KeyboardHarmony_725Exercices
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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 (
+
.
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
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
ni
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
Huchaldu. MO-A.IO A.D
THE KNOWLEDGE AND PRACTICE OF MUSIC HELPFUL BOOKS FOR EVERY STUDENT JUST ISSUED
A SHORT OUTLINE OF MUSIC HISTORY
THE STUDENT'S SHORT COURSE IN MUSICAL FORMS by CUTHBERT HARRIS
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426)
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HEACOX, ARTHUR
in
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HILL,
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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
HEACOX
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*^
'
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
-&
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 (
-fr
8.
4
6.
it
u
o 6 5,
661.
a;
5l>
|
6
5
6
_
r r r
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
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
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CAMBRIDGE UNIVERSITY From Examinations
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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
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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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