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PIANO QUINTET
THESIS
Presented to the Graduate Council of the
University of North Texas In Partial
Fulfillment of the Requirements
For the Degree of
MASTER OF MUSIC
By
Chee-Tick Tan, B.M.
Denton, Texas
May, 1997
21* mi
m . 7 J 7 y
PIANO QUINTET
THESIS
Presented to the Graduate Council of the
University of North Texas In Partial
Fulfillment of the Requirements
For the Degree of
MASTER OF MUSIC
By
Chee-Tick Tan, B.M.
Denton, Texas
May, 1997
21* mi
m . 7 J 7 y
Tan, Chee-Tick, Piano Quintet. Master of Music (Composition),
May 1997, Introduction 32 pp., Score 46 pp., 6 figures, 14 examples,
bibliography: 9 titles.
The thesis is a traditional piano quintet in the manner of Bartok,
incorporating compositional techniques such as golden ratio and using
folk materials. Special effects on strings are limited for easy conversion to
wind instruments. The piece is about 15 minutes long.
TABLE OF CONTENTS
LIST OF TABLE iv
LIST OF FIGURES v
LIST OF EXAMPLE vi
INTRODUCTION vii
ANALYTICAL NARRATIVES xii
First movement Second movement Third movement
CONCLUSION xxxi
BIBLIOGRAPHY xxxii
SCORE 1
LIST OF TABLES
Table page
1. Layout of the content of the interval selection x
2. Layout of the mvt. I xvi
3. Transpositions of my scale xxiii
4. Layout of the meter in Bartok's Mikrokosmos, no. 100 xxiv
5. Layout of the meter in mvt.III, (mm. 1-59) xxv
6. Layout of the meter in mvt.III, (mm.80-173) xxvi
7. Layout of the meter in mvt.III (mm.60-76) xxviii
TABLE OF FIGURES
figure page
1. Golden ratio xii
2. Calculation of the golden ratio of 34 and 55 xiii
3. Proportional ratio of Bartok's Music for Strings, Piano and celesta....xiv
4. Proportional ratio of mvt I of the Piano Quintet xv
5. Octatonic scale xxii
6. My scale xxii
LIST OF EXAMPLES
Example page
1. Piano part, mvt I, mm.l - 4 xvii
2. Strings, mvt.I, m.16 xvii
3. Violin I, mvt.I, mm. 16 - 17 .....xviii
4. Piano part, mvt.II, mm.51 - 52 xviii
5. Violin II, mvt.I, mm.83 - 85 xix
6. Bartok's Mikrokosmos, no. 128, mm 5 - 6 xxi
7. Violin II, mvt II, mm.58 - 59 xxii
8. Violin I part, mvt III, m.3 xxvi
9. Piano part, mvt.III, m. l l xxvii
10. Piano part, mvt.III, m.27 xxvii
11. Cello part, mvt.III, m.80 - 81 xxix
12. Cello part, mvt.III, m.94 - 95 xxx
13. Violin I, mvt III, mm. 122 - 123 xxx
14. Strings part, mvt III, mm. 144 - 145 ..xxx
INTRODUCTION
Overview
In the past few years, I have become very interested in Bela Bartok's
music and I have studied some of his scores. Among his chamber works,
Music for Strings, Percussion and Celesta is one of my favorites. As a
nationalistic composer, Bartok is famous for the use of folk materials in his
music, and this piece is no exception. Bartok's music has become a model
for my various compositions. My composition entitled Piano Quintet is my
homage to Bartok.
The instrumentation of my piano quintet is an intentional reference to
Bartok's Music for Strings, Percussion and Celesta. In my piano quintet, I
try to achieve a similar sound without using the same instrumentation.
Instead, I use the string quartet to represent the string part and the piano to
represent the percussion and the celesta parts. My piano writing is
predominantly percussive; heavy chords and dissonant intervals are
frequently used, especially in the lower register. As the piano is a
percussive instrument in nature, it can easily imitate the sound of a drum.
On the other hand, the strings do a better job for performing the legato
melodic lines. I have limited the use of special effects on the string parts so
that in the future, they can be played by wind instruments without needing
major revision.
In this piece, I try to incorporate Bartok's compositional techniques
while utilizing my own melodies and other compositional devices. Like
Bartok's music, my piano quintet incorporates folk material, thematic
transformations and the use of the golden ratio to determine the formal
structure. Yet, my compositional technique differs from Bartok's as a
result of my approach to harmonization, counterpart writing, fugal writing
and tonal planning.
Stylistic features
The first movement is toccata-like and uses short, detached,
syncopated rhythms. The movement is fast and should be played in a strict,
steady tempo. The piece is written using sonata allegro form and each
section can be clearly heard. The length of this movement is about 5
minutes.
The second movement is much more relaxed and the rhythm flows
freely. The first section is a fugue for string quartet only. The piano plays
only in the second section. There is also a theme in this movement which
resembles Bartok's folk tune. The length of this movement is about 4
minutes.
The third movement is an energetic dance movement. It contains
more metric changes than the other two movements and utilizes a large
variety of rhythms. This movement is also played in various tempos with
two andante sections embedded within this fast movement. All the themes
of the entire piece appear in the middle of this movement. This utilization
of thematic material is similar to the opening of the Finale of Beethoven's
symphony no.9. The length of this movement is about 4 minutes and 30
seconds.
In general, the texture of this piece is contrapuntal. Linear motion is
more important than the succession of vertical sonorities. Although
harmony is at times the incidental result of this contrapuntal motion, the
formation of vertical sound was carefully planned. When I composed this
piece, I tried to adjust the vertical alignments of each of the voices with
priority given to the intervals in the table 1:
Table 1. The content of interval selection.
priority interval inversion
1st A4 d5
2nd P4 P5
3rd M2 ml
4th m2 Ml
5th M3 m6
6th m3 M6
7th unison 8ve
The selection of intervals was the most important factor in
constructing melodies and their variations. Besides interval, rhythm is
another essential element since the change of rhythm can completely alter
the appearance of a melody without changing the intervallic relationship.
All of the themes are motivically related to each other. In some
places, these themes play simultaneously or follow each other in order to
create a sense of organic unity. For example, in the first movement, there
are two themes in the exposition and one theme in the development. All of
these themes reappear in the recapitulation.
The harmonic language employed in this work is an eclectic mixture
of both tonal and atonal sonorities. Different scales have been used in this
piece, they include: diatonic, chromatic, church modes, Messiaenic modes
and the octatonic scale, which was Bartok's favorite. The work starts and
ends with the note F, the pitch that serves as the tonal center for all three
movements of the composition.
FIRST MOVEMENT
The first movement is in sonata form, having sectional
division determined by golden ratio (golden section or golden means).
Many composers have use the golden ratio to compose their works;
among them, Debussy and Bartok are the most famous. The Golden ratio
is the division of a fixed length (A+B) into two segments so that the ratio
between the longer (A) and the shorter (B) segments equals the ratio of the
longer portion to the entire length, l (See Fig.l)
Figure 1 — Golden ratio
A B
II I II
(0.618) (0.382)
1. From Howat, Roy. Debussy in proportion, pg. 1 -4 . Cambridge: Cambridge University press. 1983.
In mathematical calculations:
A > B; B = A A A+B
The irrational value of the golden ratio (0.618034) is also
implied in the "Fibonacci" series. A characteristic feature of this series is
that every number is equal to the sum of the sum of the two preceding
numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.
As the series extends to higher values, it more accurately
approximates the irrational key-number of the golden ratio. For instance,
the golden ratio of 34 is 21, and that of 55 is 34. See at figure 2.
Figure 2 ~ Calculation of the golden ratio of 34 and 55
34 x 0.618034 = 21.013156
55 x 0.618034 = 33.99187
Bela Bartok is one of the composers that has used the golden ratio to
determine the structure of his music. An example is found in the first
movement of the Music for Strings, Percussion and Celesta, perhaps the
most often cited example using this proportional ratio.2
Figure 3 shows the sectional division of the first movement of
the Music for Strings, Percussion and Celesta, which consists of 89
measures and is divided into two sections of 55 and 34 measures each. It
starts at a pianississimo dynamic level, gradually rises to fortississimo at
mm.56, and recedes to pianississimo at mm.89. The section leading up to
the climax (m. 55) shows a division of 34+21 measures, and the section
following the climax is divided into 13+21 measures.
Figure 3 ~ Proportional ratio of Bartok's Music for Strings, Percussion and Celesta
89 55 34
34 21 13 21 I I I I I
21 13 *
PP 1 fff PPP
(* = climax)
2. Lendvai,Erno. Bela Bartok: An Analysis of his Music. London: Hahn and Averill, 1979.
In the first movement of my Piano Quintet, the relative length of the
three sections is determined by the golden ratio. However, the fibonacci
series was not used. Instead, the golden mean division is calculated using
the durational value of each section (0.618 and 0.382 respectively). This
calculation is based on the cumulation of eighth notes. In the figure 4
below, there is a clear calculation of the proportional ratio of the first
movement of the Piano Quintet.
Figure 4 — Proportion ratio of mvt.I
Exposition Development * Recapitulation I I 1 I < 6 x 2 3 x 3~ -->
8 4 4 4
(*= climax)
The number of eighth notes in the first section: (50x3) + (103x2) + (6x3) = 374
The number of eighth notes in the second section: 76x3 = 228
Section I : Section II
Exposition + Development : Recapitulation
374 : 228
0.621 : 0.379
Exposition + Development
0.621
Recapitulation
0.379
The first movement consists of a total of 235 measures. The
first large section is found in mm. 1-159 and includes the exposition and
development, the recapitulation lies within the second section. Table 2
below shows the layout of number of measures and the metric organization
of the first movement:
Table 2. Layout of the first movement
Section Measure no. No. of measures Meter
Exposition mm. 1-68 68 6/8 - 2/4
Development mm. 69-159 91 (85+6) 2/4 - 3/4
Recapitulation mm. 160-235 76 3/4
exposition
Piano
The movement opens with a short introduction in which the
piano plays an underlying low register F pedal point (see ex.1). The main
theme enters at m.3 in the piano and then again in m.16 in the strings (see
ex.2). The exposition lasts until m.68, where a second theme (see ex.4)
enters at m.51 in 2/4 meter, and leads to the development.
Example 1 — Piano part, myt.I, mm. 1-4
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Example 2 — Strings, mvtJ, m. 16
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The main theme (see ex.3) of the first movement contains five notes
derived from the whole-tone scale, in which the interval between each note
is a major second:
Example 3 — Violin I part, mvt.I, mm. 16-17
M2 Ag M2 , M2
The second theme (see ex.4) is derived from the first theme with the
Example 4 — Piano part, mvt.II, mm.51-52
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development
This section is the longest in the entire movement, there is new
third theme which is motivically derived from the main theme. This theme
consists of a compound line in which one part moves around a repeated A.
(see ex. 5). The interval between each note in the upper part is a second,
which is a variation of the first theme. However, this is based on an aeolian
scale rather than the whole-tone scale.
Example 5 ~ Violin II part, mvt.I, mm.83-85
intervals m2 m2 M2 ml m2 upper part C - B - C - D - E b - E
1np V * V \
* \ \
lower part
The development section is more contrapuntal and incorporates
dialogues and canonic passages throughout. This section develops material
based upon the second and the third themes. The music moves toward a
violin cadenza in m.91 which I call a " false climax." This is a term used to
describe a climatic section that sound as though it should have led into the
recapitulation; however, the music continues to develop further after this
climatic moment. From m.lOl, the music starts to build up again toward
the true climax in mm. 154-159. At this climatic moment, all of the
instruments play a unison, fortissimo passage. The meter changes from 2/4
to 3/4 and connects smoothly into the recapitulation section.
recapitulation
The recapitulation is in 3/4, which implies a hemiola effect to the 6/8
meter of the exposition section. The recapitulation starts with the piano in
the second beat of m.159, announcing the introductory pedal point of the
movement. However, instead of resounding an F, the pedal point states an
A that acts as a leading tone and moves to Bt». From m.162, the pedal point
in the piano reminds us of the exposition. The theme in the first violin part
in mm. 187-188 is the third theme. This is the first recognizable theme
from the previous sections.
There are functional harmonic passages in the recapitulation
section. The Eb section at mm. 182 exhibits a subdominant relationship to
the Bb section. However, the activities are not too busy compared to the
previous sections. The texture of this section thins after the reappearance of
the main theme at mm. 204. The whole movement ends with two
successive dyads on the piano.
SECOND MOVEMENT
This movement is in a slower tempo than the first movement.
It is divided into two parts as follows:
section 1: mm. 1-53
section 2: mm. 54-end.
I tried to imitate Bartok's folk material in this movement. Most folk
tunes are short, canatabile and in a simple rhythm. For example, in
Bartok's Mikrokosmos no. 128 (peasant dance), Bartok uses a short melody
to represent the spirit of the peasant (see ex.6)
Example 6. Bartok's Mikrokosmos no. 128, mm.5-6.
My melody (see ex.7) is an imitation of Bartok's folk tunes in the
example 6. I tried to write a short melody which shares the characteristics
of the folk tune in example 6. My melody is relatively short, rhythmically
simple, and is derived from a scale that is similar to the octatonic scale.
Example 7 — Violin II part, mvt.II, mm. 58-59
#1 #2
P 4- *
This tune is written from a scale which I deduced from the octatonic scale:
Figure 5 — Octatonic scale
I ,
— M J f 1
With F and B omitted, the note series will become:
Figure 6 ~ My scale
I , i • ' $ J J r m
This scale pattern doubles the range of the possible transposition of
the octatonic scale, allowing six transpositions, as shown in the table 3:
Table 3 Transpositions of the scale
1 C D D# F# G# A
2 C# D# E G A A#
3 D E F G# A# B
4 D# F F# A B C
5 E F# G A# C C#
6 F G G# B C# D
The whole movement is pastorale in nature. The first 15 measures
are a dialogue between the two violins, in 5/8 meter. From m.16, a fugal
section starts in 6/8. The two violins continue their dialogue, in m.23 the
viola enters as does the cello in m.25. The whole first section is played by
the strings without the piano. The piano enters in mm.54, which is the
beginning of the second section.
The second section of this movement provides a complete
contrast to the first section. This is an Allegretto in 4/8 meter and includes
the addition of the folk-tune theme. By using a faster tempo, the music
becomes more lively and dance-like. The dance keeps going with the theme
weaving among the lines. The whole movement ends on F in mm.85.
THIRD MOVEMENT
One of Bartok's compositional techniques is the use of an arch as a
structural determinant. The arch can be used to determine the formal
structure, metric organization, motivic design and other aspects of a
composition. For example, the selection of meters in Bartok's
Mikrokosmos no. 100 is clearly an arch form.(see table.4)
Table 4. Meter selection in Bartok's Mikrokosmos, no. 100.
measure 1 3 4 6 7 10 11 13 14 17 19 22 23
meter 5 3 5 3 5 3 5 3 5 3 5 3 5 8 8 8 8 8 8 8 8 8 8 8 8 8
I _ L L I
In my piano quintet, the third movement is divided into three sections:
section 1: mm. 1-59 section 2: mm.60-79 section 3: mm.80-73
This movement is composed in an arch form. The structure is
determined by using a method similar to that used by Bartok. I tried to
pre-select the meters before writing the notes. There are always central
meters that function as the axis of the symmetry. As table 5 shows, the 6/8
meter in m.4 (with an asterik indicated below the meter) acts as the axis of
symmetry for mm. 1-5. There are also axes between two arches; for
example, the 8/8 meter in m.8 is the axis for m.1-15. I used the arsch
form in the first (mm. 1-59, table 5) and the third sections (mm.80-173,
table 6). Both sections contain a total of 23 metric changes.
Table 5 Layout of the meter changes of mvt.III (m.1-59)
measure no.
meter 7 8
6 8
L
7 8
8 8
7 8
r:
11
5 8
I sk-
lS
7 8
15
6 8
16
7 8
23
7 16
27
7 8
29
8 8
30
7 8
31
6 8
32
7 8
33
8 8
34
7 8
36
7 16
40
7 8
44
4 8
48
6 8
49
4 8
50
7 8
I \z
Table 6 Layout of the meter changes of ravt.III (m.80-173)
0 00 1 112 | 130 13! ' 135 | 136 ; 144 150 j ! 154 158 t 159 161 | 162 | 163 { 164 166 ; 167 | 168 1 169 170 : i7i
CI r- 173 no. ; j i i I i I i i 1 ! j i !
• ! I ;
meter •' 5 : 6 I 5 4 5 4 ! 6 i 5 7 8 . 7 5 6 | 7 i8 ; 7 i 6 I5 ; 4 |3 : 9 : 3 10
: 8 • 8 !8
8 ; « r ! 8
I : 8 8 8 ! 8 8 8 !8 i«
i ; 8 : 8 ! 8 : 8 ! 8 ; 8 i 8
8
± _ j
Section I
* = axis of symmetry indicates the center of an arch-form passage
This movement starts with the low running bass line play on the
piano, in 7/8 meter. The main theme of this movement is an arch like
melody, as seen in ex.8. Here, the fundamental structure consists of an F -
Gb - F. In this respect, Gb functions as the axis in a small arching motive.
Example 8 -r Violin I part, mvt. Ill, m.3
i
In addition to utilizing this new theme, the themes from the first and
second movements also reappear in the opening section of the third
movement. In m.l 1 (see ex.9), the piano plays a theme derived from the
first theme of the movement. Later in m. 27 (see ex.10), the folk material
derived from the second movement appears.
Example 9 — Piano part, mvt.III, m. 11 *
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Example 10 ~ Piano part, mvt.III, m.27
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Section 2
The tempo of the second section is Andante con moto. There are
only four meter changes in this section (see table 6). The slow tempo,
with the relaxing atmosphere and the cantabile melody, is similar to the
first section of the second movement. After six measures, the music
gradually develops into a fugal passage in m.66. In mm.71-75, the texture
becomes more intense and the tempo accelerates, providing a transition to
the last section.
Table 7 Layout of the meter changes in mvt.III (mm.60-76)
Measure no. meter
60 9/8
70 7/8
71 7 / 1 6
76 5/8
Section 3
This section is the conclusion of my Piano Quintet. As a
culmination of the entire work, it includes a lot of material used in the
previous movement and the previous sections of this movement. The
figuration in the cello part at mm.80-81 (see ex.l 1) is reminiscent of the
opening of this movement. As seen in example 11, the cello part at
mm.94-95 (see ex.12) is derived from the first theme of the first
movement. The first violin part at mm.122-123 (see ex.13) is derived
from the third theme of the first movement. In mm. 144-145 (see ex.14)
the strings play the theme from the exposition of the first movment.
Unlike the other movements, the music becomes more intense toward the
end. The whole piece ends with two scales in contrary motion that each
end on F, the tonal center of the piece.
Example 11. Cello part, mm.80-81
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Example 12. Cello part, mm.94 - 95
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Example 13. Violin I part, mm.122 - 123
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Example 14. Strings part, mm.144 - 145
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CONCLUSION
In the end, I am glad that I have composed a work using a variety of
techniques that provide the trademark of Bela Bartok, my favorite
composer. Although it is not stylistically fashionable in the 1990's, this
homage is my first personal achievement to be able to apply another
composer's techniques within my own music. I hope to develop my own
personal style through this experience in the future.
BIBLIOGRAPHY
Antokoletz, Elliot. The Music of Beta Bartok: A Study of Tonality and Progression in Tweintieth-Century Music. Berkely: University of California Press, 1984.
Godwin, Paul Milton. A study of Concepts of Melody, with particular reference to some music of the Tweintieth century and examples from the composition of Schoenberg, Webern, and Berg. { Ph.D. diss., Ohio State University, 1972. )
Grout, Donald Jay and Palisca, Claude V.. A history of Western Music. 5th ed. New York: W.W. Norton and Company, 1996.
Howat, Roy. Debussy in Proportion: A Musical Analysis. Cambridge: Cambridge University Press, 1983.
Lendvai, Erno. Be la Bartok: An Analysis of his Music. London: Kahn & Averill, 1979.
Lester, Joel. Analytical Approaches to Tweintieth - Century Music. New York: W.W. Norton and Company, 1989.
Maxwell, Judith Elaine Shepherd. An investigation of Axis-Based symmetrical Structures in Two Composition ofBela Bartok. ( Ph.D. diss., University of Oklahoma, 1975.
Randell, Don. The New Havard Dictionary of Music. Massachusetts: The Belknap Press of Havard University Press, 1986.
Schoenberg, Arnold. Fundamentals of Musical Composition, ed. by Strang, Gerald and Stein, Leonard. London: Faber and Faber Press, 1967.
PIANO QUINTET
1996
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