THE MELODIC MINOR SCALE IN SELECTED WORKS
OF JOHANN SEBASTIAN BACH
by
SHARON LOUISE TOWNDROW, B. M.
A THESIS
IN
MUSIC THEORY
Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for
the Degree of
MASTER OF MUSIC
Approved
Accepted
December, 1977
I ^-f* ^
c.^r ^
ACKNOWLEDGMENTS
I wish to express my sincere appreciation to my thesis committee,
Dr. Judson Maynard, Dr. Mary Jeanne van Appledorn, and Dr. Richard
McGowan. I am especially indebted to Dr. Maynard, chairman of my com
mittee, whose suggestions and assistance proved most valuable during
the preparation of this study. I also gratefully acknowledge the cour
tesies rendered by the staff of the Texas Tech University Library.
11
i"&e''
CONTENTS
INTRODUCTION 1
I . TONIC HARMONY 3
I I . HARMONIES OF THE FIRST CLASSIFICATION 13
I I I . HARMONIES OF THE SECOND CLASSIFICATION 24
IV. MISCELLANEOUS HARMONIC FUNCTIONS 34
CONCLUSION 45
NOTES 47
BIBLIOGRAPHY 48
1 1 1
LIST OF EXAMPLES
TONIC HARMONY
Sixth and Seventh Scale Degrees as Nonharmonic Tones
Ex. I-l. Fugue No. 20, P. 179., m. 25 3 Ex. 1-2. Ricercare a 6 voci, p. 17., mm. 78-79 4 Ex. 1-3. Prelude No. 4, p. 105., m. 39 5 Ex. 1-4. Concerto No. 1 for Clavier, p. 38., mm. 5-6 6 Ex. 1-5. Cantata No. 106, p. 15., mm. 3-5 6 Ex. 1-6. Suite No. 3, p. 37., mm. 17-18 7 Ex. 1-7. Suite No. 3, p. 40., m. 24 • 7 Ex. 1-8. "Von Gott will ich nicht lassen," p. 52., m.2 8 Ex. 1-9. Musical Offering, p. 36. , m. 11 . . 8 Ex. I-IO. Mass in B Minor, p. 2., m. 5 9 Ex. I-ll. Mass in B Minor, pp. 2-3., mm. 19,1 9 Ex. 1-12. Cantata No. 106, p. 16., mm. 4-5 10 Ex. 1-13. Concerto No. 1 for Clavier, p. 37., m. 2 11 Ex. 1-14. Fugue No. 20, p. 179., mm. 26-27 11
HARMONIES OF THE FIRST CLASSIFICATION
Sixth Scale Degree as Nonharmonic Tone
Ex. II-l. Suite No. 3, p. 39., mm. 15-16 14 Ex. II-2. Suite No. 3, p. 44., m. 23 14 Ex. II-3. "Von Gott will ich nicht lassen," p. 53., m. 8 15 Ex. II-4. Concerto No. 1 for Clavier, p. 32., mm. 1-3 16 Ex. II-5. Mass in B Minor, p. 25., mm. 7-8 17 Ex. II-6. "Jesu, meine Freude," p. 128., ma. 32-33 18 Ex. II-7. Suite No. 3, p. 44., m. 22 18 Ex. II-8. Cantata No. 106, p. 7., mm. 11-12 19 Ex. II-9. Cantata No. 106, p. 18., mm. 6-8 19 Ex. 11-10, Prelude No. 4, p. 104., mm. 9-11 20 Ex. 11-11. Fugue No. 20, p. 178., mm. 7-8 20 Ex. 11-12. Musical Offering, p. 4., mm. 13-15 21 Ex. 11-13. Suite No. 3, p. 39., mm. 40-41 21 Ex. 11-14. Mass in B Minor, p. 85., mm. 1-2 23
HARMONIES OF THE SECOND CLASSIFICATION
Seventh Scale Degree as Nonharmonic Tone
Ex. III-l. Suite No. 3, p. 39., mm. 20-21 24 Ex. III-2. Cantata No. 106, p. 21., mm. 7-8 25 Ex. III-3. Mass in B Minor, p. 193., mm. 10-11 26 Ex. III-4. Musical Offering, p. 35., mm. 7-8 26 Ex. III-5. Cantata No. 106, p. 15., mm. 3-4 27
iv
Ex. III-6. "Von Gott will ich nicht lassen," p. 51., m. 2 . . . . 28 Ex. III-7. Fugue No. 20, p. 179., m. 26 28 Ex. III-8. "Jesu, meine Freude," p. 127., mm. 27-28 29 Ex. III-9. Cantata No. 106, p. 23. , m. 9 30 Ex. III-IO. Mass in B Minor, p. 26., mm. 4-6 31 Ex. III-ll. Concerto No. 1 for Clavier, p. 31., mm. 5-7 32 Ex. III-12. Ricercare a 6 voci, p. 6. , m. 2 33
MISCELLANEOUS HARMONIC FUNCTIONS
Ex. Ex. Ex. Ex. Ex. Ex. Ex. Ex. Ex. Ex. Ex. Ex. Ex. Ex. Ex. Ex. Ex.
I V - 1 . I V - 2 . I V - 3 . I V - 4 . I V - 5 . I V - 6 . I V - 7 . I V - 8 . I V - 9 . I V - I O . I V - 1 1 . I V - 1 2 . I V - 1 3 . I V - 1 4 . I V - 1 5 . I V - 1 6 . I V - 1 7 .
Concerto No. 1 for Clavier, p. 35., m. 5 Concerto No. 1 for Clavier, p. 15., m. 3 Suite No. 3, p. 39., mm. 34-37 . . Musical Offering, p. 32., mm. 4-5. Ricercare a 6 voci, p. 13., m. 62. Mass in B Minor, p. 2., mm. 1-2. . Cantata No. 106, p. 10., mm. 1-4 . Cantata No. 106, p. 6., mm. 3-4. . Suite No. 3, p. 41., mm. 26-28 . . Suite No. 3, p. 43., mm. 39-42 . . Musical Offering, p. 36., mm. 7-8. "Von Gott will ich nicht lassen," p. 52 "Herzliebster Jesu," ram. 1-3 . . . Mass in E Minor, p. 121,, mm. 10-12 "Von Gott will ich nicht lassen," p. 53 Suite No. 3, p. 40., ram. 2-3 . . . Mass in B Minor, p. 118., mm. 1-4.
m
mm. 6-7
34 35 35 36 37 37 38 39 39 40 40 41 41 42 43 43 44
Conclusion Ex. Suite No. 3, p. 34., mm. 5-9 46
INTRODUCTION
There is some disagreement among theoreticians as to the applica
tion of the melodic minor scale in tonal music. It has usually been
taught that the sixth and seventh degrees are raised in the ascending
form and lowered in the descending form. Examination of music litera
ture of the eighteenth century and particularly that of J. S. Bach
shows, however, that the melodic minor scale has exhibited the raised
sixth and seventh in both ascending and descending forms, with the use
of natural minor in both directions also. It is important to note that
a single piece of music may have employed various forms of the minor
scale at different points in accordance with its particular harmonic
structure.
Since the works of J. S. Bach have often been used to support
theoretical conclusions in these areas, representative pieces have been
selected from the various genres to serve as vehicles through which a
practical conclusion concerning melodic minor scales may be reached.
Selections include Cantata No.106 "Gottes Zeit ist die allerbeste
Zeit," Chorale "Herzliebster Jesu, was hast du verbrochen," Chorale
for Organ "Von Gott will ich nicht lassen," Concerto No. 1 for Clavier
in D Minor, English Suite No. 3 in G Minor, Fugue No. 20 and Prelude
No. 4 from The Well-Tempered Clavier-II, Mass in B Minor, Motet No. 3
"Jesu meine Freude," and the Musical Offering. The number of selec
tions has been limited necessarily in order to eliminate needless
repetition.
The examples were taken from modern editions, but articulations
are those of the Bach-Gesellschaft. Some of the examples have included
r-^-rf
2
piano reductions of orchestral parts or editorial realizations of
Bach's continuo parts. Where necessary, notes were changed to agree
with the Bach-Gesellschaft edition. Measure numbers for the examples
have begun with the first measure of the given page unless measure
numbers have been printed in the score. In the analyses of the ex
amples the lower case letters and numerals have been used to represent
minor keys and chords, while major ones have been indicated by upper
case. The following symbols have been used to identify non-chord
tones: passing tone - P, lower auxiliary (or neighboring tone) -jO »
upper auxiliary -^f, appoggiatura - Ap, escape tone - E, suspension -
S, retardation - R, anticipation - A, and changing tone - C.
^m ' "%.
CHAPTER I
TONIC HARMONY
Sixth and Seventh Scale Degrees as Nonharmonic Tones
It has been traditional for teachers of music theory to stress the
concept of melodic minor scale with the sixth and seventh tones raised
in the ascending form and lowered in the descending form. This tra
dition apparently had its origin in music where tonic harmony prevailed.
When the minor scale occurred with tonic harmony, it was usually writ
ten in this traditional manner. However, in examination of the actual
music, it appeared that the usage of the melodic minor where associated
with tonic harmony was not totally predictable. Since neither the
sixth nor the seventh scale step was a part of the tonic chord, both
appeared as nonharmonic tones. Usually they were seen as adjacent
passing tones, but it was not uncommon to find them functioning other
wise.
Ex. I-l. Fugue No. 20, p. 179., m. 25.
a: I
In Example I-l the melodic minor scale was used in the fashion
described in most theory textbooks. The tonality is A minor, with
tonic harmony. The sixth and seventh steps here function melodically
3
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as adjacent passing tones. They are raised in the ascending scale and
lowered in the descending scale.
Ex- 1-2. Ricercare a 6 voci. p. 17., ram. 78-79.^
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Example 1-2 shows the raised ascending and lowered descending form
of the scale with a slight shift in harmonic function. The first two
beats after the bar line are obviously tonic and utilize the raised
tones in the ascending scale. Had the harmonic content remained tonic
throughout the measure, the lowered sixth and seventh would probably
•3s.
have appeared as they are. However, the D-flat in the first tenor
part did change the harmonic and melodic function somewhat. The sixth
scale step in the alto voice (which would have been a passing tone if
used with a tonic chord) became a chord member, and the harmonic func
tion and color moved toward the submediant.
Ex. 1-3. P r e l u d e No. 4 , p . 1 0 5 . , m. 39.
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In Example 1-3 the A-sharp and -sharp have been used as passing
tones with the tonic harmony. The lowered B and A do not form dis
sonances with the tones in the upper voices; therefore, they are not
nonharmonic tones in the strict sense. It is similar to Example 1-2
in that the A has caused a momentary harmonic shift to the submediant.
Nevertheless, the underlying tonic harmony is evident.
The preceding examples have illustrated the melodic minor as it
has appeared in both ascending and descending forms coupled with tonic
harmony. In Example 1-4 the scale descended in the bass, with the
sixth and seventh as passing tones (C -natural and B -f lat). The ascend
ing form of the scale did not appear at this point. Most often the
adjacent tones were found either in ascending or descending passages.
rather than both. (The procedure concerning dominant harmony is
discussed in Chapter II.)
^^' ^~^' Concerto No. 1 for Clavier, p. 38., mm. 5-6.
mm.m
d: n Ex. 1-5 . Can ta t a No. 106, p . 1 5 . , mm. 3 - 5 .
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Ex. 1-6 Suite No. 3, p. 37., mm. 17-18.
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Examples 1-5 and 1-6 were written in a similar fashion, with the
lowered sixth and seventh in the descending scale over tonic harmony
Ex. 1-7. Suite No. 3, P. 40., m. 24.
fe F ^ ^
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In Example 1-7 the lowered form of the scale was present, but the
leading tone was used to mark the cadence. After the subdominant chord
(formed initially on the second beat), a feeling of dominant function
may be construed, with the interval of a diminished seventh ( -flat
down to P -sharp) outlining a leading tone seventh chord.
It would appear that the descending form of melodic minor was
employed more frequently than the ascending form in instances of tonic
harmony. Perhaps the great preponderance of root progressions down
8
a fifth could provide an explanation for such a phenomenon. The ascend
ing scale did occur alone, however, as evidenced in Example 1-8.
Ex. 1-8. "Von Gott will ich nicht lassen," p. 52., m. 2.^
• f ; lb
On many occasions the raised sixth and seventh were found (whether
in ascending or descending form) in conjunction with dominant harmony,
followed by the descending scale with lowered sixth and seventh degrees
over tonic harmony. Such is the case in Example 1-9.
Ex. 1-9. Musical Offering, p. 36., m. 11.
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Ex. I-IO. Mass in B Minor, p. 2., m. 5.
>^^^[j;^)f# [ ^X!lj f {i(i\ vii'' 5"' I
The dominant to tonic function is also clear in Example I-IO. The
temporary tonal center is F-sharp minor, regardless of the key signature,
Ex. I-ll. Mass in B Minor, pp. 2-3., mm. 19, 1.
\\J viij 1 \
The above example in B minor further illustrates this procedure.
The diminished seventh chord on the third beat in the first measure of
Example 1-11 necessitated the use of the raised sixth and seventh tones.
The members of the tonic chord in the second bar were connected by the
lowered sixth and seventh scale degrees.
From time to time there were evidences of interesting cross-rela
tions in the harmonic content resulting from the melodic lines. In
Example 1-12 the raised sixth and seventh scale tones have been used at
the beginning of the first measure to make possible the dominant harmony,
Ex. 1-12. Can ta t a No. 106. p . 1 6 . , mm. 4 - 5 .
10
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After the tonic chord appeared, the sixth and seventh were lowered.
This is not dissimilar to previous examples, except the lowered tones
are followed closely by the raised sixth and seventh in anticipation of
the succeeding dominant harmony. The resulting cross-relation is quite
obvious and provides a striking effect.
In a brief cadenza contained in Example 1-13 an exception has been
noted. The melodic augmented second (F-sharp to E-flat) has been writ
ten in the scale pattern over tonic harmony, probably to introduce va-
riety and maintain melodic interest.
11
Ex. 1-13. Concerto No. 1 for Clavier, p. 37., m. 2.
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Ex. 1-14. Fugue No. 20, p. 179., mm. 26-27.
a: ^ip \\){p 1P'6 '''k %' \(p
Another exception to melodic minor usage with tonic harmony has
occurred in Example 1-14. The raised sixth and seventh appeared in the
descending scale over tonic harmony (first beat of the first measure).
Perhaps the composer was indicating the approaching dominant harmony.
due to the imminent final cadence of the piece. The effect of the sub-
12
dominant with the lowered sixth and seventh was thereby also heightened.
CHAPTER II
HARMONIES OF THE FIRST CLASSIFICATION
Sixth Scale Degree as Nonharmonic Tone
As stated earlier it has been maintained that the raised sixth and
seventh scale degrees in minor belonged to the ascending melodic minor
scale. Most theoreticians up to the present day have adhered to this
principle, either by implication or actual statement. The following
passage" is from a modern textbook but merely echoes the teachings of
many older texts:
"The melodic form of the scale is the same as the natural form but with two exceptions: (a) the sixth and seventh degrees are raised when ascending, thereby producing a whole step between 6 and 7 and the desired half step between 7 and 8, and (b) the sixth and seventh degrees are lowered to the natural form when descending."
As noted above, however, the raised sixth and seventh appeared in both
ascending and descending scale passages. Examination of the music re
veals that the harmonic background was the criterion for deciding
whether the sixth and seventh should be raised or lowered.
In harmonies of the first classification (those having dominant
function)' the sixth and seventh were usually raised when they appeared
melodically. The decisive note in first classification harmony was the
leading tone. The leading tone is probably the single most significant
factor in tonal music. In order to have a leading tone in a minor key,
the seventh scale step must be raised. Therefore, the raised seventh
degree will be present in almost every instance of dominant harmony in
minor keys. When the seventh tone functions in this capacity as a chord
member and the sixth is with it as a passing tone or an auxiliary, the
13
14
sixth will also be raised. Whether the scale is ascending or descend
ing appears to be irrelevant. It is the leading tone that is essential
to the harmony in this case, and the sixth is adjusted in order to avoid
the melodic interval of an augmented second. The following examples
illustrate the raised sixth and seventh within dominant harmony.
Ex- II-l- Suite No. 3, p. 39., mm. 15-16.
iS^ ^m
9- T i
In Example II-l the scale passage is ascending with the E function
ing as a passing tone and j;-sharp as the third of the dominant chord.
There are many such examples to be found in tonal music. Most theorists
have taught this usage (coupled with the lowered sixth and seventh in
the descending scale) as the typical application of the melodic minor.
Ex. I I - 2 . Sui te No. 3 , p . 4 4 . , m. 23.
r - ^ - u ^ ^ u Lti
^ ^ p 9- T )J\\ ly Viio,
15
Another such occurrence can be observed in Example II-2. The tonal
center at this point is G minor. The harmonic function again is domi
nant, the scale passage ascending, with the sixth degree as a passing
tone. Example II-3 illustrates the same procedure in a different key.
Ex. II-3. "Von Gott will ich nicht lassen," p. 53., m. 8
[ I f^^ "^ i fT
i ^^ Pedal U' .
^: 3r^ I IIlp i l l
Example II-4 illustrates a descending scale passage in D minor. In
the second measure the harmony is dominant and makes use of the raised
seventh tone, necessitating the raised sixth as well (third beat). No
tice, however, that the raised sixth was not used for the appoggiatura
at the beginning of the passage, since the seventh scale tone was not
present in the melody and the danger of the melodic interval of an aug
mented second did not exist.
It was not uncommon for the raised sixth and seventh to appear in
the bass line, although it was probably used more frequently in the
other voices. Example II-5 illustrates the use of the melodic minor in
the bass of the continuo part. Here the entire first measure is ob-
16
E^* ^^"^- Concerto No. 1 for Clavier, p. 32., mm. 1-3.
viously first classification harmony, even though the dominant note (£-
sharp) did not appear as a chord member until the last beat. At first
glance, the abundant embellishing tones may seem to form separate
chords. These chords are merely melodic coincidences, however, and the
prevailing harmonic function of the segment remains dominant.
Example II-6 shows the raised sixth and seventh in the bass with
first classification harmony. Although the raised sixth did appear
occasionally as a chord member (Chapter IV), chord tones were usually
taken from the harmonic rather than the melodic minor scale. Therefore,
the raised sixth could appear in the bass without affecting the harmonic
content of the music. In the last beat of the first measure, the D-
sharp is a chord member and the £-sharp functions as a lower auxiliary.
Ex. I I - 5 . Mass i n B Minor, p . 2 5 . , mm. 7 - 8 .
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17
In Example II-7 the raised sixth was used as a passing tone in the
first beat of the measure. Notably, the became JE-flat on the third
beat in order to preserve the usual major quality of the submediant
chord. It would have been exceptional for the &-flat to have appeared
sooner since the F -sharp was needed for the dominant chord (second beat),
and an -flat would have resulted in a melodic augmented second within
one beat.
Example II-8 illustrates again the necessity for the raised sixth
and seventh in the descending scale. It can be observed in the upper
18
Ex. I I - 6 . " J e s u , me ine F r e u d e , " p . 1 2 8 . , mm. 3 2 - 3 3 . ^
~Saf)t VLKJri:
"€& p fa.mil:
m^^ ^ ^
T ti n o r
^
sicK r e r l^uK;
V n .1, -in
= ^ ;
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^ 5icK
bt i ^
1 •
^
S 3 :
5icK "^e 'T- g,yh ^ \ y\
*\ m ^s=3^^
TJt If/ f i
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e: VM ff|
Ex. I I - 7 . S u i t e No. 3 , p . 4 4 . , m. 2 2 .
h" J 1' M ^^ ii h!s lUl ^'-^^ ^ ^
±ri r n i n ' f l 9- X i j j 5: IT
voice. The harmony is simply dominant to tonic. Both A-flat and A-
natural have appeared here as nonharmonic tones. The leap to the lead
ing tone (A-flat down to ]B) reinforces the tonality.
Ex. II-8. Cantata No. 106. p. 7., mm. 11-12.
19
• ftV.f F n — ^ r. r
^
^=f ±=t
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i = = = ? =
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Ex. II-9. Cantata No. 106, p. 18., mm. 6-8.
A\t e> Solo
at^i -•^c- »^iA-ele te-CeVx\' icK .rve^A^ewGcist^l
N It
f > ( 'ft'J n 1' i •. t \v I'VX \
Example II-9 is in B-flat minor and exhibits the raised sixth and
seventh over dominant harmony. The raised tones can be seen in the
continuo part (ascending G-natural to A-natural) and in the solo part
as well (descending A-natural to G-natural). It is interesting to no
tice the half-step nonharmonic tones (£-flat to _F and A-natural to -
flat) that give expressive reference to the text: "into Thy hands I
commend my spirit." (The raised sixth and seventh were also used in
the ascending scale with tonic harmony.)
20
^^- ^^"10- P r e l u d e No. 4 . p . 1 0 4 . , mm. 9 - 1 1 .
M mr f
'"• ' • ' - f 'I f f l i t
r
c : x"" 9 '- '\^
The raised tones in the descending scale are also seen in Example
11-10. Notice the overall harmonic sequence and the melodic sequence
in the bass voice (second and third measures). The raised sixth and
seventh scale degrees appear on two different tonal levels, the first
being -sharp and the second, £-sharp, the dominant.
Ex. 11-11. Fugue No. 20, p. 178., mm. 7-8.
a-. ^"5
Example 11-11 shows an entire measure of first classification har
mony. The first half of the measure consists of the leading tone sev
enth chord, with the addition of the dominant note, , on the last half
of the bar. The raised sixth and seventh scale degrees were used in both
ascending and descending motion; the sixth degree is employed as a non-
21
harmonic tone.
Examples 11-12 and 11-13 further illustrate the raised sixth and
seventh tones in descending scale movement with dominant harmony. Such
cases were abundant and appeared in almost every instance of downward
scalewise motion over, or in close proximity to first classification
harmony in music written in minor keys. (Example 11-12 also contains
the raised tones within tonic harmony.)
Ex. 11-12. Musical Offering, p. 4., mm. 13-15.
[}V^ Us^]
^ ^
^
X^^T] f
^ = ^ ^
f 9- x* IV \(„ •STt
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Ex. 1 1 - 1 3 . S u i t e No. 3 , p . 3 9 . , mm. 40-41
The practice of writing the raised sixth and seventh tones in as
cending and descending scale passages in association with first clas
sification harmony was so consistent and predictable that instances of
exceptions were exceedingly rare. Most seeming exceptions to the prac-
22
tice have had other harmonic functions or purposes and only appeared to
be unusual. Such cases will be discussed in Chapter IV.
One exceptional case can be cited here, however. In Example 11-14
the presence of the cross-relation between the natural and raised sev
enth (A-natural and A-sharp) is surprising. The harmony after the bar
line is obviously of dominant function. Probably the A-sharp was not
written in the bass because it would have added a fourth whole tone to
the melodic line. Therefore, the tonality established in the first half
of the measure is momentarily obscured by the appearance of the minor
dominant (fourth eighth note). A modal quality is heard briefly at
that point with the resumption of the major dominant on the last eighth
note of the bar. (Occasionally the augmented mediant chord, in first
inversion and containing the leading tone, is employed as a dominant
functioning chord. In such instances the raised seventh appears as a
chord tone and the raised sixth, when present, is a nonharmonic tone.)
23
Ex. 11-14 . Mass i n B Minor, p . 8 5 . , mm. 1-2.
^i>K> I f-)—^
5vp IE
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if/' ' i j , | " f ff !• 1 [ A- mcn, A
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7 7
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t
CHAPTER III
HARMONIES OF THE SECOND CLASSIFICATION
Seventh Scale Degree as Nonharmonic Tone
When the minor scale has been supported by harmonies of the second
classification (those chords having subdominant function) it has ap
peared in natural form; that is, the sixth and seventh scale degrees
have remained unaltered. The direction of the line was apparently un
related to the scale form used, for ascending passages of natural minor
were as common as those which descended. Since the desired quality or
qualities of second classification harmonies were usually dependent
upon the lowered sixth scale degree, that note was not raised. When
the seventh scale degree was written adjacent to the sixth, it was also
in lowered form. This practice was to provide a smooth melodic line
and to avoid the occurrence of the interval of an augmented second.
In any case, the sound of the leading tone was undesirable in passages
based upon the subdominant because it would detract considerably from
second classification function and color. The natural minor scale has
been used in the following examples.
Ex. I I I - l . S u i t e No. 3 , p . 3 9 . , mm. 2 0 - 2 1 .
t ^ gE i> f- I
3- '
4agf lU
24
25
Example III-l is obviously tonic to subdominant harmony in the key
of G minor. The E -flat in the second bar is a chord member and the ¥_
is an upper auxiliary. The descending scale with the tonic chord in
the first measure is also in natural form.
Ex. III-2. Cantata No. 106. p. 21., mm. 7-8.
In Example III-2 the sixth and seventh scale tones have been writ
ten in both ascending and descending motion and in the three voices.
Despite the three-flat signature, the passage is in G minor at this
point. The -flat is a chord tone each time it appears and the F's
are nonharmonic tones. This is the typical appearance of the minor
scale when associated with subdominant harmony.
The seventh scale degree (F) appears as a nonharmonic tone (beat
one of the second measure) in Example III-3. However, due to the me
lodic figure and the harmonic rhythm, the sixth scale step also functions
26
Ex. I I I - 3 . Mass i n B Minor, p . 1 9 3 . , mm. 1 0 - 1 1 .
'4^^=^fTr^. 9> J' X i' \ ^^\ to\ - \ i 5 ?«c.- CO.
9- -^^s vva ^ Wv -X^ u
as a non-chord tone at one point (second beat of the second measure).
The overall harmonic effect is one of subdominant harmony with domi
nant punctuation.
In most cases the natural minor was used as long as second class
ification harmony prevailed, while surrounding scale passages contained
the raised sixth and seventh degrees with first classification harmony.
Ex. III-4. Musical Offering, p. 35., mm. 7-8.
27
Example III-4 illustrates the unaltered sixth and seventh tones in the
first half of the first measure where the harmony is subdominant. In
the second measure the sixth and seventh have been raised to antici
pate the first classification harmony.
Ex. III-5. Cantata No. 106, p. 15., mm. 3-4.
^SJL
^^^T^
IK. r\ •
g«,55
"•"1 n I n i l # ^ ^ \<^ \ o ^ Komm^ \^ ISoh K Wer>- 3^€- su.^
t^ s te
'I a
^
^ s
i V b ^ i> s > ? t p- M i v
•. r \V ii 2:
i
i
' 1 ' f L L
5
I The same approach was used in Example III-5. The composer wrote
E-natural in the dominant chords (first and last chords of the measure)
but used the E-flat passing tone to precede the £-flat in the subdom
inant chord.
28
Ex. III-6. "Von Gott will ich nicht lassen," p. 51., m. 2.
h^ i± vv hiJ^j'^'^
^
^
J
m=^ 4 LA
^g
^ ^ ^
^
c". j^ Wi
In Example III-6 the raised sixth and seventh scale degrees were
used with tonic and dominant harmony in the first half of the measure.
They were lowered on the last beat of the measure with the appearance
of the subdominant chord.
Ex. III-7. Fugue No. 20, p. 179., m. 26.
^1
M i f
a ; ifc
' "V ' ^^ '.'jn ^'^]
|0(o
? ^
iL(p
Notice in the above example that the only appearance of the lowered
sixth and seventh was with the subdominant harmony. The raised tones
were written even with the descending passage over tonic harmony (Exam
ple III-7). The second chord in the measure could be interpreted by
some as a submediant chord. However, the bass tones do represent the
functions of tonic - subdominant - dominant if one considers the fact
29
that each bass tone is the third of a chord.
Since the supertonic chord has strong implications of subdominant
function, it was not unusual to see it in conjunction with the natural
minor scale. The submediant chord has been considered here to possess
some subdominant characteristics, even though it is a chord of the
third classification. The submediant chord is built on the sixth scale
tone and scale passages used with it have of necessity employed the
sixth and seventh scale degrees in unaltered form. Example III-8 shows
the lowered sixth and seventh scale steps in proximity with subdom
inant, tonic, submediant, and supertonic chords. The sixth scale tone,
Ex. I I I - 8 . " Je su meine F r e u d e , " p . 1 2 7 . , mm. 27 -28 .
5c>i>T
^^^^^
w^
TZA
^ ss:
^^f f l±
-^
u\
± 5i
t sick
r\ \ sicK - rer
^ ^
r^r
m g a r 5icK
I J \-tx-
R,itK' irv 90L^ S\V^ - re
^§
t\ \v
^ m m ; yv o^a^r s \cVv - r e r
3zr V»t X '
30
£, is a chord member wherever it has been used; with the -natural, or
the scale seventh, functioning as a non-chord tone.
Ex. III-9. Cantata No. 106. p. 23., m. 9.
• A ^ t »
tnk $ s
Tod f
a l^'i^^J-^'
^ ^ m^
c\
The lowered sixth and seventh in Example III-9 have prepared the
way for submediant harmony. The ascending passage at the beginning of
the measure contains the raised sixth and seventh as passing tones over
tonic harmony.
The natural sixth and seventh tones were used in the descending
bass line in Example III-IO. The last half of that measure is second
classification harmony, with the subdominant chord having been followed
by the Neapolitan sixth chord.
In Example III-ll the supertonic harmony is found in the second
measure, with the unaltered sixth and seventh in the top voice. The
ostinato figure in the bass is interesting but does not affect the har
monic function.
Example III-12 is perhaps a little more ambiguous but illustrates
the same procedure. The ambiguities resulting from the chromatid sm
31
Ex. I I I - I O . Mass in B Minor, p . 2 6 . , mm. 4 - 6 .
^^' - .7 •
32
Ex. IIl-ll. Concerto No. 1 for Clavier, p. 31., mm. 5-7.
I
1'
^m s - ^ ^N
*
Tifrzr^r^r-^-T^
j—Lj • ' s ^ ^
^
^ ^ a
> . - 4 I I 4 I J I—* ** =?=^—«=a < \4=
g : i. ' » ^
T^
i &
f
Iff
Ex. 111-12 . R i c e r c a r e a 6 v o c i . p . 6 . , m. 2 1 .
33
— i-tT-fe
^ ' f C!(
'i> .' J i .n n ,i J
'/,. T f T , r t ^
V-.>i ' J i s
^ a 'V
c; X \v^ lU |V
have not destroyed the basic function of the second classification har
mony in the last half of the measure. The lowered sixth and seventh
scale degrees were used in the second soprano voice.
There are other chords belonging to the second classification that
have not been included in this chapter. Because their usage has dif
fered from that of pre-dominant chords in support of the natural minor
scale, they are discussed in Chapter IV.
CHAPTER IV
MISCELLANEOUS HARMONIC FUNCTIONS
Upon examination of the music of Bach it became clear that on many
occasions the sixth and seventh scale degrees had been altered for rea
sons not related to the employment of the melodic minor scale. In
these instances the interval of a major second between the sixth and
seventh steps in the natural minor was either increased to encompass an
augmented second, or decreased to a minor second.
Ex. IV-1. Concerto No. 1 for Clavier, p. 35., m. 5.
I<
11,' T,'i , , i - i . f r Y r f f f i
s ^
^ n %
^
-it ^
vin XI In Example IV-1 the interval of an augmented second appeared in the
second group of sixteenth notes ( -flat to J^-sharp). This was not un
common, since the lowered sixth and the raised seventh were both mem
bers of the leading tone seventh chord which was used extensively as a
dominant functioning chord during the period of common harmonic prac
tice, 34
^^* ^^"2- Concerto No. 1 for Clavier, p. 15., m. 3
35
I
H
[ i i i ' ^ i I
3 ^ i 3
g s? ^ ^ ^
/'v, -^
y- >K
3- I' ,>
^
viij ii^, vu\
Example IV-2 again illustrates the use of the augmented second
melodically in association with the leading tone seventh chord (beats
two and four). It has been preceded by the supertonic seventh chord.
Ex. IV-3. Suite No. 3, p. 39., mm. 34-37.
5 f E p ^ 9: 1
Example IV-3 shows another common occurrence. The appearance of a
secondary dominant in the third measure has caused the alteration of the
scale in the bass. In cases such as these the scale tones have fol
lowed the key represented in the dominant-tonic relationship rather
36
than staying in the key of the piece. In other words, the piece of
music has remained in the key of G minor but the scale of the major
subdominant has been borrowed temporarily.
Ex. IV-4. Musical Offering, p. 32., mm. 4-5.
Ibrt E il: \ I 'C. 1 7 K
h^ m
^ *ff=fe
c: ^/5r ^' ^K > n
The sequence of secondary dominants in Example IV-4 called for a
number of altered notes, including the sixth and seventh degrees in
the scale of C minor. The alterations were used to maintain the qual
ity of the major-minor seventh chords in the sequence and they do not
indicate any particular scale.
Episodic and transitional passages have of necessity employed
altered scale tones. Example IV-5 shows the change in the F minor
scale as it moves to E-flat.
The procedure followed in Example IV-5 could be extended to include
passages with temporary changes of tonal center, or modulations. Exam
ple IV-6 illustrates the accidentals encountered in a modulation from
B minor to F-sharp minor. The half-step from -sharp to A is not found
37 Ex. IV-5 . R i c e r c a r e a 6 v o c i . p . 1 3 . , m. 62.
^m =d^\'i f ^
^ ^ ? ^
bi i^^ J ^ $
7x\ f f H
^ ^ H E ^ ^ ^
II'A,\ f LLr t f j ^
l\
Ex. IV-6 . Mass i n B Minor, p . 2 . , mm. 1-2.
^
at fe -i J—-j"^
^ ^ ^
^ ^. »J' Q^^r] r ^ t ^
V
38
Ex. IV-7 . Can ta t a No. 106, p . 1 0 . , ram. 1-4
te ioprft-KO
I S£
te Alto
S ^ ' i H J 1 hi J i ^1 ts (st der Ij^,^ ^^ g^^j,^ ^ J
Tcn."-V . ' cn .*- ^
gccss
Es i s t det- a l - ^^ Banci: r'\eAv:K,«iitin/5S^s-^e»-- - ken cla »nusft"
fs i»t
•"•'j'J J 4 ^ s
1 :
•y 'i^ If
^ if^g ii: ^ ^
W f
J' ^muiSi ^m \v U ^ ' T )>/(.
in any B minor scale, but it does appear in the scale of F-sharp
minor.
The scale tones have also been altered in cases of imitation. In
Example IV-7 the imitation (tonal answer) at the fifth, beginning on
the last beat of measure two, has used the scale of the dominant (in
this case, C minor). The tonality imraediately preceding and follow
ing the imitation at the fifth is clearly F minor.
In Example IV-8 a change of register and melodic direction has
made it possible to use the lowered sixth and raised seventh without the
Ex. IV-8 . C a n t a t a No. 106. p . 6 . , mm. 3 -4 .
S EEEZ U fc ( HI- n IMf
g ^
t ( u ^ -I'l u.ns be - den
§ ^ri .fl
zzt ^
^ ^ v _ ^
c: I Xfc IVb 3zr
39
occurrence of the melodic augmented second (at the bar line). The
harmonic and melodic structure have adhered to the harmonic form of
the minor scale.
Ex. IV-9. Suite No. 3, p. 41., mm. 26-28.
There are some pre-dominant functioning chords that have employed
the raised sixth scale degree as a chord tone. An example of this
usage can be observed at the beginning of Example IV-9. The example
is in G minor with the -natural functioning as the root of a super
tonic seventh chord for the dominant (D).
40
Ex. I V - 1 0 . S u i t e No. 3 . p . 4 3 . , mm. 3 9 - 4 2 .
:TrfrtTi'i
» V I I , , \ (p \\^ 1 ^ " 2 : \
The same type of occurrence is shown in Example IV-10. The raised
sixth scale degree again is the root of the chord (bass voice). In
this case the raised seventh is also present, functioning as an appog
giatura in the soprano.
Ex. IV-11. Musical Offering, p. 36., mm. 7-8.
C-- ^ % w i ' 5 (V i
In Example IV-11 the raised sixth scale step functions as the
third of the dominant seventh chord of the subtonic (third eighth note).
At the end of the measure the raised sixth and seventh degrees are seen
with dominant harmony.
When the leading tone chord for the dominant has appeared, the
Ex. IV-12. "Von Gott will ich nicht lassen," p. 52., m. 5.
^^^m f: X
ffl!^^-^.
•')i X'
41
raised sixth scale tone has been employed as the third of the chord as
seen in beat two of Example IV-12. In cases such as these the arpeg-
giated figure has been used to strengthen the harmonic function and the
absence of scalewise motion has prevented the use of the seventh scale
degree. (The seventh scale tone does appear in the succeeding dominant
seventh chord, however.)
Ex. IV-13. "Herzliebster Jesu, was hast du verbrochen," mm. 1-3.
^op^a^ i i P J J >' i m ^ ^ ATf : f E f=^ ^=f T&/<p>^
Wie.
j?.^.(|V-V-^f
t i 1 a 1
r.
f H t t ^
1 ^ £
b-. % iu '% 3r U(. xs 1 VII \ TC
On some occasions, especially in chorales, the raised sixth scale
degree has been employed as a chord member and has changed the usual
quality of the chord in which it is found (Example IV-13). Here (sec
ond measure, beat one) the subdominant chord, normally of minor qual
ity, becomes major,
Ex • IV-14. Mass in B Minor, p . 1 2 1 . , mm. 10-12.
J_ 5o/;.Tr-
i M ^
iszn
bu.'^i's
^ u /Ov
fat * = ^
•VSV
se - p ul ^ ^ -5-. tu5 e s t
?-) c 'J H 11'°') 3
•v^V
S€ - p« l -
^ ^.^
*i r f :^5 :
se - p u.(
i t * t a s e s t
ii
^ i j jl i i Ger X
42
The augmented sixth chords have employed the lowered sixth scale
tone. Example IV-14 illustrates the German augmented sixth chord in G
major in its less common "root position." Again the seventh scale tone
is not included because it would reduce the effect of the altered sixth,
When a scale passage appears with a tonic seventh chord (third clas
sification) the seventh scale degree is a chord tone and the adjacent
passing tones that have normally been seen with tonic harmony are not
present. The sixth scale degree would then function as a nonharmonic
tone as in Example IV-15. Notice here, however, that in this example
43
Ex. IV-15. "Von Gott will ich nicht la
^ ^ ^ ^ ^
11 ssen," p. 53., mm. 6-7.
IT H i -Xl^
the scale is not melodic minor, but rather F Dorian. The cantus firmus
for this particular chorale prelude is in the Dorian mode and that mode
has appeared in the piece, with the various forms of the minor scale
having been employed also. With the appearance of the D -natural the
tonal center has moved toward the dominant.
Ex. IV-16. Suite No. 3. p. 40., mm. 2-3.
^ £ ^
^ ^ ^ ^ ^
^r^-^Ulrf ±
^ ^
m*' -XT ••' ^ 7
3'' ^ I iv^ /^ j ^ ^
In Example IV-16 the tonic-seventh chord has appeared in arpeg-
giated form in the first beat of the measure. The seventh scale tone
functions as a chord member. The sixth tone did not appear at that
point.
IMT^
Ex. IV-17. Mass in B Minor, p. lis., mm. 1-4.
44
iZTip VH1 \U \\i, l*- "SL
Example IV-17 has combined all the tones of the melodic and natu
ral minor scales in a descending chromatic passage encompassing the
tones from tonic to dominant in E minor. The alterations are in the
bass, with chords from E minor in the treble. Even though the notes
in the treble combined with the bass notes do form chords, the de
scending chromatic line would seem to have more significance melod
ically. The chromaticism is the result of textual expression in the
"Crucifixus" portion of the Mass.
^
CONCLUSION
It has been found that the application of the forms of the minor
scale has most often followed the pattern of:^^
(1) raised sixth and seventh (ascending and descending) over
first classification harmony (with sixth scale degree as non
harmonic tone)
(2) lowered sixth and seventh (ascending and descending) over
second classification harmony (with seventh scale degree as
nonharmonic tone)
(3) traditional usage (raised sixth and seventh in the ascending
scale and lowered sixth and seventh in the descending scale)
over tonic harmony (with sixth and seventh degrees as non
harmonic tones)
The essential tones of the harmony have adhered to the harmonic minor
scale, with adjustments having been made in the embellishing tones in
order to avoid the occurrence of the melodic augmented second. The
preservation of harmonic function, which has been so important through
out the period of common harmonic practice, has been the controlling
factor in the use of the minor scale. Perhaps if theory texts would
include a fuller explanation of the harmonic basis for the employment
of the minor scale, students would be better equipped to use the mate
rials of music.
The following example illustrates the minor scale as it has nor
mally appeared in association with tonic, dominant, and subdominant
functioning harmony.
45
jT
_Suite No. 3. p. 34., mm. 5-9.
46
i ^ ^ ^
The manner in which Bach handled the melodic minor scale is now
relatively clear. Studies of the music of other composers might fur
ther illuminate the subject. Research into the works of some com
posers before Bach (particularly Henry Purcell) could be interesting.
Examination of the music of the Viennese Classicists and the nine
teenth-century Romanticists could prove helpful as well. Comparisons
of the employment of the melodic minor scale in the different styles
are excellent possibilities for future studies.
-•^x
NOTES
1. Johann Sebastian Bach, The Well-Tempered Clavier: 48 Preludes and Fugues, vol. 2 (Huntington Station, L. I., N. Y.: Edwin F. Kalmus, 1968), pp. 178-179.
2* > Ricercare a 6 voci, edition for organ by Helmut Walcha (New York: C. F. Peters, 1964).
^' . > The Well-Tempered Clavier: 48 Preludes and Fugues, vol. 2 (Huntington Station, L. I., N. Y.: Edwin F. Kalmus, 1968), pp. 104-105.
^* » Six English Suites, ed. Hans Bischoff (New York: Edwin F. Kalmus, 1945), pp. 34-45.
5« , Eighteen Large Chorales for the Organ (Bryn Mawr, Pennsylvania: Oliver Ditson Company, 1952), pp. 51-53.
6. Joseph Brye, Basic Principles of Music Theory (New York: The Ronald Press Company, 1965), p. 14.
7. Allen Irvine McHose, The Contrapuntal Harmonic Technique of the 18th Century (New York: Appleton-Century-Croft3. Inc., 1947), p.9.
8. Charles Burkhart, Anthology for Musical Analysis, 2nd ed. (New York: Holt, Rinehart and Winston, Inc., 1972), pp. 124-131.
9. Johann Sebastian Bach, 371 Chorales, compiled and ed. by Frank D. Mainous and Robert W. Ottman (New York: Holt, Rinehart and Winston, Inc., 1966), p. 96.
10. Neale B. Mason, Essentials of Eighteenth-Century Counterpoint (Dubuque, Iowa: Wm. C. Brown Company, 1968), p. 24.
47
^^: • > > > .
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, Concerto in D Minor. Edited by Edwin Hughes. New York: G. Schirmer, Inc., 1928.
, Eighteen Large Chorales for the Organ. Edited by Albert Riemenschneider. Bryn Mawr, Pennsylvania: Oliver Ditson Company, 1952.
, Mass in B Minor. Edited by Frank Damrosch. New York: G. Schirmer, Inc., 1899.
, Musical Offering and Three Trio Sonatas. New York: Lea Pocket Scores, (n.d.)
, Ricercare a 6 voci. Edited by Helmut Walcha. New York: C. F. Peters, 1964.
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The Well-Tempered Clavier: 48 Preludes and Fugues. Vol. 2 Huntington Station, L. I., N. Y.: Edwin F. Kalmus, 1968.
, 371 Chorales. Compiled and edited by Frank D. Mainous and Robert W. Ottman. New York: Holt, Rinehart and Winston, Inc., 1966.
Buckhart, Charles. Anthology for Musical Analysis. 2nd ed. New York; Holt, Rinehart and Winston, Inc., 1972.
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Bach, Johann Sebastian. Concerto No. 1 for Clavier in D Minor (Vol.
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48
> "
49
"Gottes Zeit ist die allerbeste Zeit" (Cantata No. 106 of "Vol. 23, edited by Wilhelm Rust). Leipzig: Breitkopf & Hartel,
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, "Jesu, meine Freude" (Motet No. 3 of Vol. 39, edited by Franz Wiillner). Leipzig: Breitkopf & Hartel, 1851-1926., p. 61.
, Mass in B Minor (Vol. 6, edited by Julius Rietz). Leipzig: Breitkopf & Hartel, 1851-1926., p. 3.
, Musikalischen Opfer (Vol. 31 ii, edited by Alfred Dorffel) Leipzig: Breitkopf & Hartel, 1851-1926., p. 3.
, Prelude No. 4 in C~sharp Minor from Das Wohletemperierte Klavier - Teil II (Vol. 14, edited by Franz Kroll). Leipzig: Breitkopf & Hartel, 1851-1926., p. 104.
, "Von Gott will ich nicht lassen" from Achtzehn Chorale (Vol. 25 ii, edited by Wilhelm Rust). Leipzig: Breitkopf & Hartel, 1851-1926., p. 112.
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Brye, Joseph. Basic Principles of Music Theory. New York: The Ronald Press Company, 1965.
Goetschius, Percy. Exercises in Elementary Counterpoint. New York: G. Sfchirmer, Inc., 1910.
Grove, Sir George. Dictionary of Music and Musicians. Edited by Eric Blom. 5th ed., 1955. 10 vols. Rpt. New York: St. Martin's Press, Inc., 1960.
Kennan, Kent. Counterpoint. Englewood Cliffs, N. J.: Prentice-Hall,
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^
50
McHose, Allen Irvine. The Contrapuntal Harmonic Technique of the 18th Century. New York: Appleton-Century-Crofts. Inc., 1947.
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Piston, Walter. Harmony. 3rd ed. New York: W. W. Norton & Company, Inc., 1962.
Rameau, Jean-Phillippe. Traite de I'harmonie reduite a ses principes naturels. Paris: Jean-Baptiste - Christophe Ballard, 1722. English translation by Philip Gossett. New York: Dover Publications, Inc., 1971.
Shirlaw, Matthew. The Theory of Harmony. 1st ed. London: Novello & Sons, n.d. 2nd ed. DeKalb, Illinois: Dr. Birchard Coar, 1955.
jT