
-*-*-
V
V
nVI Special rules violated.
The VI as a connecting chord. The ii" a* a substitute for the subdominant. (Far oftc-ner used in its first inversion, $2l). The III' as a simple triad, best resolved to the VI (the cadencing resolution).
20. In Mrirt writing no voice may progress an augmentod interval, and while this restriction quite properly disregarded under certain circumstances, as for example, in chord repetition, the student should rigidly adhere to the following-. is
TWO SPECIAL RULES FOR THE MINOR KEY Ffule
r.
In the progression ir-V, give
up
the
common
tone and lead the upper three voices in
contrary motion to an -ascend ing bass, Ex. ill (b). Rule 2: In the progression, V-VI or VI-V, double the third voices
move contrary
VI and do not omit the
fifth.
Two
to the bass (d).
The n, HT and VI 156.
iri
minor keys
in
_J
\
8
^
158.
v
*
s.
r
ir
r
159.
^ ^
*
irrir"
ir
160.
r
irriNi"
161. ,
>:
V^ii
ylliU
8
11838*
T* I
^
^r
163..
APS
P
P .g
f i
iJ
r
;:
^P
^
,
'
fe^Jg
r
ir
--
r
%
i
1
r
r
iJ
H
Bad.
Bad.
r
j
i
164.
170.
m. 8 |jjr
fa
24
The Triad on the Leading Tone .
The Triad on
the Leading-Tone is a dissonant, or
inant Seventh Chord from which
it
is
derived
(fl-36)
it
tendency, chord and
like the
Dom-
resolves regularly to the Tonic, rarely
to the VI.
GENERAL RULE FOR THE LEADING TONE TRIAD Use the Leading Tone Triad all parts siepwise to a
complete
in the first
I
or
I6
The
inversion only, double the third, or fifth, fifth progresses
up
or
down.
and resolve
The consecutive
fifths
which result from the proper treatment of this chord are unobjectionable, one of them being diminished and not appearing with the bass (outer part). Sometimes the third, and more rarely the
may be left by a leap. All the progressions in Ex. 18 are equally good in both major and niinor, except that the deceptive resolution is best restricted to major only.
fifth,
(c)
Ex.18
(d)
(e)
(h)
m
(i)
25
Advanced Exercises in Triads 180.
5,
6
6
*
U- H
lisas-
,
6
26
V
vn-
T
r r r
P r
^ 199.
n
2
2' Unfigured
V
vn
IV 6
V6
^
^
^
2
vn6
p
n<5
je
iPP f
m
201.
I-
^^
P
3t
TT~
^
-
i
202. LiHtf,
Pa
4,
(b
=z p
p
r=
F
J
I
J
J
I
p
r
IP
rJ
203.
The Sequence The Sequence
is
a succession of similar harmonies resulting from a symmetrical pro-
gression of the given part. The initial design, or pattern, is usually repeated twice,or more, in an ascending or descending series, and usual rules for chord progressions, doubling, etc., are in order to obtain the required symmetry. Practice in both writing and playing sequences is strongly urged as one of the practical ways of gaining freedom at the keyboard, and familiarity with the vocabulary of chords, and chord progressions, in all the
frequently disregarded
keys.
Cadence I
7
(a)
I
Design
Ex.21
Transpose
to every
major key
'
a cadence
204
A* ft.
uaaH
*
''"^ e " end
^ ^^
throu
^
-ever.l bars and add
28
209,
3
m
29
Phrygian Cadences. Transpose(b)
.(a)
(d)
fTT
o Ex.23
if* 51,
2 212.
3
213.
I
214.
rfr
I
3
ao
220,
rv
221.
^ .
bass note.
A
triad in fundamental position
The figuring
--
3H
is 5
may precede
or follow a chord of the sixth on the
6 or 6 5 according to the ord'erof the two chords.
The
same
intervals,
6 and 5, must not be doubled and should appear in succession in one voice, usually, but not ne-
In most cases one of the two intervals (the 5 or 6) is a passing tone and usually both taken and left stepwise (Ex.24,).
cessarily, the soprano.
as such
I7k7h
is
n
31
General Review in the use of Triads 33. suaded
Mr. Walter R. Spalding in his treatise on Counterpoint says, "So let the stud ant be per. sound and facile technique in the treatment of triads. Nothing will give him
to acquire a
such a good foundation for future development when he comes to free chromatic writing." In the following review exercises the problems are grouped under four general headings, according to their character* and the grade of advancement expected. Thus the first set of sopranos can be
used as review before any inversions are reachedi-while the last list, selected from examination papers, demands a comprehensive grasp of all that has been presented in the foregoing pages.
Basses- easy
moderately difficult
to
^^
228.
230.
229.
231-
m
36
J r r
;
ii
iv
^
{
j
233
.
J
j
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if
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8 4
6
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I
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224.
^
u
if 3
J
6
i
^
i
s
237.
B 4
B 4
B
11
238.
5 6
2
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J J
J
666
239. Ll
240.
{.
241.
f
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6
e
ii 8
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6
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32
243.
r A
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245. ...
iJ
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[A
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o. 8
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249.
65
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8
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Ifg 6
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Tr 6
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E 250.
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[*
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6
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i I
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*
li
r
Sopranos- vrwjabulary,
all the triads (except vn,)
251.
i
r
->-
in fundamental position only 252.
-e-
RS33:
253.
Q
1
i
r^
fr
-<0
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J
^
254.
ft*
J r
255.
J
r
r
<
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rJ
256.
? 8.
11338 J
n
33 857.
258.
J
J
J
|J
|
259.
rrr Sopranos- All the triads and their inversions, including
vii-
'
r
J
|J
I
..
262.
261.
r
Ji r rr
J
i
r
r
263. -e-
J 264.
r 265.
VJJlrJJJI 266.
r 267.
I*
i.j
IV
Sequence ^i-v^uriiuc
ir
ir
288.^
r^
J
fe
.ii
\\
J r
.
r'
r i
'r
ii
1
i
ijjjjij
269. i
.
9m
I
I
J M'
IU
l^
>
|rJ
J
[J
f
f
'r
1
1
1
34 270.
-jfr
Old French Noel.
280.
"
t
*
?
I
r
rr
5
r r
282.
m
6
283.
Unfigured
I l
!_
v4 y?
IV*
IH
n
I''
J
P
r
r-rr At the
4-
use" chords, otherwise
,
These
6'8
mean
ti
r^ i
B
first inversion, root in
Supply alto and tenor
2HH.
(5
this is
t
I
an unfigurcd problem.
i
soprano. (Not usual marking)
6
u
I
6
36
Chap. II. Chords of the Seventh 34r.
A
added third
Chord of the Seventh
is
formed by adding another (upper) third
to
any triad.
This
a seventh above the root and, since the interval of the seventh is a dissonance, <5r tendency chords, requiring resolution; that is-
is
chords of the seventh are dissonant
all
they must progress (sooner or
later) to
consonant chords, chords of repose. The chord of most
complete repose is the final tonic triad and toward this, as an ultimate goal, all the dissonant elements of a musical phrase tend to progress. The charm of many a passage depends chiefly upon an artistic treatment of these dissonant elements as they emerge from and disappear in
The dissonant chord which most conclusively
the stream of the music.
resolves to the tonic, is
the Dominant Seventh.
The Chord
Dominant Seventh
of the
(Primary Dissonant Chords)
35. The Chord
of the Dominant Seventh consists of the
next (upper) third, a minor seventh from the root. Ex. 20 (a) jor and minor yet different from all other seventh chords.
Dominant triad
(b).
This chord
is
to
which
is
the same
added the
in both
ma-
always the leading tone, a major third, its fifth is perfect, and its seventh, minor. Containing as it does the most important tones of the scale except the tonic it may be said to hold a strategic position in the key as
Primary Chord of the Seventh. as seventh, while
its
flanked by the dominant as root, by the subdominant third, the leading tone, unmistakably defines the key by its tendency
toward the keynote, Ex.2(>
36. The may be
as
Its third is
triad VII
is
seen at Ex.26
It is
(c)
not an independent chord but an in incomplete dominant seventh chord (d).
See also
par. 22.
Tonic
(d) VII
Introduction of the Dominant Seventh 37. the
V
7
In general dissonances require careful introduction as well as resolution.
however enters with almost the freedom of a consonance.
ceding chord >(a)
it
is
usually kept as a (b)
common
(d)
(c) |
When
the seventh
tone and then said to be introduced by
|
(e) |
(f; ,
The seventh of is in
the pre-
preparation.
37
Resolution of the Dominant Seventh
38
The regular.resolution of the V? it> to I. the seventh descending a degree; the third ascending to the tonic, or leaping downward a third if in an inner voice with the bass ascending; the root le; .Jng upward or downward to the root of. the tonicj and the fifth usually descending a degree, but sometimes ascending for special melodi( reasons. solve to
vi
(deceptive).
the seventh
Among
may be found
The following examples mental position as
the
many
the
stationary (delayed resolution or none
at all)
are representative and, except (h), equally
at (b), fifth
is
complete
or
good
it
ff*
in
n
-*-
Ex.29
common tone -
-.
/
ff
(h
Foor
)po98ib]o,maj.only
m
BFSF
-*>^
H 7
O
-firri r
re-
In funda-
minor.
il
*
may
I.
(f)
ZEE
it
may even ascend.
omitted and root doubled, the upper root becomes a
(c)
*
V
irregular, or less usual resolutions, shown later (Kx.3i)
very good since this provides a complete triad on the
Ex.28
If
Distinguish carefully the interpretations of * and 87.
m
n
38
295.
3 n
G
I fr
39 Inversions of the Dominant Seventh
39. There
are three inversions of the
V7
,
all
of which are useful.
Regular resolution
to the
tonic triad is by far the most usual. In this resolution the voices usually progress as when in the fundamental position except the root itself which is generally retained as a common tone. Complete figuring is seldom used unless needed to indicate certain intervals altered, as the raised
seven
in the
minor scale. Unless the seventh
is in
the bass
two figures are indispensable, those
dicating the root and seventh.
>(a)
(c)
(d)
(e) ,
in-
40
662
4
308.
6
3
6
6
e
8
4
7
-O-
309.
4v ft
8532
6
6
487
6
_
6
7 6.
41
321.
M
s
322.
m P
323.
c/ |rj
r 324.
A.
IT
J
^
J
U
^ '^
r
ir
J c/ i^ LT
j if
'^
42
Exercises containing some irregular resolutions of the Dominant Seventh Chord 326. *V.|
7
8
6 4_
43 334.
44 In the dominant ninth and its resolution to the tonic triad
struction and resolution of all the
is
Primary Dissonant Chords.
found the basis of conIn other
words the
pri-
mary dissonant chords, in both content and tendency, show themselves to be more or less com3 7 plete foi'ms of the V (orV ). That an incomplete form whose apparent root is the leading tone, does not take a cadencing resolution (ty 44)' is additional proof that the always the dominant, is omitted. Before going further it will be well to examine a table of the primary dissonant chords. as for example the
real root,
which
VH,
is
Table of the Family of Primary Dissonant Chords The root of all these chords, whether present or not, solve regularly to their tonic triad.
dominant and
they all re-
In minor
In major Leading tone
is the
triad
V***
)
fl8
(?
qtim*
Leading tone triad
im seven th chord
Leading tone seventh chord
-
Dom. major ninth
__ A3.*
(Never used in minor)
(Frequently borrowed for use in major)
1
Dom. minor ninth (Sometimes appears in major by chromatic inflection)
Dom. seventh
Dom. seventh
V7
I
Introduction and Resolution of the Dominant Ninth (b)
(a)
.
(c)
(e)
(d)
i Ex.
(f
Bad
positions
9th
V9 rt
f
36
rs
V (f
9
P
me
n 9th
On
the use of the Dominant Ninth Chord
the ninth, like the seventh, being a primary dissonance, requires no presmoothness of entry, especially in minor. paration, but preparation of either ninth or root conduces to be approached in contrary motion. should nor root is When neither ninth (d) prepared they
43.
In Ex. 3
(a) (b) (c)
This excludes contraction to a second and also makes the ninth below the root impossible. (The ninth below the root can be found in modern works). the root in < (f) (g) In four-part writing, only two inversions are possible. Exactly as with (e)
Keep
the ninth a full ninth above the root
V
an inversion is best kept as a common tone, the other voices following their tendency. (h) Conservative treatment places the ninth in the highest voice. At (*) the ninth is
in the
tenor
clearly a passing tone.
important to study these figurings (b) (i) is likely to be confronted with similar problems. When (j)(k) for in higher examinations the student the figures are given in full as here, it is a suggestion of the required interval for each voice respectively. Not a good practice but sometimes unavoidable. (i)
Here
the ninth in the alto is a suspension.
It is
Interchange of chord members. 7 There is usually ultimate resolution but this is not necessary. (k) Passive resolution as with V must be in the octave a (1) Giv-n to illustrate necessary procedure with this figuring. The 7 above th'e e-, otherwise a second will appear between the root and ninth. Compare with (P). Note in addition to these points the apparent resolution to 1$ and to the III" in (-|). These are (j)
.
They
scarcely more than accidental chord formationsorcasioned by the flowing parts. ively between two forms of the dominant harmony. '
(It
The descending
(MA
Ex.37
Models to be transposed to other keys is important to study closely every full figuring)
scale usinff vr
(,) ..
U
.
'
*
lie
pass*_
46 Exercises containing the Dominant Ninth Chord 4
337.
47
The Chord
of the Seventh on the Leading-Tone in
Major
(Also called the Leading- Tone Seventh).
44.
The Chord
Seventh on the Leading Tone
of the
chord with root omitted.
The omission
acter of the remaining chord
In
Major
is
a dominant major ninth
of the generator (the dominant) does not affect the char-
members which
are introduced and resolved essentially as in
V.
Like the complete major ninth, this chord can not resolve to a minor tonic. For simplicity this chord is figured as a chord of the seventh, and as such should be complete. The best positions keep the seventh (original ninth) in the soprano, or at least above the leading tone.
The
third inversion
is
rarely used since the original ninth
is
too harsh in the bass,
except where
skillfully handled. Arensky in his "1000 Exercises" and Tschaikovsky in his For a typical example "Harmony" use this third inversion, always resolving it to a lH chord. see Ex. 38 (e) below.
The typical resolution of the root position is to a tonic triad with double third- The consecutive fifths which result in this resolution when the third of the tonic is not doubled are objectionable and must be avoided, except as
at
() where
the fifths in the inner voices
come
under f 23. In 38
(-X-X-)
the vn
}
is
such
to the
eye only.
passing tones and therefore the bass (root of IV>
It
is
may be explained free to leap, or
downward to the root of the tonic. The resolution to some inversion of the Vi and the passive
if
that the
b and d are
preferred that the bass
in
vir| leaps a fourth
of the regular
V
progressions.
Study the progressions them to other keys. The seventh
Ex.38
resolution are natural derivatives
in
Ex. Ss u\ ear as well as eye.
Learn the best ones and transpose
(original ninth) in soprano: these positions are best.
48 Exercises containing the Leading Tone Seventh 351.
-vi
49
The Diminished Seventh Chord 45. The Chord.
chord of the seventh on the leading-tone
Like the dominant minor ninth chord from which
the tonic minor triad. (By alteration
Dim. 7th-chord
thtt
in
minor
it
is
i*
is
called th- Diminished Seventh
derivcd,its regular re>olution
often used
in
major*.
is
to
Composed as
it
is
of three minor thirds, this chord presents no perfect interval in any position or inversion.
It
is
used with great freedom
in
fundamental position, and
can be spelled piano (enharmonic notation) see also f 64.
of
its
peculiar construction,
in
it
in all
three of
inversions.
its
To be sure
Because
same on the
several ways, though sounding the
chord
of the correct notation of the
any given key, place the leading tone of the key at the bottom and spell three minor
for
Thus
in
succession above
is
b-d-f-a!>, not gS because f- gl
it.
for example, the diminished seventh chord of the key of c
thirds
minor
not a minor third.
is
Introduction and Resolution of the Diminished Seventh Chord (b)
*-
Ex.39
(c)
^ff ;;
ir
1
u
4>
*V Possible
Not
*V
(g)
*>
i>
ti
^^
(e)
(.1)
11
O
tt
--
TT
TT >
'
(m)
(J)
(n)
(o)
*s
>
<9
f
ffll-fcV
-*-
*>
o
Pass. rrs. to J
Passive res to 6
t 31: 4
^--
vnj.VJ
5
fl
Typical approach and resolution
(a)
(b)
(c)
Leap down,
(e)
(f) (%)
(j
)
(I)
Passive resolution,
(k),
a
B^B -
5
4
S
4
"
augmented
6 4
a
-e-
4th.
fifths-
resolution to the dominant seventh.
Intervals are permissible in chord -repetition.
in more than one way. The F major triad alternates with the dim. be called an F major triad as long as the F continues, enriched by the may use of passing-tones and embellishments. The main point for the student to grasp here is that figuring of this kind is not infrequent, and requires care to obtain a good melody.
(m)
7th.
May be analyzed
chord, or
it
Transpose Ex.40
Ex.40
I
!
ti
ris
-
to other
minor keys
IE
-4-
i
to the tonic.
not up, to the root, avoiding thus the
Various consecutive
Augmented
**
4
50
Exercises containing the Diminished Seventh Chord 364.
Supply
th'e
Alto and Tfenor
n
PPi 7
*
S
P^P 365.
56
7
6
-t
5
.S
ep5
6 4
6
-S-
4
6
f^W -5
-4-
B
3
/?
--
P
366.
3 P 6
5
3
^-tf-
-4-565
6
^
6
8
8 7
4 2
4
^p
7
^^JJIJnJ
6
(5
6 -w I_ (5
fl
i
JJI^^
367.
fj
o rr
i
^
,
j ji| j r
"~
'J
.
i
t
B
r
TJ
rr
^ 6
j
i3
^
'
,
|f
j
371. .
I
.
"I
'-'
Z.
J
ir^r
ir^iiJ-'ir
frirr 'rP
8 7
65
"6"
566,
6
5 3 3 2q
370.
J/
"[
6
(5
4,
4,
6 2t|4
-+ 3
6 4
-5
6
M tf,
51
The Secondary Seventh Chords (Secondary Dissonant Chords) are called SecAll chords of the seventh other than those on the decrees V and dissonant than for the most more Seventh Chords. primary sevenths these ondary Being part chords are generally introduced with greater care, the seventh, especially when major, requiring preparation or entry stepwise from above. While the modern tendency is toward an increasing freedom in the use of all dissonances the student should prepare and resolve every dissonance that needs it.
46.
When
tt
the student's technic in the handling of dissonant sevenths
established along con-
is
rule study the possibilities under a broad general like the one laid down by Frank E. Ward (Columbia University) as follows: "The seventh or the root must be prepared in every instance,although many of the preparations are by substi-
servative lines
it
him
will be well for
to
advanced work 1 am guided more by my own musical experience and a decided taste for the rich dissonances of modern music than by what is set down in text books." This is excellent doctrine for every earnest student. Let him prepare all secondary dissonances at first directly if possible, later by substitution where the effect is not too harsh and the passage gains by it, and still later judge every dissonance on its own merits and use it as
tution.
it
In
best serves a musical purpose.
The Cadencing Progression 47. The
step toward an understanding of all the seventh chords is to construct sebased on the cadencing resolution of the dominant seventh chord to its
first
of the sevenths
quences tonic.
Chords of the Seventh
of all
In such
sequences every seventh chord will be led
to the triad (or
seventh chord) situ-
ated a fifth lower (fourth higher) just as V 7 resolves to I. The seventh of seventh chord will be prepared and resolve stepwise downward.
Play Ex.41
rK
'
'
'
many other keys
(a),'b),(c), etc., in '
'
Nn
VT
II
(c)
In
minor
o o "o -o-
-o-
o o .1
LJ -*>-
-tHar. sc.
Ex.41 :EL:
*-
v7
-*-
rv7 viMipvi
IF
v
V7
I
7
7
I
8
B
f
!
IMIIV t>
V7
7
(K)
(f)
6
i
7 I
Har. sc.
*>
--
-*v 1
nCT
Orig. sc.
oo
" "**"**"" o
(e)
i
every secondary
4 3
4 .1
48. Double function of the Leading Tone Seventh, in a sequence of cadencing. seventh chords the vu , loses its character, as fncompletc V* progressing to the tonic, and resolves like the other seventh chords. See Ex. 41, N.B. 3
On account
49.
of the
sequence the IV 7
to vir is tolerated,
Cadencing chords of the seventh
In
though
in itself a
fundamental position omit the
poor progression.
fifth in alternate
chords.
The third of one chord prepares the seventh of the next. Ex. 41 (b) In minor keys the original form of the scale is used except where the leading tone is needed, as in the Cadence. See again f 31. Sequences using inversions ft) (ei 'flfg) also consist of the cadencing resolution, that in (aj(b) and (c). roots bear the same relationship
u
1I338*
is
the
52
The cadencing **'*
3
7,7
resolution of all Chords of the Seventh
77
'*>
3
3
7,
3,
7
53
Significance of the Cadeneing Resolution 50. Before examining other aspects of-the secondary seventh chords it will be profitable to read again $34 and study more closely the significance of the cadencing progression of chords. Mr. Benjamin Cutter in his "Harmonic Analysis" says: "The succession in, vi,u,V, with or without sevenths, and in whatever form, is one which confirms the ultimate tonic; it is one in which -the total impression is that of pushing on to the close in that final tonic harmony which rounds out the whole." Now the roots of these chords are the successive fifths reckoned upward from the keynote, and the chord farthest removed .tonally from its ultimate tonic is the one built on the most distant namely the in"). The cadencing resolution is therefore a progression downward toward the tonic by stages of fifths. Thus the resolution of V' 7) is direct. Between 11 '> and I is the V* 7> Between vi'3 and I are both the u (7) and V">; while iu'', farthest removed and least used, must touch three intervening chords on Its way (cadencing) to the ultimate tonic. This will be made deafer, perhaps, by the following table. fifth in the series,
.
Table of Secondary Seventh Chords in their Relation to the Ultimate Tonic Triad I "
Chart f\
Ex.
1
remove.
A*
'i^
remove.
1*J
remove
Ultimate Tonic.
54
The
Supertonic Seventh Chord
55. The most important secondary seventh is that on the supertonic. It is almost as valuable as the dominant seventh and is introduced with nearly the same freedom. The fundamental position may omit the fifth, the inversions should be complete. The finest form of this chord is the first inversion (Rameau's "Chord of the Added Sixth"). All inversions are possible, but the second inversion is rather
weak
Ex.43
in the
major
key.
The chord
is
treated the
same
in
both major and minor.
390.
V"L9
3
6
6
-3-
7
4,
7,
391.
1
6
6
5,
5
56
Various Resolutions of the Secondary Sevenths 57. The-general
principles regarding resolution of the seventh stated as follows (under three heads):
(ft
52)
may now be
concisely
A. The seventh resolves downward, one degree to the root, third, fifth, or (rarely) sevof the succeeding chord. This is the true (active) resolution of a genuine seventh, whether enth, prepared, passing, or taken by a leap.
remains Stationary
(passive resolution) becoming the root, third, or succeeding chord. This is frequently a rriere delay of the downward resolution; but
B. The seventh fifth of the
when the seventh has become passive, by becoming
a root, third, or fifth,
it
ceases to
demand
resolution. C.
The seventh IS led
Upward
one degree
it
the bass drops a third to the note of re-
solution (resolution by substitution), otherwise bad covered octaves would result, see Ex.32(g).
The major seventh may ascend whenever
it
functions as a retardation.
It is
not then
a true seventh, nor can its progression be called "resolution of a seventh", but lists of secondary sevenths usually include it.
fl
Ex.45
(a) va>
1' v* (a)
iu;
t.c;
\.c>
^
c*
^.
57
Various Resolutions of the Seventh 408.
87
87
409.
7'
j
IP
8 7
=z
77
87
410.
78
2
7 8
a,
*
7
*
4
i
,
P
ES^E^ IP ^
-*-
n
412.
6
*v
i
rr
->-
413.
y ^
87
414.
8
6
7,
..
w
if 7
I
If 415.
7
78
.;.
m^T P
rtFMJrUM 41G.
87
8 7
,
7
1
U'-O
F=]
I
1
I
R
_
_7
a
Jt
:>
_
7
*:
7
S
i
..
i
:
7
'
4
41IS.
H
5
? 8
f
7
_6.
-
^
"
7
/1*J1 ^ 41
-
8
3, J
,
4
85
419.
\
II
1,
/
/
f)
T
r ir r
766 fl
y 425.
>i
r
ft
B
R
r
"l
r
7
fl
-ft-
n
87
422.
5
75
5
a
'
"57
.
7 8
7
7,
7
1
7,
i..
rV 7,
-
5
87
44
76
i
7
.IX "
"5 i
**
fl
4 4
5
.1
X
7 B
44
5
a 2
Ji.
**
^
?
i
g
5
4 S
-*v
7
==P^
Mr
423.
8 7
4
7/
if
r if r 'r
4 4 3 2
7 S
s
B
*
7 8
u jin 424.
^
72
76
87
8 7
i]
78
^^s^
**=f
'I 6
i
I
,
420.
I
i
.-.,
v*
6
r
6,
7
M
J
ir i
n
58
426
Ravel.
Ex.47
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Playing Tests Set for Advanced Students,
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E.
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Table of Contents (N.
B.
The numbers
refer in every instance to the paragraphs)
PART Chap.
I,
I
Triads
Page 4
The Primary triads in Fundamental Position, to harmonize a bass, i- To harmonize a soprano,*- The soprano leaps, 3. Change of chord, 4, Bass repeats, 5- Rule for no common tone, 6- Cadences, 7_ Rale for common tone, 8- Harmonizing first six tones of scale, 9- Tendency of scale steps, io_ Review primary triads, 11- First inversion, 12- Successive Chords of the Sixth, 13- Second inversion, 14- Secondary triads in major, 16- Thirds of sec. triads, doubling, 16- Rule for n-V, 17- Rule for n-I|, 18- Secondary triads in minor, 18- Acgmented interval, Special rules for minor key, 20- Inversions of secondary triads, 21- Triad on Leading Tone,22- Permitfed Consecutive Fifths, 23- Three successive chords of the sixth, 24- Doubled third in successive chords of the 27sixth, 25- Similar motion of all the voices, 26- The Sequence in mi design, 28, 29, or,
30-
Phrygian cadence, 81_ The figuring
(5 e),
Sequence, Sequence General review, 83-
32-
Chap. n. Chords of the Seventh Page 36 Chords of seventh formed, 34. Dominant Seventh, 35- Triad (vu) not independent, 36- Introduction of Dom. The Dom. 9th, 417th, 37_ Resolution of Dom. 7th, 38- Inversion of Dom. 7th, 39- Licenses in resolution, 40Table of all the primary dissonant chords, 42- Use of Dom. 9th, 43- Leading-Tone seventh, 44- Diminished seventh, 45- Secondary sevenths, 46- Cadencing progression, 47- Double function of Leading-Tone seventh, 48Cadencing sevenths in. fundamental position, 49- Significance of the Cad. res., 50- Tendency of IV, 61- Other resolutions, 52- Introduction of sevenths, 53- Resolution, 64- Supertonic seventh, 55Supertonic ninth, 56Various resolutions, of the secondary sevenths, 67- Freer use of the sevenths, 58Mastery of conservative usage, 59-
Chap.
III.
PABTH Alterations
Paged
Alteration presented, 60- Rules for, 61- Application and exceptions, cross-relation, 62- Special alterations in major, 63- Dim. 7ths by alteration, 64- Augmented Sixth, 65- Aug. sixth chords in harmonizing a melody,66Progressions compared, 67- Augmented sixth chords "not of the key", 68- No limit to resolution, 69-
Modulation
Page 12 a Modulation by means of triads, 7O- Half and deceptive cadence, 71- Suggestions choral, 72harmonizing The tendency chords of a key,73- Modulation through the Dom. 7th, 74- Removes in the key-circle, 76- Mod. Passing by the Dom. 7th to next-related keys, 76- Modulatory inflection, 77- Reaching a new tonic, 78 from key to key, deceptive resolutions of the Dom. 7th, 79,80- Modulation by the Dim. 7th, 81- Modulation by the Aug. six- five chord, 82- Sequences, and use of any form of the Aug. sixth chords, 83- Modulation by the
Chap.
IV.
for
Dim. 7th on the raised fourth degree, 84_ Sequences byway of the dim. 7th on raised fourth, 85- Modulation by the Neapolitan chord, 86- Special intervals, enharmonic notation, pivot chords, (Ex.65).
Chap. V. Non -harmonic Tones The Suspension, 87- The Preparation, 88- The Suspension embellishments, 91-
Appoggiatura, 92-
Page 28
itself, 89- The Resolution, 90- Passing-tone and Anticipation, 93- Comparing the unornamented harmony, 94-
Chap.VI. The French System of Figured Bass Examinations by eminent Frenchmen, 95-
---
,
Page 41
.
Page 44
Significance of special figures and signs, 96-
Chap.VII. Examination Papers from Various Sources
numbers refer to the exercises, not pages) bass from Bachs Bass" made "for his fig. "Thorough scholars", 642- Eight different basses on one choral, Kittel (Bach's last pupil), 648- American Guild of Organists, sight-playing examinations from 19O7 to 1916, (in this list the
to
A
644-677. Knox Conservatory of Music, 678-79- Cornell Conservatory of Music, 680-81- Oberlin Conservatory of Music, 682-86-. Harvard University, 687-90. Columbia University, 691-93. New England Conservatory of Music, 694-96. Royal Conservatory of Music, Moscow, Russia, 697-99. Trinity College of Music, London, 7OO703- Royal College of Music, London, 704- 14- Oxford University, 715-16Cambridge University, 717-18Paris, The National Conservatory of Music, Chapuis, 719-21. Lavignac, 722. Gabriel Faure, 728-Gnflmant,7MVincent D'lndy, (The Schola Cantorum), 725-27, Facsimile of M. D'lndy's solution of No. 726, Page 62.
A.V*. 11888*
in Harmony Keyboard Training PART II
Chap.
ARTHUR
HEACOX
E.
in. Alterations
60. One or more tones of a chord may be chromatically altered without producing a modulation or essentially affecting its original relation to the key. The alteration may be introduced chromatically or diatonically, that Is the unaltered form of the chord may or may not precede the alteration. Furthermore all such alterations are essentially melodic and the tone combinations resulting therefrom should be considered ornamental variants of the original chord. In this sense only is it well to use the term "altered chord." Certain combinations containing the interval of the augmented sixth are as Neapolitan Sixth, usually termed Chords of the Augmented Sixth, another is popularly known terms are convenso on. These another the Diminished Seventh on the Raised Fourth degree, and but with the older on treatises development of modient and are used in practically all the harmony, broader lines the and ern harmony along chromatic and horizontal conception of the charresulting to chords seem to have less claim these acter of alteration in general independence than was formof view While this does not them. change point essentially change the treatment of erly accorded the altered notes
it
does simplify the subject of alteration
In playing alterations from a figured bass there are exceptions to them all. although
61.
it
is
in general.
best to observe the following general rules
Rules for Alterations The alteration is never doubled. The note which Is to be altered
t.
2.
in the 5.
is
not doubled unless one of these progresses stepwise
opposite direction. Raised notes continue to ascend, lowered notes, to descend.
alteration is made in one and the same voice. Chromatic alterations usually follow the chromatic scale* which always lowers the seventh degree and raises the fourth degree, while all others are raised in ascending and lowered In descending. (A good rule but frequently ignored.) 4.
The
6.
JdJ:
(b; -ft-
s
i
w
g =
te.
Ex.48
o
'
-*-
*
i:
CIV
I' (i)
xc
o
XE
-e-
-e-
N
V*
C(k)
(j)
(D
e
e jg
e
Poor
v:
Good
Bad
crotB- relation
J
62.
The
rules observed:- (a) Third lowered, introduction chromatic; (b) Fifth lowered, introduction diatonic; (c) The note that is to be altered, correctly doubled (rule X). Ex.48, A.
B. Legitimate exceptions to the rules:- (d) Altered ton.- doubled in (so called) Neapolitan Sixth -exception to rule 1; (e) (f) (g) rule t broken, but poor only as indicated; (h) Raited note does not continue upward (rule 3); (i) (j) Altered note not kept in the same voice (rule 4). C. Cross -relation (or false -relation). This not avoided by an intervening chord as at (1); but aside from such open contradictions, which are obviously offensive, very little attention is now paid to cross -relation, especially in modulatory or chromatic
passages.
* Thu
HMD
it
mot the only form of chromatic scale in use. 1917 by The Arthur P.
Hchll Oo.
Wrurrd
Exercises in Alterations (General) 8
435.
,
436.
,
S
3 31
8 7
6-
6
437.
6
5*-
6
2
1
,,5
E
6
-e-
6
440.
4 7
5
8
5sl
67 5
7
1
367
439.
9 7
438.
,
|
e-e-e
_
-eeb 39
6 3
441.
ii
e
442
4 7
E
ITU
443. '[/I.
C*^
<&
"
i
-o-
45.
-n~
o 6
p bp
i
i
/r
6
8 7
4 3
r<
5
-
4
2
^ Some Special Alteration 63.
in the
Major keys
m> and
vi, may appear by alteration as major triads, or as apparent most seventh dominant chords, taking frequently but not necessarily, the cadencing resolution (^50). (See also ft 77). The usual indication is n-, n', etc.; with inversions the* being
In the major, H,
placed in brackets to distinguish
it
from other figures
(11! ).
Other alterations frequent enough to justify special mention, are V in major with minor ninth (V 9 ''); the ii7 with lowered fifth (np; and the I 7 with lowered seventh (pt), which functions as a dominant seventh, (apparently in the subdominant key).
Ex.49
4U>S.11338t
m
Some Special 446.
Alterations in
Major keys.
Supply the alto and tenor. Inversions as desired. All the tones are chord-tones.
6
The Diminished Seventh Chord
448 /Lit.
n
i
(by Alteration) on Various Degrees
Exercises
in
the Augmented Sixth Chords
T
In the following exercises the
fched third or tenth.
463
u
augmented sixth sometimes becomes, by inversion, a diminNo new principle
The dim. tenth is the better, but the third is admissible. involved- the altered tones follow their tendency. 454
8
The Augmented Sixth Chords
in Harmonizing a
Melody
66. To use the augmented
sixth chords in harmonizing a melody (or in modulation, ^83 ) it be able to think their spelling and resolution accurately and readily. Here the support of figured bass is lacking and the problem demands mental concentration and more
is
necessary to
than ordinary care in leading the voices. Learn first to construct the augmented sixth chord
low the keynote. This
whose bass is a major third be"chord of the key" having subdominant function tonic, or dominant harmony. To build the chord at the
is the legitimate
(derived from IV or H.) and resolving to piano proceed as follows:
Strike the keynote) add the major third
1.
above the bass
below
it
for the bass, to these two add the aug-
(These three notes are the same in all four forms). Then, for the fourth voice doable the third (above the bass) in a 6+> use an aug-
mented sixth
in
any upper
part.
6+ 4+ a doubly augmented S
6+
04.
fourth in 4-H-> and a perfect fifth in 5 8 process is illustrated in Ex. St. Resolve as indicated in the example.
mented fourth
In
C
in
maj. or c min.
The four forms of Angm. Sixth Chord (The ang. ftth chord of the key)
Xk Ex. 52
Their regular resolution in the key
.
This
Some (a)
i
,
67.
_
_
Ex. 53 C,
I
The bass
(a)
and ak chromatically;
an inner part;
(e)
(d)
exceptional progressions permitted
<
fifths In reaching the chord, fl
Some
progressions better avoided
bad
Bad
In a
weak
six- four Is better led stepwise; (b) Consecutive
Unnecessary cross- relation, - approach outer parts in resolving to V (now freely written with
in outer voices; (c)
fifths in
Beethoven, op. 57 (transposed), the true resolution to If
is elided,
the sus-
pension improves the progression; ff) Fifth* now written freely; (g) Regular resolution, but by substitution, ujivocal but possible; (h) For instruments any altered tone may be taken by a leap of an augmented interval, smoother in an inner voice.
The following simple sopranos
invite regular use of the
Augmented
There is no need of any bat the smoothest
Sixth chords "of the key". progressions
^
+
!*
8+
84-8
ft
P
469.
tt
8
S
rr irrr irrr'r
^^ nr Mr
FT
ir
^ e-*-
^fe
AMMMtl
"r
'
6+
6+
r
J
1
irrr^
r r ir r
r
T
it* 8
^
m
6+
^
r
J
'
J>
'
tfn "
11
479.
666+ 480.
tt
r
J
'rr
'r
481. 3
69.
Finally, there
is
no limit to the ways these augmented sixthchords
cept that set by the taste of the composer. to following its conventional tendency
The
outward
the great composers progressing in all the
interval of the
to the octave,
ways shown
lar motion may be found, and either part may leap.
may be
augmented sixth
may
at 55 (a).
resolved ex-
itself, in
also be found in the
addition
works of
Here contrary, oblique and simi-
In 55 (b) note excerpts from the masters
illustrating this variety of treatment.
Wanner
(b)
The
and tenor may be added to the following:
may be omitted by the student who has not studied modulation, on account of the obvious inflection to related keys.)
(This
482.
alto
Chap. IV; Modulation Modulation by means of Triads TO.
This means of modulation
is
best illustrated in the Choral
where the melody leads simply
and naturally to cadences in nearly related keys, thus providing an interesting variety in the harThe succeeding monic setting. Keys so reached are usually points of but momentary repose. line of the choral may resume the original key directly if desired. That is, such modulations as we are considering are more in the nature of mere inflections to one side or another of the principal key. In the following models from Bach's Chorals note the brackets which indicate how one may consider the two keys as in a sense overlapping. The triad which seems to belong to either key and thus falls within both brackets is sometimes termed a pivot-chord. In Ex.56 (e) a pivot-chord is lacking, but the modulation
is
quite satisfactory.
In 66 (g) note the accented six-four and
how
Let the pupil solve strongly
it
this using
a pivot-chord.
declares itself a tonic chord
(fl-14).
Ex.56
CN
I
c min.
rrr
r-
J^u mod. by thefchd.
Harmonize the following choral lines simply and modulate in each one by means of triads. It is assumed that V87, n| etc., will be used ,
as desired. 483.
484.
485.
J| 487.
r'riTr
nr'r'r'
i" 488.
From a
to
G
also
C
to-
G
13
490.
489.
J
I'J
II
J
if
I
491.
From K
to B!, then to F, then
back
^
to g.
493.
492.
cf.
Ex. 10
A
494.
HP y
P
~
T *
J
d
i
r
49?..
t> Phrygian cadence (see again f 3l) is now added the half cadence, usually and the deceptive cadence, usually V^-vij we shall have sufficient vocabulary to harmonize many chorals. Note the following cadences and transpose them to other keys.
71.
If to the
I-V, IV-V, or
ii-V-,
Half Cadence
Ha)f Cadence
Ex.57
V
API. tlt8"
I
IVI
Deceptive Cadence
14
Suggestions for Harmonizing a Choral The following suggestions will be found in line with the best general usage. The triad at each hold is usually in fundamental position and has tonic function, i.e., jt can be figured as a tonic chord in the key of the choral, or as tonic in the related key to which the '.
1.
line
may have
led.
Since the hold marks a point of repose more or less complete, a chord of the seventh is obviously inappropriate at this point and is very rare. 3. If not tonic in function, the triad at the hold may appear as the V in a half cadence, Ex.57 2.
as the vi (really a tonic) in the deceptive cadence (c); or as the final major triad in the Phrygian cadence (fl'Sl)- The V in the half cadence may be reached through the 11 or IV as well as
(a) (b);
through the I, but is less usual. The last two chords of a line may be I-IV, but this again is a cadencing formula explainable as V-I in the subdom. key. 4. In .general do not introduce a chord on a weak beat and carry it over to the succeeding There may be strong beat, unless beginning a line. Compare 57 (d) 1 and 2, and (e) 1 and 2.
how many
occassional valid exceptions, but let the student find
Bach
5.
It is
one hundred lines of the
generally hi better taste to harmonize a repeated line in a different manner the
second time, 57 6. 7.
(f).
The parts may cross occasionally, but do not cross the soprano. Avoid many six-four cadences. Avoid many of any one form of cadence.
In the following
496.
in
chorals.
list
the more difficult chorals are mostly placed toward the end.
Ach Qott und Herr .'
.
j 497.
Christus der
r
i
.
rr rnrrr
mein Leben
ist
,. I
I
I
I
I
J Ji J J 498.
Errett mich,
O
mein
j
fdtt
lieber
Herre
rr
iJ
j
Ji r
Jjji Es
r 600.
i
r
J j j
Freu dich
sehr,
O
u meine
j.
j
r
ij j j
j
ist
gewisslich an der Zeit
ij J
P
j
i
rr
r
r
|
eele
v J
-
r r r
J
u
j
i
16 801.
602.
B03.
Oott Act Hinmels and der Erden
Oott dich loben
allr
wir
an Gottea Segi-n
Ermuntre dich, mein achwacher Geiat
g04
1,1
I
JJ|J
1 JIJJJJU 605.
Erqnicke mich, dn Heil der Sander 1
It
I
l
r
'j
l,.JJJJl Oottes Sohn
too
kommen
iit
jj Herr, ick hab
miagehandelt
^
^^ '
BOS.
y~
r
a
Ach wie
irrrrirr
nichtig
1 &^$ '
r r r r ir S09
HanHct tkvt mich
verlangen
!
'
'r A
I'hry^i.tn
melody
J i
J3_
MI ijji
16
510.
dank
ich
Machs mit
dir schon durch deinen
mir, Qott,
Sohn
nach deiner Gut
jNl.j|JJJJ|JJ?J| f |||l r Heine Hoffnnng stehet feste
513.
Frohlieh soil mein Herxe springen
E
JJ I
514.
&1
m
a .
St. Ann's
5
i
.
I
i
(With
i
-
rrr
J
f H as signature this is
a true Lydian melody)
Dundee (Scotch Psalter)
',
au
&
J
*-e
i Ein feste Burg
ist
1 1B46
unser Qott
'
r
"
J
.r
r
rr
r
'r
517.
J r
ir
r
ir
r
^
4
\4
J
^W
|ZM
Hannover 1648
17
518.
ich>
^ nr
pp
JJJ
519
Der liensch hat nichU to eigen
ir
520.
>-v
rr JiJ.
Verlieh on* Prieden gnadiglich
Aeolian melody
IMO
-
521.
Von Oott
will ich nicht lassen
M7JUJJJM.
? !--
Dorian melody, Not.
522.
I
m
_^
A.
Singen wir aus Hercensgrund
Abont 14tO
^^^_
t
&
IJ
"-
J
IJ
J
J
IJ J
'l
1 *
Mit Ftied and Rrend ich fahr dahln
j
j
r
i
lit*
fV>
j
r
r
J?L
JJr 524.
A Myxolydian melody Komm, Oott Schopfer,
heiliger Oeitt
Fr -
ij
Beethoven, Op. ia, Lydian (The d
"J
I.J
J
HJJjT nijjiij Ji
is
rr rirrr
r irr r
lower than the old rale permitted.)
1
11,111
in
i|l|M|
18
Modulation to a key through one of
its
Tendency- chords
73. The
tendency-chords of a key which resolve most emphatically to its tonic triad are Dim. 7th, (c) its Aug. Six-five, and (d) the Dim. 7th on its raised fourth of means degree. By anyone of these chords one may modulate from any key major or minor to other key, major or minor; but some modulations are much smoother than others and some any (a) its
Dom.
7th, (b) its
are too abrupt to
(a)
be
satisfactory, especially
when made through the Dom. 7th.
Modulation through the Dom.7th of the nev key
This modulation will be used first to next-related keys, do not differ by more than one sharp or flat. The next-related keys its Dominant, Subdominant, and their three relative minors; and The tonic inant, Subdominant, and their three relative majors. formed from the scale of the given key, using the ascending major,
whose signatures any given major key are
i.e.,
to
to those
for any given minor its
Dom-
triads of these keys can be
and descending original
minor, Ex. 58. Next-related keys to
C major
*
Ex.58 di
ei
FI
Next -related keys to a minor
*EE*
TT
GI
al
ar
I
GI FI
t ei
*=t CI di
signatures differ by but one sharp or flat are said to be one remove the difference in the signatures expressing exactly the number of removes from one key apart, to another. From C to D is therefore two removes, C to P| six removes, C to f (minor) four re-
75. Keys whose
all the keys maybe seen in the following chart. The arms will always inclose the next-related keys of any to which the arrow points. Brackets inclose enharmonic
moves. The relation of keys.
76. Modulation from any key to its five next-related keys may be made by progressing from the old tonic to the new Dom. 7th. Common tones are best kept, the other voices going to the nearest chord-tones. On reaching the new tonic it should be established by adding a closing cadence. Modulation from (a)
I
Modnlation
t
1
C major
to its five next-related keys:
Icioiing cadence
tb)
i
(c)
tt
\>&
M
Ex.59
m
CI
GV
(d>
=E CI* dV*
I
6
f IV
IS
y
I
(e) (a) (b)
^ndC
*
*d
m CI
V7
tt I
and Cad.
d
FV>
!
c dence
Modulation through V*.
inversion of the
It
Cad
In general modulation
Dom. 7th conduces
through an and re.
to greater plasticity,
serves the Vft for the closing cadence. (c) Modulation by Vj, chromatic soprano. 0) Begin with a I*, a fine road for this particular modulation. (e) No common tone, the third of the old tonic must be doubled to avoid an augmented second- (A rather abrupt modulation, made smoother by using a pivot chord, e.g., C I-vnV
rv/'
Modulate by the Dom. 7th from every major key Modulation from a
HSn
Ex.60
$
ok~
minor
to its five next-related
to its five next related keys:
keys
20
Modulatory Inflections Through Apparent Dominant Sevenths . In the following exercises the apparent Dom.. 7th resolving to its apparent tonic, can not be said to produce other than a fleeting impression of modulation. Such progressions See termed inflections. be 63 under the which fl may following exercises could modulatory
also be placed.
Exercises Which Contain Modulatory Inflections 536.
3
-6-
7
f 2 6
6
537.
,
It
e
6
4
aSiEg
6
i
P 538.
6
6
6
R
6
5.
4 3
6
4
-e-
o'
W -,
4
6
......3 J
6
4
5
^*
540.
7
g^
r r |J
-6-
4
541
542
5
65*
4-3-2,
8
3
645
4
6
3
5
6
66
5
5.
4,
7,
6 5
_ .
78. Through some
6
7
4
JL
544.
3
8
6
6
*
=r,
-
1t O^O-
i
:
r'
-*
6
3
&
?
'0ffri j
2
5.
6,
j ii
6
6
r
V7
(or fundamental position if necessary) reach a new as in the following model. As has ajready been shown, it may be questioned whether these are modulations at all. In any case the impression of the successive (apparent) to-
tonic at
6
6
T
-6-
6
-e-
^
543.
h
inversion of the
each+
nics is fleeting.
Ex.61
aV*
i
GVf
I
CV 2
e
FV|
I
dV|
I
CVg
I
21
The bass
is practically "unfiguredr
the needed accidentals as needed. 546.
-y^-t
Use
inversions and supply
The model
is
Ex.61.
22
(b)
Modulation through the Dim.7th chord of the new key (<| 45). Exercises which modulate by the Diminished Seventh Chord 6
n
556.
f r
t
*
g
6
i
if
r 4
557.
7
3
6
m
558.
m
7
*
si
3
8
T
ir
ir
i
T
-6-
559.
560.
6
^
65
-4-
8J
8
4
6
3.
I
7,
6.
67
64-%-
6.
2.
tt
7
4
7J>
-fr
8.
4
6.
it
u
o 6 5,
661.
a;
5l>
|
6
5
6
_
r r r
i
r
3 2
562.
-e
3 6
7
^
6l|
48.
J
4
6
n
i
r
r
r
J
J &
4
-6-
6
5
745
6 4
*
e
6
6 *
6
JL
ir r
H
564.
33
i
7_
6
7
W
6l|
6 7
5
-6-6O Tr
4
*
I
rt
,n
-e-
81. Pass from key 11888?
to
key
in exercises
550 to 555, by way of tbeir Dim. 7th chords.
Modulation through the Aug. Six-five chord of the new key
re)
The new
.
tonic
is
reached as an accented six-four, to which
is
added V?
- I.
Other
positions are sometimes used.
.()
(b)
(c)
3
3E Ex.
^
62
9+ ft
8+ ft
_|
--
3
i
te
I
D
CI
6-*-
4+
K
II
Some of the smoothest ways of reaching the Aug. Six- five:- at (b) from a I* an Aug. Six- four-three to avoid con. Kths, (d) the Aug. Six-five first in other than (c) through conventional form to escape con. Bins, or a cross -relation. Free yet quite permissible approaches to the Aug. Six-five. One should avoid (e) 9)(g)(h) con. Bths, but may disregard augmented intervals and cross-relation in any modulation by alter(a)
(t)($(d)
,
ed chords. 6 4
*
I 688
r
H
Jl,
ic
i-
r
I
i
i
^^ ^ e
588.
.
T
T
s
Modulator? unrction
i
1 "
^ e-*-
an
;,
through 3
l
r
(V r
l|-
J
l
n
24 570.
Sequences of modulations by the use of
j 571.
*
CI
V
II
aV
j
7
DJ*
I
II
'
7
|"t
Extend through the octave, ascending by half steps. This and similar sequences from F. J. Lehmann/by permission)
j * I
Ascending by whole steps.
CI Dg*
V7
II
II
E|*
I
V7
83. Also
invent and play sequences similar to 570-1. Finally modulate from any key to every other in the circle, f 75. (The other Aug. Sixth chords are also available for these modulations, but the Doubly Aug. Fourth leads to major only).
(d)
Modulation through the Dim. 7th on the raised fourth degree of the new key
84:. Use
chord preferably in its fundamental position (permissible in first inversion) through the nearest chord -tones. Resolve it to the new tonic six- four chord, on any and add V?- I. The chord is often indicated by accent,
and reach
this
it
(c)
(b)
rr
Ex.63
J=J:
3? f CI
%
-o-
fT" ibt f
(d)
r r
" Jo *i ITp
-o-0-
*
3=4 ?^r
_
o
'^JL^
-*
P
t
ci
r
r.
(e)
#
f
^
=Jt
J=tt
^^
-&-
*
r=i
BHVJ
Gng
(d)
Typical models. The old tonic taken in first inversion avoids an augmented second. The modulating chord taken in its first inversion.
(e)
Cross- relation
(a)(b) (c)
is
unobjectionable as in practically
all
progression
to
modulatory
(altered)
chords, see under Ex. 6Z. (f)
(g)
The augmented second, good.
is
This chord
major keys
is
Compare this modulation with (b,, which sometimes spelled as a Dim. 7th on the raised second of
identical in sound.
(f 64).
Exercises which modulate by the Dim. 7th on the raised fourth
572
-
866 r r
i
J
r
r
fi
574.
-e-
AP*. 11888^
A y* r
573.
4
.
8
i
25
4
6
67
-4
-e-
,
t
4
2.
1
|.| 575.
576.
r
*
*
*
e
Beethoven
5.
|J>^^
vj^jitj 85.
Pass from key to key
fourth degree of the In the
new
key,
exercises 660 to 666 by way of the Dim. 7th on the raised Add to each new Ij a V 7 -I cadence. in
same manner modulate from any key
in the circle Of 76) to every other key.
Sequence of modulations by the use of the Dim. 7th on the raised fourth
J
J
J
J
Extend through the octave, ascending by half steps.
i
Extend through the octave,
7
ascending by major seconds.
V7
EiV7.IIete
I
Also invent and play sequences similar
to B78-9 ascending or descending
by other intervals.
Modulation through the Neapolitan Chord of the new key 86. The Neapolitan Chord by alteration: but
key
entitle
it
its
to a place
among
1
fa)
(Vo) (Knharmonir)
T
^
MI* Typical modulations using the
(c;
The N'' The N* doubles
(A)
If
its
own
(c)
resolves to its
its
accented it
N" with or without,
Its
passing seventh.
.
root and reaches the
simpler to notate, the
V
FlN
V
:
te ?-8-
Z
chord although produced
the musician's modulating materials.
r
g>
Ex.64
BN
not, properly speaking, a tendency
=^
-o-
g
rs
characteristic resolutions to the tonic six -four or to the dominant of
new
tonic through
V*
.
enharmonic equivalent of the Neapolitan
chord may be used, (here e-gf-b for fV-aV-ct).
Exercises which modulate by the Neapolitan chord of the new key 8
580.
6
5
/3 .
fcy
f^
y-ti
r
IT (B>N
581.
s
i
(gN6 )
8 7
Supply
-the
alto
& 5
582
7^
6
*2
A U
^
4
"eb !
(EN 6) *
6
I
|
,
r rrif r'r
Unfigured bass. Introduce an
|"*~,
a
fj
ir
1
j
2
P
sl
and tenor
56
J
)
i
P
if 583.
$ P
8
i'
6
3
56 387
a
5
.
fa
J
si
-
i
7
5*
j rrir
and modulate through the
NB
.
984. -e-
6+
6+
5
N8
5
?
*fr Analyze fully and transpose
J
P
j
Sequence of modulations by the use of the
N
8
of the new key
Extend through the octave ascending by half steps through major keys.
CI
586
V|
P
8
JCI Jr> 1SJ8 587.<
BN
I
DN8"VJ J
V
Vv *
letc.
IV
J
f^^
Extend through the octave descending by half steps through major keys.
letc L etc -
Extend this ascending by minor thirds through major keys.
Invent and play sequences similar to 585-7, ascending or descending by other intervals. Also modulate from any key in the circle (f 75) to every other key by 8 or N*.
N
27
Modulation to more or less distant keys, Special Intervals up or down, Enharmonic Notation, Deceptive Resolution, Pivot Chords o
(t)
i
**
Ex.65
i per
4* h
Up a
00
u
o >-J
4*
ang.
a half -stop
(8)
(f)
(e)
Up an
Down
half -step
Down
a half -step
e
P Down two
Dp a mln.jd
o
min. 84*
(or dim. 5th)
(k)
0)
Too abrupt
Down a
maj.
Ex. dulate
Up a min. 39
3*?
65.
all
Add
a closing cadence to each of these except
(e)
which needs a V?-
The old tonic is a The new Dora. 7th is the Aug. 8ix-five(enhannonicaHy notated) The old tonic is N in the new key (a pivot- chord). The N* of the old key is the V in the new, to which is added
(a) (b)
(c) (d)
I
only,
and mo-
same way from every major key. pivot -chord quitted as V in the new key.
these distances In the
bent in the third inversion.
Note that
Dom. 7th
Ok) is
The chord and must always be complete. The (f) (ft) Deceptive resolutions. old
(e)
is
the
the enharmonic equivalent of
of the old key (a pivot -chord;.
A
the seventh. (d);
pivot -chord,
avoid fifths as
Aug. Six-five (enharmonicatty notated) of the new,virr- of the old
key
at (1).
a pivot
-
enharmonically vn-i<- of the new, By this means one reaches those keys is
a pivot-chord usable in both minor and major keys, par. 45. one, two x or three minor thirds distant (or enharmonic equivalent).
Modulations by the Dom. 7th to rather distant keys. Good because the third of the new tonic does not produce any unpleasant, or too abrupt, contradiction of the old key. With (h)
(1)
scarcely an exception those modulations by Vi which come within Mr. LehmannV rule for pure modulation 4' are sufficiently smooth for most purposes. The rale includes all the next related keys. However within the rule, C to aV (or pi) is poor. On the other hand C to f breaks the rule but (j),
*
Note.
good, see (a) above. Not a pure modulation, obviously too abrupt.
is
RULE: A
modulation
is
pare in
may be
mode when
the third of the
new
tonio triad or
enharmonic e. harmonic fo
its
In minor key* the notation of either the original or used. F. J. Lehmann- Lessons in Harmony.
qaivalent, i* contained in the old key.
Chap.V Non-harmonic Tones 1.
The Suspension
87. The Suspension is a prepared discord a degree higher (or lower) than the chord-tone which temporarily displaces, and to which it logically resolves. Three factors are involved:- the Preparation, The Suspension itself, and the Resolution.
it
In the following suspensions, locate the part to which each figure refers. 8-
# Ex.66
(f }
"
a
$
29
The Suspension 7 Su.
,
Sui.
tx
6; Suspensions in the bass Sat.
,_ v
Ret.
Ex.67
(f)
(g)
*
a
a triad in first inversion with delayed root. (a) The figures (7 G) or(J ) indicate to be considered a chord of the seventh. Compare with the next example. (b)
Or
The figures(-)
indicate what
is
here shown,
i.e.
In no case
two complete chords of the seventh,
a six-five chord with delayed root, the analysts depending on environment. a retardation. The context makes this so obvi(c) A triad in first inversion with a suspension and
ously a tonic with delayed root, that analysis as a chord of the seventh is illogical triad in first inversion with delayed root, through a retardation. (d)
A
Triads with suspension In the bass. Note the figures. Either Interval may be doubled. (e) ft)
(g)(b)
Chords of the seventh with suspensions
in the bass.
Add no
intervals to those indicated.
Three figures are here required
to
indicate the chord.
The Suspension with Change
of
Harmony, with the Six-four Chord, and
Double Suspensions () l^ f
Ex. 68
xl
I
.
I
(c)
,
(d)
(e)
30
The Suspension 6 5; Reduplication of the Resolution (a)
j Ex.69
Ex.70
(b),
fe
(c)
(d)
(e).
(f)
Suspensions In the soprano only
988
.
J "J
9 8
589
l|
"
I I
5
y
r
I
I
[
>ixr
"
II
I I
I
I
5 7 I
I I
1 I
I
i^
590.
57
8
J
43
8
54
78
43
I
I
I
I
77
t
ir
'
8 5
B92.
43
.
yur JL. Rft9 '
'
'
43
J
j
7 6
i
9 8 6
48
ft
43
4
___
u
in
any voice except the bass
438
08
4398
B--43
rJ
ip 5 4
595.
7 6
8
11. s
596.
i*
o
i
8
7
ft
j
6
7.
r
..
i
7
78
open position
Suspensions
J
98 __
48
M 7
4 -
ft
76
3
u Beftia in
.
_ _ u u u
'
76
.
7
1 t
98
6
"
r
988
r
if
ir
^
597.
7
9
8
t
f
r
'
r
r
7
I
7 5443 8
04
8 5
5 4 8
if
r
O.S.D.
J
iJ
.
T
M
780ft
ft
_
r
75
,
43
A
i
J 7 4
=B
..
A
iJ
j
43
898
,8,
1
ft
*
^
98
Z
7 *
*.
4 B1
9 8
4 3
"
j
J .A" "
I
* 3
ft
j
4
1
r
O.8.D.
rrrn .
i.J
7
ft
u
.>
r
3
S
irrr
s
i"
J
iy i
i
5 o
"
599.
s I
y
J
^
T^ r
.T^
[f
Suspensions in the bass only
_
5
_
5
5
2
p
rp 5
5
5
3
32
600.
6
-fcfH
r
ir
r
if
r
r
r
i"
5
2
ir
n
33
^65 4356 5663
_8
Ij6
610.
*
7
< .
Note. In
many paprB
thetf it
placed before the figure as
in those
:i
_
7 H
6
6
-6
3
4
7 8
_
.6
6-6 4
from the Guild examinations.
611.
7
One solution upper figures, one the lower
987 765 -IS-
4
APltMU*
34
Passing Tones and Embellishments
.
91. When Passing-tones and embellishments are to be used in a figured bass, dashes are used after the usual figuring as in the following example. (a)
.,
I
(b)
(c)
,
Ex.71
6
5
Bad
9
Correction
*
p T
5
7
8
_
4
6
(a)
=? T_
r~i A 7
<8
'5
2_
A 4
The chords are indicated as usual and
the dash continues the chord while the bass moves.
Unaccented passing -tone, (o) Accented passing-tone, (E) Embellishment. These ornaments, together with the passing sevenths, afford a very flexible bass, as will be seen in the following chorals from J.S.Bach. (+)
Signs;
Some common
(b) (c)(d)(e) (f)
ond
No
Good.
fifth is not a
(a) It
.
,
J
J
fault
faults
and their correction.
can be found with consecutive perfect
fifths if either
member
of the sec-
chord-tone.
+
(b)
(P)
ill
In Ex. 72 the fragments are from Bach's solution of the chorals which follow. (616-619) (a)
(b)
Passing tones in two voices. Passing tones and an embellishment.
the tenor.
Let the student consider
Here also a passing tone prepares a suspension
in
this exceptional.
The passing seventh temporarily crosses the bass. Par. 72. (c) This resolution into a unison may be jus(d) Bach here reduces the suspension, 9 8, to 2 1. tified between the tenor and bass by assuming that the latter will be played on a iC-foot stop, thus sounding an octave lower than written. Not recommended when 9 8 is available. e) Oblique motion of a passing tone into a unison. Generally forbidden in the books though be found rather often. To avoid it makes for clarity. "Let each voice respect its neighbor's /
to
territory" 1133S
1
?
is
a
good general
rule.
Bach Chorals containing
suspensions, tones and embellishments. passing
Supply the 616.
r*
Der Tag, der
iit
m 8 7 5
<
P *
r - J
and tenor.
*
to freadenreich
f^PP 3
alto
"T
5-7 8_
8 4
326
78
5-
587 5 8
it
3
2
31 565
1
36 618.
A_
An Wasserflussen Babylon *-
37
3 .t
-
u
5
8
*
-
-- 6 4 _. a
"~
Ol'
1
L_J
Harmonize simply
*
5 6
P f Hp HP tm ti^rz^ra r
620.
iI
in
g tf
* .
m
65766
sl l
i
four parts
Bach
622.
Play an accompaniment to this, one harmony to a measure except in the final cadence. A1 non-harmonic tones must be passing tones or embellishments. '
38
3.
ive
Appoggiatura, Anticipation
92. The Appoggiatura is briefly defined as an unprepared suspension. It is most expressIt is when on the accent, but unlike the suspension it may appear on the unaccented beat.
taken by a leap of an augmented second or more-
It is
commonest
in the highest voice.
93. The Anticipation is the opposite of a suspension in that it becomes a discord by taka tone of the following chord before that chord enters. The anticipation is unaccented. ing It usually enters stepwise but need not do so.
Ex.73
(c)
Appoggiaturas on the accent, and on the second half of the beat respectively. Anticipation in the soprano. Sign, A.
(d)
Simultaneous appoggiaturas.
(a)(b)
(e;,
Sign,Ap.
Simultaneous anticipations.
A
9-4. Compare Ex. 74 and B. If the unornamented harmony is correct the appoggiaturas to enrich it may enter with great freedom, e. g. leaps of a major seventh, augmented and diminished intervals, apparent cross- relation, consecutive perfect fifths^if the second one con-
used
tains an appoggiatura) are permissible.
This general principle applies to the use of all ornaThe appoggiatura should ments, especially as regards consecutive fifths and cross-relation. not resolve obliquely into a unison.
melody which contains appoggiaturas or other non-harmonic tones, think without any ornaments, choosing a harmonization that is clear and logical, with a decided predominance of the primary chords. This accomplished, the resumption of the ornamental tones should seem a simple matter. In harmonizing a
it
A.S 8. 11838 b
first
Exercises containing the Appoggiatara and the Anticipation
An appoggiatura, anticipation or passing
tune at the +.
Ornamental Resolutions of the suspension, appoggiatura, passing tone and embellishment The
suspension ornamentally resolved,
(.,
IEJ
S.,.
,,
*"
sign: s. c,
oma. *<>
40
The 628.
s
oma
41
Part VI. 95. The Ben
The French System of Figured Bass
Harmony Lessons
Examinations prepared by
and
such eminent French-
as Albert Lavlgnac, Auguste Chapuis, Alez.Guilmant,
Theo.Dubois, Gabriel Faure, Ch. M. Wider, Vincent D'Indy, Caesar Franck, and many others, afford such a wealth of material for advanced study and sight playing that it has seemed best to give here a brief explanation of the French system of figured bass.
96.
In general the French system employs the
same characters
to indicate inversions,
we
find in the American, English and German figured basses. alterations, suspensions, etc., that For instance the use of 6 to represent a first inversion, a (f) to refer to the third above the bass, are universal. The figuring of all secondary seventh chords that contain a per-
fect fifth is the same in all systems. But the figures used to denote the V, V?, vn7, vur> (that is the whole family of primary dissonances) and the n ? in minor are peculiar to the French system and must be committed to memory if any facility in their use is desired. In sequential modulatory passages, and anywhere that the primary dissonant chords are used, the special signs used by the French obviate the necessity of numerous signs of alterations impossible to avoid
in
our
own method, as
will be seen a little later in the
examples
to be
given.
The French figuring (a)
A
stroke
a diminished
/
fifth-,
through a figure indicates a diminished interval. For example standing alone it means a diminished triad.
%
means
A
(b) plus sign (+) before a figure denotes the leading tone, the (4) alone applies to the third above the bass, the figure 3 being then omitted. (c)
A
zero (O) alone indicates silence; above or below other figures, the suppression of
some chord member, (d)
A
e.g.,
O
denotes a triad with the third omitted.
major or minor triad
some authors placed over every
is
indicated by 5, 3 or 8; most often by the B which is by Some reserve the S for minor triads. When a f,
triad- root.
t or ^ is used to indicate the third, the perfect fifth is always understood. The inversions of these triads (with any necessary signs of alteration) are expressed in the same manner as in our figuring. (e)
The special arrangement of chord members, as with
us,
is
sometimes suggested by
unusual groupings, e.g., 5, 8. 6
(f)
A +
before 7 (thus +7) denotes the Dom. 7th chord over the Tonic, (the French
accord de 7me sur-tonique), (g)
Note carefully
sonant chords
the +7, the Dom. 0th chord over the Tonic.
that the plus sign
(4} is
always used
in
connection with
primary dis-
to designate the leading tone (unless already present in the bass). It is not Is reserved for chords of four
however used to denote the leading tone in the triad on vu, but or more tones. N. B. + denotes our V) not vn.
Examples of French figuring The/
The
+
The
+
Suggested
arr.
The $, V
4-6
7
7
Ex.77
+
The
-6-
O
The- 5, 5, or
O
5
The Leading Tone 7th.
V? -
[
The Dim.
The
7th.
V7 and V9 over-tonic.
8
Alterations
if
VH7 and
TheV 9
necessary.
Dim. 7 over
This when 1I7 in minor.
tonic.
A
few Suspensions.
chords. Simplicity in denoting primary dissonant Let the student figure this by the usual method and compare.
Exercises in French figuring 6
7
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Conservatories,
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made MS!
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for his
Instructions for Playing
Accompaniment in Pour Parts, in music by Johann Sebastian Bach"
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and
'09,
The papers for
'07,'08,
contained no sight-playing from figured bass.
Given Melodies
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Harmony John W. Thompson, by per.
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in these
Horace A.
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Dim. 7th chords
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Various Alterations
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Parentheses indicate unconventional positions-
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52
COLUMBIA UNIVERSITY Examination papers (written work) "i.
Secondary seventh chords .
Frank
E.
Ward, by
per.
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Waltz time
Write
(or play)
an accompaniment to this melody.
ROYAL CONSERVATORY CF MUSIC, MOSCOW, RUSSIA Three figured basses
Aug. 6fh Chords
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NATIONAL CONSERVATORY OF MUSIC, PARIS From 721.
Given Soprano.
APt. 11338*
the competitive Examinations, men's class, 1900
Chapuis, by per. Duranri A (Mr. Paris.
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61
THE SCHOLA CANTORUM, PARIS Three
final examinations in
advanced harmony; by permission
of the composer,
M.Vincent D'Indy.
to
H y
pyp
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D'lndys own solution of this melody (facsimile from his pen, p.2), Theme B, transmade to serve as bass in the first six bars, and both A and B appear entire unposed der the tonic pedal. Such possibilities however are intended to be discovered by the candidate, the themes being merely indicated. The following problems from the Schola Cantorum (also Nos. 719 and 723) are of this nature, demanding a high degree of skill and some good trainIn M.
to Eb, is
ing in counterpoint. Vincent D Indy, leio,
fVi fci:)|A
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62
The
following beautiful manuscript from the hand of the composer, is his own solution of N2 725. By permission.
M. Vincent D' Indy,
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MacDOWELL, EDWARD
.60
Critical and Historical Essays. America's great composer has furnished one of the outstanding books on the history and development of the art of music. It contains twenty-one chapters in which Mr. MacDowell outlines somewhat the technical side of music, and gives a general idea of the history and aesthetics of the art 2.50
SPALDING,
From
WALTER R.
An
SIGHT READING
Nt
FAELTEN, REINHOLD
be read for general in1.75
**
MAXWELL, DOROTHY Sight Reading. A first
sight reading book for students of any age, designed to teach the student to think before touching the keys, and to hear mentally before producing the musical sounds (Schmidt's Educational Series No. SS7)
HARRIS, CUTHBERT
First Steps in Ear Training. An easy and practical method of ear training up to a stage sufficiently advanced to meet the needs of the average music student. A knowledge of the rudiments of music up to key signatures and time signatures is all that is needed to precede
SOME PRACTICAL THINGS
may
AND EAR TRAINING
in Progressive Order. Deals with rhythm, pitch, intervals, chords, etc. . $ .50
A
Palestrina to Grieg. (First
for reference purposes, or struction and enjoyment.
One Hundred Ear Training Exercises
the course (Schmidt's Educational Series No. S59)
1.76
Year Music Biography). Each chapter is concerned with a single composer, and has at the end a synopsis and review questions which serve to emphasize the main points and test the student's knowledge. The book may be used for class work,
Art and a Language. Presents a working knowledge of the structure and modes of presentation of standard works in music, and is written primarily with a view to training listeners 2.50 Music:
Net
First Year Music History. The narrative, though direct and concise, nevertheless includes enough detail to render the story human and interesting, and to indicate the natural relationship of persons, causes and events. Questions at the end of each chapter outline the principal topics discussed
76
TAPPER, THOMAS
Sight Reading and Memory Lessons. Exercises and pieces accompanied by analysis and suggestions for correct 1.00 procedure in reading at sight and memorizing. (Schmidt's Educational Series^ No. If)
75
IN
PIANO PLAYING by ARTHUR FOOTE
practical handbook giving musical precepts and principles of artistic playing. Discusses the mechanism of the piano, relaxation, Price 60 cents net touch, pedalling, voice leading, etc., and contains numerous illustrations as well as practical exercises.
THE ARTHUR BOSTON:
120 Boylston Street
P.
SCHMIDT CO. NEW
YORK:
8
West 40th
Street
