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An Analysis of formal determinants in theFuneral Music for String Orchestra (1958) and
the String Quartet (1964) of Witold Lutoslawski
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Authors Bailey, Shad Culverwell
Publisher The University of Arizona.
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AN ANALYSIS OF FORMAL DETERMINANTS IN
THE FUNERAL MUSIC FOR STRING ORCHESTRA
(1958) AND THE STRING QUARTET (1964)
OF WITOLD LUTOSLAWSKI
by
Shad Culverwell Bailey
A Thesis Submitted to the Faculty of. the
DEPARTMENT OF MUSIC
In Partial Fulfillment of the Requirements
For the Degree of
MASTER OF MUSIC
In the Graduate College
THE UNIVERSITY OF ARIZONA
1 9 8 1
STATEMENT BY AUTHOR
This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.
Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
SIGNED: JilLzJ
(
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below:
E. W. MURPHY Professor of Music
r h J y /Date
ACKNOWLEDGMENTS
Profound gratitude to:
My parents9 James and Berneal Culverwell, for providing the
opportunity for me to pursue an early curiosity about music theory.
My teacher, Josephine Clark, for directing my curiosity in
a highly disciplined and progressive program.
My teachers. Dr. Leonard Pearlman and Mr. William Pflugradt,
for their patience and willingness to share some of their vast
knowledge of twentieth century music and compositional techniques.
My advisor, Mr. Pflugradt, for his guidance in the initial
stages of this project.
My reader and advisor, Dr. Edward Murphy, for his assistance
in the revisions and final draft of this document.
My husband, Robert, for his quiet and enduring encouragement.
TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS ................... vi
ABSTRACT . , . . . „ ......................... - x
1 o INTRODUCTION .............. 1
Need for the Study ................... 2Plan of the Study . ................. 3
2. FUNERAL MUSIC . . . . . . . ............................ . . . 5
Formal Concerns .......... . . . . . . . . . 6Formal Diagrams........................... 12Prologue and Epilogue ................... 18
Pitch . ............................. 18Rhythm ................... 24Timbre. ........................... 28Dynamics . . . . ............. . . . . . . . . . . . 32Texture . . . . . . . . . . . . . . . . . . . . . . . 33
Metamorphoses ............ 35Pitch ......................... 35Rhythm . ..................... 43Timbre . .............. . 48Dynamics ................ 48Texture ........................... 48
A p o g e e .............................. 50Pitch .......................................... 50Rhythm .............................. . . . . . . . . 51Timbre ..................... 51Dynamics ................ 52Texture.......... 52
Larger Formal Concerns . . . . . . . . 52Prologue and Epilogue . . . . . . . . . . . ........ 52Metamorphoses ............... 53Apogee ............ 54
Summary ............................... 54
3. STRING QUARTET ............ 57
Formal Concerns........................... 60Formal Diagrams . ................... 63X Motive . ........................... 68
iv
V
TABLE OF CONTENTS— Continued
Page
P i t c h ........................................................................ o o e 76Aggregates . . . . . . . . . ................ « 76Tritone and minor second . . . . . . . . . . . . 79
Rhythm . .......... . 84T i m b r e ........... • ............ 88
Con sordino . . . ..................... 88Non vibrato .............. 89Pizzicato............ 89Sul Ponticello ................ 91Glissandi . » 91
Dynamics .......... 93Texture ..................... 93
Larger Formal C o n c e r n s ........................... 95P i t c h ...................................... 95R h y t h m ............................... 96T i m b r e ......................... 96D y n a m i c s ................ 97Texture . . . . ............................. . . . . . 97
Summary................................................... 98
CONCLUSIONS .............................. . . . . . 101
P i t c h ...................................... . 102Duration . . . ............................... 103Timbre . ............................... 105Intensity............................................ 106Texture................... 107
5. BIBLIOGRAPHY .............. . - 108
LIST OF ILLUSTRATIONS
Figure Page
1. Funeral Music, Twelve-note r o w ......... 5
2. Funeral Music, Transition from Prologue to Metamorphoses 7
3. Funeral Music, Transition from Metamorphoses to Apogee . 9
4. Funeral Music, Transition from Apogee to Epilogue . . . 11
5. Funeral Music, Prologue, Form . . . . . . . . . . . . . 13
6. Funeral Music, Metamorphoses, Form .................. 14
7. Funeral Music, Apogee, Form . . ........................ 15
8. Funeral Music, Epilogue, Form . .........................17
9. Funeral Music, Prologue canon entry points ............. 19
10. Funeral Music, Epilogue canon entry points ............. 20
11. Funeral Music, Epilogue, Multiple entries on one pitch . 20
12.' Funeral Music, Epilogue, All entries on one pitch . . . 21
13. Funeral Music, Distribution of Prologue dyad pitches . . 22
14. Funeral Music, Epilogue,' Solo row statement interruptedby c a n o n ................ . . . .2 3
15. Funeral Music, Epilogue, Systematic deletion of pitches 24
16. Funeral Music, Epilogue, Measure of silence ........... 25
17. Funeral Music, Epilogue dyad durations............. 26
18. Funeral Music, Prologue dyad durations .................. 27
19. Funeral Music, Prologue, Irregular canon entry ......... 29
20. Funeral Music, Prologue and Epilogue comparative ranges 31
vi
viiFigure Page
21o Funeral Music, Metamorphoses, Vertical pitch class sets 36
22o Funeral Music, Metamorphoses, Sequence . ................ 37
23o Funeral Music, Metamorphoses, Sequence . . . . . . . . . 38
24. Funeral Music, Metamorphoses, Inversion, Sequence andretrograde inversion • • • • o 0 .o . . . . . . o.- 40
25. Funeral Music, Metamorphoses, Four-part Sequence . . „ . 41
26. Funeral Music, Metamorphoses, Repetition . . . . . » . . 42
27o Funeral Music, Metamorphoses, Syncopation withoff-beat accents.......................................44
28. Funeral Music, Metamorphoses, Off-beat accents . . . . . 45
29. Funeral Music, Metamorphoses, H e m i o l a ............. .. . 47
30. Funeral Music, Metamorphoses, Range . ........... 48
31. Funeral Music, Metamorphoses, Sparse chordalaccompaniment................................... 49
32. Funeral Music, Apogee, Aggregates ...................... 50
33. Funeral Music, Apogee, Instrument ranges ............... 51
34. String Quartet, Mobile 4, Single x motive . ............61
35. String Quartet, Mobile 4, Multiple x motive . . . . . . 61
36. String Quartet, Introductory Movement, Form . . . . . . 64
37. String Quartet, Main Movement, O v e r v i e w ........... 64
38. String Quartet, Main Movement, F o r m ........... 68
39. String Quartet, Mobile 4, x motive delineation............69
40. String Quartet, Introductory Movement, Octaveplacement of x motive . . . . . . . . . . . . . . . 70
41. String Quartet, Introductory Movement, Transformedx motive . . . ............................ 71
viii
Figure Page
42. String Quartet, Mobile 12, Transformation of x motive . 72
43. String Quartet, Mobiles 16 and 22, Transformationof x motive . ........................ 73
44. String Quartet, Mobile 38, Transformation of x motive . 74
45. String Quartet, Mobile 39, Transformation of x motive . 74
46. String Quartet, Mobile 41, Transformation of x motive . 76
47. String Quartet, Mobiles 1 and 2, Aggregate as aconnecting link . . . . . . . . . . . .............. 77
48. String Quartet, Mobiles 2 and 3, Aggregatefunctioning as a bridge . ............................ 77
49. String Quartet, Mobile 7, Fixed aggregate pitches foreach instrument ..................... .. . 78
50. String Quartet, Mobile 13, Overall tritone/minorsecond relationship . . . . . . . . . . . . . . . . 81
51. String Quartet, Mobile 27, Cadence pitches relatedto tritone and m2 ......................81
52. String Quartet, Mobiles 29-31, tritone/minor secondrelationship .........................................82
53. String Quartet, Mobiles 29-31, tritone/minor secondrelationship ............................... 82
54. String Quartet, Mobile 42, tritone/minor seconddistribution ............................ 83
55. String Quartet, Mobile 42, 0, 1, 2 , 3 set . . . . . . . 83
56. String Quartet, Mobile 46, Tritone arrangement . . . . . 84
57. String Quartet, Mobile 3, Use of full score . . . . . . 85
58. String Quartet, T e m p o .............................. 85
59. String Quartet, Mobile 42, Variable length fermatas . . 86
60. String Quartet, Mobile 7, Gradated note values ......... 87
ix
Figure Page
61. String Quartet, Mobile 25, Duration gradation inbowing patterns . . ........... 88
62o String Quartet, Mobile 50, Pizzicato used todelineate m o b i l e s ................... 90
63. String Quartet, Mobile 42, Extended glissandi at climax 92
64. String Quartet, Mobile 49, Glissandi on a repeatedpitCh 0 0 0 0 0 0 0 . 0 0 0 . 0 . 0 . 0 . 0 . 0 0 . 92
65o String Quartet, Mobile 9, Drone accompaniment ofVioloncello solo ........... 94
66. String Quartet, Mobile 12, X motive as a "quasihocket" t e x t u r e ..................... ............. 94
67o Funeral Music, Duration as it relates to overall form . 104
68. String Quartet, Imitation as it relates to overallform . . ............ 105
ABSTRACT' /
Both the Funeral Music for String Orchestra and the
String Quartet represent new directions in the music of the con
temporary Polish composer, Witold Lutoslawski<, The Funeral Music
offers his first use of serial composition, albeit applied only
to the first and last divisions of the work. Likewise, the
String Quartet contains his first usage pertaining to the elements
of aleatory, or chance, music. Unlike the Funeral Music, this
latter technique is applied throughout with but a few exceptions.
Analysis of the two scores by a parametric study of pitch,
rhythm, timbre, intensity and texture reveals a certain predilection
of this composer for favored intervals, twelve-note aggregates,
rhythmic gradation, uniform dynamics and imitative texture.
Aspects of larger formal concerns also reveal certain
tendencies common to both the Funeral Music and the String Quartet.
x
CHAPTER I
INTRODUCTION
Witold Lutoslawski, born January 25, 1913, is one of Polandf
leading contemporary composers. His works span from 1936 to the pre
sent and are representative of many genres. Large works include:
Symphonic Variations 1936-38First Symphony 1941-47Second Symphony 1966-67Overture for strings 1949Little Suite for chamber orchestra 1950Concerto for Orchestra 1950-54Five Dance Preludes 1955 rev. 1959Musique funebre for string orchestra 1958Three Postludes 1958-60Jeux venitiens 1961Livre 1968Cello Concerto 1970Mi-parti 1976
Chamber music is equally represented:
Trio for oboe, clarinet and bassoon 1945 Recitativo e Arioso for violin and piano 1951 Five Folk Melodies for strings 1952 Bucoliche (five pieces for viola and piano) 1952 Preludia taneczne for clarinet and piano 1954 String Quartet 1964Preludes and Fugues for thirteen solo strings 1971
Works for voice and instruments include:
Belated Nightingale and Mr. Tralala for voice and orchestra 1947
A Straw Chain for soprano, mezzo-soprano, flute, oboe, two clarinets and bassoon 1951
2
Five songs for female voice and thirty solo instruments 1958
Silesian Triptych for soprano and orchestra 1951 Three Poemes dTHenri Michaux for choir, wind instruments,
percussion, two pianos and harp 1963 Paroles tissees for tenor, string ensemble, harp, piano
and percussion 1965 Les Espaces du Sommeil for baritone and orchestra 1975
As the title suggests, this thesis will examine two of these
works, the Funeral Music for String Orchestra and the String Quartet,
in detailo
Need for the Study
At the time of writing, only one survey of the music of Witold2Lutoslawski was availablee The broad scope of Mr. Stucky?s study
does not allow a critical analysis of any one composition. In the
present writer's opinion there is a need to examine in detail at
least two representative works, one from an earlier and one from a
later style period, on order to establish consistent formal determinants.
The works list, performance reviews, numbers of awards and newly
commissioned works underscore the importance of this composer. It is
hoped that further studies of his compositions will be undertaken.
1. Nicolas Slonimsky, Baker's Biographical Dictionary of Musicians (New York: Schirmer Books, 1978), pp. 1053-1054.
2. Steven E. Stucky, "Part I: Kenningar (Symphony No. 4) Original Composition. Part II: The Music of Witold Lutoslawski:A Style-Critical Survey.", D.M.A., Cornell University, 1978.
Plan of the Study
An insight into the musical aesthetic of Witold Lutoslawski has
long been the object of Balint Andras Varga, publisher of the Editio
Musico Budapest. A series of taped interviews conducted on the
afternoons of March 12-17, 1973, in Lutoslawski’s home provided the3material for Varga’s book, Lutoslawski Profile. There is a decided
philosophical leaning to the Profile; Lutoslawski candidly discusses
his interest in composition, other twentieth century composers, and
his views on the worth of artistic endeavors in today’s society.
Gradually, a dualism may be perceived by the reader. On the
one hand, Lutoslawski acknowledges that he is not a "one school" com
poser, continually applying his craft to a single methodology. Along
with his claims of each work’s individualism, he also acknowledges
that there are compositional traits which remain a part of a composer’s
craft from one work to the next, i.e. a musical trademark. "If you
compare the works of a composer written in different periods of his
life, you will always find the same man behind them."
The bulk of this thesis consists of a parametrical analysis
of the Funeral Music and String Quartet to discover "musical trademarks"
which might exist. Each work is examined in separate chapters. Each
chapter begins with a general discussion and formal diagram; each
concludes with a look at larger formal concerns and a summary.
3. Balint Andras Varga, Lutoslawski Profile (London: J. & W.Chester, 1976).
4
Two of the large sections of the Funeral Music9 the Prologue
and the Epilogue, are discussed together because they share similar
compositional techniques. Canonic treatment utilizing different forms
of a twelve-note row and extended sections limited to pitch classes
f and b are studied. Rhythmic and dynamic augmentation and diminution
are touched upon. The combination of pitch, rhythm, timbre and
intensity into various texture types is discussed.
The Metamorphoses and Apogee are treated separately. The
gradual increase in both the simultaneous and successive densities
and overall dynamic level is examined in the Metamorphoses; the gradual
decreases in simultaneous and successive densities is studied in con
junction with an eventual dynamic decrease in the Apogee. Tabulations
of vertical pitch class sets found in the Metamorphoses are included
in this chapter. Resultant textures in both the Metamorphoses and
Apogee are briefly outlined.
The third chapter begins with an examination of the unique
use of aleatory techniques in the String Quartet. The x motive and
its transformations are shown in context and their uses are discussed.
The importance of the aggregate, tritone and minor second are examined.
The limited use of meter and rhythmic augmentation and diminution
provide materials for rhythmic analysis. Timbral concerns play an
important role in the Quartet. Each is discussed in a separate category.
Typical examples of textural and dynamic imitation are highlighted.
The paper ends with a summary and conclusions.
CHAPTER II
FUNERAL MUSIC
The Funeral Music for string orchestra is dedicated to the
memory of Bela Bartok. It consists of one large movement, divided into
four distinct divisions: Prologue, Metamorphoses, Apogee and Epilogue.
The measures are numbered consecutively throughout:
Measures 1 - 5 8 Prologue
Measures 59 - 233 Metamorphoses
Measures 234 - 245 Apogee
Measures 246 - 305 Epilogue
The Prologue and Epilogue will be discussed together in this
chapter. They represent Lutoslawski's only incursion into serial
composition. The row used in these two divisions is shown in Figure 1.
E z A _ D :g o V o ^ -
Figure 1. Lutoslawski, Funeral Music, Twelve-note row.
This twelve-note series consists of alternating tritones and minor
seconds never exceeding the span of a major seventh. Its presentation
is always linear and most often canonic. These canons range from two
to eight voices.
5
Sections in which all instruments repeat pitch classes f and
b alternate with the row canons. Each group (Violin I - II, Violin
III - IV, Viola I - II, Violoncello I - II with Contrabasses I - II
where applicable) is assigned a particular octave and duration. Entry
and exit points are staggered. Three of these tritone units are found
in the Prologue; two similar sections are contained within the Epilogue.
The Metamorphoses, longest of the four sections, is motivic.
Continuity is created by repetition and extension; rhythmic diminution
of motivic shapes creates an ever increasing sense of momentum. Verti
cal alignment of pitches reveals a predilection for certain pitch class
sets. Contrapuntal dynamics delineates particular tone colors but as
the Metamorphoses progresses, louder dynamics become more and more
commonplace; from measure 201 to measure 233 no dynamic except forte
or fortissimo is employed.
The Apogee is divided into three units. Each is begun with
a sustained chord made of a twelve-note aggregate. The first and
second units retain assigned aggregate pitches throughout. Each employs
a similar increase in successive density. The third unit gradually
decreases its successive density and does not retain its original
aggregate pitches; they, too, are decreased in number until all parts
are playing either pitch class na!l or pitch class "b^".
Formal Concerns
The four divisions are separated by different means. A grand
pause separates the Prologue from the Metamorphoses. A reduction of
simultaneous and successive density and intensity precedes the grand
7
pause. This provides a transition to the pianissimo irregularly
spaced pitches of the Contrabasses which begin the Metamorphoses
(Figure 2).
P.G
PC
ppP.G .
Vie I ell
P.G.Vc.IcD
P.GCb.
(attacca)
Metamorfozy • Metamorphoses
Figure 2. Lutoslawski, Funeral Music, Prologue-Metamorphoses, mm. 52-64, transition from Prologue to Metamorphoses.
8The immediate reduction of successive density from continuous
sixteenths of the Metamorphoses to the sustained tutti chord which
begins the Apogee creates a strong division (Figure 3).
3
Apogeum • Apogee
m dto appassionato}muisi vubalo)
, i i, w
m
m,n
m
f f i
M
Figure 3. Lutoslawski, Funeral Music, Metamorphoses-Apogee, mm. 231-235, Transition from Metamorphoses to Apogee.
10
The reduction of pitches to ja and coupled with a lessening
of successive density provides a smooth transition from the Apogee
to the Epilogue. The Epilogue immediately returns to the durations
and pitch content of the row forms; no value less than half note is
found in the canons. Likewise, no value is greater than a dotted
whole note, except in measure 249 (Figure 4).
Vni
Vc.
Cb.
11
Epilog • Epilogue
eul sol
Vn. n
DU IV
PPsul sol
Vie sul sol
Vc. I e 11
aCb.Icfi
PP
Figure 4. Lutoslawski, Funeral Music, Apogee-Epilogue, mm. 242-250, transition from Apogee to Epilogue.
f
12
The alternation between row canons and sections limited to
pitch classes f and b is illustrated in the formal diagram of the
Prologue (Figure 5).
Prologue
Section: A 1 2 3
Measures: 1 - 5 6 - 1 0 11 - 15
Dynamic: piano mezzo piano . mezzo forte
Device: two-voice canon three-voice canon four-voice canon
Instruments : VC I - II VLA I
VC I - IIVLA I - II VC I - II
4 5 6
16 - 20 21 - 26 26 - 30
quasi forte forte forte
six-voice canon eight-voice canon eight-voice canon
VLN III - IV VLA I - II * VC I - II
VLN I - II VLN III - IV VLA I - II VC I - II
VLN I - II VLN III - IV VLA I - II VC I - II CB I (doubling VC
B A B
29 - 35 33 - 38 37 - 43
- fortissimo mezzo forte fortissimo
f-b dyads eight-voice canon f-b dyads
(order of entry)
CB I - II VC I - II VLA I - II VLN III - IV VLN I - II
VLN I - II VLN III - IV VLA IVC I - II CB I
(order of entry)
VLN I - II VLN III - IV VLA I - II VC I - II CB I - II
Section: A B
Measures: 41 - 46 45 - 57 58
Dynamic: mezzo forte fortissimo pp grand pause
Device: eight-voice canon f-b dyads
Instruments: VLN I II (order of entry)VLN III - IV CB I - IIVLA I II VC I - IIVC I II VLA I - II
VLN III - IV VLN I - II
Figure 5. Lutoslawski, Funeral Music» Prologue, Form.
14
Formal design of the Metamorphoses is determined by the increase,
in which all parts share, in successive density. As each new value is
introduced, it first undergoes a period of irregular usage before
becoming the standard value (Figure 6).
Metamorphoses
Section:
Measures:
Fastestduration:
Attackdensity:
A
59 - 76 77 - 85
jirregular regular
86 - 101 102 - 112Jirregular regular
Section:
Measures:
Fastestduration:
Attackdensity:
113 - 128
D
129 - 141 142 - 221 222 - 233
irregular regular irregular regular
Figure 6. Lutoslawski, Funeral Music, Metamorphoses, Form.
15
Three distinct divisions in the Apogee delineate its form.
Both aggregates in the first half illustrate an increase of successive
density without changing assigned pitches until the cadence. In the
second half, assigned pitches are not retained; there is a reduction
in both numbers of pitches and successive density (Figure 7).
Apogee
mm.A 1
234 - 236
i236 - 238
P P0
pitch range pitch range
238 - 245
ityzr
o -
pitch range
Figure 7. Lutoslawski, Funeral Music, Apogee.mm. 234-236, 236-238, 238-245, Form and vertical range.
16
The Epilogue incorporates more diversity in its content than
did the earlier Prologue, In addition to the row canons and f - b
dyads the Epilogue employs a unison row statement, single measures
of rests and fragments of the row by a single instrument (Figure 8),
Epilogue
Section:
Measure:
Dynamic:
Device:
Instrument:
A1 B A
246 - 250 251 - 254 255 - 260
fortissimo pianissimo piano fortissimo piano
unison row
full ensemble
f - b dyads
VC I - IIVIA I - IIVLN III - IVVLN I - II
seven-voice canon
VLN I - IIVLN III - IVVIA I - IIVC I
B
261 - 266
piano fortissimo
f - b dyads
VC I - IIVLA I - IIVLN III - IVVLN I - II
A 1
265 - 268
fortissimo mezzo forte
eight-voice canon
VLN I - II VLN III - IV VLA I - II VC I - IICB I - II (doubling VC I)
269 - 273
mezzo forte piano
six-voice canon
VCVLA IVLN III - IV
274 - 278 279 - 284
piano pianissimo pianissimo
A
285 - 287
piano
A
288 - 289
pianissimo
four-voice canon two-voice canon solo row fragment six-voice canon
VLA I - II
VC I - II
VC I - II VC I VLA I - II VLN III - IV VLN II - I
17
290
Grand Pause
A
291
piano
single voice
VC I
A
292 - 294
pianissimo
six-voice canon
VLA I - II VLN III - IV VLN I - II
295
Grand Pause
A '
296
piano
single voice
VC I
297
Grand Pause
A
298
piano
single voice
VC I
299
Grand Pause
A
300 301
piano-dim. Grand Pause
single voice
VC I
A
302 303
piano-dim. Grand Pause
single voice
VC I
A
304
piano-dim.
single voice
VC I
305
rest
Figure 8. Lutoslawski, Funeral Music, Epilogue, Form.
18
Prologue and Epilogue
Pitch. Both Prologue and Epilogue employ canonic treatment
of the row (see Figure 1). Starting pitches of each canon are not
limited to the initial pitch of a row form. New entries in each of
the eight Prologue canons are related by tritone to the preceding
entry (Figure 9).
two—voice canon three-voice canon
V ■ • - i ') cf rm. 1 m. 6
four—voice canon six-voice canon
v n -----
¥-fei i vi
m. 11 mm. 16-17r
eight-voice canon
i f l B l \ 1 'I J
mm. 21-22
19
eight-voice canon
ir i 1
ram. 26-27
eight-voice canon
1r " tram. 33-35
eight-voice canon
i f Iram. 41-43
Figure 9. Lutoslawski, Funeral Music, Prologuemm. 1, 6, 11, 16-17, 21-22, 26-27, 33-35, 41-43,
Prologue canon entry points.
20Similarly, each new voice in the four adjacent Epilogue canons
(mm. 265-284) enters a tritone higher than the preceding last voice (Figure 10).
TV" - o o •--^ ----- T -- 1 ---e---tH2— : — X o
— cz___________________
Figure 10. Lutoslawski, Funeral Music, Epilogue, mm. 265-284, Epilogue canon entry points.
Other Epilogue canons employ different entry procedures for ensuing2 1 1voices. Figure 11 shows two entries on f , b , and f .
IVno l solo
W no D solo
IVno msolo
. IVno IVsolo
IVla I sola
I Via U sola
1 Vc. 1 solo
Figure 11. Lutoslawski, Funeral Music, Epilogue, mm. 255-259, Multiple entries on one pitch.
21
All voices enter on the same pitch in the canons beginning on measures
288 and 292 (Figure 12).
Violin II
Violin III
Violin IV
Viola I
Viola II
con sord
viir
f p non Jibr.
ppnon uibrcon sord.
ppnon wbr
non vibr.
Measure 288
Violin II
Violin III
Violin IV
Viola I
Viola II
Measure 292
Figure 12. Lutoslawski, Funeral Music, Epilogue,mm. 288, 292, All entries on one pitch.
22
The distribution of the dyad pitches is the same in all
three Prologue appearances (Figure 13).
Violins I and II Violins III and IV
$Ie e I
Violas I and II Violoncellos I and II Contrabasses I and II
Figure 13. Lutoslawski, Funeral Music, Prologue, distribution of Prologue dyad pitches.
In contrast, a particular octave is not constant for each part in the
two Epilogue dyad statements.
As shown in the formal diagram, three unique row structures
are found only in the Epilogue. The first is a unison row statement
made of P^ plus the first five pitches of 1 ^ (see Figure A). The
second is a solo 1^ row statement interrupted by a six-voice canon
derived from the same 1^ form (mm. 286-294) (Figure 14).
23
con surd
con lord
Jtpnon vibr
Vie
non vibr
Figure 14. Lutoslawski, Funeral Music, Epilogue, solo row statement interrupted by six-voice canon.
The third unique Epilogue row structure is a successive decrease in
the end of the row beginning with pitch nine of 1^. Rests are
interpolated between each segment (Figure 15).
3 5 rit. al f3 ^ 4
PC.
PGP .G .
PG P.G.
PGP.G
PC
PG.
p diminmtndo al finr
24
4 . 3p,® *r 2 3 r c2i'/ - j'jjj-jt i- ,j_ j i ---T iJ I I -. j i - = 3
Figure 15. Lutoslawski, Funeral Music, Epilogue, mm. 296-305, systematic deletion of pitches.
Rhythm. Each of the two types of pitch selection (row forms
or alternating f - b dyads) has a particular rhythmic association.
Only half and dotted whole notes are used in the row forms. As each
new canon begins, entries follow at half-note intervals. The dyads
are more diverse and use values ranging from one to five units of the
basic half-note duration.
Rhythmic contrasts exist between the Prologue and Epilogue
as shown in the following examples. The Epilogue contains measures
of silence (mm. 290, 295, 297, 299, 301, 303, 305). Each complete
measure of rest is a "grand pause" except the last instance which
substitutes a fermata in place of the "grand pause" (Figure 16).
25
*ord
PC
VniP -G .
P .G .
PC
P.G.
IV c. 1 solo
5 rit. al fine 3 P G4P.G
PC. PC.
Vni P.G.P .G .
P.G P.G.
P G .P .G .
Vie PCP .G .
PG.IV c. I
solo
p d im m m m do al finr
& ^4 . 3 p.c.®____pC 2 3 po 2 0 ̂i'f - j ,g i T - , 3 t - f -
Figure 16. Lutoslawski, Funeral Music, Epilogue,mm. 289-305, Measures of silence.
The Prologue has no periods of silence. Both Epilogue dyad sections
employ longer durations in each lower instrument (Figure 17).
Vni II
A'
Figure 17. Lutoslawski, Funeral Music, Epilogue, mm. 251-254, Epilogue dyad durations.
27The second of the three Prologue dyad sections, however, employs
shorter durations in each lower instrument (Figure 18).
.40.a
Vni U tuftiiVno 111 svlo
Vni m tutti
IVnoIV
Vni TV tutti
IVla Isola
IV la II sola
Vic U
IV c .I a =so lo ■■ S —
ahri
tubjf \ t u t t la l tn
\ t u t t i
Cb 1 • I tn
Figure 18. Lutoslawski, Funeral Music, Prologue,mm. 38-41, Prologue dyad durations.
28
The Epilogue expands its variety of meters by the inclusion
of ^ and ̂ the final eight measures (see Figure 15), This particular
arrangement allows the remaining pitches of the final 16 tetrachord
a starting position on the second half-note of the measure (mm. 298/ 300,3302, 304) preceded by a measure of ̂ "grand pause".
Timbre. There are no short articulations in either Prologue
or Epilogue. The only distinction between row forms and dyads is
the accent ( ) accompanying each separated dyad pitch. Notes not
associated with a slur do occur in the row forms but there are no
accents.
Dyad pitches are always doubled by instrumental pairs.
Doubling occurs in both Prologue and Epilogue row forms but not with
such consistency. Row doubling is limited to Violoncelli I and
Contrabasses (measures 26-30, beat 2; 265-269).
The addition and deletion of instrumental colors is in score
order for both row and dyad structures with one exception. Contra
bass I becomes the eighth voice in the seventh Prologue canon,
measures 33-38. Viola II does not enter (Figure 19).
29
l Vno I solo
*lln
1 Vno IIsolo
subffehri
Vni U
1 Vno HIsolo
sub.ffVm HI
attri
1 Vno IVsolo
Vni IV
sola
Vie
solo
IVc IIsolo
IC b .Isolo
Cb.
Figure 19. Lutoslawski, Funeral Music, Prologuemm. 33-36, irregular canon entry.
30
The only unusual range demand is for Contrabasses in the
opening Epilogue row:
\ e
A comparison of ranges between the Prologue and Epilogue shows that
each instrument employs a wider range in the Epilogue (Figure 20).
Prologue Epilogue Prologue Epilogue
-CL
Violin I
IViolin II
Violin III Violin IV
Prologue Epilogue31
Prologue Epilogue
y D .... ' .. - 1 * 0 . . ..... . b ^ — t ;-----A : — — N I - b ------ - - 1 ? ■ K ---- :
0
Viola I Viola II
Vo bo-bo.
* -e
Violoncello I Violoncello II
e e ^ *
Contrabasses I Contrabasses II
Figure 20. Lutoslawski, Funeral Music, Prologue and Epilogue comparative ranges.
Dynamics * The number of voices employed in the Prologue
and Epilogue canons is relevant to the dynamic level. As the number
increases in the Prologue* there is an accompanying increase in the
dynamic level:
number of voices dynamic level starting measure
2 piano 1
3 mezzo piano 6
4 mezzo forte 11
6 quasi forte 16
8 forte 21
As the number decreases in the Epilogue, there is a corresponding
decrease in the dynamic level:
number of voices dynamic level starting measure
8 fortissimo 265
6 mezzo forte 269
4 piano 274
2 piano 279
A similar correlation is shown in those canons which are immediately
preceded and followed by dyad structures.
33
number of voices dynamic level starting measure
8 mezzo forte 33
8 mezzo forte 41
7 piano 255
5 pianissimo 288
6 pianissimo 292
After each Epilogue voice enters, a diminuendo is begun» No
corresponding crescendo exists in the Prologue,
All Prologue dyads begin fortissimo and end with a diminuendo.
The final dyad extends its diminuendo to "pianissimo perdenosi".
Both Epilogue dyads begin piano and crescendo to fortissimo.
The row structures unique to the Epilogue are a dynamic4realization of larger formal concerns. The opening unison P row
begins fortissimo but diminuendos to pianissimo during its last note
and the five-note fragment which follows illustrating a descent
from the Apogee (mm, 249-250), As pitches are deleted from the
final tetrachord, a corresponding dynamic reduction takes place
signalling a further decline (see Figure 15),
Texture, The contrapuntal texture resulting from canonic
treatment of the row is shared by both Prologue and Epilogue; the
dyads also represent a contrapuntal texture because of the different
note values employed in each instrumental group. Both Prologue and
Epilogue employ a decrease in simultaneous density at the end of the
movement; both include alternating solo(i) and tutti sections
with resultant textural changes as shown in the following:
34Prologue
Solo
mm. 1 - 1 5
mm. 33 - 36
mm. 41 - 44
Tutti
mm. 16 - 32
mm. 37 - 40
mm. 45 - 58
Epilogue
Solo
mm. 255 - 260
mm. 285 - 287
mm. 291
mm. 296 - 305
Tutti
mm. 246 - 254
mm. 261 - 284
mm. 288 - 289
mm. 292 - 294
One notable difference may be seen in the canons of the
Prologue and the Epilogue. Proliferating canons from two to eight
voices begin the Prologue. Conversely, a reduction from eight to
two canonic voices is begun in the twentieth measure of the
Epilogue. Canons with an absolute number of voices both preceded
and followed by dyad structures are found only near the conclusion of
the Prologue. They occur, however, in both the beginning and middle
parts- of the Epilogue. These isolated Prologue canons have eight
parts. Those in the Epilogue have seven, six and six parts
respectively. The dyads in the Prologue and Epilogue are also
differentiated by simultaneous density; more varied and expanded
usage is found in the Prologue.
35
The unison row and fragmented for solo Violoncello found
in the Epilogue represent the only example of monophony in both sections.
Metamorphoses
Pitch. Pitch class sets, subsets and IC 1 provide harmonic
continuity in much of the Metamorphoses. All vertical chords from
measures 59-89 are 0, 2, 7 sets. The same 0, 2, 7 is a subset in
all but three of the vertical chords from measure 90-127 and in all
but one chord from measure 132-136. The 0, 1, 3 subset is common
to all but two vertical configurations from measure 137-158. IC 1
continues as the initial interval in sixty-six percent of the sets
from measure 159-188. Subset 0, 1, 2, 7 (variant of the original
0, 2, 7 set) is common to all sets from measure 188-224 with four
exceptions. A high incidence of an initial IC 1 is included in the
vertical sets from measure 225 to the conclusion of the Metamorphoses.
In summary, the vertical pitch class subset occurring most
often and thus providing the greatest unity is 0, 2, 7. It occurs
in forty-two percent of the vertical pitch class sets. The
following table is an itemization of all Metamorphoses vertical
sets and a tabulation of their number of occurrences (Figure 21).
36Vertical Pitch Class Sets
0. 1, 2 - 10
0, 1, 3 - 8
0, 1, 4 - 11
0, 1, 5 - 9
0, 1, 6 - 1 3
0, 2, 4 - 4
0, 2, 5 - 7
0, 2, 6 - 7
0, 2, 7 - 9
0, 3, 6 - 3
0, 3, 7 - 10
0, 4, 8 — 3
0, 1, 2, 3 - 2
0, 1, 2, 4 - 20, 1, 2, 5 - 2
0, 1, 2, 6 - 4
0, 1, 2, 7 - 1
0, 1, 5, 6 - 3
0, 1, 6, 7 - 2
0, 2, 5, 7 - 5
0, 1, 2, 5, 6 - 2
0, 2, 3, 5, 7, 9 - 12
0, 1, 2, 6, 7 - 2
0, 1, 3, 5, 6 - 1
0, 1, 2, 5, 7 - 1
0, 1, 3, 7 , 8 - 1
0, 2, 3, 5, 7 - 4
0, 1, 3, 5, 7 - 2
0, 2, 3, 5, 8 - 1
0, 1, 3, 5, 8 - 1
0, 1, 3, 6, 8 - 4
0, 2, 4, 6, 9 - 1
0, 2,4, 7, 9 - 12
0, 1, 2, 5, 6, 7 - 2 0
0, 1, 2, 6, 7, 8 - 1 1
0, 1, 2, 5, 7, 8 - 22
0, 1, 3, 4, 7, 8 - 1
0, 2, 3, 5, 6, 8 - 1
0, 1, 3, 5, 6, 8 - 17
0, 1, 3, 5, 7, 8 - 7
0, 1, 2, 4, 7, 8, 9 - 1
0, 1,-2, 5, 6, 8 - 2
0, 1, 2, 5, 6, 9 - 1
0, 2, 4, 5, 7, 9 - 5
Figure 21. Lutoslawski, Funeral Music, Metamorphoses, Vertical pitch class sets.
37Much of the horizontal profile is motivically organized and
extended by sequence, repetition and inversion. A sequence is
shown in Figure 22.
Vni »ul ponlir
aul pontic
Cb.
Figure 22. Lutoslawski, Funeral Music, Metamorphoses,mm. 70-73, sequence.
Figure 23 is a sequential pattern which moves from Viola I to
Violin III.
I
nVni
m
IV
IP'M)I
Vie
II
I
Vc.
II
Cb. 1 e U
Vni
Vie 'ord
mpVc.
JS1 d j
Figure 23. Lutoslawski, Funeral Music, Metamorphoses,mm. 79-85, sequence.
39Inversion, sequence and retrograde inversion are shown in Figure 24.
The exchange between instrumental groups is common.
JOOj
Vni
UlelV
Vie
Vc.
Cb. D
JO 5.
lell
Vni Dl
Vie
Vc.
Cb.
40
no]
VlB ■
IcE
Cb.
— : /
leD
Vie
leD
/
Figure 24. Lutoslawski, Funeral Music, Metamorphoses, nun. 98-114, sequence with inversion.
41
A varied sequence is illustrated in Figure 25. The fourth statement
is in retrograde and is also inverted.
Vni in
y* pesantf
v ie nJpesantt
Vc.
ptsantr
Cb.
fp esa n tr
125,
Vni IB
Vie II
Vc.
Cb.
Figure 25. Lutoslawski, Funeral Music, Metamorphoses,mm. 121-126, four-part sequence.
42Aural but not visual repetition is seen in the exchange of parts
between Violin I-II, Violin III-IV and Viola I-II (Figure 26).
I
D
Vra
Cb.
ff
Figure 26. Lutoslawski, Funeral Music, Metamorphoses,mm. 201-203, repetition.
43Unique to the Metamorphoses is the inclusion of complete
scalar patterns. Their name, type, instrument and measure number(s)
are listed below:
Name Mode Instrument Measure
Bb Major Violin I 169
E Major Violin I 170
Eb Major Violin II 171
Eb Major Violin I 172
E Mixolydian Violin II 173
Bb Dorian Violin.I 176-177
b Natural minor Violin II 177
bb Natural minor Violin I 181-182
B Phrygian Violin II 182
a" Natural minor ' Violin I 184
D. Dorian Violin I 185
C# , Dorian Violin II 186
C Mixolydian Violin II 187
Rhythm. Rhythm delineates form in the Metamorphoses. The
increase in successive density moves from irregular quarter-notes
with interpolated rests to a continuous sixteenth-note attack density.
Each new value is heard first on an irregular basis but becomes the
value of the attack density before a faster duration is introduced
(see Figure 6). Clear divisional lines are created.
44
This is not to imply that other durational values do not
exist in the Metamorphoses. Rhythmic variety is exemplified in the
Metamorphoses by syncopation, hemiola and off-beat accent. Syncopation
with accompanying off-beat accents is illustrated in Figure 27.
Vie
Vc. u
Figure 27. Lutoslawski, Funeral Music, Metamorphoses, mm. 90-93, syncopation with off-beat accents.
45
Figure 28 is typical of the off-beat accents found in the Metamorphoses.
Vni
Vc.
— //Cb.
Figure 28. Lutoslawski, Funeral Music, Metamorphoses,mm. 142-144, off-beat accents.
46Hemiola illustrated in Figure 29 sets Viola II against Violin III-IV
and Viola I; it is indicative of the rhythmic variety found in the
Metamorphoses.
j30Jle ll
Vni
Vie
Vc.
Cb
/
47
y ptsantr
Vni
Vie
Vc.
Cb.
/
Figure 29. Lutoslawski, Funeral Music, Metamorphoses, mm. 127-134, hemiola.
The use of many different meters is unique to the Metamorphoses.
(Meters of ^, 2* 2* and 2 occur in the Epilogue but ̂ and ̂are foundonly in the last eight measures.) Duple, triple, quadruple, and
quintuple units occur in irregular order from the beginning of the
Metamorphoses to measure 129 (seventy measures). A simple triple 3meter, ^ , begins in measure 129 and continues to the end of the
Metamorphoses (one hundred-four measures). This implies a quicker
succession of down-beat pulses which complements the increasing
successive density. The quarter-note as the basic duration is found
only in the Metamorphoses.
48
Timbre. Regular arco bowing is employed in most of the
Metamorphoses. Contrasts include combinations of sul ponticello
and pizzicato which occur from measure 59 through 85 (see Figure 2
for pizzicato) and combinations of measured tremolo and glissando
found in measures 232-233 (see Figure 3).
Ranges for all members of a particular string instrument
type are the same (Figure 30).
IViolins I - IV
I IViolas I - II
I iVioloncelli I - II Contrabasses I - II
Figure 30. Lutoslawski, Funeral Music, Metamorphoses, range.
Dynamics. Contrapuntal dynamics add variety to the overall
increase in dynamic levels from pianissimo to fortissimo during
the Metamorphoses.
Texture. An increase in simultaneous density continues
throughout the Metamorphoses with polyphonic and homophonic
49textures predominating. Monophony occurs only in the opening six
measures (see Figure 2). Homophony, often associated with sparse
accompanimental chords as illustrated in Figure 31 below, occurs with more frequency.
,120J
Vm m
Vc.
Cb
Figure 31. Lutoslawski, Funeral Music, Metamorphoses, mm. 118-120, sparse chordal accompaniment.
The increase in successive density from quarter to eighth and
sixteenth notes is first articulated in Violins I and II. Each occurs
in a homophonic setting. The polyphony which follows each increase
is a result of the faster durations having been incorporated into
the lower timbres. Motivic exchanges are common with this
assimilation.
50
Apogee
Pitch. Each of the twelve chromatic pitches is assigned1 2to a particular instrument in both A and A . Each aggregate is
arranged differently but remains unchanged in these two units; section
B, also consisting of a twelve-note aggregate at its inception,
employs a gradual reduction of pitches to a m2 dyad. This pitch
reduction is complemented by a gradual narrowing of range. The
three aggregates, arranged on either treble and bass clef staves or
on just a bass clef staff, show the distribution of the twelve
pitches as they occur in each of the three sections (Figure 32).
A* Composite B Composite
8vaV q I
pA Composite
a *
Figure 32. Ludoslawski, Funeral Music, Apogee, aggregates.
51
Rhythm. The Apogee meter of ^ is unchanging. However, slight
variations may exist becuase of the "molto appasionato, quasi rubato"
indication. Each of the three divisions is begun with a sustained
chord and each is separated by a rest. All parts move together.1 2Sections A and A each employ three increases in successive
density. The increases take place within the duration of a half
note. Section B employs six reductions in successive density. The
durations of the reductions vary in length but each takes the length
of at least two half notes.
Timbre. No special effects are employed. Ranges vary for
each part, including those from like instrument groups (Figure 33).
Violin I
IViolin II Violin III Violin IV
Viola I Viola II Cello I Cello II Contrabass I
£V s
33=
Contrabass II
1Figure 33. Lutoslawski, Funeral Music, Apogee,
Instrument ranges.
52
Dynamics. The Apogee is sempre fff.
Textureo A thick simultaneous density is created in sections
a V and A^ by the twelve-note aggregates; all but two chords within
the first nine measures include twelve pitch classes. As the number
of pitches is reduced in the final section, a parallel reduction in
density takes place.
Larger Formal Concerns
The larger formal concerns of the Funeral Music are reflected4in the definitions of each division:
Prologue - the preface or introduction to a discourse or performance; specifically,, the discourse or poem spoken before a dramatic performance or play begins; hence, anything which precedes an act or event.
Metamorphoses - the result of metamorphic action; any change of form, shape, structure, or nature; transformation.
Apogee - figuratively, the culmination of anything.
Epilogue - in oratory, a conclusion; the closing part of a discourse, in which the principal matters are recapitulated.
The literary connotations of "prologue" and "epilogue" are expanded in
this instance to include musical considerations.
Prologue and Epilogue. Parametrical comparison reveals a
balance and direct relationship between the two framing divisions.
Unity is created by their similar canonic treatment of the same row
with alternating f - b dyads. Canon and dyad durations and a soft
4. Webster's Twentieth-Century Dictionary (Unabridged)
53
dynamic ending are also shared. Similar articulations and instrumental
combinations (including solo and tutti groups) are found in both
divisions. The Prologue and Epilogue add and subtract canonic voices
to create a thinner-to-thicker or thicker-to-thinner texture. A
similar addition and subtraction process is shared in the dyads.
Contrasts are created by dynamics (in parts other than at
the ends of the divisions), timbre (by the inclusion of "con sordino"
and "non vibrato" in the Epilogue), rhythm (by the inclusion of periods
of silence in the Epilogue), and texture (Epilogue monophony).
Metamorphoses. In a larger sense the purpose of the Meta
morphoses is to break away from the confines of the Prologue and to
create a strong rhythmic, dynamic and textural build-up to the Apogee.
These ends are accomplished in the following four ways. First, the
rules of pitch selection ascertained by the row canons and dyads
in the Prologue are abolished; motivic treatment, modal scales and
a multitude of different intervals create strong contrasts to the
tritone, minor second arrangement of the row. Secondly, there is
a gradual increase in successive density. Each duration is first
established on an irregular basis but it becomes the characteristic
value of the attack density before the next increase in successive
density. Third, there is an overall increase in intensity. (Motives
are delineated by dynamics and thereby create some diversity to the
overall dynamic rise.) Finally, there is a gradual increase in
simultaneous density. This is accomplished by the addition of
instruments and is a by-product of the increased rhythmic activity.
54
Apogeeo The Apogee represents the culmination of the
Metamorphoses and is the high point or climax of the composition.
Simultaneous twelve-note aggregates are found in all but the last
three measures. The Apogee telescopes the successive density increase
of the Metamorphoses in its initial two statements. Each employs
a series of progressively faster durations. The intensity level (fff)
is the highest level of the composition. Timbral and textural contrasts
are created by different arrangements of the twelve-note aggregates.
Not sacrificed, however, is the dynamic level or number of instru
ments. The dynamic remains fff, and as the pitch content is reduced,
doubling of the remaining pitches retains the instrumentation of the
full ensemble.
The Apogee also represents a descent from the climax of
the composition. To facilitate the descent the twelve aggregate
pitches are gradually reduced to a dyad of two, the range is
diminished from over four octaves to a minor second and the successive
density is gradually reduced.
Summary
Unity and contrast create form on both intra- and inter-
divisional levels in each of the four divisions of the Funeral Music.
Intra-divisional unity is created in the Prologue by the
recurrence of both the canonic row and f - b dyad sections. Contrast
in the canons is created by the number of canonic voices included,,
the instrumentation and the order of instruments as they are added.
55Although the f - b dyads retain specific octaves for each instrument
as they appear in new dyad sections, contrast is created by duration
both in terms of the overall length of the different dyad sections
and with regard to durations for a particular instrument in different
sections.
Intra~divisional unity is created in the Epilogue by a similar
recurrence of the canon at the tritone and f-b dyads. Contrast is
created as the functions of the row are expanded to include unison
statements, solo statements and canons which allow entries at inter
vals other than the tritone. Contrast in the dyads includes
duration, both in terms of individual note values for different
instrument groups and in overall dyad section length, similar to
that shown in the Prologue. The use of different octaves of pitch
classes f and b for each instrument as they appear in different
dyads is a contrast unique to the Epilogue.
Unity is created in the Metamorphoses by the repetition of
certain vertical pitch class sets, the increase in successive density
and the overall increase of intensity and simultaneous density.
Contrast is created by the many different motives that make up the
horizontal profile, the rhythmic variety (hemiola, syncopation)
appearing as an adjunct to the overall increase in successive density
and the momentary shifts away from the overall increase of intensity
and simultaneous density.
Unity is created in the Apogee by a continuous successive
density gradation, one dynamic level and one meter. Contrast is
created by the change from two smaller sections employing an increase
in successive density to one long section of continuously decreasing
successive density. Contrast is also created by the reduction in
pitch content from a twelve-note aggregate to a two-note dyad in
the final section.
Inter-divisional unity and contrast is created by similar
and dissimilar pitch, rhythms, timbre, dynamic and textural controls
applied to each division. The Prologue and Epilogue create unity
because each is made of the same two compositional devices with
similar durations, simultaneous densities and timbral concerns. The
Metamorphoses and Apogee are contrasting divisions because each is
dependent on different unifying and contrasting parametrical controls
to create intra-divisional form and neither resembles either the
Prologue or Epilogue.
CHAPTER III
STRING QUARTET
The String Quartet was commissioned by the Swedish Radio on
the occasion of the tenth anniversary of the series of contemporary
music concerts, "Nutida Musik'% It was premiered by the La Salle
Quartet (Stockholm, March 12, 1965)» In a letter to one of its
members, Mr. Lutoslawski describes the work as "consisting of a
sequence of mobiles which are to be played, one after another, without
any pause if there is no other indication". In the ordinary sense,
"mobiles" refer to hanging art objects in which several parts are
suspended by nearly invisible filaments; air movement allows each
part its own freedom or mobility without disturbing the artist'sr
overall spatial conception. Lutoslawski has adapted the mobile
technique to music in the String Quartet. Each mobile is made of
from one to four parts and is governed by certain cues (aural and
visual) which serve as musical filaments. In turn each mobile,
with its connecting cues, retains a particular level of importance
to the formal plan as a whole. The mobiles are organized into two
divisions, "Introductory Movement", an introduction and mobiles
one through the first half of mobile thirteen, and "Main Movement",)
the latter half of mobile thirteen through mobile fifty-one.
57
58
The Quartet is unique because it represents the first
instance of aleatory, albeit controlled, in the music of Lutoslawski.
An explanation of its application and basic technique used in the
Quartet is excerpted from the aforementioned letter.
Within certain points of time particular players perform their parts quite independently of each other.They have to decide separately about the length of pauses and about the way of treating ritenutos and accelerandos. However, similar material in different parts should be treated in a similar way. You wrote that you ’must have a score so that each one knows what the other one is doing and at what points events coincide1. The point is that one of the basic techniques used in my piece is that in many sections of the form each particular player is supposed not to know what the others are doing, or, at least, to perform his part as if he were to hear nothing except that which he is playing himself. In such sections he must not bother about whether he is behind or ahead of the others. This problem simply does not exist because of measures which have been taken to prevent all undesirable consequences of such freedom. If each performer strictly follows the instructions written in the parts, nothing can happen that has not been foreseen by the composer. All possible lengthenings or shortenings of the duration of the sections as played by each particular performer cannot affect the final result in any decisive way. The lack of a score is partly compensated for by a whole system of signals written in the parts, fragments of the piece scored traditionally, frequent use of cues, etc. In a given part I have often written the part of another instrument when the first instrument is to accompany the second one.
You may ask me why I attach such a great importance to the non-existence of a score of my piece. The answer is quite simple: if I did write a normal score, superimposing the parts mechanically, it would be false, misleading, and it would represent a different work.This would suggest e.g. that the notes placed on the same vertical line should be always played at the same moment, which is the contrary to my intention. Further, it would prevent each performer from being free enough in his rubatos, ritenutos, accelerandos, pauses and above all in his own tempos. That would deprive the piece of its "mobile" character which is one of its most important features.
59
The "whole system of signals written in the parts" refers to
the aural and visual cues. The following examples typify the kinds
of performance cues employed in the Quartet.
Aural Cues
Mobile
Introduction
37
45
Instrument
Violin I
Violin II ViolaVioloncello
Violin I Violin II
Violin I Violin II Violoncello
Direction
repeat the phrase between repeat marks until the audience has become completely quiet
repeat until the entrance of Violin I then stop immediately
repeat until the ’cello’s ff pizz. chord, then play as far as the nearest rest and go on to 38
sustain this note until everyone reaches his A-flat. Then general pause for about one second
Visual Cues
42
Violin I give the viola a signal
Viola the first violin will give you asign before the beginning of the cue
Violin I repeat only if the viola and ’celloViolin II have not yet turned over their pages
Aural - Visual Cues
35 Violoncello
Violin II Viola
wait until everyone has finished before ff pizz.
go on immediately after the ’cello’s ff pizz. chord
60
Tempo flexibility is also indicated at certain points in the
score:
mobile 14 Each performer should play his part asif he were alone. Changes of speed (acc. and rit.) generally relate to individual parts and should be so treated
mobile 4 the wavy line suggests unequal distancebetween entrances
The reference to "fragments of the piece scored traditionally"
is illustrated in mobiles five, ten and eleven. In these instances
a different meter is assigned to each part and the tempo, "40
measures/min." is given. Metronome markings are indicated in mobile
five because less than a minute's worth, only seventeen measures,
is included. In mobile forty-three, also scored traditionally, all
parts change their fermata whole notes together. There is no tempo
or meter indication.
Formal Concerns
Two basic structures are contained in the Introductory
Movement. One, motive x, is made of separately articulated octaves
of pitch class "c". It occurs either singly (Figure 34) or in
extended groups of alternating instruments in different registers
(Figure 35).
61
Figure 34. Lutoslawski, String Quartet, mobile 4, Introductory movement, Single x motive.
vno I
vno II
via
vc.
) Uotr felufcct oiB*ct»x BlertiDne odxcpv e l td iy • I be e*vy Unr•uggeen unequal diataaor* befveeo entrances
Figure 35. Lutoslawski, String Quartet, Introductory Movement, mobile 4, Multiple x motives.
Usually the motive x occurs at the end of a mobile signalling the
beginning of a new imitative texture. As shown in Figure 35 the wavy
line suggests unequal distances between entries.
The second basic structure may be expressed in terms of
texture. Motivic fragments are shared among the four instruments in
many mobiles by imitation. Often, these fragments incorporate only
three pitches with a different set being assigned to each instrument
resulting in a combined twelve-note aggregate. Other times, pitch
selection overlaps without negating the effects of rhythmic imitation.
62A third subsidiary structure centered around the activities
of a single instrument for an entire segment is seen only in the
introduction and in mobile two. Unity in these monophonic segments
is created in large part by imitation and extension. Dynamic and
registral differences provide contrast in the introduction; durational
twists create a variety of patterns in mobile two.
The Main Movement is similarly organized into mobiles. The
x motive is no longer limited to a single pitch class but does retain
the same shape, unequal time allotment between entries and single
instrument order of presentation. The function of the x motive (to
separate textures) as seen in the Introductory Movement is found
only in two instances of the Main Movement, mobile thirty-nine and
at the end of mobile forty-seven. Moreoften, a transformation of
the x motive is employed as an integral part within many of the Main
Movement mobiles.
In addition to an expanded usage of the Introductory Movement
structures and materials, the Main Movement includes new compositional
techniques. Imitation may be shared among three instruments allowing
the fourth a more soloistic role. Two kinds of imitation may be seen
in one mobile by pairing. A set of the same materials may be included
for all parts within a mobile but in different orders of presentation.
Each part may be derived from a different contrasting Introductory
mobile thus creating a collage effect. Many mobiles of the Main
Movement are grouped into large divisions. These divisions are
determined by similarities of pitch, duration, timbre and intensity.
63
Formal Concerns and Diagrams
The formal design of the Introductory Movement is determined
by a recurring imitative texture, rather than specific pitch or
durational properties. Contrasting materials alternate with the
imitative texture; motive x which occurs at the beginning and end
of mobile four, at the end of mobiles five through ten and which is
the total substance of mobile twelve, delineates the textural changes
to establish a rondo form. Mobile thirteen is the Coda; its materials
are derived from motive x and the introduction (Figure 36).
Introductory Movement
Mobile:
Tempo:
Dynamic:
Texture:
x motive:
Introduction
recitative
variable
monophonic
A
1
slow
soft
imitative
B
2fast, sporadic
medium loud
monophonic
A
3a
fast, intermittent
soft
imitative
C
3b
slow
very soft
polyphonic
A
4
very fast
med. soft-very soft
imitative
before and after
D
5
moderate (metered) very soft
imitative
after
A
6fast, intermittent
very soft
imitative
after
64
E
7
varied
soft
freely imitative
after
A
8fast, intermittent long durations very soft
imitative
after
F
9
slow accel. fast
melody - varied accomp. - very soft melody with accomp.
after
D
10
slow(metered), very soft
freely imitative
after
11mod. slow
varied
imitative
x motive
12
fast
quasi loud
x motive
Coda
13
slow-recitative
very soft-varied
imi tat ive-melody with accomp.
Figure 36. Lutoslawski, String Quartet, Introductory Movement, Form.
Tempo, texture and intensity are key factors in the formal
organization of the Main Movement. The movement is divided into
four large divisions, the first two of which are largely determined
by textural controls; tempo and intensity share equally with texture
in determining the third and fourth divisions. An overview of the
movement is given in Figure 37.
Divisions: A B\ C (Dev.) D Coda
Mobiles: 13-34 35-38 39-42 43-50 51
Figure 37. Lutoslawski, String Quartet, Main Movement, Overview.
65
The mobiles of the first division are mainly imitative.
Sub-divisions are created by grouping together those mobiles which
employ a similar imitative device. The second large division is made
of mobiles which employ a double imitation or split texture. The
third division is the most complex and developmental. It contains
a variety of textures including a collage of assorted fragments from
mobiles of the Introductory Movement, an x motive design from assigned
aggregate pitches and imitation similar to that found earlier in the
movement. The highest dynamic of the Quartet is found in this
division; durational values are short providing an added element of
tension. The last division begins with a decided dynamic contrast
(subito piano) which prevails throughout the remainder of the movement.
Durations are slow for the most part with an occasional very fast,
excitable line designed to balance a slower, more soloistic part.
Figure 38 is a more detailed formal plan. The tempo, dynamics,
texture and any unique characteristics of each mobile (or groups of
mobiles, if applicable), is given.
Main Movement
Large division: A
Mobiles: 13 - 34
Sub-section(s): 1 13 2 14-23
Tempo (a), Dynamics (b), Unique Characteristics (c) Texture (d):
b) f«^>p, p ^ fc)d) imitative
a) very fast a) fastb) loud (soft in 14)c) all aggregates.
assigned pitches d) imitative
66
3 24-28 4 29-31 5 32-34
a) slow (variety by bowing patterns), fast
b) p<Kf, fc) slides, repeated
pitches form two tritones
d) imitative
a) VLN I recitVLN II, VLA, VC fast
I variedVIA, VC very
b) VLNVLN II, soft VLN II,c)
d)
VLA, VC eachassigned two pitches melody with accomp.
a) very fastb) VLN I p<ff>p, pp
VLN II, VLA pp VC p<Cff5=>p, pp
c) increased presence of motive
d) imitative
35 - 37
1 35 2 36
a) VLN I,II slow a) VLN I, VC fastVLA,VC varied VLN II, VLA very
b) VLN I,II cresc. b) VLN I, VC loudVLA, VC varied, final cresc. VLN II,, VLA pp<f
c) paired texture c) paired textured) double imitation d) double imitation
3 37
a) VLN I,II slow VLA, VC variable
b) VLN I,II pcf (repeated) VLA, VC variable
c) paired textured) double imitation
C (Dev.)
38 - 42
1 38
a) VLN I slowVLN II, VLA, VC variable
b) variablec) collaged) quasi imitative, polyphonic
67
2 39 3 40 4 41
a) moderateb) very loudc) motive x
aggregated) hocket
a) variable, fastb) soft, very loudc) collaged) imitative/collage
a) VLN I,II, VIA fast-slow alternationVC slow
b) VLN I,II, VIA med loud VC very loud
c) VLN I,II, VLA gradual revealing of x motive shape
d) imitative
D (textural recap)
5 42 43 - 50 2 45
a) variable, accel., slow 1 43-44 a) slowpresto, gradual ritard b) soft =-)
b) loud, soft^ff, very loud. a) very slow c) siciliano char., allsubito piano b) soft parts use same
c) aggregate reduced to four c) scored pitchespitches d) chordal d) imitative
d) imitative
3 46 4 47
a) slowb) very softc) made of VLA,d) imitation
VC slides
a) VLN slowVLN II fast, intermittent VLA, VC fast=v>slow
a*) continued ritardb) VLN I quasi loud
VLN II softVLA, VC very, very soft
b*) medium loud=£>ppc) VLA, VC mirrord) imitative with VLN II support dl) x motive hocket
68
5 48 6 49
a) VLN I variable VLN II fastVLA repeated, fast intermittent
b) VLN I soft, VLN II, VLA very softc) collaged) polyphonic
a) slowb) soft^>very softc) VLN I,II only
descending slidesd) imitative
7 50
a) VLN I,II, VLA very fast VC slow
b) VLN I, II, VLA med loud^=>soft VC (little) loud
c) three parts imitative, one independent
d) imitative with VC intro
CODA
51
a) VLN I,II, VLA fast-intermittent VC slow
b) VLN I,II VLA very soft, very very softVC med sof t<^ med loud
c) three parts imitative, one independent
d) solo, with accompaniment
Figure 38. Lutoslawski, String Quartet, MainMovement, Form.
Overall, the Main Movement appears to be one of continuous
development. Many of the mobiles employ the same intervals (minor
second, tritone, aggregate), textures (imitative, melody with
accompaniment, collage of unrelated materials) and duration patterns
(written out accelerandos and ritardandos) but no group of parameters,
including pitch, rhythm, timbre or intensity, ever returns in exactly
the same (or in a slightly modified) pattern.
X Motive
The x motive described earlier as repeated octaves of pitch
class c unifies the Introductory Movement because of its frequent
69
recurrence. It is found at the end or beginning of diverse imitative
textures and helps to create strong divisions. The first appearance
of the x motive is brief but with the help of a five second pause,
it delineates a diverse polyphonic texture from one that is highly
imitative (Figure 39).
vc.
vno II
Figure 39. Lutoslawski, String Quartet, IntroductoryMovement, mobile 4, x motive delineation.
70
All x motives of the Introductory Movement are taken from a
selection of the following four octaves of pitch class c_. Each of
the four octaves is represented by a numerical figure; the ordering
of the octaves as they occur in the different motive x patterns is
shown in Figure 40. The x motive is found at the beginning and/or
ending of the mobiles listed in the left column; a small x is placed
before or after the number according to its placement except for
mobile twelve which is made exclusively of motive x.
" , ".::o : ~
—
oO : — : -• =-/::z ---O _ o. ------------------
*Octave 1 2 3 4
Mobile Ordering of pitch class c octaves as they occur in motive x4 14 X 1 2 4 3 1 4 3 1 2 45 X 2 2 1 4 36 X 3 3 2 4 17 X 2 2 4 3 1 28 X 2 1 49 X 1 310 X 412 1 4 3 2 4 1 4 3 1 4 2
4 3 1 4 2 4 2 1
Figure 40. Lutoslawski, String Quartet, IntroductoryMovement, Octave placement of x motives.
71
The Main Movement does not include repeated octaves of c but
does incorporate a transformation of the x motive in many of its
mobiles. This transformation relates to both pitch and duration
but the basic shape of low-high alternation is retained. The
Introductory Movement includes two instances of x motive transfor
mation. The first is found in the introductory mobile for Violin I
(Figure 41). Here, neither repeated pitches nor perfect octave
leaps are retained but an alternating low-high shape is evident.
praripifsnrfo
Figure 41. Lutoslawski, String Quartet, Introductory Movement, Transformed x motive.
The second instance is at the conclusion of the movement.
After its initial presentation in mobile twelve, the x motive
creates a bridge to the recapitulation of the opening solo statement.
Rather than octave c's each instrument is assigned pitches from
an 0, 1, 2, 3 set made of pitch classes b, c, d^ and d. The
disposition of the pitches remains constant for each instrument;
their low-high alternation resembles motive x's basic shape
(Figure 42).
72
vno I
vno II
via
vc.
Figure 42. Lutoslawski, String Quartet, Introductory Movement mobile 12, Transformed x motive.
In the Main Movement mobiles fourteen through twenty-three
offer many good examples of x motive transformation. In mobile
sixteen the Viola employs an alternation of and b^* with frequent
repetition of one or both pitches. Again, the high-low alternation
resembles the x motive. In mobile twenty-two an intermediate2 y/ipitch (c ) is interpolated between the alternating low-high f and
2g , each of which is further emphasized by the inclusion of an
accent. Figure 43 illustrates the transformed x motives as they
occur in mobiles sixteen and twenty-two.
73
via■ rifaal tfcu pee here
Mobile 16
via
Mobile 22
Figure 43. Lutoslawski, String Quartet, Main Movement, mobiles 16 and 22, transformation of x motive.
Transformed x motives are illustrated in mobile thirty-six
in both Violin I and Violoncello against the background of fast-
moving thirty-second notes in the other two parts. Accents and
separate articulations help to set them apart.
A transformed x motive is included in one of the collage
mobiles (mobile thirty-eight). Here the Violoncello retains the
low-high shape of the x motive but rather than the exclusive use of
pitch-class c, the alternation is between the single lower d and
the higher two-pitch pattern of e ^ and d^\ The motive stands
74
out against its surroundings because of the dynamic (f), articulation
( » , and dotted eighth rests placed on either side (Figure 44).
vc.
Figure 44. Lutoslawski, String Quartet, Main Movement, mobile 38, transformation of x motive.
Mobile thirty-nine illustrates two x motive transformations.
The c’s are no longer used. Rather, each instrument is assigned
different pitches from twelve-note aggregates. Their positioning
and rhythmic placement provide the low-high alternation characteristic
of motive x (Figure 45).
pUi ca rvno I
cm V
vno II
ca I"
viaca rca I'-
V C .
odmlcpv esmmoive pomlfd&y posmcsegdlnymt mkofdemt pourtnny supetole ^ednmkoivr Uk disimnces bctveen penkulmr chord# should not be mbmoluiely equal
Figure 45. Lutoslawski, String Quartet, Main Movement,mobile 39, transformation of x motive.
75
Mobile forty-one illustrates a gradual unraveling of a
transformed x motive. In the three upper parts certain pitches are
set apart by interpolated rests, separate articulations and poco
ritard markings. These pitches, separated from the etc.
background pattern, retain the x motive shape by their low-high
alternation and retention of a specific ordering of pitches. The
Violoncello builds an outline of the x motive by adding one pitch
with each repetition of the pattern. Again, the c?s are not
employed;, pitches are chosen which typify the x motive high-low
basic design. Once established, the ordering of pitches is
constant (Figure 46).
76
vno IHi.
Vvno II
via
via
V C .
Hi.
ex; peuxa llcxp e*t od tale)
Figure 46. Lutoslawski, String Quartet, Main Movement mobile 41, transformation of x motive.
Pitch Aggregates.
Aggregates are an integral part of both the Introductory and
Main Movements. They create unity within individual mobiles and on
occasion serve as connecting links between two adjacent mobiles.
In many instances individual pitches remain assigned to particular
instruments for the duration of the aggregate. Figure 47 demonstrates
77
the aggregate as a connecting link between mobiles one and two
utilizing fixed pitches for each instrument.
Mobile 1 Violin II f e b^
Viola a d#
Violoncello g^ d c^
Mobile 2 Violin I c f^ g b
Figure 47. Lutoslawski, String Quartet, Introductory Movement, mobiles 1 and 2, aggregate as a connecting link.
In the above example the completion of the aggregate represents not
only a change in instrumentation but also a change in texture from
imitative polyphony to monophony. In Figure 48 (a bridge between
mobiles two and three) Violin II and Viola are added but the single
note chromatic line begun in mobile two is continued without a
change in character or texture.
vnoll
Figure 48. Lutoslawski, String Quartet, Introductory Movement, mobiles 2 and 3, aggregate functioning as a bridge.
78
In the Introductory Movement it is common to exclude the
pitch c from the aggregate until the x motive at the close of the
mobileo This occurs in mobiles six, seven, eight, and eleven.
Mobiles five, six, eight and eleven allow a sharing of pitches c^
through b among the members of the quartet. Mobile seven, one of
the rhapsodic and freely stated mobiles, employs fixed pitches for
each instrument. The Viola part is unique. In the first half of
mobile seven its pitches are the same as those of Violin II
(a^, c^, b, d); in the second half they duplicate those found in
Violin I (g^, f, a, f^) (Figure 49).
Violin I f f^ g^ a
Violin II c c# d a# b
Viola
Violoncello
c# b d
f a
e g eb (d^)
Figure 49. Lutoslawski, String Quartet, Introductory Movement, mobile 7, fixed aggregate pitches for each instrument.
Aggregates are often used to coalesce groups of mobiles into
larger units in the Main Movement. Many mobiles include all twelve
pitches shared freely among the ensemble but of particular interest
are those which employ fixed aggregate pitches for each instrument.
Mobiles fourteen through twenty-three represent such an example.
Only mobiles sixteen and eighteen present unique circumstances;
mobile sixteen does not include an f and mobile eighteen, begun with
79
a complete aggregate9 gradually reduces its complement to include only
c^9 d eb, e and f. (Each instrument includes d and one other pitch.)
Mobile thirty-seven is an excellent example of intra-mobile
unity achieved by assigning aggregate pitches to particular instru
ments. Violins I and II share pitches d f b; pitches d^ a g^ and
a^ are assigned to the Viola. The remaining pitches, c^ g a and d
are found only in the Violoncello.
Two examples of the basic x motive shape are found in mobile
thirty-nine. Each motive includes a twelve-note aggregate with assigned
pitches for each instrument (see Figure 45).
Mobile forty-two represents the longest single unit of the
Quartet. Its second half is begun with a wide-spread twelve-note
aggregate. The aggregate is prolonged by each instrument as it
divides its assigned pitches into two sets of alternating double
stops before continuing repeated articulations of the complete chord.
A final example of aggregate usage is found in mobile forty-
eight. Unlike many of the earlier assigned pitch mobiles, forty-
eight does not employ an equal distribution. Violin I controls
c c# f^ g a*3 a b^ and b ; Violin II has d e^ and f; Viola articulates
repeated e vs and the Violoncello is tacet.
Pitch. Use of the tritone and minor second. .
The recurrence, both in melodic and harmonic form of the
tritone and minor second is a second important pitch consideration.
Both the Introductory and Main Movements employ these two intervals
to create unity.
80
The first instance in which these intervals predominate
is the opening introductory statement for solo violin. Only three
kinds of pitch relationship are present: 1) no motion, 2) movement
by tritone above or below, and 3) movement by minor second above
or below. Octave displacement is allowed in each of these categories.
In the second half of mobile one, Viola employs only pitches
of the tritone a-d^. Violin II and Violoncello employ motives made
of one tritone and one minor second. Each of the Violin II and
Violoncello patterns is repeated in different octaves.
Mobile four is restricted to mostly minor seconds. Violin II
and Viola each have one instance of a melodic whole tone but the
effect of inconsistency is negligible because a sixteenth rest with
a fermata is interpolated between the two pitches which form the
whole tone. The starting pitches (Violin I, b^. Violin II, b^^, and
Viola, a^) are related by semitone but all parts resolve on a unison
d^ ̂before the return of the x motive (see Figure 39).
An overall tritone/minor second relationship exists in the
second part of mobile thirteen which is also the beginning of the
Main Movement. All parts begin the passage with an e^ and end
on e*, a minor second higher. The highest pitch is a^; the lowest
is a^. In addition to being related by semitone each of these two
pitches is related by tritone to either the beginning or ending
pitches (Figure 50).
81
i a
Figure 50. Lutoslawski, String Quartet, Main Movement, mobile 13, overall tritone/minor second relationship.
Mobiles twenty-four through twenty-eight all cadence on four
pitches related by both tritone and minor second. Mobile twenty-
seven illustrates this pattern (Figure 51).
vno I
U t fu n k e d begin [21]
(ID
vno II. . ------------ . — . ebigpkJem[II] together w*h Ike 1* Ttotin
viaI) [Ml remem s p*er— f > mkrmgp [111 u g e tk er e k k Ike 1* rlolln
V C .r e e g m ekngpkU mIke I* rlolln
Figure 51. Lutoslawski, String Quartet, Main Movement, mobile 27, cadence pitches related to tritone and minor second.
82
Mobiles twenty-nine through thirty-one each retain specific
pitches for Violin II, Viola and Violoncello. A vertical alignment
of these pitches reveals an on-going tritone/minor second relation
ship. In the following illustration, tritones are enclosed in
boxes; minor seconds are connected by lines (Figure 52).
Violin II
Viola
Violoncello
C
G
Mobile 29 Mobile 30 Mobile 31
Figure 52. Lutoslawski, String Quartet, Main Movement, mobiles 29-31, tritone/minor second relationship.
The initial pitches for Violin I consist of those which form two
tritones and are related by minor second (Figure 53).
Figure 53. Lutoslawski, String Quartet, Main Movement, mobiles 29-31, tritone/minor second relationship.
As the segment progresses, however, the above pitches in Violin I
are often ordered to form consecutive perfect fourths or fifths rather
than tritones or semitones.
Each of the x motives of mobile thirty-nine is made of a
different arrangement of the twelve chromatic pitches (see Figure 45).
Once established the pitches are fixed for each instrument. In both
83
instances the chords thus formed in each part are made of semitones
(with octave displacement).
The climatic twelve-note aggregate at the fff "poco largo"
in the mobile forty-two is distributed so each instrument includes
either a tritone or minor second in its chord spelling (Figure 54).
IB E I V o
Violin I Violin II Viola Violoncello
Figure 54. Lutoslawski, String Quartet, Main Movement, mobile 42, tritone/minor second distribution.
An 0, 1, 2, 3 set is created by combining the pitches from all four
instruments after the long bowed slide near the conclusion of this
same mobile (Figure 55).
— — — ——^
iFigure 55. Lutoslawski, String Quartet, Main Movement,
mobile 42, 0, 1, 2, 3 set.
A tritone (A - d) is formed at the conclusion of mobile
forty-six. Both parts are begun on a unison f but on its second
repeat the Viola's bottom pitch (d) forms a tritone with the bottom
pitch of the single major sixth Violoncello slide (f - A^) (Figure 56)
84
bafte erfth ike cello
viarr —-— rrr rf~H— — rrr rr — =“ rrr m̂ rnJo
VC.rr rrr ew n W o
Figure 56. Lutoslawski, String Quartet, Main Movement, mobile 46, tritone arrangement.
Only one of the normally scored sections (mobiles forty-three
and forty-four) employs the same basic duration for all instruments
thus making a traditionaly analysis of vertical structures possible.
A study of these chords reveals that eighty percent contain a semi
tone. The presence of both a semitone and a minor third is relatively
high (60%); chords containing both a minor and major second (30%) and
chords containing both a major second and perfect fourth (25%) are
somewhat less common.
Rhythm. Mobiles five and ten-eleven are the only ones that
employ meters, albeit a different meter, for each instrument.
(The same meters are retained in both instances.) A relative tempo
is indicated as there are no note values which have the same length
in any two of the four parts but vertical dashes are used in place
of traditional measure bars to aid in performance.
A full score is used to denote x motives to insure the proper
ordering of parts; it is also employed to insure chromatic pitch
ordering as found at the beginning of mobile three (Figure 57).
85
c»r cm I
vnoll
via>
Figure 57. Lutoslawski, String Quartet, mobile 3, use of full score.
Throughout the remainder of the Quartet, Lutoslawski has
indicated tempo by giving a time allotment in which a certain number
of a specific duration could be executed (Figure 58).
Introduction-Mobile 1 ca 5 J^/sec.
Mobile 2 piu mosso 7-8 ^ /sec.
Mobile 3-4 ca 5 ^/sec.
Mobile 5 metered
Mobile 5 (x motive) - 9 Tempo I
Mobile 10-11 metered
Mobile 12-13 ca 5 /sec.
Mobile 13-42 ca 7 f /sec.
Mobile 42 Presto ca 10 ^ /sec.
Mobile 43-44 no tempo indicated but slow because of the fermata whole notes.
Mobile 45-46 Funebre ca 5 J^/sec.
Mobile 47-51 5 ^/sec.
Figure 58. Lutoslawski, String Quartet, Tempo.
86
Innumerable tempo nuances are marked throughout each part.
In mobiles which require a certain ensemble relationship, written-in
musical cues are standard. Other visual and musical cues necessary
for "ensemble" within this aleatory context have been cited (see
pp. 59-61).The most common values in the Quartet are sixteenth and
thirty—second notes. Only a few mobiles have textural rhythms which
do not include sixteenth and thirty—second notes. Fermatas over
a value of rest and fermatas over which has been placed a duration
of time are common methods by which the flow of these faster note
values can be abated. The inclusion of a myriad of rests exerts
a considerable influence as well.
Another important rhythmic element includes a gradual
increase or decrease in the length of note values, rests or fermata
values. The first example illustrates how the length of fermatas
may be increased (Figure 59).
P R E S T O (ca 10 J/*ec.)
*mwc*koiu*mle por unlit)
I be bowing above
e a l-
da) aggnal loaym, te akodciylei give ibe otberaa you have finished
Figure 59. Lutoslawski, String Quartet, Main Movement,Violin I, mobile 42, variable length fermatas.
The beginning of mobile seven illustrates this same principle as
applied to note values. Violin I and Violin II parts have been
chosen for this example (Figure 60).
vno I
viavno II
Hi
Figure 60. Lutoslawski, String Quartet, Introductory Movement, mobile 7, gradated note values.
Instances similar to the above are found throughout both movements.
Another form of rhythmic gradation found only in the Main Movement
pertains to bowing patterns over a glissando. Figure 61 includes
three examples of this form of rhythmic gradation; it is not
unique.
88
m h i)vno I
■efecp •*o4ci* u cxa l) [M)I tanytn t
ev rrfoee hes llelsbed. begin1S6J together v ttb the t* h rn
vno II
:r e iib the 1st
V C .
>1) (MlMem Ik
Figure 61. Lutoslawski, String Quartet, Main Movement, mobile 25, duration gradation in bowing patterns.
Timbre. Instrumental sounds and effects are used extensively
in the String Quartet. Not only do they play an important role in
the delineation of form but they also highlight contrasts within
mobiles, between adjacent mobiles and between groups of mobiles.
Con sordino. Con sordino complements the introductory nature
of the opening violin statement and mobile one. Violin I employs
motives similar to those in the introduction in mobile forty-eight.
89
Con sordino is again employed; its return is initiated in this latter
mobile by a three-note Violin II pattern, also con sordino.
The only instrument not employing con sordino from mobile
forty-eight to the end of the Quartet is the Violoncello, Its
position at the end of mobile fifty-one as the solo line is similar
to the close of the Introductory Movement; con sordino in the
remaining instruments allows the Violoncello to be easily heard. One
of the three upper strings finishes the movement and thus brings back
the con sordino of the introduction. Which one of the three is never
known because of the aleatory factor.
Non vibrato. Non vibrato is associated with notes of longer
durations and is normally found following a release from previous
tension or heightened activity. Its first appearance is shortly
before the conclusion of the introductory statement for solo violin.
An important instance of non vibrato is found in mobiles forty-three
and forty-four following the most climactic mobile of the Quartet.
The non vibrato "indifferent" indication helps emphasize the release
of tension.
Pizzicato. Pizzicato is employed in the first normally
scored mobile (mobile five). It does not appear elsewhere in the
Introductory Movement with any degree of regularity except in the
three upper strings of mobile thirteen. In this capacity it allows
the solo Violoncello line to be heard much like the effect of con
sordino at the end of the Main Movement.
90
Pizzicato is first used in the Main Movement as an integral
part of mobiles fourteen through twenty-three. In mobile thirty-
five pizzicato in the two lower strings helps delineate the first
instance of split texture.
Pizzicato is also used to identify fragments within mobiles,
as in mobile thirty-eight which pairs pizzicato with those fragments
employing rhythmic gradation.
Pizzicato chords are used to signal the beginning of new
mobiles. This is exemplified in mobiles thirty-seven and thirty-
eight by the Violoncello. Pizzicato on a single note followed by
a glissando fulfills the same function in mobile fifty (Figure 62).
F°ccf
Figure 62. Lutoslawski, String Quartet, Main Movement, mobile 50, pizzicato used to delineate mobiles.
Pizzicato is used to help contrast the character of two
adjacent mobiles. The dark, sombre mood of mobiles forty-five
and forty-six (sub-titled Funebre) is immediately contrasted by the
fast ppp pizzicato of the Viola and Violoncello in mobile forty-seven.
The last primary use of pizzicato is to delineate the
Violoncello solo line in mobile fifty-one. Other uses of pizzicato
are strictly for momentary color and do not contribute to the
identity of a particular mobile or group of mobiles.
91
Sul ponticello. Sul ponticello provides unity and contrast
in mobiles twenty-nine through thirty-four of the Main Movement.
Initially? it is used exclusively in mobiles twenty-nine through
thirty-one in the three lower instruments to provide freedom for the
more soloistic first Violin. Later, mobiles thirty-two through
thirty-four employ a gradual replacement of sul ponticello by short
scalar motives in regular bowing. Single repeated pitches in mobiles
forty-seven (Violin II) and forty-eight (Viola) are the only other
examples of sul ponticello in the Quartet.
Glissandi. Glissandi are also found only in the Main
Movement. They create unity by being an essential part of mobiles
twenty-four through thirty-one (see Figure 51). Later, as mobiles
become more diverse, glissandi are used to identify certain recurring
fragments within two or more parts.
The longest glissandi are reserved for the most climactic
mobile of the Quartet (mobile forty-two). Viola and Violoncello
parts have been chosen to illustrate this instance (Figure 63).
92
PKESTO (c* loi/acc.)
lytmkowwUt pof my**l
p o iu line j a t do »u@niictelUiu. po cjpni pru
repeal 10 lbe cello' a »
ca 2" n ca 3" n ca <" c a T
P R E S T O (cm 10^/»ec.)
r™if i i H M M M ; :n ;
f l l j i see ibc bowing above
(* * ij p
Figure 63. Lutoslawski, String Quartet, Main Movement, mobile 42, extended glissandi at climax.
Other uses of glissandi are found in the Funebre mobiles
(forty-five, forty-six) and in the repeated pitches of Violin I in
mobile forty-nine (Figure 64).
vno I
Figure 64. Lutoslawski, String Quartet, Main Movement,mobile 49, glissandi on a repeated pitch.
93
Dynamicso Dynamics is one of the least utilized parameters
in the delineation of form within the Introductory Movement because
the overall level is. soft. Only during solo mobiles (including
the introduction) and mobiles which have a clearly defined solo part
does the dynamic level rise above mezzo forte.
Dynamics are used to establish both intra- and inter-mobile
identity in the Main Movement. The more diverse mobiles found in
the latter part of the movement use dynamics to unify particular
fragments found in different parts. Earlier, whole blocks of mobiles
retain one dynamic throughout. The climax of the Quartet (mobile
forty-two) reaches the highest dynamic (fff) and is made even more
effective by the subito piano which follows immediately and is
retained until the end.
Texture. Only a few mobiles in the Introductory Movement
do not have an imitative texture, the result of all instruments
sharing similar pitch, rhythmic, timbral and dynamic elements. The
exceptions are the introduction, mobile two and the end of mobile
thirteen (solo instruments), the last part of mobile three (independent
poloyphony) and mobiles nine and thirteen (homophony). An example
of the homophony found in mobile nine is given in Figure 65. Here
the Viola acts as a drone accompaniment to the Violoncello. Its
very soft dynamic and exchange of long-short durations is a strong
contrast to the variety of dynamics and rhythmic patterns illustrated
by the Violoncello.
94
Figure 65. Lutoslawski, String Quartet, Introductorymovement, mobile 9, drone accompaniment of Violoncello solo.
The only other texture found in the Introductory Movement is
the "quasi hocket" of mobile twelve. This is an extended x motive
which encompasses the entire mobile rather than assuming its normal
function as a transitory element between two adjacent mobiles
(Figure 66).
nVftvno I
n V
vno IICM 3"
via
vc.
Figure 66. Lutoslawski, String Quartet, Introductory Movement, mobile 12, x motive as a "quasi hocket" texture.
95
An analysis of pitch, rhythm, timbre and dynamics in mobiles
of the Main Movement has shown them to be coordinating factors in
the identity of certain groups of mobiles. Textural analysis of
individual mobiles reveals a variety of types ranging from imitation
in which all parts share one pitch pattern, one rhythmic pattern,
one timbral effect and one dynamic (or pattern of dynamics) to a
diverse kind of collage in which parts share facets of pitch and
duration taken from different mobiles of the Introductory Movement,
Other textures found in the Main Movement exhibit pairing of instruments,
melody with accompaniment and chordal arrangements. The textural
organization of the Introductory and Main Movements is included in
the formal diagrams (Figures 36 and 38),
Larger Formal Concerns
The mobiles of the Introductory Movement provide a nucleus
of materials to be expanded and transformed in the Main Movement.
Each of four parameters (pitch, duration, timbre and intensity)
along with textures resulting from their interaction contribute to
an understanding of larger formal concerns.
Pitch, Aggregates, both those which allow a sharing of
pitches and those which assign each of the twelve notes to specific
instruments, create unity by their recurrence in both the Introductory
and Main Movements,
Intervals, especially the tritone and minor second, share
equally in the responsibility of creating unity by their return.
96
The x motive? firmly established in the Introductory Movement
by its rondo-like return is transformed in the Main Movement by the
use of different pitches and durational values. By its reappearance,
in a variety of guises, unity is preserved.
Rhythm, Rhythmic gradation is present but does not play an
important role in establishing the identity of particular mobiles
in the Introductory Movement, Its use in the Main Movement, however,
is greatly expanded. Whole sections of mobiles include this rhythmic
device as an important means of creating unity.
The use of sixteenth and thirty-second notes is extensive
in both movements. In each, variety is achieved by different degrees
of rhythmic continuity. Some mobiles employ a motivic treatment
with the inclusion of many rests and fermatas; other exercise the
near exclusion of rests and fermatas.
Timbre. Con sordino occurs in both the beginning and ending
mobiles of the Quartet• Its return provides a unique balance of
color. Non vibrato is found in earlier mobiles but the only ones
which can include this effect as being critical to their identity
appear late in the Quartet (mobiles forty-three and forty-four).
Pizzicato is used sparingly in the Introductory Movement
appearing nowhere except in mobile five. In the Main Movement it
works in conjunction with twelve-note aggregates in establishing
the identity of a larger group of mobiles (mobiles fourteen through
twenty-three); elsewhere in the Main Movement it is used to delineate
intra-mobile fragments. Sul ponticello, found only.in the Main
97
Movements helps create unity in mobiles twenty-nine through thirty-
one and in mobiles thirty-two through thirty-four,
Glissandi are also important in establishing the identity of
mobiles twenty-nine through thirty-one. They perform the same
function in mobiles twenty-four through twenty-eight and in mobiles t
forty-five and forty-six. The importance of this effect in single
mobiles is seen at the height of the climax in mobile forty-two and
in the collage mobiles, i.e. mobile thirty-eight, as well.
Dynamics. Dynamic levels are not an effective means of
delineating larger formal concerns in the Introductory Movement
because the dynamic level is relatively soft throughout. The Main
Movement maintains a relatively high dynamic profile until after the
climax in mobile forty-two. The immediate contrast to a lower level
from the end of mobile forty-two to the conclusion of the Quartet
creates two large sections of dynamics in the Main Movement.
Texture. Divergent textures are created in the Introductory
Movement. Most important to the delineation of form is the continued
return of imitation and the recurrance of the "quasi" hoeket x motive.
Four large divisions can be articulated from the different textures
found in the Main Movement. These four divisions represent an
increase (divisions^ one through three) and subsequent decrease
(division four) in complexity.
The first division (mobiles thirteen through thirty-four)
continues the imitation established in the Introductory Movement
with some modification created by homophony in mobiles twenty-nine
through thirty-one.
The second division (mobiles thirty-five through forty-two)
allows fragments from earlier mobiles to interact in an exchange
among the four parts. The resultant "collage” effect represents the
most complex texture of the Quartet.
The final division (mobiles forty-three through fifty-one)
is created by a return to imitation (with modifications).
"Modification” includes reminders of the collage effect, quasi-
hocket 9 and melody with accompaniment along with the addition of a
new chordal texture. A strict recapitulation to imitation does not
exist.
Summary
The String Quartet does not follow regular scoring procedures.
The setting of parts is done with the understanding that each per
formance will necessarily be different due to the aleatory nature
of the Quartet. Complete freedom of performance, however, is not
allowed. Each player is made aware of his position by certain aural
and visual cues and must respond according to printed directions.
The work is divided into two sections, the Introductory
and Main Movements. Each movement is organized around a series of
self-contained units referred to by the composer as mobiles. The
movement from one mobile to the next is dependent on the afore
mentioned cues.
The Introductory Movement is centered around imitative
mobiles and x motives. The x motives create strong divisions in
99the Introductory Movement as they occur between adjacent mobiles
of diverse texture.
The Main Movement is also concerned with imitative mobiles
and x motives which undergo transformation. Both are adaptations
borrowed from the introductory Movement. An expanded use of imitation
is seen in the Main Movement as well as other representative textures.
Among these are monophony, homophony and a collage of different
fragments from earlier mobiles.
Pitch aspects are shared between the two movements. Of
particular importance are recurring twelve-note aggregates. Some
mobiles employ these aggregates as fixed pitches for particular
instruments; others allow a freer adaptation of instrumentation.
Specific intervals, the tritone and minor second, also play an
important role in many mobiles from both movements.
The same rhythmic concerns are not always found in both
movements. The use of assigned meters is limited to mobiles five,
ten and eleven, all from the Introductory Movement. The tempo of
other mobiles in both movements is determined by a given time
duration within which a specified number of notes of a particular
duration may be executed. Rhythmic gradation is included in the
Introductory Movement but its use is greatly expanded in the Main
Movement where gradation is seen in notes, rests, length of
fermatas and bowing patterns over glissandi.
Both movements employ an extensive use of timbral effects.
Included among these are con sordino, non vibrato, pizzicato, sul
ponticello and glissandi. These effects are used for momentary
100
color and/or to create unity among fragments9 mobiles or larger
groups of mobileso
Dynamic levels do not play an active role in the delineation
of form in the Introductory Movement because the dynamic is soft
throughout. They do, however, create unity and contrast in the
Main Movement. Of particular interest is the extremely soft ending
found in the three upper strings and the overall soft closing section
of the Quartet.
CHAPTER IV
CONCLUSIONS
The Funeral Music for String Orchestra and the String Quartet
each represent a new direction in the music of Witold Lutoslawski.
The Funeral Music is the first of his experiments in dodecaphonic
composition; similarly? the String Quartet is the first of his works
to explore the vast world of aleatory, or chance, music. Ironically,
the Funeral Music is not entirely a row composition nor is every facet
of the String Quartet decided on by chance. Rather, the particular
twelve-note row (see Figure 1) is only applicable to the first and
last divisions of the Funeral Music, the Prologue and the Epilogue,
and there are a few instances in the Quartet that are scored normally
and have a reasonable chance of sounding alike on repeated occasions.
Both works have separately named longer divisions, i.e., the
Prologue, Metamorphoses, Apogee and Epilogue of the Funeral Music
and the Introductory and Main Movements of the Quartet. Though
each work contains sectional divisions, both are performed without
pause between divisions. "Attaca" connects the two movements of
the Quartet and the first two divisions of the Funeral Music.
Continuous sound between the Metamorphoses and Apogee and between
the Apogee and Epilogue makes even "attaca" unnecessary.
101
102
Both works are for stringed instruments» This medium is
not new to Lutoslawski nor is it one that he has abandoned since the
Quartet; the Overture for Strings (1949) came nine years before the
Funeral Music and the Preludes and Fugues for thirteen solo strings
was written in 1971, seven years after the Quartet.
As one might expect the Quartet is more adventuresome with
regard to string writing than is the Funeral Music which was written
for a much larger ensemble. Even in the sections of the Funeral
Music written for solo strings, one on a part, durational and timbral
concerns are much less complex.
As suggested in the Introduction, the purpose of this paper
is to discover aspects of pitch, rhythm, timbre, intensity and texture
which create form, by either their recurrence or contrasting nature,
in both the Funeral Music and String Quartet. Analysis has shown
certain properties in each of the above categories to be operative
in both works; attention will now be directed to a summary of these
findings.
Pitch. A short recurring pattern, very limited in pitch
content, is used in both works to provide contrast to an otherwise
thick, multi-voiced texture. This pattern in the Funeral Music is
a tritone dyad (f - b) and in the String Quartet is a simple alter
nation of low and high statements of pitch class c which undergoes
considerable transformation (see Figures 17 and 39 as representative
illustrations). The recurrence of the dyad is not used throughout
the Funeral Music but rather is limited to the first and last
103
divisions; the x motive with its transformations is found in both
large divisions of the String Quartet.
Important to the structure of the String Quartet is the
use of tritones built from a variety of pitches. Likewise, the
entries of all subsequent canonic voices in the Funeral Music are
at the tritone.
Another interval equally important to both works is the
minor second. One of its main functions in the Funeral Music is to
alternate with the tritone in the formation of the row used in the
Prologue and Epilogue canons. This same kind of alternation is
shown in the introductory segment for solo Violin in the String
Quartet; this segment contains only tritones and minor seconds.
The third division of the Funeral Music, the Apogee,
exhibits an almost total pitch dependence on twelve-note aggregates.
Indeed, its first two sections maintain complete aggregates in all
but a very few instances; the last section employs a gradual
reduction of aggregate pitches to its concluding minor second.
Many mobiles of the String Quartet are based on aggregates.
Often the pitches are assigned in groups of three to each instrument
for an entire mobile; in other instances, pitches are not fixed
and move freely among members of the ensemble but there is a strict
avoidance of pitch class c, the twelfth member, until the use of
the x motive.
Duration. Duration plays an integral part in the shaping
of the Funeral Music. The Prologue and Epilogue employ mostly long
durations; both canons and dyad structures are limited to a
104particular selection of these durations." In a decidedly different
manner the Metamorphoses is dependent upon a gradual increase in
successive density to determine its overall shape. This gradation
moves from irregularly spaced quarter notes with interpolated rests
to regularly occuring sixteenth notes. Likewise, rhythmic gradation
is the basis on which the Apogee is formed. It maintains a peak of
activity in its first two segments, each of which begins with long
durations followed by increasingly shorter ones, thus creating an
internal acceleration. This peak is soon reduced in the third
segment by a gradual ritardando facilitated by using increasingly
longer durations. An overall view of rhythmic organization illustrates
the balance which this parameter provides to the Funeral Music
(Figure 67).
Prologue Metamorphoses Apogee Epilogue
stable increase decrease stable
Figure 67. Lutoslawski, Funeral Music, duration as it relates to overall form.
Similarly, rhythmic gradation plays an important role in the String
Quartet. Many mobiles employ increasingly shorter or longer
durations with regard to notes, rests and sometimes fermatas. At
times, only one instrument will exercise this technique (as in mobiles
twenty-nine through thirty-one) to establish its soloistic role
against a more regular rhythmic background of the other members■ ' <• ■ . .
of the quartet.
105
The rhythmic relationships exercised among the various
instrumental groups in the Funeral Music provides an example of
imitation. Rhythmic imitation is also operative in the String
Quartet in a decided way; the integrity of many of the mobiles in
the Introductory Movement is dependent on a similar rhythmic
pattern being found in all parts. The Main Movement also illustrates
this rhythmic imitation as it pairs instruments in groups of twos
(mobiles thirty-five through thirty-seven) or distributes a set
or group of rhythmic patterns taken from different Introductory
Movement mobiles into collage-like patterns. This latter culminating
effect is found particularly near the climax of the Quartet, most
explicitly in mobiles thirty-eight through forty-two. Not to be
forgotten are those early and late mobiles of the Main Movement
which are treated in much the same manner (one imitative pattern
for all instruments) as seen in the Introductory Movement. Overall
the imitative aspect of duration creates form in the String Quartet
much like rhythmic gradation is able to do in the Funeral Music
(Figure 68).
mobiles 1-34 mobiles 35-37
simple more complex
Figure 68. Lutoslawski, it relates to overall
Timbre. There is a decided difference in the use of timbral
effects in these two works. Their very absence in parts of the
Funeral Music is important; nowhere in either the Prologue or
mobiles 38-42 mobiles 43-51
most complex simple
String Quartet, imitation as form.
106
Epilogue is there anything but straight arco bowing. The only
distinguishing type of articulation is in the dyad sections which
employ single strokes, each of which is accented. The alternation
between soli and tutti groups is yet another timbral difference;
it is employed only in the Prologue and Epilogue of the Funeral
Music and is not found in the String Quartet at all. The most
similar of the Funeral Music divisions to the timbral effects of
of the String Quartet is the Metamorphoses but its use of sul
ponticello and pizzicato is limited and does not affect larger formal
concerns.
Nowhere in the Funeral Music is there the use of timbral
effects, other than the solo-tutti alternation, to establish larger
divisions as found in the String Quartet. Here, whole sections of
mobiles employ a single device, i.e. glissandi (with or without bowing
patterns) and sul ponticello. Single mobiles employ a particular
technique, i.e. pizzicato, to establish their own identity while
others employ a variety of effects to help distinguish motives
borrowed from earlier mobiles.
Intensity. Intensity is an important factor in the delineation
of form in both the Funeral Music and String Quartet.. In the Funeral
Music the same intensity level is usually retained for the entire
ensemble; contrapuntal dynamics are employed to some extent in the
Metamorphoses but even in this longest of divisions an overall dynamic
increase predominates. The most climactic of mobiles (number forty-
two) and the most climactic of divisions (Apogee) reach the highest
intensity level (fff) in their respective works. Similarly, the
107conclusions of both the Funeral Music and the String Quartet illustrate
a dramatic lessening of intensity allowing both works a rather intro
spective, soft endinge
Textureo Textural properties are also an important form
delineating technique in both compositions. The number of voices
constituting the various canons of the Prologue and Epilogue determine
their texture; generally this is shown to be a matter of increase in
the first instance resulting in a progressively thicker texture and
the opposite, or a decrease in the number of voices with a corresponding
progressively thinner texture, is true in the latter case. The
increased rhythmic complexities of the Metamorphoses create its
progressively thicker texture which is continued through the opening
of the Apogee before its eventual decline.
The String Quartet is organized in a different manner. It
moves from a single textural control (imitative) to a more complex
system (paired imitation) and finally to an arrangement of many
diverse fragments within a single mobile (collage) before returning
to a more simplified imitative texture in its last section.
Although both works include some instances of melody with
accompaniment and monophony, the main textural control is by imitation.
Finally, it has been shown that the four parameters (pitch,
duration, timbre and intensity) and their resultant textures do
delineate form in both the Funeral Music and String Quartet and that
certain elements from each of the above parameters are utilized in a
similar manner in both works.
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Heyworth, Peter. "A Thorn Grows in Warsaw." Hi Fi (1965) : 60-65.
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Lutoslawski, Witold. "Doctoral Speech." Polish Music 8 (1973):18-19.
Lutoslawski, Witold. "Funeral Music" (et al.). Orchestra Symphonique de la Philharmonic Nationale de Varsovie, conducted by Witold Rowicki. Philips 6500 628.
Lutoslawski, Witold. Musique Funebre. Warsaw: Polskie WydawnictwoMuzyczne, 1958.
Lutoslawski, Witold. "Reflections on the Future of Music." Polish Music 7 (1972): 3-6.
Lutoslawski, Witold. "String Quartet" (et al.). La Salle Quartet. Deutsche Grammophon 2530 735.
Lutoslawski, Witold. String Quartet. Warsaw: Polskie Wydawnictwo Muzyczne, 1968.
Marek, Tadeusz. "Contemporary Polish Composers." Polish Music 8 (1973): 4-17.
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