comparative study of three sonatas brass thesis/67531/metadc699576/... · horn sonata,. movement...
TRANSCRIPT
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,A&I
A COMPARATIVE STUDY OF THREE SONATAS FOR SOLO BRASS
INSTRUMENTS AND PIANO BY PAUL HINDEMITH
THESIS
Presented to the Graduate Council of the
North Texas State College in Partial
Fulfillment of the Requirements
For the Degree of
MASTER OF MUSIC
By
Edward Lee Alley, B. Mus.
Denton, Texas
June, 1957
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TABLE OF CONTENTS
PageLIST OF TABLES . . . . . . . . . . . .. . . . . . . . . iv
LIST OF ILLUSTRATIONS . .. v........... v
Chapter
I. THE HINDEMITH CONCEPT OF ANALYSIS . . . . . . 1
II. THE SONATAS FOR SOLO BRASS INSTRUMENTSAND PIANO . . . . . . . . . . . . . . . . 7
General StructureHarmonic TensionTonality
III. STUDY OF THE SONATA ......... . . . 13
Sonata for Trumpet and Piano byPaul Hindemith (1I9)
Sonata for Horn and Piano byPaul HindemitW1939F
Sonata for Trombone and Piano byPaul Hindemith (191) Ny
IV. SUMMARY YAND CONCLUSIONS ..... .... . .85
General StructureTonalityHarmonic Tension
APPENDIX . . . . . " ...... . ..,,91
BIBLIOGRAPHY................ . . . . 92
iii
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LIST OF TABLES
Page
I. Harmonic Tension Fluctuation in FirstMovement of Trumpet Sonata . . . . .
II. Harmonic Tension Fluctuation in SecondMovement of Trumpet Sonata . . . .
III. Harmonic Tension Fluctuation in ThirdMovement of Trumpet Sonata . . . . .
IV. Harmonic Tension Fluctuation in ThirdMovement of Trumpet Sonata . . . .
V. Harmonic Tension Fluctuation in FirstMovement of Horn Sonata . . . . .
VI. Harmonic Tension:Fluctuation in SecondMovement of Horn Sonata . . . . .
VII. Harmonic Tension Fluctuation in ThirdMovement of Horn Sonata . . . .
VIII. Harmonic.Tension Fluctuation in FirstMovement of Trombone Sonata . . .
IX. Harmonic Tension Fluctuation in SecondMovement of Trombone Sonata - . . .
X. Harmonic Tension Fluctuation in ThirdMovement of Trombone Sonata . .
XI. Harmonic TensionFluctuation in FourthMovement of Trombone Sonata . . .
. . . .
. " . .
. . . .
. . . .
. . . .
. . . .
* . . .
. . 9 0
" 0 . .
. 0 9 .
0 . ."
XII. Frequency of Usage of Intervals in Tonal CenterRelationships in the Sonatas for Trumpet,Horn,. and Trombone . . . . . . . . . . . .
20
26
32
34
46
53
65
71
75
80
84
88
iv
Table
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LIST OF ILLUSTRATIONS
Series 1 . . . . . .
Series 2 . . . . . . .
Trumpet Sonata, Movement
Trumpet Sonata, Movementand 4'-487T.....
Trumpet Sonata,
Trumpet Sonata,,
Tr upet Sonata,Trumpet Sonata,
Trumpet Sonata,
Trumpet Sonata,
Trumpet Sonata,,
Trumpet Sonata,
Trumpet Sonata,.
Trumpet Sonata,
Trumpet Sonata,
Trumpet Sonata,
Trumpet Sonata,
Trumpet Sonata,
Movement
Movement
Movement
Movement
Movement
Movement
Movement
Movement
Movement
Movement
Movement
Movement
Movement
Movement
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
Figure
1.
2.
3.
4.
.
.
. . . . . . . . . . .
I, mm. )-6 * . .*. .
I, mm. 30-31, 37-42,. . . . 0 9 . . . .0
I, Tonal Centers . .
II, mm. 1-4 . . .
II, mm. 30-31 . . .. "
II, Tonal Centers .
II, mm. 35-36 . . ..
II, mm. 44-45 . .
III, mm. 1-3 . . .
III, mm. 17-20 . . .
III, mm. 51-52 . . .
III, mm. 68-69 . .
III, Tonal Centers .
III, mm. 10-12 ..
III, mm. 22-25 . .
III, m. 34 . . . .
mm. 1-4 . . . . . .
mm. 1-2 . . . . . ..
A-mm. 23-27; B-mm. 45-. . . 9 . 0 . . . 0 . .
Page
2
3
13
14
17
21
21
23
24
25
27
27
28
29
31
32
33
34
36
36
37
V
9
9
"
9
f
9
."
Horn Sonata, Movement I,
Horn _Sonata, Movement I,
Horn Sonata, Movement I,49 . . . . . . . . .
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Figure
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
Horn Sonata,: Movement
Horn Sonata, MovementHorn Sonata, MovementHorn Sonata, MovementHorn Sonata,, MovementHorn Sonata,. Movement
Horn Sonata, MovementHorn Sonata, Movement
Horn Sonata, MovementHorn Sonata, MovementHorn Sonata, MovementHorn Sonata, Movement
Horn Sonata, MovementHorn Sonata, Movement
36. Horn Sonata,, Movement III,. Principal Motivessof Group I . . . . . . . . . . . . . . .
37. Horn Sonata,,.Movement III,, Principal Motivesof Group II - - . . . . . . . . . . . .
38. Horn Sonata,, Movement III, mm. 38-39 . . . .39. Horn Sonata, Movement III, mm. 50-51. . . .
40. Horn Sonata, Movement III,, Rhythm of mm. 77-7841. Horn Sonata,. Movement III, Rhythmic Alteration
of Motives of Group II . . . . . . . . .
42. Horn Sonata, Movement III, Tonal Centers . .
43. Trombone Sonata, Movement I, mm. 1-2 . . . .
44. Trombone Sonata, Movement I, mm. 19-20 . . . .
vi
Page
I,, mm. 60-62 . . . . . . . 38
I, mm. 78-79 . . - . . . . 38
I, mm. 102-103 . . . . . . 39
I, Tonal Centers . . . . . 42
I, mm. 1-2 . . . . . . . . 43I, mm. 23-24, 45-46 . . . 43
I, mm. 78-79 . . . . . . . 44
II, mm. 1-10. . . . . . . 47
II, mm. 18-21 . . . . . . 47
II, mm. 58-66 . . . . . . 48
II, mm. 90-93 . . . . . . 48
II, Tonal Centers . . . . 51
II, mm. 44-45 . . . . . . 52
II, mm. 105-107 . . . . . 53
54
56
56
57
58
58
62
66
67
.0
.0
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Figure
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
vii
Trombone Sonata, Movement I, mm. 40-42 . . .
Trombone Sonata, Movement I, mm. 72-73 . . .
Trombone Sonata, Movement I, Tonal Centers .
Trombone Sonata, Movement I, m. 2 . . .
Trombone Sonata, Movement II, mm. 19-26 . .
Trombone Sonata, Movement II, Tonal Centers
Trombone Sonata, Movement III, mm. 1-6 ...
Trombone Sonata, Movement III, mm. 32-35 ..
Trombone Sonata, Movement III, Tonal Centers
Trombone Sonata, Movement IV, Tonal Centers
Page
. . 67
. . 68
. . 69
.. 70
. . 72
. .74
. . 76
. .77
. . 78
. 83
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CHAPTER I
THE HINDEMITH CONCEPT OF ANALYSIS
In 1937, Paul Hindemith published his now well known
theoretical work, Uterweisun im Tonsatz, in which he set
forth his own ideas and theories for a new approach to musi-
cal composition and analysis. This work was translated into
English as The Craft of Musical Composition, and published
in this country in 1942. This work is "primarily and exclu-
sively a study of musical material . . . establishing the
legitimacy of chords never before welcomed in conventional
harmony."
Hindemith's system of analysis is based on the twelve
tones of the chromatic scale, and each of these twelve tones
can become a tonal center. This tonal center serves as an
axis around which the other eleven tones group themselves.
In establishing the order for the grouping of tones in his
Series 1, Hindemith turns to the natural harmonic series
and alters the order of the notes by assigning them a new
harmonic number above or below the original number. The
next step is to establish their corresponding new fundamen-
tals and to continue this procedure until twelve different
1Bernard Heiden, "Hindemith's System--A New Approach,"Modern Music, XIX (January-February, 1942), 103.
1
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fundamentals are found, which produce the twelve note chro-
matic scale.
The basic steps in the derivation of Series 1 are best
summarized by Mosco Carner:
Suppose that we use the harmonic series on C . . . Wemove the second overtone down and give it the functionof a first overtone, giving us the fundamental of a newharmonic series which is merely an octav- higher thanour original one. The new fundamental C represents theupper note of the basic octave. We now proceed to thethird overtone G and move it first two points lower orgive it the function of a first overtone, but since itlies outside the basic compass of our basic octave itcannot be used. The third overtone is consequently movedone point lower assuming the role of a second overtone.Its corresponding fundamental is then a lower octave G,which is ranged in the basic octave.
The next three overtones of the series on C aretreated in the same way, then the procedure is reversedwith the overtones being moved one or more points up-wards. 2
The order of the derivation of the twelve tones of
Series 1 (Figure 1) is important, because these intervals ;.n
reference to C) represent values in tonal relationship.
Fig. 1--Series 1
This Series 1 is not a "tone row" or a series representing a
melody, but a formula for governing the relationship of large
21osco Carner, Contemporary Harmony, Vol. II of A Studyof Twentieth Century Harmony, 2 vols. (London, 1942), p. 73.
19 :p
be ____'
5 b-
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tonal masses. The relationship shown is that between the
fundamental or progenitor note (in thisecase C) and the other
eleven notes. The further to the right in the series one
moves, the lower becomes the degree of relationship to the
original note (C), until the final note (F#) is reached,, and
the relationship is zero. In setting forth the purpose of
Series 1, Hindemith states: "The value of the relationships
established in that series will be the basis for our under-
standing of the connection of tones and chords, the ordering
of harmonic progressions, and accordingly the tonal progress
of compositions." 3
The smallest unit involved in composition or analysis.
is the interval,. which may serve in two capacities: as a
melodic interval, when the two tones are used successively,
and as a harmonic interval, when used simultaneously. As
Series 1 showed the tonal relationship of the eleven notes
of the chromatic scale to the tonal center, Series 2 (Figure
2) illustrates the decreasing harmonic value of the intervals.
Fig. 2--Series 2
3 Paul Hindemith, The Craft of Musical Composition, trans-lated by Arthur Mendel, I (New York,, 1942), 56.
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Two intervals stand at the outside of Series 2: the octave
and the tritone (which is an interval of harmonic uncer-
tainty).4 The order of these intervals in Series 2 is based
on the acoustical phenomenon of combination or resultant tones
which influence an interval more or less favorably in respect
to its harmonic strength.5
All intervals have roots, and in the interval the domi-
nating tone is the root (indicated by an arrow in Figure 2).
The root of an interval is that tone most reinforced by the
combination tones. Hindemith6 maintains that the tritone
has no root because of its tonal uncertainty. The tritone
does, however, have a "root representative" which is the tone
which proceeds by the smallest step to the root of the reso-
lution interval.7
Hindemith8 states that the conventional theory of harmony
is far too limited in its system for the determination and in-
terpretation of chords. His system classifies chords accord-
ing to their quality, worth, or lack of tension. Hindemith
defines a chord as a group of at least three different tones
sounding simultaneously. 9 Also, the tritone, because of its
'Hindemith, op. cit., p. 82.
5 Heiden, of. cit., p. 106.
6 Hindemith, op. cit., p. 89.
7lbid. 8lbid., p. 90.
9 Ibid., p. 95.
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instability as an interval is the governing principle of this
system of chord classification. This is the first division
of the chordal material. Chords which do not contain a tri-
tone are classified as Group A, and chords with a tritone
are classified into Group B. In Group A, there is also a
further division: Group I,1 consisting of chords without
seconds and sevenths, and Group III containing chords with
seconds and sevenths. Group B is also subdivided into two
groups: Group II, containing chords with minor sevenths and
major seconds, and Group IV, containing chords with major
sevenths and minor seconds. There are two more divisions which
do not have a definite root. These are Group V (containing
augmented triads and the three-note fourth chord) and Group VI
(containing diminished triads and diminished sevenths).
In Groups I, II, III, and IV there is one final sub-
division which Hindemith makes. If the root and the bass tone
in the chord are identical, the chord is classified, for ex-
ample as IV1. If the root is located above the bass tone in
the chord it would be classified as IV2 , and so on.
In discussing chords further, Hindemith states that
chords, like intervals, have roots,11 In a chord of several
tones the strongest interval is responsible: the root of the
strongest interval is determined by Series 2. A series of
The labelling of the chord groups refers to the chartin the back of The Craft of Musical Composition, and not toscale degrees.
11 Hindemith, _o. cit., p., 96.
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roots of chords is referred to as a "degree-progression" by
Hindemith, and a satisfactory degree progression is the
foundation of a given composition. The intervals of the de-
gree progression when analyzed according to Series 1 estab-
lish the tonality of the composition.
The table of chord classificationsalso serves another
purpose than to establish a set of available tone combina-
tions. It also serves as a basis for evaluating any given
progression. If a composition were to progress through
Groups I, II, III, IV and back again, the resultant curve
of harmonic stress or harmonic tension would be one of gradu-
ally increasing and decreasing tension. Thus chord succes-
sions can now be evaluated and studied according to the ratio
between tension and stability by the use of Hindemith's table
of chord classifications. 1 2
Under Hindemith's system the traditional concept of "key"
is greatly expanded. Any tonal combination is now possible
as long as its use is justified by a satisfactory degree pro-
gression.. Hindemith justifies this by stating that "the
juxtaposition of intervals,, or of chords, which are the ex-
tensions of intervals,, gives rise to the key." 1 3
1 2 F. B. Muser, "The Recent Work of Paul Hindemith,"Musical quarterly, XXX (January, 1944), 34.
1 3 Hindemith, pj. cit.,.p. 107.
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CHAPTER II
THE SONATAS FOR SOLO BRASS INSTRUMENTSAND PIANO
In the years during the writing of The Craft of MusicalComposition, and for the next few years afterwards, Hindemith
was engaged in writing a solo sonata for each of the instru-
ments of the orchestra. Muser1 states that this aeries of
sonatas continues a definite policy of providing music for
people who want to play music, and not merely to listen to
it. The three sonatas for solo brass instruments and piano
were written during this period. The sonatas,2 written for
trumpet, horn, and trombone, were written in the following
order:
Sonata for Trumpet and Piano--1939Sonata for Horn and Piano--1939Sonata ? Tohmbone and Piano--1941
These sonatas, being written rather closely together, should
have certain stylistic characteristics in common, and there
should also be certain features peculiar to each sonata. To
study these sonatas and compare them with each other struc-
turally and stylistically is the purpose of this work.
F. B. Muser, " The Recent Work of Paul Hindemith,"Musical Quarterly, XXX (January, 1944), 34.
2Published by Schott and Co., Ltd. through AssociatedMusic Publishers, Inc.
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Each sonata will be examined for three specific features:
general structure (musical form), harmonic tension, and to-
nality. Before the studies of these sonatas are presented
it would be well to state specific points about each factor
to be taken into consideration.
General Structure
The object of this study is not to compare the form of
these works with their traditional analogues, but with each
other. In order to do this, however, some point of reference
must be taken, and in the study of musical form, reference
will be made to the traditional forms. Since it is known
that Hindemith is one of the contemporary composers who uses
traditional forms, even though they are at times greatly
modified, the labelling of the structure of the various move-
ments will be done in the conventional terminology. The forms
will be analyzed as found in almost any text on form analysis,
and any deviation from the traditional form that is in common
with the three sonatas will be noted in the concluding
chapter.
Harmonic Tension
The study of harmonic fluctuation and tension will be
based on the method explained in The Craft of Musical Composi-
tion, briefly outlined earlier. One explanation should be
made here, however. The main purpose of this study of har-
monic tension is to derive the "over-all" or "general" tension
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design of each movement, and not to extract a "chord-by-chord"
analysis. For this reason in the discussion of harmonic ten-
sion, the various sub-groups- of the chord classifications have
been omitted, both in the discussion and in the graphed har-
monic tension of the movements. While in some examples of
Hindemith' s writing, such an exclusion of the sub-groups might
prove fatal to a true study of harmonic tension, in this case,
the general classification of the chord is of main importance.
Thus, a chord of Group 1112 will be considered simply as a
chord of Group III, making the generalization of harmonic ten-
sion more simplified in this study.
Also in the discussion and study of harmonic tension
there arises another problem. When and when not are chords
to be extracted for study of harmonic tension? In this study
chords will be extracted for tension study only when they
form a primarily harmonic accompaniment. Therefore, accom-
paniments essentially of contrapuntal or linear nature will
not be considered. If the contrapuntal lines are complex
enough to form chords briefly, then they will be listed as
chords, but two-voice counterpoint independent of the solo
line will not be considered for purposes of tension. Since
this work makes no effort to analyze the various contrapuntal
devices employed by Hindemith in composing these three sona-
tas, all contrapuntal writing will be referred to as counter-
point, with an occasional mention of a fughetta or stretto
section.
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In other sonatas by Hindemith, as well as the three
brass sonatas, the use of ostinato rhythms is predominant.
At times these ostinato rhythms employ chords or chord se-
quences which may or may not fluctuate harmonically. The
analysis for harmonic tension of such patterns will be limi-
ted to the general tension implied by the measure or passage,
for in many cases- the resultant chords are secondary to the
purpose of advancing the ostinato rhythm and building the
rhythmic tension.
Some ostinato rhythms are constructed not with. chords,
but with sustained passages consisting of octaves, thirds,.
fifths, or other intervals. In such cases, when the accom-
paniment is placed in a linear role with the solo part, the
tension rating given the accompaniment will probably be from
Group I. The reason for this arbitrary decision is that
usually the ostinato rhythm will not contain enough voices
to make up a complete chord, so that the resultant tension
cannot be given a higher classification.
Accompanying each discussion of harmonic tension will
be a graph illustrating the general plan of harmonic fluc-
tuation for the movement as a whole.. This graph will be
based on the general harmonic tension, not the tension of
each individual chord. In the instance of the very slow
section (Movement III of the Trumpet Sonata), the graph. will
contain the harmonic fluctuation on each beat of the measure.
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Tonality
The determination of the tonal centers and tonal axes
of the compositions, will be based on the root progressions
and degree progressions: as outlined earlier. In the final
summation of the tonality of a movement, the tonality listed
will be the primary tonal axis for a certain section, i.e.,
the tonal center of Group I in the exposition of a sonata-
allegro movement. By this method, it will be easier to see
the relationship of the tonal centers and the "key schemes"
of the separate movements, whereas if smaller units of
tonality were used, the number of different tonal centers
would be large, and difficult to handle. In the discussion
of tonal centers of development sections of sonata-allegro
movements, only the more important key centers will be noted.
Since the development sections in some movements are longer
than in others, a comparison by this method will be more
comprehensive than if all possible tonal centers were
extracted.
One final point in the discussion of the analyses for
tonal centers: in some passages the solo part will be accom-
panied by a contrapuntal figure, or the passages will not be
complete enough harmonically to derive the tonality from a
root progression. In these cases, the tonality will be de-
rived from a melodic analysis based on Series 1 as in the
root progression analysis.
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The following studies and analyses will be more com-
prehensible if they are supplemented by the scores of these
compositions. In the study of the horn, trumpet, and trom-
bone sonatas the measure numbers cited refer to each
movement.
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CHAPTER III
STUDY OF THE SONATAS
Sonata for Trumpet and Pianoby PaulHindem ith TI99F
Movement I
General structure.--Part A- -Exposition (mm. l-84 )
Gro I (mm. 1-26) Group I contains only one theme,
and it is presented five times in this section, three times
by the trumpet, and two by the piano. Throughout this sec-
tion the piano plays an ostinato rhythm accompaniment. In
Figure 3 below, (A) shows the theme of Group I as stated by
the trumpet in the opening measures, and (B) illustrates the
ostinato rhythm of the piano.
A.rtPT.)
B. (PIAMfO)
IL - . a I;1 :
Fig. 3--Trumpt Sonata, Movement I, mm. 1-6
The transition (mm. 27-29) consists of staccato chromatic
notes in the piano followed by a short fanfare on the trumpet.
13
IL_-A-A . - " s _- a
W=ML
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Group II (mm. 30-62) Group II is introduced by a
six-measure statement in the piano of a new ostinato rhythm.
This new rhythm (shown in Figure 4-A) accompanies the entire
statement of Theme A of Group II (mm. 37-45). In Figure 4-B
and C below are shown the second ostinato rhythm, and Themes
A and B of Group II.
AEC
B. e4
C.
Fig. 4--Trumpet Sonata, Movement I, mm. 30-31, 37-42,and 47-48.
Measure 46 serves not only as a transition to Theme B
of Group II but also to set up a third ostinato rhythm of
triplets. Theme B of Group II contains four statements of
the two-measure motive, two each by trumpet and piano.
The transition to the closing section of the exposition
occurs in measures 63-66. The closing theme (mm. 67-84) is
merely a restatement of Group I accompanied by tremolo chords
in the piano. Group I is quoted for four measures, then
stated again with slight variation by the trumpet. The
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exposition ends with a final cadence and fermata in measure
84.
Part B--Development (mm. 85-126) The first part of the
development section is centered around the two-measure motive
from Theme B of Group II shown in Figure 4. This two-measure
motive is stated by the piano and then the trumpet with a
cadence being reached in measure 106.
The second section of the development begins with an
eight-measure introduction (mm. 107-114) in which the piano
again states the ostinato rhythm used to introduce Group II
in the exposition (see Figure 4). The development in measures
115-123 is centered around Theme A of Group II.
The retransition (mm. 124-126) uses the rhythmic motive
in the piano with a repeated three-note sequence in the trum-
pet to lead to the recapitulation.
Part A' -- Recapitulation (mm.. 127-142) The recapitulation
involves only the theme from Group I. The theme is stated in
the trumpet with the piano providing an accompaniment of trip-
lets. The theme is altered slightly beginning in measure 133.
In measure 131 the piano again returns to the second ostinato
rhythm which served earlier as an introduction to Group II
and the second section of the development. Beginning in
measure 138 the trumpet sustains a pedal point while the
accompaniment continues the ostinato rhythm, reaching a final
cadence in measure 142.
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Tonality.--In the exposition of Group I, the principal
tonality is "Bb" although the theme is stated in several
different tonal centers briefly. In measure 9 the piano
states the theme in "F," followed by a trumpet statement in
"F" in measure 12. The piano states the theme in "B" in
measure 16, but the next time the trumpet states the theme
(mm. 24-26) it is again in "BbtI
The seven-measure introduction (mm. 30-36) to Group II
serves only to set up a rhythmic pattern for the exposition
of Group II. This is the primary function of the accompani-
ment during the exposition of both themes of Group II. The
basic tonality of Theme A of Group II is "A," and Theme B is
also primarily in "A." In measures 54-55 there is a partial
statement of Theme B in "Db but this key center is only
transient. A statement of Theme B in "A" occurs in the
piano part in measures 56 and 57.
The closing section of the exposition (mm. 67-84) is in
"D." The trumpet briefly states the main theme of Group I
against tremolo chords in the piano. The exposition closes
with a definite cadence in "D."
The first section of the development (mm. 85-106) is
introduced by the piano stating Theme B of Group II in "B."
During the motival development of Group II in the first sec-
tion of the development, the motive is stated first in "F"
(mm. 92-95) and then in "B" (mm. 100-106).
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The second section of the development (mm. 107-123) is
centered around "EbH with the last few measures (mm. 118-
122) implying a center of "D."The recapitulation implies a use of bitonality. The
trumpet is definitely in "Bb' from measures 127-142, although
the piano accompaniment is in "Gb and cadences in that key
in measure 130. The piano resumes the ostinato rhythm of
Group II in measure 131 while the trumpet continues with the
theme of Group I in "Bb.#t The final cadence of the movement
begins in measure 138 with the trumpet holding a dominant
pedal, and the final "Bb" cadence is reached in measure 142.
Figure 5 shows the tonal centers derived from the root
and degree progressions of the first movement.
F!ZZI~j~Njw
Fig. 5--Trupet Sonata, Movement I, Tonal Centers.
Harmonic tension. -- During the greater part of the first
movement, the use of the aforementioned ostinato rhythms makes
a detailed analysis of the harmonic tension impractical. In
this movement, general harmonic tension will be used instead
of a chord by chord analysis.
The exposition of the first group begins with chords
from tension Group III in the ostinato rhythm, except the
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18
initial chord in measure 1, which is from tension Group I.
The tension shifts to Group I in measure 4, where it remains
through measure 18. The accompaniment assumes the role of
a linear,. rather than a harmonic one, and the tension remains
at zero until measure 24. The final measures of the exposition
of Group I (mm. 24-26) are accompanied by the ostinato rhythm
using chords of tension Group I.
The second ostinato rhythm used to introduce and accom-
pany the exposition of Group II keeps the harmonic tension at
zero until measure 42, where the motive is accompanied by
chords of tension Group III. In measure 47 the accompaniment
is based on recurring triad patterns from tension Group I,
and is then shifted to chords from tension Group III in
measures 51-53.
Chords from tension Group I are used again beginning in
measure 54, and continue until measure 62 where the transition
to the closing theme of the exposition begins. The transition
(mm. 63-66) is based on chords of tension Group III, and the
entire closing theme (mm. 67-77) uses chords of the same ten-
sion group. In measure 78, the chords are from tension Group
I, and remain there until the final cadence of the exposition
in measure 84, with the exception of one chord from tension
Group III in measure 83.
The development section begins in measure 84 using chords
of tension Group III, and in measure 89 the accompaniment as-
sumes a contrapuntal rather than harmonic role, with the
-
19
tension reduced to zero.. A series of thirds in the accompani-
ment beginning in measure 96 returns the tension to Group I
chords, where it remains until measure 99.
Beginning in measure 99 the accompaniment becomes linear
again, and the tension returns to zero. The second ostinato
rhythm is resumed in measure 107, and the tension does not
shift from zero. A series of parallel fifths in the bass of
the piano part implies chords from tension Group I beginning
in measure 115; this same figure also occurs in measure 121,
continuing through measure 126. Although this tension is
actually only an implied one, it will be shown on the tension
graph in Table I on the following page.
The recapitulation is marked by an increase in harmonic
tension to include chords of tension Group III in measure
127. The harmonic tension drops to zero in measures.128-
129, but is resumed in measure 130 with chords from tension
Group III. The rhythmic motive begins again in measure 131
dropping the tension once again to zero. Chords implying
tension Group I are present in measure 135. The chords
accompanying the rhythmic motive increase the tension to
Group III in measures 137-139. The final measures of the
first movement (mm. 140-142) contain chords from tension
Group I.
-
20
TABLE I
HARMONIC TENSION FLUCTUATION IN FIRST MOVEMENTOF TKJMPET SONATA
-~ -,
4- , + -- -
t *.
-~Li-
'iV77tV $K1
T
4 +
4 iI"
1-.
1 t-t-4
+. t t
.f
i
-- - . -- -_ ._ r - s _. -
1
" -t
_ t
t - ---
1 1
It4s- 1 i i M; i i ; iz ! ! in 1 1 i d-
i .
- t + - ,
i _.
- , _.._
_. ., ,
.
_ .. ,.
1_
_.,__
.;
;._
-"
__{ _.
. {. _.
.. t"r
r-
.
. ~
._ .1_. ,
-t--
- --- i-
-- -- +
. y .. .
-- 4 -4
t .
'I t y41 - 7 -!
*Roman numerals in this and succeeding tablesrefer to Hindemith' s chord classifications (see antep. 5, fn. 10).
**Arabic numerals in this and succeeding tablesrefer to measure numbers.
Movement II
General structure.--Part A (mm.. 1-25) The theme of
Part A is in the piano with the trumpet playing short fanfare-
like passages in measures 3 and 4, then resuming the theme in
measure 13. In measure 23 the trumpet briefly states a f rag-ment of the piano theme leading to the introduction of Part B
of the movement. Figure 6 shows the main theme of Part A and
also the trumpet fanfare passage.
1'
II
0
4 --- *---0 r- ~--1 ''"'Ipr'
- -r.
-- -F - ' t - --- -__ -i-
- 1
i i
+
,1
.-
i
. .. tr T
i
. y ... } . j ..... 1... t - .tr f..
i S f
i t
t
t
f }
i i
-,- -- -i
r 1-
... f _. 4....
f -- ' -
1 '..
t v
.. - -
s ,
T .
.
t"'
-
21
Fig. 6 -- Trumpet Sonata, Movement II, mm. 1-4
PrB (mm. 26-58) Part B consists of two contrasting
ideas, the first carried by the piano, and the second intro-
duced by the trumpet. The piano introduces a rather lyrical
theme in measures 26-29,. and in measure 30 the trumpet states
the short rhythmical motive shown in Figure 7.
Fig. 7--Trumpet Sonata, Movement II, mm. 30-31
The rest of Part B (mm. 32-58) consists of the repetition. of
these two basic ideas. In measure 48 the piano again states
its theme followed by the trumpet motive in measure 52. Sec-
tion B ends with a two-measure transition to the next part
(mm. 57-58).
Part A' (mm. 59-76) Part A' consists of a repetition of
the thematic material from Part A, but this time the trumpet
has the melody with the piano supplying a contrapuntal accom-
paniment. Beginning in measure 72 and continuing through
-
22
measure 76 the trumpet repeats the first five measures of the
theme.
Coda (mm. 77-87) The short coda section makes uses of
thematic material from Part B, principally the short rhythmic
motive stated in Part B by the trumpet, and shown in Figure 7.
During the entire coda the trumpet holds a tonic pedal point
above the piano accompaniment, and in measure 85 states the
short motive bringing the movement to a close.
Tonality.--The tonality of Part A of the second movement
is centered around "F," with the piano assuming the total
melodic and harmonic interest.. The trumpet plays several
fanfare-like passages, but the main emphasis on the key
center is in the piano.
Part B (mm. 26-58) has ass its tonal center "A," which
remains constant throughout the entire section. In measure
32 there begins a rhythmic repetition of a simple figuration,
(Figure 7), but the cadence of this sequence in measure 39
is in "A"). The motival figures played by the trumpet
throughout this section only tend to reinforce the "A' key
center. The last two measures of Part B (mm. 57-58) serve
as a modulation or connecting link with the next part of
the movement.
Since Part A' duplicates melodically Part A, the only
difference being the accompaniment, it, too, is centered
around "F." In measure 59 the piano is definitely in "F,"
-
23
and the tonality remains in "F" throughout this section. with.
the exception of a few measures which imply a slight shift in
tonal center. These are too brief to be considered here.
The section closes with a sustained "F" in the trumpet, which
also introduces the short coda.
Throughout the coda the trumpet holds the sustained "'FT"
establishing the tonality for this section. The piano again
hints at bitonality through its statement of the rhythmic mo-
tive of the trumpet from Part B, but the trumpet pedal point
keeps the tonality centered around "1F," where a definite ca-
dence occurs in measures 86 and 87.
Figure 8 below shows the principal tonal centers of the
second movement as derived from the root and degree progres-
sions, and a melodic analysis of the movement.
t J& 6 ~
Fig. 8--Trumpet Sonata, Movement II, Tonal Centers
Harmonic tension.--In the second movement of this sonata
the most used chords fall into Group III of Hindemith' s chord
classifications. In the first section of the movement (Part A:
mm. 1-25), the accompaniment uses chords from tension Group I.
The piano states the theme with Group I and III chords occur-
ring when the contrapuntal voices overlap and form these
-
24
chords. The only purely harmonic accompaniment occurs in
measures 15-17 when the trumpet states the theme. These
chords are from tension Group I. The section ends with chords
from tension Group III in measure 25.
In Part B (mm. 26-58) the most important harmonic tension
fluctuation of the movement occurs. In measure 30 the piano
begins a repeated motive using chords from tension Group III.
This repeated motive occurs through measure 39 where the trum-
pet states the short motive again. The trumpet motive is
shown in Figure 7 in the discussion on general structure, and
the repeated chord progression is shown below in Figure 9
taken from measures- 35-36.
PIANO
Fig. 9-Trumpet Sonata, Movement II, mm. 35-36
The most striking harmonic fluctuation occurs when chords from
tension Groups I and IV are alternated in the accompaniment
beginning in measure 40, and continuing through measure 48.
Chords from tension Group IV are used on the strong beat of
the measure, alternating with chords from tension Groups I and
III on the weaker beats of the measure. This fluctuation is
shown below in Figure 10 from measures 44-45.
oft"Now
Ask a -j I" AM a
k. A
-
25
FMNI ? 7
II
Fig. 10--Trumpet Sonata, Movement II, mm. 44-45
Part A' (mm. 58-76) of this movement is based entirely
on a linear accompaniment with trumpet playing the theme from
Part A.
The final section (mm..77-87) of the movement features
a harmonic fluctuation between chords of tension Groups I and
III, much in the same manner of those in measures 40-48.
The tension graph in Table II on the following page
illustrates the fluctuation of harmonic tension in this move-
ment. It will be observed that only the general tension for
each measure is given, because the important tension changes
have already been mentioned and illustrated. In the follow-
ing graph these changes are briefly notated to show their
relation to the general tension of the entire movement.
Part A' (mm. 58-76) of the movement is rated on the
graph as having a harmonic tension of "0" since the accom-
paniment is linear and completely independent of the melody
line in the trumpet.
-
26
TABLE II
HARMONIC TENSION FLUCTUATION IN SECOND MOVEMENTOF TRUMPET SONATA
1 11
Movement III
General structure. -. The third movement of the Sonata for
Trumpet and Pia is subtitled Trauermusk, or "Music of
Mourning," and is characterized by the extreme slowness of
the tempo. This movement is divided into four sections, the
last being based on the chorale Alle Men chen misen sterben.
The entire movement is ninety-four measures long and is best
divided as follows-:
Part A (mm. 1-16) The piano opens the movement with a
somber statement of its theme. In measure 7 the trumpet
sounds a quiet fanfare over the repetition of the theme in
the piano. The principal motive of this section is shown
on the next page in Figure 11.
-
27
PIAI
Fig. 11--Trumpet Sonata, Movement III, mm. 1-3
The trumpet and piano build in intensity until in measure 11
the trumpet plays a recitative-like passage over tremolo
chords in the piano. The section then decreases in intensity
with the trumpet resuming the short fanfare motive (m. 14)
bringing the section to a close in measure 16 with a tran-
sition to the next portion of the movement.
Part B (mm. 17-) The tempo marking for this section is
SRuh Bew or a little more moved. The piano opens the
section stating the theme in the first four measures as shown
in the figure below:
fo-
Fig. 2o--Trumpet Sonata, Movement III, mm. 17-20
A short interlude follows (mm. 23-25) and the trumpet states
the theme beginning in measure 26. The climax of this sec-
tion comes in measure 35 when the trumpet states the theme
"G
-
28
accompanied by very strong chords in the piano. This state-
ment continues until measure 42 where the trumpet states the
second phrase of the theme accompanied by a linear piano ac-
companiment. This section ends in measure 50 following two
measures for trumpet unaccompanied.
Part A' (mm.. 51-6?) This section introduces no new
thematic material, all of it being derived from Part A of
this movement. Beginning in measure 51 the piano plays an
ostinato rhythmic figure which continues throughout this
section. Figure 13 shows this rhythmic figure, and the
trumpet part with Theme A.
TKPr(whaTrtAI
1- ---
Fig. 13--Trumpet Sonata, Movement III, mm. 51-52
The trumpet plays Theme A from the first section of the move-
ment. In measure 58, the trumpet resumes its fanfare motive
from Part A, while the piano continues the rhythmic motive in
the left hand and also carries on its accompaniment of the
trumpet with chords as in Part A. The climax. is reached in
measure 61 with the trumpet and piano playing a figure identi-
cal with that in measure 11. There is an extension of this
-
29
idea, and, in measure 63, the trumpet holds.- a pedal point
while the piano resumes the rhythmic motive. The section is
brought to a close by the piano in measures 65-67.
Chorale (mm. 68-9) The sonata is brought to a close by
the trumpet playing the chorale melody Alle Menschen mtssen
sterben, while the piano plays an ostinato rhythmic accompani-
ment. This is shown in Figure 14 below.
PI At~
Fig. 14= Tr Sonata, Movement III, mm. 68-69
This ostinato rhythm, once established, is continued
throughout the entire section, even during the final measures
of the chorale. The chorale melody ends in measure 91, but
the trumpet sustains the last note as a tonic pedal point
through the piano's final cadence in measure 94.
Tonality.--Because of the slowness of the tempo of this
work, and the use of chords of rather high harmonic tension
(see discussion of harmonic tension for this movement) the
tonality is, in places, a little obscure, but for the most
part it is rather clear.
-
30
The introduction and Part A of the third movement are in.
"Bb,"f and this tonality is principally reinforced by the re-
curring trumpet fanfare. The final measures of Part A (mm.. 15-
16) lead to a "Bb" cadence in the trumpet part.
The second part of the movement begins with the statement
of the theme in the piano in "A." In measure 29 the trumpet
states the theme in "A" also.. The restatement of the trumpet
theme in measure 35 is the climax of a two-measure build up
of both harmony and tension. This statement is centered in
"A." In measure 43 there is a full cadence on "D," but it
serves mainly a sub-dominant function in "A." The final ca-
dence in "A" occurs in measure 45, with the last five measures
of the section serving to introduce the next section of the
movement.
The trumpet enters in measure 51 with the main theme of
Part A centered around "F," while the ostinato rhythm accom-
paniment in the piano is centered in "Bbt In measure 58,
both trumpet and piano cadence in "Bb"i with the piano and
trumpet resuming their original parts as in the first of the
movement (mm. 7-9). In measure 63 the trumpet holds a domi-
nant pedal point on "F" and the section closes in measure 67
with a half cadence in "Bb."
The tonality of the last section of the third movement
is "Bb" both in the trumpet part (which is the chorale Alle
Menschen mtsssen sterben) and the ostinato piano accompaniment.
-
31
The final cadence in the trumpet occurs in measure 91, and
the trumpet sustains a "Bb" while the piano completes the
cadence in measure 94 ending the sonata.
Figure 15 below illustrates the tonal centers of Move-
ment III as derived from the root and degree progressions.
Fig. 15--Trumpet Soonata, Movement III, Tonal Centers
Harmonic tension.--From the viewpoint of harmonic
fluctuation, the third movement of the trumpet sonata is
the most interesting of the three.
The first section of this movement (mm. 1-16) uses
chords from tension Groups, I, III, and IV. The distribu-
tion of these various chords is illustrated graphically in
Table III on the following page.
-
32
TABLE III
HARMONIC TENSION FLUCTUATION IN THIRD MOVEMENTOF TRUMPET SONATA
z
r i
- - -, 1- a - + -t
,
1
_4---t- +--- +-_ _.r._.
i r _-t
;_ .. _ : _ _
a ,
r i x t- --, I
. ,,_..:.. ,t _.,, _
- _ t
t
-+
! _;
r T "-r -
f
i
' _.t. _ __,._._..
r- r
1 -h :
... ,T. _ " ,_
- }aLfAf tiIIYK
1 4__ _ _ _ _ _ _ ;L _ _ _ 1
By comparing the illustration in Figure 16 below with the
score, it can be seen that the point of highest harmonic
tension (mm. 10-11) coincides with the melodic climax of
this section.
I- . . r w Aa".
a A Lim. 4b#~*
bFi 6-Tbnta, Moeen:b
Fig. 16-.Trumpet Sonata, Movement III, mm. 10--12
BL /or-AWL
-
33
The use of a highly dissonant chord of tension Group IV in
measures 10 and 11 provides a moving accompaniment for the
trumpet recitative passage. Immediately after the melodic
climax. is reached,, and the melodic tension decreases, the
harmonic tension follows in like manner. The chords from
tension Group IV descend the ladder of dissonance to tension
Group III in measure 12 and remain there until the end of
the section.
In the second section of this movement (mm. 17-w50) the
first important harmonic fluctuation occurs in measures 22-
25. Beginning in measure 22 a recurring melodic motive is
used, accompanied by chords of tension Groups I and IV in
alternation with tension Group III chords. Figure 17 illus-
trates measures 22 and 23.
. I
1*16 1 "
Fig. 17--Trumpet Sonata,. Movement III,, mm. 22-25
Table IV shows graphically the harmonic fluctuation of measures
20-25.
I
-
34
TABLE IV
HARMONIC TENSION FLUCTUATION IN THIRD MOVEMENTOF TRUMPET SONATA
' 2 3 4 ~ & M 2 3 2 4 2.
*Underscored Arabic numerals refer to beats in eachmeasure.
The next place where an increase in harmonic tension
is in evidence is in measure 34, where a series of chords
of tension Group III raise the harmonic tension a great ex-
tent. This is illustrated in Figure 18 below. This measure
preceeds the trumpet statement of the main melodic idea of
this section.
my J
Fig. 18--Trumpet Sonata, Movement III, m. 34
-
35
Throughout the rest of this section the harmonic tension
remains centered around chords of Group III, with the excep-
tion of measures 33-35, where the accompaniment assumes a
linear role.
The third section of this movement (Part A'--mm. 51-67)
contains no fluctuation in harmonic tension, the accompani-
ment being based on an ostinato rhythm shown earlier in
Figure 13. In measure 59 the piano again assumes the accom-
paniment figure of the first section of the movement, and in
measures 61-62 the melodic climax is again accompanied by
sustained chords of tension Group IV. In measure 63, as the
climax is reached, the tension immediately drops to zero with
the piano presenting a. unison figure that resolves the chord
of tension Group IV of the preceding measure to the tonic of
the tonality in measure 64.
The entire chorale (mm. 68-94) is accompanied by a rhyth-
mic motive in the piano based on octaves and varying very
little from chords of Group I. In measure 76 the accompani-
ment is based on the parallel movement of triads in the rhyth-
mic motive shown earlier in Figure 14. The final cadence of
the movement begins in measure 91 with the trumpet holding a
tonic pedal point as the piano completes a sequence of chords
in Group I, consummating the final cadence in measure 94.
-
36
Sonata for Horn and Pianoby Paul Hindemith
(1939)
Movement I
General atructure.--The first movement of the Sonata for
Horn and Piano is in sonata-allegro form, using three themes.
The sections can be divided as follows:
Part A--Exposition (mm. 1-71)
Group I (mm. 1-22) Group I contains three state-
ments of the main theme, one by the horn, and two by the
piano. In the beginning the main theme (see Figure 19) is
accompanied by an ostinato rhythm in the piano shown in
Figure 20. This ostinato rhythm is used by the piano
throughout the exposition of Group I.
Fig. 19--HornSonata, Movement I, mm. 1-4
PIANO
I , - -T - I - w ' w 117A L j. b I
Fig. 20--Horn Sonata, Movement I, mm. 1-2
-
37
Group II (mm. ?3-54) Group II contains two motives,
the first being stated by the horn in measures 23-30, and the
piano in measures 31-39. The first motive of Group II is
shown in Figure 21-A and the second motive in Figure 21-B.
The second motive of Group II is stated by the horn in
measure 45 after six:measures of transitional material
(mm. 40-46). The horn sustains a pedal point while the piano
states this second motive of Group II in measures 49-53.
Five measures of transition (mm. 55-59) lead to the intro-
duction of Group III.
Fig. 21--HorSonata, Movement I,
Group III. (mm. 60-70) There are three statements,of the main idea of Group III in the exposition. This rhyth-
mical idea is shown below in Figure 22. The horn states the
idea in measures 60-63, followed by a fragmentary statement
in the piano in measures 64-66, and another horn statement
in measures 67-70.
-
38
Fig. 22--Horn Sonata, Movement I,
Part B--Development (mm.. 7 }-139) The development section.
of this movement is clearly divided into three sections-, each
employing the development of a separate theme or idea.
Section 1 (mm. '0- 1) This section is based ex-
clusively on the development of a short motive from Group III.
This motive (shown in Figure 22) is stated by piano and horn
a total of five times in this section. The horn statements
occur in measures 74-75, 76-77, and 79-81; the piano state-
ments occur in measures 75-76 and 81-82.
Accompanying the horn statements of this motive is a
rhythmical figure derived probably from a segment of this
motive. This accompaniment figure is shown in Figure 23.
Fig. 23--Horn Sonata, Movement I, mm. 78-79
Section-2 (mm. 92-104) Preceding this section of
the development is a five measure transition containing no new
-
39
thematic material or development and serving as a continu-
ation of the rhythmic accompaniment figure shown above.
Measure 92 begins a short statement of Group I by the
horn, still accompanied by the rhythmic figure of the pre-
vious section of the development. This statement is somewhat
altered from the original beginning in measure 95, and serves
as a transition to the last and longest section of the de-
velopment. A rhythmical sequence based on sixteenth notes
rounds out this transitional sequence in the development in.
measures 97-104. The sequence, and the method by which it
gradually slows down into first triplets and then eighth
notes, is illustrated in Figure 24.
P ANO
Fig. 24--HorrSonata, Movement I, mm. 102-103
Section.2 (mm. 105-139) This section of the de-
velopment is centered around the two ideas of Group II. In
measures 105-112, the horn states in full the entire first
idea of Group II, followed in measures 113-118 by a piano
statement of the same motive. Beginning in measure 124 the
piano states the second idea of Group II, followed by a horn
statement of the same idea in measures 129-132. In measures
-
40
134-135, and 137-138 the horn states the first six. notes of
Group II in stretto with piano statements of the same motive
occurring in measures 135-136, and 137-138. This section of
the development ends with a fermata in measure 139.
Part A'--Recapitulation (mm. 140-162 In this movement,
as in others before, Hindemith chooses to recapitulate only
the group not used in the development section. In the case
of this movement, Group I was not used in the development
except for a. partial statement in the middle section of the
development (mm. 92-98); therefore this entire recapitulation,
or coda, is centered around a treatment of Group I.
This seems more in the spirit of a recapitulation rather
than a coda because the rhythmic motive of the exposition
appears. as well as a statement of Group I in the original key
of the exposition.. Both: ideas of Group I are stated, with
the final statement of Group I occurring in measures 153-158.
Beginning in measure 158 the movement gravitates toward the
final cadence which occurs in measures 161-162.
Tonality.--The principal tonal center of Group I of the
exposition (mm. 1-22) is "F." In measures 1-4 the horn states
the theme in "F," followed by a statement of the theme in "C"
by the piano in measures 4-8. Measures 8-11, the second mo-
tive of Group A, are also in "F." The piano states the
theme in "F" from measures 16-22.
Group II of the exposition (mm. 23-54) is centered around
the key of "A" with both statements of the first motive of this
-
41
theme (mm. 23-29, mm. 31-38) being in "A." The second motive
of this group (mm. 39-54) is also in "A," with the cadence
being reinforced by a tonic pedal point in the horn in
measures 49-54.
Group III of the exposition (mm. 55-70) is centered in
The enharmonic notation in the piano part suggests; a
center of "Gb, but enharmonic notation in this case is
principally for convenience of performance. The main motive
of Group III is stated in "F#" by the horn in measures 53-63
and by the piano in "F#" in measures 64-66. The motive ap-
pears in "Bb" in measures 67-70 and there is. no transition
to the development.
The first section of the development (mm. 71-86) con-
tains statements of the motive of Group III in "B" (mm. 74-
77) and "E" (mm. 78-86).
The second section of the development (mm. 87-104) con-
tains a statement of the theme of Group I in "F" and the rest
of the section is devoted to a rhythmic sequence preparing
for the third section of the development.
The last section of the development (mm.. 105-139) is
based on the theme from Group II and contains several state-
ments of that group in different tonal centers. The first,
mm. 105-112, is in "E," and in measures 113-123 it is stated
in the piano in "A." A short development of the second motive
of Group II in measures 124-132 is in "Ab," followed by five
-
42
stretto statements of the first motive of Group II in measures
133-139 in "Abti
The recapitulation (mm. 140-162) is in "F" with the osti-
nato rhythm is the piano reinforcing this tonality. The final
cadence in measures 160-162 ends with four "F" major triads.
The tonal centers for this movement as derived from the
root and degree progressions are shown in Figure 25 below.
Vf.
Fig. 25--Horn Sonata, Movement I, Tonal Centers
Harmonic tension.--As is: the case with the other first
movements of the three brass sonatas, this first movement is
divorced from a. truly harmonic accompaniment because of the
use of several recurring ostinato rhythms. As explained pre-
viously,, these ostinato rhythms and the measures in which they
occur are not being examined for harmonic tension on the basis
of individual chords. The basic pattern of tension for the
entire section accompanied by the rhythm, and the implied ten-
sion of the ostinato rhythm give a general tension for the
entire section.
The accompaniment of the first movement of this sonata is
based primarily on three major and two minor ostinato rhythms.
The first of these rhythms, used in measures 1-22, implies
-
43
chords of tension Group I because of the prominence of fifths
and sixths in it. Figure 26 shows the first major ostinato
rhythm and its implied tension.
PANO
Fig. 26-- S~ Sonata, Movement I, mm. 1-2
The first minor ostinato rhythm begins in measures 23-
29, where it accompanies the exposition of Group II. It is
found again In measures 45-49 in a slightly expanded harmonic
version, but it retains the same harmonic tension level. Fig-
ure 27 shows the two versions of this first minor ostinato
rhythm, together with the implied harmonic tension ratings.
oAiI
Fig. 27{--Horn Sonata, Movement I, mm. 23-24, 45-46
-
44
Both of these examples are assigned to Group I, because
of the predominance of fourths and fifths.
The second minor ostinato rhythm is found first in
measures 39-40. It is based on octaves in contrary motion,
and is also given an implied tension of Group I.
The second major ostinato rhythm is found first in
measures 61-63, where it accompanies the exposition of
Group III. A rating of tension Group I is given this rhythm
also, because of the presence of only two voices, which are
not enough to make up a chord (see explanatory material in
Chapter I). This second major ostinato rhythm is constructed
of sixteenth notes moving in scale-like passages.
The final ostinato rhythm of the first movement begins
in measure 78 and continues through measure 81 in its first
appearance. Later in the movement it is again found in
measures 85-97. This rhythm is again based on only two
parts, with their octave doublings, and must be rated with
a tension of Group I for the same reason as the preceding
rhythm,. An illustration of this rhythm (Figure 28) shows
that while some other tensions may be implied, the strongest
implied tension is from Group I.
PINO -b- r -I' I ~ r t r ~ r,
Fig. 28--Horn Sonata, Movement I, mm. 78-79
-
45
Other than the tensions implied by the five ostinato
rhythms, the accompaniment in this movement is for the most
part contrapuntal, there being only four instances in the
movement when a harmonic accompaniment is used. These occur
in measures 124-128, 134-138, 151-153, and 157-162.
In measures 124-128, tension Group III is implied in
the piano statement of the second motive from Group II of
the exposition.
The final statements of Group II by the piano in the
closing measures of the development serve also as a harmonic
accompaniment figure. These measures use chords from tension
Group III, and serve to close the development section.
The final use of chords that can definitely be assigned
a harmonic tension rating occurs in measures 152 and 153
where the first ostinato rhythm figure is increased dynami-
cally by the addition of triads and in measures 157-162, when
the movement is brought to a close by the statement of a
fragment of this first ostinato rhythm augmented by the use
of triads. In both cases the assigned value is from tension
Group I.
The harmonic tension graph of the following page (see
Table V) implies that tension Group I is the predominant
tension of this movement.
On listening to the movement, however, one will find
that the use of the ostinato rhythm figures compensate for
the lack of chord progressions exhibiting varied harmonic
-
46
tensions and that the rhythmic tension created by these osti-
nato rhythms provides enough diversity to prevent monotony.
TABLE V
HARMONIC TENSION FLUCTUATION IN FIRST MOVEMENTOF HORN SONATA
7050 0
'5 0,10
130; -- 1I35 p!~ jl
Movement II
General structure.--The general structure of the second
movement in this sonata may be considered either a five-part
compound song or a rather brief first rondo. The movement
contains 126 measures, and can be divided as follows:
Part A (mm. 1-16) The entire theme is stated first by
the piano and consists of two ideas, the first stated in the
first five measures, and the second appearing in measures 6-11.
-
47
The remaining four measures constitute a repetition of theI
first idea. These two ideas are shown in Figure 29.
Fig. 29--Horn Sow, Movement II, mm. 1-10
Part B (mm. ) The horn enters with the theme of
this section (shown in Figure 30) and the piano follows with
a fughetta of the theme in succeeding measures. The entries
of the subject are made in measure 17 (the original horn
statement), in measure 22 (soprano voice in the piano), in
measure 26 (bass voice in piano), and in measure 31 (a com-
bined entry with horn and octaves in left hand in piano).
Fig. 30-.-Horn Sonata, Movement II, mm. 18-21
Part A' (mm. 36-53) This section consists of a state-
ment by the horn of the complete theme of Part A in its
-
48
entirety accompanied by the piano. The piano accompaniment
is of secondary importance throughout this section.
Part C (mm. 54-77) The piano accompaniment shifts to
9/8 meter while the horn remains in the 3/4 meter of the
previous sections. A new theme is presented in this section,
first by the horn in measures 55-65, and then in variation
by the piano in measures 66-76. During the variation of this
theme the horn sustains a pedal point on "B." The theme of
this section is shown in Figure 31.
HORN
Fig. 31--Horn Sonata, Movement II, mm. 58-66
Part A'' (mm. 7126) This closing section of the move-
ment presents again the thematic material of Part A with a
short development of the first idea of the theme. The theme
is stated in measures 79-89, and in measure 90 the piano
states the first idea in a new key with aome rhythmic vari-
ation. The new form of the theme is shown in Figure 32.
Fig. 32--Horn Sonata, Movement II, mm.. 90-93
-
49
In measure 97 the horn plays the idea as just introduced by
the piano, and the new form of the theme is continued until
measure 111 where the original of the first idea is stated
in the piano. In measure 115 the horn resumes the theme,
and continues until the movement is brought to a close in
measure 126.
Tonality.--The principal tonality or key center of this
movement is "D," although there are several passages which
do show a tendency toward a different tonal center.
Part A of the movement (mm. 1-16) is centered in "D"
with the second idea (mm. 5-10) gravitating toward "E." The
return of the first idea in measure 12 resumes the key center
of "D."
Part B begins with the horn stating the subject of the
fughetta in "D" in measures 18-21. All of the entries in
this short fugal exposition are centered around "D" with the
exception of the last double entry in piano and horn (mm. 31-
34) which is centered around "E."
Part A' has the same key centers as Part A with the
first idea being presented in "D" both times, and the second
idea again having a tonality of "E."
Part C is presented in "B," both in the horn statement
(mm. 55-66) and in the piano variation (mm. 66-76). The
final cadence in measure 77 leads to a strong cadence on
"B."
-
50
Part A'' begins with a statement of the first and second
ideas of Part A in their original keys ("D" and "E"), but in
measure 90 the piano begins a statement of the first idea in
a key center of "C." This in reality is more like the key
of C minor in the traditional major-minor system, but accord-
ing to Hindemith's system of tonality (in which there is no
major or minor system) it is labelled as "C." Beginning in
measure 97 the horn takes up the first idea, also in the key
of "C." In measures 106 and 107 the accompaniment comes to
a half cadence in "A" before returning again to a statement
of the first idea in "G" in measure 111. Again this state-
ment of the theme (in measure 111) is more in a minor mode
than major, but for the purposesof this thesis, it is la-
belled as "G." The horn states the idea in "G beginning inmeasure 115, but the cadence of this phrase gravitates to
"D" in measure 119. Beginning in measure 120, the theme is
restated in "D," and the movement closes in measures 125 and
126 on a "D" major chord, providing a strong cadence and
conclusion to the movement in "D."
Figure 33 on the following page shows the tonal axes of
this movement as derived from the root progression and the
degree .progressions. The example is labelled to show the
relationship of each of the key centers of the five sections
to each other.
-
51
Fig. 33--Horn Sonata, Movement II,, Tonal Centers
Harmonic tension.--The two predominant chord groups used
in this movement are I and III. Part A of the movement (mm. 1-
17), stated by piano alone, is centered chiefly around these
two tension groups.. For the most part the tension is extraa-
ted when the contrapuntal voices are grouped to form a chord
lasting for at least one beat in the measure.
Part B (mm. 18-35) consists of a short four-voice fughetta
in which the only chords extracted for tension occur in meas-
ures 26 and 27. The rest of this part is constructed so that
an extraction of harmonic tension is not useful.
Part A' (mm. 36-53) uses the same tension structure as,
measures 1-17 with the exception of measures 44 and 45, in
which a chord from tension Group IV is used for the first
time in the movement (Figure 34).
-
52
3
'
-9-~-
PIANO JIPTi I
_______L1~z-
Fig. 34--Horn Sonata, Movement II, mm.. 44-45
Part 0 (mm. 54-77) is based on an ostinato accompaniment
figure in the piano which alternates chords of tension Groups I
and III. This alternation extends from measure 54 until meas-
ure 63, where the accompaniment becomes linear. The balance
of this section (mm. 66-76) contains a variation of the mel-
ody accompanied by counterpoint in the piano.
Part A'' (mm. 79-126) contains the same harmonic material
as the preceding sections of A and A'. The fluctuation in
harmonic tension is varied only slightly from the pattern of
the earlier sections. The climax of the movement (mm. 104-
107) employs chords of tension Group* I in measures 104 and
105, a chord of tension Group IV in measure 106, and a chord
of tension Group I in measure 107. Figure 35 illustrates
this climax--in measures 106-107.
d bn . -V ---7 - 4=3
I
-
53
PAll
4 4-f ..=..
Fig. 35--Horn Sonata, Movement II, mm. 105-107
The remainder of the movement is constructed primarily
with chords from tension Groups I and III, with the final ca-
dence in measures 124-125 using chords from tension Group III
and resolving to chords from tension Group I. The following
graph (Table VI) illustrates the fluctuation of harmonic ten-
sion in Movement II.
HARMONIC TENSION
V -i~~F7i11;
TABLE VI
FLUCTUATION IN SECOND MOVEMENTIN HORN SONATA
1-
b0 -0--- a- 4
!--tY 7
KiLL J4. ._JL . - - {i ..
r- -
._ __
-o - -.----IQ z~
T 1
E
" -" , {
_ , ___ i
-- i
t
L_I.I
Wrl
r 1
J Ah J
r
i
f
_ {
==--w .,. ..- w---.
._ , - _. __. .. f
._ .. _ __
__
i ..
TI
06: . IR 1l5.; . 110 Tr_ 1 ,.. .
I
-
54
Movement III
General structure.--This movement is essentially in
sonata-allegro form, but because of extensive use of recur-
ring motives, both in the exposition and development sections,
it will be treated in a different manner from that of the
other movements in this form.
Part A--Exposition (mm. 1.-61)
Group I (mm. _ In Group I there are four impor-
tant motives which make up the principal thematic material of
this section. These four motives are shown below in Figure 36.
V IOWMM 3-9
(P A NMM.8-9
u W.
JIM I-Em
Fig. b--Hor Sonata, Movement III, principal motivesof Group I.
Throughout the discussion of this movement, the different
motives will be referred to by number, e.g., Group I, Mo-
tive 1, Group II, Motive 3.
-
55
Following a short introduction, the horn states Mo-
tive 1 with a rhythmic accompaniment in the piano. In meas-
ure 8, Motive 2 is introduced in the piano, with the horn
stating it in measures 10 and 11. In measure 11 the piano
takes up the statement of Motive 2,. extending it, and leading
through a two-measure transition (mm. 12-13) to another state-
ment of Motive 1.. This statement of Motive 1 in the piano is
accompanied by a stretto statement of the same motive enter-
ing one beat later in measure 14.
In measure 21 Motive 3 is introduced in the piano, which
continues alone until measure 26, where Motive 4 is stated in
both piano and horn. Motive 4serves as a closing "theme" to
Group I,, which ends in measure 37.
Group . (mm. 38-61_) Group II is very sharply con-
trasted to Group I for two reasons- first, the abrupt change
in tempo (Group I is in 3/2 meter, marked Lebhaft withJ= 92-
100, and Group II is in 6/8 meter, marked Langsam with"=66)
and second, because of the involved rhythmic. patterns in the
accompaniment of Group II. These rhythmic figures, while not
a point of specific consideration in this study, certainly de-
serve mention, and they will be illustrated a little later in
this discussion.
Group II, like Group I, also contains four motives which
serve as the basic. thematic. material for this: section. In
Figure 37 on the following page are shown the four basic mo-
tives of Group II.
-
56
HORN,MM 1SiO
HRN 3 t--3
NQRV M 42-45
i~~l, MM .6573 3
t ww p
Fig. 37-Horn Sonata, Movement III,of Group II.
principal motives
In measure 38, Motive 1 is stated by the horn, and again
by the piano beginning in measure 40. Motive 2 is introduced
in measure 42 by the horn. The accompaniment in these meas-
ures (mm. 38-44) eonsista: of an ostinato rhythm based on
dotted sixteenth and thirty-second notes, shown in Figure 38.
Fig. 38--Horn Sonata, Movement III, mm. 38-39
t
"ii'
-
57
In measure 50 the piano begins another ostinato rhythm
which continues for six measures, and accompanies the state-
ment of Motive 3 by the horn in measure 53. Figure 39 shows
the basic outline of this ostinato rhythm.
Fig. 39--Horn Sonata, Movement III, mm. 50-51
Motive 4 is actually a continuation of Motive 3, but since
it is used separately in the development section, it has
been listed separately. In measure 57 the piano begins the
statement of Motive 3 (and 4) which continues through meas-
ure 61 leading to the development.
Part B--Development (mm. 62-8) The development is in
3/2 meter marked L= 92-100, and begins simply enough, with
the piano repeating the short introduction to the movement,
and the horn stating a variation of Group I Motive 1 begin-
ning in measure 64. In measure 67 this is expanded to in-
clude Motive 2 of Group I also. Beginning in measure 71
there are several entrances of Motive 2 of Group I in stretto
between piano and horn.
Beginning in measure 77 and continuing through measure
93, the piano plays another ostinato rhythm which serves as
-
58
basis for this section of the development. This ostinato
rhythm is shown in part in Figure 40.
Fig. 40--Horn Sonata,. Movement III, rhythm of mm. 77-78.
In this section of the development Hindemith alters
rhythmically the principal motives of Group II and they are
played by the horn against the ostinato rhythm in the piano.
Figure 37 shows the principal motives of Group II in their
original notation, and Figure 41 below shows them -in their
augmented notation into 3/2 meter.
Fig. 41--Horn Sonata, Movement III, rhythmic alterationof motives of Group II.
-
59
The rest of this section of the development (mm. 79-93) con-
sists of the statements of the motives of Group II against
the ostinato rhythm of the accompaniment.
In measure 94 the piano takes up the development melod-
ically, stating the rhythmically transposed version of Mo-
tive 1 of Group II. This is followed by a short transition
beginning in measure 97 which ends the development and intro-
duces the recapitulation.
Part A'--Recapitulation (mm. 102-154) In measure 102
Motive 1 from Group I is stated by the horn with the piano
providing an accompaniment similar to the beginning of the
movement. Motive 2 from Group I is stated in the piano in
measure 107, and then there occurs another short development
based on this motive (mm. 107-122). This motive is used by
horn and piano with stretto entries occurring in measures
110 and 120.
Measure 123 begins.. the only recurrence of any motive
from Group II in the recapitulation. Motives 3 and 4 from
Group II are stated in their rhythmically transposed form
first by the horn (mm. 123-127) and then by the piano
(mm. 127-136).
The recapitulation then returns to motives from Group I,
beginning a short development of Motive 3 from Group I in
measure 137. In measure 140 the horn states Motive 3 from
Group I, and this development is handled in the same manner
as was the development of Motive 2 in measures 107-122. The
-
60
development of Motive 3 extends from measures 137-147 where
the transition to the coda begins.
The transition to the coda is seven measures long
(mm. 147-153) and is:based on the short introduction to the
movement and also on Motive 4 from Group I.
Coda (mm.. 155-179) The entire thematic material of the
coda is derived from Motive 4 of Group I. The motive is
stated three times by the horn in measures 155-161, and two
stretto statements occur between horn and piano beginning in
measure 162. The piano then takes up the statement of Mo-
tive 4 with the horn playing an accompaniment figure (mm. 165-
170). Measure 172 begins the final statement of Motive 4,
with the rhythm returning to that of the introduction of the
motive (see mm. 26-28) in the exposition. This rhythm con-
tinues as the movement reaches its final cadence and concludes
in measure 179.
Tonality.--In the exposition of the last movement, the
tonal centers are not as clearly defined as in the previous
movements studied. The general tonality of Group I Motive 1
of the exposition (mm. 1-8) is "Eb, " with Motive 2 (mm. 8-
14) being stated in "F," "Bb," and t"Ftt alternately by horn
and piano. The key center returns to "Ebt in measure 15
when the piano states Motive 1. Motive 3 of Group I (mm. 21-
25) is in "Bb" in the piano statements. The closing motive
of Group I (mm. 26-37) is in "F" with the group ending on a
half cadence in "F" in measure 37.
-
61
Group II (mm. 38-61) has two primary tonal centers, "A"
and "F." The first two motives of Group II (mm. 38-49 and
mm. 50-53) are centered in "A," with the accompaniment re-
inforcing this tonal center through the ostinato rhythm.
The last motives (mm. 54-61) are centered in "F" with the
ostinato rhythm centered around this tonality.
The development section opens with a motival develop-
ment of the first motive from Group I in "G" (mm. 62-66).
In measures 67-76 the motive is again stated alternately by
piano and horn in changing tonal centers which are too
transient for the purposes of this study. The second sec-
tion of the development (mm. 79-98) is based on the themes
from Group II of the exposition accompanied by one of the
major ostinato rhythms. In measures 77-80 the tonal center
is "{#," and the tonal center is obscure in measures 80-84,
although in measure 84 a tonal center of "Bb" is predominant.
This "Bbu tonal center remains throughout the rest of the
development section (through measure 97).
The recapitulation section uses& the same tonal centers
for the statement of Group I (mm. 98-122) as did the exposi-
tion, i.e., the tonal center for Motive 1 is "Eb, " and Motive
2 is "Bb." The statement of the idea from Group II (mm. 123-
136) in the recapitulation is in "Bb" in both statements by
the horn and piano. The tonal center shifts to "F" in meas-
ure 137 and remains there until measure 147 where it shifts
-
62
to "F#" for three measures in a transition to the coda
section.
The entire coda section (mm.. 154-179) is centered
around "F," although temporary key centers of "Bb,t" "A,"
and "Ebt are found. The final cadence of the movement is
reached in measure 179,. climaxing several measures in which
the primary tonal center is "F."
Figure 42 illustrates the tonal centers of the third
movement as derived from the root and degree progressions,
and a melodic analysis.
Fig. 42--Horn Sonata, Movement III, Tonal Centers
Harmonic tension.--The accompaniment in Movement III of
the Horn Sonata is based primarily on the previously outlined
ostinato rhythms and contrapuntal devices. Therefore, with
the exception of a few isolated cases, harmonic: tension for
this movement is almost exclusively from tension Group I.
In the exposition of Group I (mm. 1-37) the accompani-
ment consists entirely of ostinato rhythms and counterpoint
of tension Groups I and III. In measures 1-3 there are three
chords from tension Group III, and the ostinato rhythm in
measures 4-7 is from tension Group III. The tension drops to
-
63
tension Group I in measure 8 and remains there until meas-
ure 26, when a few chords of tension Group III are used in
a restatement of the initial ostinato rhythm.
The exposition of Group II (mm.. 38-61) is. also based
on an ostinato rhythm in the accompaniment with a rating of
tension Group I, and with the exception of two chords from
tension Group II in measure 61, tension Group I is predomi-
nant throughout this section.
The development (mm..62-101) begins with a restatement
of the initial motive of the movement, with tension Group III
implied in measures 62-67. The accompaniment assumes- a linear
role again in measures 67-74 and the rating is again tension
Group I. With the return of the initial motive in the expo-
sition in measures 74-76 the tension is again raised to chords
from tension Group III.
In measure 77 the ostinato rhythm of Group II in the ex-
position is resumed (with the rhythmic transposition) and the
tension level remains at tension Group I throughout the rest
of the development.
The tension fluctuation of the recapitulation is almost
identical with that of the exposition, containing very few
passages with a construction that would permit the extraction
of absolute tension. The ostinato rhythm of the first motive
of Group I is stated in measures 102-106, and is again given
an implied tension Group III rating. The contrapuntal accom-
paniment of measures 107-122 returns to tension Group I. In
-
64
measures 123-127 the level is raised to tension Group III
through the use of the ostinato rhythm of the first motive
of Group I. A piano statement of the theme in measures 127-
136 contains a few chords from tension Group III, but there
is a predominance of tension Group I chords, both from the
rhythm and the actual harmony.
In measure 137 the third motive from Group I is stated
by the piano with an implied Group III tension in the accom-
paniment. This use of tension Group III chords continues
through the end of the section (m. 154) with only occasional
chords of tension Group I being used.
The coda (mm. 155-179) contains the principal use of
a harmonic accompaniment in the entire movement. The rating
remains at tension Group I level until measure 166, when the
piano begins the statement of the thematic material used in
the coda.
In measures 166-179, the harmonic accompaniment fluctu-
ates between chords of tension Groups I and III, with chords
of tension Group II being used in measures 172 and 173. The
final cadence of the movement (mm. 176-179) uses four chords
from tension Group III followed by the final chord from ten-
sion Group I.
The accompanying graph (Table VII) illustrates the
fluctuation of harmonic tension in Movement III.
-
HARMONIC
TABLE VII
TENSION FLUCTUATION IN THIRD MOVEMENTOF HORN SONATA
797
wINo
I -i
Y 777ij
Ism
C -+-
LLF~qs' 1SD
gS' Igo. ,., .
._
1
t
j
... .t ..
t. , ,
2 4, 71
1 or nto
b -
-
i. , .
,. .
_. - -_ .. i._ . _..
- t t
Lrr1,1
..
. ,
. ,
i ,
" . -
- - -
Sonata for Trombone and PianobyPau HindemithTI94+IF
The Sonata for Trombone and Piano: is written in four
distinct movements. to be played without pause. For the pur-
pose of this study, each movement will be treated separately.
Movement I
General structure.--Part A-4Exposition (mm. 1-3)
Group I contains two themes. Portions of Theme I are re-
peated four times in the first eighteen measures, twice by
the trombone, and twice by the piano.. During the entire
65
.}""'.'M" "
L- --
._-__.._._i-. _-. r
L- -i - - -
-- .
. _
. . ,
-
66
statement of Group I, an ostinato rhythmic figure is used in
the accompaniment to build the rhythmic tension. This rhyth-
mic figure is shown below in Figure 43.
VIAND 4
Fig. 43--Trombone Sonata, Movement I, mm. 1-2
This rhythmic figure is also very important in the cyclic
recapitulation of Group I in the fourth movement. Group I
ends with a two measure transition (mm. 18-19) to Group II.
Group II (mm. 19-27) contains- two presentations of its_
theme in eight measures, one by the trombone, and one by the
piano. The statement of Group II by the piano leads into
the development section.
Part B--Development (mm. 27-64) The development section
is centered around the principal five-note motive from Group
II, and its motival development. This five-note motive (shown
on the following page in Figure 44) is the basis for the en-
tire development section, and also recurs in the fourth move-
ment.
-
67
Fig. 44--Trombone Sonata,, Movement I, mm. 19-20
Following the transition to the development, the piano begins
the development of Group II by stating it in its entirety with
a counterpoint below it.. The trombone holds a pedal point
during this statement. In measure 37 the trombone states the
motive from Group II, while the piano begins a new rhythmic
figure, which is repeated in measures 40-45, again building
the rhythmic tension. Figure 45 shows the new rhythmic fig-
ure introduced in measure 45.
Fig. 45--Trombone Sonata, Movement I, mm. 40-42Group II returns in a fragmentary statement in measure 53 and
the piano resumes the development of the motive of Group II
(see Figure 44). This motive is stated by trombone and piano,
with stretto statements appearing in measures 60-64.
The retransition section begins in measure 65 with the
piano again stating the rhythmic motive used in measures 37-45
-
68
and shown in Figure 43. This: retransition begins with the
rhythmic motive stated very softly in measure 65, increasing
to forte in measure 71.
Part A'--Recapitulation (mm. 72-84) The recapitulation
is centered around a brief statement by the trombone of
Theme I of Group I accompanied by a canonic figure in the
piano. Figure 46 shows this rhythmic canon used in the ac-
companiment.
c
Fig. 46--Trombone Sonata, Movement I, mm. 72-73
New material is added in measure 74 wit