symmetry and pitch-duration associations in boulez' le

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Symmetry and Pitch-Duration Associations in Boulez' Le Marteau sans maîtreAuthor(s): Steven D. WinickSource: Perspectives of New Music, Vol. 24, No. 2, (Spring - Summer, 1986), pp. 280-321Published by: Perspectives of New MusicStable URL: http://www.jstor.org/stable/833238Accessed: 13/06/2008 08:02

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SYMMEIRY AND PITCH-URATION ASSOCIATIONS IN BOUTE7,' LE MARTEA U SANS MAITRE

STEVEN D. WINICK

e Marteau sans maitre is one of Boulez' most widely known compositions and yet it remains one of his most enigmatic. In contrast to Polyphonie X

(1951), the two Etudes (1951-52), and Structures, book one (1951-52) which immediately preceded Le Marteau (1953-54, revised 1957) and whose pitch, duration, dynamics, and modes of attack are strictly serialized and relatively easily analyzed, the compositional processes in Le Marteau are obscured by transformed serialization, veiled relationships, and speed and complexity of texture.

One aspect of Le Marteau which has been generally overlooked is that of pitch-duration association. This technique usually associates pitches of an ascending chromatic scale with durations which increase arithmeticlly by small increments, such as a sixteenth note. For example, C = , C = , D = ,

Boulez' Le Marteau sans maitre

DO = J, etc. I will refer to this as a pitch-duration association based on C, or a PDA = C. What I will attempt here is to share a few discoveries and observations of my own concerning the use of PDA's and their influence on the overall structure of movement VI ofLe Marteau.

Le Marteau's glassy, ethereal sound of pulverized, constantly changing pitches, dynamics, timbres, and rhythms mirrors the surrealist poetry of Rene Char upon which the composition is based. This kaleidoscopic soundscape seems as fragmented as the text, and both transmute the irrational chaos of our

age into music. It is well known that Boulez is reluctant to explain his own compositions.

When asked to supply program notes for the first performance ofLe Marteau in 1955 at the Baden-Baden International Society for Contemporary Music, Boulez laconically wrote, as quoted by Friederich Saathen: "Le Marteau sans Maitre, after a text by Rene Char, written for alto, flute, viola, guitar, vibraphone, and percussion. The text is partially sung, partially interpreted through purely instrumental passages."' In a fashion typical of many writers on this subject, Saathen commented that it was unlikely that anything more could be said and that his own article would provide random reflections and impressions.

In his recent book on Boulez' music, Paul Griffiths notes that Le Marteau "resists any kind of conventional serial analysis"2 and according to Joan Peyser, "the machinery oftwelve-note organization [in Le Marteau] is so complex that it is impossible to trace the steps which lead from one pitch to the next."3

Boulez himself has said that an analysis ofLe Marteau would be very difficult because

There is in fact a very clear and very strict element of control, but starting from this strict control and the work's overall discipline there is also room for what I call lcal indiscipline: at the overall level there is discipline and control, at the local level there is an element of indiscipline-a freedom to choose, to decide and to reject.4

Yet reportedly, Boulez is annoyed at suggestions that Le Marteau's success is due

merely to the fact that he had greatly relaxed the rigor of his serialism. On the contrary, he says, it was precisely the serial experience of "Structures" that enabled him to turn at once to the composition of what has proved his first fully mature (and still his best-known) work. "People say it 'sounds well,' but that is not merely because I have a good nose for sound-it is also because the textures and harmonies are absolutely con- trolled," he explains. "Serialism provided me with a syntax. In 'Le Mar- teau,' I used it to formulate thoughts. "5

281

Perspectives of New Music

The analytic literature is replete with accounts of the development of the serialization of note duration (termed variously as "chromatic rows," chiffrge siriel orgrilles d'enchainement), tracing its use from Wladimir Vogel's Varitudes (1939-40) to Babbitt's Three Copositionsfr Piano (1948), and Mes- siaen's Mode de valeurs et d'intensites (1949) to Boulez' Structures, book one (1951-52). However, only a few analyses ofLeMarteau discuss the use of pitch- duration associations and they do so only briefly, noting occasional and appar- ently unrelated examples.6

Boulez uses pitch-duration associations with varying degrees of consistency in movements II, VIV, VIII, and IX ofLeMarteau. The technique is used in a most interesting fashion in movement VI, where it is employed throughout. Entitled "Bourreaux de solitude," the movement is scored for voice, flute in G, xylorimba, vibraphone, maracas, guitar, and viola. It begins with single PDA's employed for one to three measures each. (Due to the pitchless nature of the maracas part it is necessarily omitted from the pitch-duration association analysis.)

Analytic examination begins easily, with PDA's on D, GO, At, CO, A, and E being quite discernible (measures 1-13: see Example 1, pp. 288-89). In measures 1-2 PDA = D. All twelve chromatic pitches and all twelve durations in sixteenth note increments from D = 1 through C# = 12)s are utilized.

From measure 2, last quarter note through the first part of measure 4 in the vibraphone, guitar (D), and viola, the PDA = G#. Again, all twelve pitch- duration associations are utilized although a bit less strictly. Here Boulez exchanges the increments of duration in the case of two pitches: the vibraphone's F, which should have ten sixteenths has only nine, while the guitar's D has eight instead of seven sixteenths.

In the last part of measure 3 in the flute, xylorimba, and viola (D) through measure 5 the PDA = A#. As in measures 1-2, all twelve chromatic pitches and all twelve durations from A# = 1l through A = 12)s are employed.

In measures 6-8, eight of the twelve notes of PDA = C# are "disguised" by using irrational durational values which do not exactly follow the system of sixteenth note increments. The following chart was constructed in an attempt to discover whether or not Boulez used any apparent method in his employment of these triplet rhythms.

The left column lists the durational values as actually used in measures 6-8 while the right column shows the values as they should be notated to conform to the normal progression of sixteenth-note increments. The center column indicates the fraction of a quarter note by which the left column differs from the right and which of these two durations is the larger. It can be observed that there is no apparent pattern or method by which the durations are altered, yet they conform basically to the PDA = CO. Since this is also the case in a number of other instances it was decided that notes written under triplet signs would be considered as though they were not written under triplet signs, even though a small degree of inaccuracy might occur in the analysis.

282


PITCH-DURATION ASSOCIATION ON Ct

AS USED IN MM. 6-8 DIFFERENCE AS NORMALLY USED 3

1 C ' '

4/12 *-1/12 3/12 3

2 D 7 none 6/12 none

3

3 D ' '

4/12 5/12-+ 9/12 . 3

4 E 7 ,J 14/12 ,-2/12 12/12 3

5 F 7 J 14/12 1/12-* 15/12 J

6 F J' 18/12 none 18/12 J 3 3

7 G 7''i} J' 18/12 3/12-- 21/12 J

8 GO J 24/12 none 24/12 J

9 A 2 4lJ.) ' 24/12 3/12-* 27/12

3 3

10 A# '

J'h '

18/12 12/12- - 30/12 J4 3 3

11 B , J 18/12 15/12- 33/12 J.

12 C J' 36/12 none 36/12

Pitches in measure 8 through parts of measures 10 and 11 belong to the PDA = A. Again, pitches in measures 10-14 conform to the PDA = E if the notes written under triplet signs are considered as though they are not under triplet signs.7 Thus, in measures 9-12, the vibraphone's

B-D Ab -C

283


printed in the score as

are considered as being written as

r _ P? _ _ t P t G 6'

with sixteenth note durational values of

8 -11 12-9.

Similarly, in measure/s: the: pitch/es: printed in

the score as: is/are considered as with sixteenth- being written: note durational

values of:

11 xylorimba's E 6 1

18-19 vibraphone's CO ~ , t- 12

18 guitar's A 8 c 8

21 viola's G P 2

40-42 flute's F-CO-E rfr' r r "t rfr 124-10

41 xylorimba's C-F t 2-1

41-42 vibraphone's E r t r r11 F 4

40-41 guitar's A-G-EbI i tt 5-5-1

F-F4 9 3Jola'sri fr ^-12 40-43 viola's D [.t Lp_f_ . r 9 12

Beginning with measure 13, at the first entry of the voice, matters become complicated and the clean-cut scheme disintegrates: PDA's are only partially used while, at the same time, new PDA's are introduced. Further inspection shows that Boulez utilizes all twelve possible PDA's simultaneously throughout the rest of the movement. At this point, no structural plans or relationships are readily apparent.

Quite startling relationships are revealed, however, by dissecting the movement into its twelve individual pitch-duration associations and examining the pitch order of each. In Examples 2 through 13, pitch names in each pitch-

284

'3.

crttFr;`


duration association are listed under the measure numbers in which the pitches begin. Pitches placed vertically are attacked at the same time.

Palindromic, symmetrical, and otherwise ordered arrangements of pitches in most PDA's are now made evident in surprising quantities. In Examples 2

through 13, symmetrical arrangement occurs in pitch order, groups of pitches (cells), and single pitches. This is shown by lines connecting the pitch names.

Although a few PDA's possess weak symmetrical tendencies and no apparent symmetry exists for PDA = D, the instances of strong symmetry are far too pre- ponderant and ordered for them to be considered merely coincidental.

What is discovered when the twelve individual PDA's are considered simul-

taneously, as presented in the music itself? Certain pitches from various PDA's synthesize or cluster to form new, symmetrical relationships on a "macro- level. " The effect is somewhat analogous to twelve gears in a machine rotating at different rates, some of whose cycles synchronize from time to time.

Twelve points of synchronization or clusters of PDA's have been identified and are illustrated below as Examples 14 through 25.

These twelve PDA clusters impart a camouflaged, symmetrical structure to the array of pitches, durations, and resultant harmonic and intervallic rela-

tionships inherent in the music. A linear presentation of the PDA clusters, (Example 26), allows the symmetrical structure to be readily observed.

Recalling Weber's influence on Boulez, this structure is a logical extension of other symmetrical relationships which permeate Le Marteau in various ways. Some representative instances of symmetry are presented in Examples 27

through 31. As may be seen from the examples above, Boulez' cerebral compositional

style employs complex structures not immediately (if ever) perceivable to most listeners. In this musical context, the occasional use of imitation is all the more noticeable and remarkable. I would suggest that the numerous pitch repetitions in movement VI are subtle examples of text painting on the part of the com- poser. It is interesting to note the relationship between the text of "Sur le cadran de l'Imitation" (On the dial of Imitation) and the conspicuous preponderance of pitch imitation in the section beginning with measure 44 (Example 32).

The "D" in the guitar in measure 44 is imitated by the voice in measure 45, reinforced by the "D" in the xylorimba. In measure 46 the voice's "B" is dou- bled by the vibraphone. The flute's "B-flat" in measures 46-47 is transferred to the voice in measure 47. The guitar's "E-flat" in measure 47 is echoed in the viola. The vibraphone's "E" in measures 46-48 is repeated after a sixteenth rest by the guitar. In measure 49 the "D" in the vibraphone is imitated by the viola, etc.

If one is immediately attracted by the unique beauty ofLe Martau's shim- mering sonorities, one must also be intrigued by the reali7ation that, beyond the first or second hearing, there is much more comprehension to "master" in this music.

285


NOTES

1. Friederich Saathen, "Le Marteau sans Maitre," SchweizerischeMusikzeitung, 97 (July 15, 1957): 290. Translation by the author.

2. Paul Griffiths, Boulez (London: Oxford University Press, 1978): 37.

3. Joan Peyser, Boulez (New York: Schirmer Books, 1976): 102.

4. Pierre Boulez, Conversations with Celestin Deliege, English translation (London: Ernst Eulenburg Ltd., 1976), 66. First published in French under the title Par Volonmt etpar Hasamd: Entretiens avec Cilestin Delige (Paris: Les Editions du Seuil, 1975).

5. Peter Heyworth, "Profiles: Taking Leave of Predecessors-I," New Yorker (March 24, 1973): 64.

6. Susan Bradshaw and Richard Rodney Bennett, "In Search of Boulez," Music and Musicians, 11 (Aug., 1963): 17-18. The authors state that "the second and sixth movements employ various techniques of 'chiffrage sriel ' " but quote an example from movement IX (measures 79-81).

7. In measures 10 and 11 the duraton of the two upper notes in the guitar (DO and Ft) should be r and J P respectively, instead of [ and J as printed in the score. This is printed incorrectly in both the London Univer- sal Edition, copyright 1957 (front cover marked "UE 12652," page 1 marked "Universal Edition Nr. 12450 LW") and the re-engraved Philhar- monia score printed in Austria (front cover marked "No. 398," page 1 marked "UE 12.450 LW W. Ph. V. 398," succeeding pages marked "UE 12450-12652 LW").

While we have our correcting pencils handy, we should also correct the mistake in measure 78 in the viola. The London edition score prints this as

p m

Obviously, these two notes are too long in duration to be contained in a 3

measure. The re-engraved Austrian score attempts to correct the mistake by changing the double-dotted half note to a double-dotted quarter, thus neatly completing the I measure:

- >

p mf

286

Boulez' Le Marteau sans moftre 287

However, a careful listening to the recording made with Boulez conducting (Turnabout TV 34081S/TV 4081) reveals that the last note in this measure should be a natural harmonic sounding B, a twelfth higher. Probably it was written originally as

p rmf

but printed mistakenly as a double-dotted half note rather than as a harmonic with a duration of a double-dotted quarter note.


VI <bourreaux de solitude ,

IG"=, Fin.

I~~g.- ~??-?-- . L 7 ,mp J - 11 I

_suilvant les dynamiques, employer baguettc douces ou dures f ooooto hi

.-y I< ^ P?F

1P T ,T I. I.. I - .h

_ I - vi P07 I

, I

sF i 6- r-

-

7

!q-

- ? r I f ~d -d I

If ly L.

pp 4tfPP

(kI - TI . . I (sul D)

Y, J -, --

Alto |. -, v r V H I '~ - avec sourdinel' f | ~ I !- I

l.f P

wE 4? Alf=>g '

' I 'l ' - ff ~ n -d To l ~e n i .r

' * '

pp 1 6Li1A 4 4

Gt,,. 7,I IJ r i i

MPJT ]~.; i

-" 6 - r Alto

avttc sourd~~~~~~~~~~~~~~~~~~~~~~~' jij~~~~~~~,=A p

*) Battre los croches pendant deux mesures pour itabllr le mouvement; battre ensuite la noire. Revenir a la croche quand cela est nrcesalre.

EXAMPLE 1: PITCH-DURATION ASSOCIATIONS

288

Assez lent(;- 5)

)Tempo rigoureux

I AD=J -

-1-.

,,da -f =- -

Flfte en sol

Xylorimba

Vibraphone

Maracas (ou sonnailles)

Guitare

Voix d' alto

3 pp empre - sans nuances

4

a - e22

arco-60 hl.

8~r I & r Y r r ' I i r r r Y I I r t- .' rloi

I

-E , ff "m

I I I. ' I' 1

? -1 -r, Pr I

_ - - .- .


cedez - - -

9

8

7

6

5

4

3

2

1

B C CO D D E F FM G

Al B C CO D DO E F FM

A AM B C CO D D E F

GO A AM B C CO D DM E

G GM A At B C CM D DO

FM G GM A AM B C CM D

F FM G GO A AM B C CO

E F Fl G GM A AM B C

DO E F FM G GM A AM B

D D E F FM G G A AM

CO D DM E F FM G GO A

C CO D DM E F FM G GM

GO A AS

G G A

FM G GM

F FM G

E F FM

DM E F

D D E

CO D DM

C C D

B C CO

AM B C

A AM B

Pimur Boulez-LE MARTEAU SANS MAITRE ? Copyright 1954 by Universal Edition (London) Ltd., London. Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. AU Rights Reaved. Used by permiion of European American Music Distributors Cotporation, sole U.S. agent for Universal Edition.

EXAMPLE 1 (CONT.)

289

Fl. en sol

Vibr.

Mrc. (sonn.)

Gutll.

Voix

12

11

10

9

8

7

6

5

4

3

2

1

measure no. \O ....25 26 27 28 29 30 31 32 33 34 ....46 ....75 76 77 78 ....87 ....91 92 93 94 ?

Fl. DB D#G en sol

Xyl. C# c c E c C# cc D

Vibr. E F G .B D D E A# FA F# B B

Mrc. n

?o Guit. D# G# A# D# C# A#G

Voix

Alto F# E A F E F#

Sv2 r)

EXAMPLE 2: PITCH-DURATION ASSOCIATION BASED ON C = )

.-

measure no.

..,.6 7 ..25 26 27. .34..38..45 ..47. .49. .5355. .66 67..73 74 75 76 77. .79. .81. .84 85..87 88 89 .. 91

Fl. E F G# C# C C# A en sol

Uo Xyl. D# D D C# C# D 0

c# C (D N

Vibr. C B A# G# G# F

Mrc. cD

Guit. F# G A# F# C# G D# F# C# A#

Voix D C#F A C C# |

Alto G# A D# G# C# D C#

(predominance of C#)

EXAMPLE 3: PITCH-DURATION ASSOCIATION BASED ON CO = P NJ t'0 I'D

..16..18..26..34..36..38..41..45..49..65..67 68..71..74

F# A A

)#

B C# E G# B C F C

A A# F D#

D# F

A F F

A D

..77..79..81..84 85 86 87..92..94

E

D# D

F# A E

A

D# D

EXAMPLE 4: PITCH-DURATION ASSOCIATION BASED ON D =

G

D E

X C#

measure no.

1

Fl. E en sol

Xyl.

Vibr. A

Mrc.

Guit. G

Voix

Alto A#C

N-J Nx

CD

CD

CD ~t,

CD

ci

F#E

measure no.

.. 31.35.7 38. .41. .45 46..48. 51 52..58..60..63 ..66. .68 69 70..76 ..80 81 82..84..87..92 93 94

Fl. A I

I Fl. D AG# A# G# G# G#

en sol

Xyl. E F /D# D#F. F D#

03 B--

Vibr. (F G# F C# A# G# A# C F# F# F# C C' G N

Mrc.

Guit. G#D G D D A# oB- A A G o f -F# c

Voix F# G#

Alto C# C# D D C D F F F# A# D G# D# F#

EXAMPLE 5: PITCH-DURATION ASSOCIATION BASED ON D = WA

NO -p

measure no.

10 11 12 13..15..33 34 35 36..39..42..44..46..51..59..63 ..67..70..76 77..79..82 83..85..87..92 93 94

E B

G GG# A D

G

F

B G

F# E

A#- G# F

C- A B A#

B

D

EXAMPLE 6: PITCH-DURATION ASSOCIATION BASED ON E = I

Fl. en sol

Xyl.

Vibr.

Mrc.

Guit.

Voix

Alto

G# A#

F#F E

B D C

D# A

A

C#G

F

-o CD

CD

C' n

CD

CD

A-'

E

measure no. . .20.. 25 26 27 28.. 30 . .33 34 35 36 37..40..43 44..46..50..52..63 64..69..75 76 77 78 79..81 82 83 84 85..87..93

F

EXAMPLE 7: PITCH-DURATION ASSOCIATION BASED ON F =

Fl. en sol

Xyl.

Vibr.

Mrc.

Guit.

Voix

Alto

cG 0 C cD N

r- rD>

0 CD Qj 0 C

0

?5 (0

\0 Un

measure no. r

..16..18 19..21 22 ..24..31..34 35 36..40 41 ..44..46..50 51 52..54..59..63..65..67..70 71..75 76 77..80 81 82..84 o

Fl. A# D# A# F A# G F

en sol

Xyl. F# F#F# G A F# G# G# F# G G G F#

Vibr. F# BE C A# C# A D# B B C B C

Mrc. CD n

Guit. B C A# A# D# D C B G# A D

0

Voix G# G Z

Alto A E G C D A# D# C A# F A#t E V .

0

EXAMPLE 8: PITCH-DURATION ASSOCIATION BASED ON F =

measure no.

. .18. . 26 27 28 29 30. . 32. . 36 . . 38 39 40 41 42. .46. .49. . 53. . 55. . 58 59. . 61. . 63. . 65. .70. . 72 73 74. . 80. . 82. . 85. .93

D D#

G

C* G#F

G# A

D

C# G#

A# A E

D# C

C# C

G

B

F1

G

D A

D

F C# c

Ij

D

G G G

E

CD 0

N_

CD

CD A

CD

F

G

EXAMPLE 9: PITCH-DURATION ASSOCIATION BASEDoN G =

-4

Fl. en sol

Xyl. G#

Vibr.

Mrc.

Guit.

Voix

Alto

k

I

measure no. -

co ..2 3 ..36..39..47 48..52 53..56 57..61..63 64 65..67 68..70 71 72 73 74..77..85..88..93

Fl. F# A# en sol

Xyl. AG# A# G# A A#

Vibr. D# F A# D C# B F E F# C A# B

Mrc.

Guit. E C#D C# E F# G A F D C# E B R,

Voix A A# a

o

Alto B C G G D# D D E A G#

I I I (

EXAMPLE 10: PITCH-DURATION ASSOCIATION BASED ON G# =

measure no.

...8 9 10..27..38..40..42..46 47..49..52 53 54..57..61..63 64 65 66..69..71 72..74..76..92 93

Fl. D# en sol

Xyl.

Vibr. D

\

Mrc.

Guit. A#

Voix

Alto ((

A# A

A

EXAMPLE 11: PITCH-DURATION ASSOCIATION BASED ON A =

0 0

(D N

I- CD

Q

C A

5 0

c

C,

:3 (A

9

\D ',D

measure no.

...3 4

Fl. A en sol

Xyl. A#

Vibr. I

Mrc.

Guit. C G

Voix

Alto D

C C) ..32..37..41..44..48 49 50..53..56..62..66 67..75 76..79..81..85 86 87 88 89 90 91 92

D C# B D DC#

C B

FE

# D#F#

G# D

A# B A#

-o (D

0- rD

CD

S.

EXAMPLE 12: PITCH-DURATION ASSOCIATION BASED ON A =

measure no.

..13 14. .17. .21 22. .24. .26. .3C. .37 18. .41. .47. .49. .53 54. .58. .61 62 63 64. .67 68 69. .71. .73 74. .76 77..87.93

Fl. C# A# A G D# E D en sol /

Xv. GB C B C C G# F BC C# B

Vibr.

Mrc.

Guit.

Voix A#DE C# G F#B D#C

Alto

F

E C#D F

F D

EXAMPLE 13: PITCH-DURATION ASSOCIATION BASED ON B = P

Co OD 0 c_ CD 0

C

I--

0

(D)

Q

C 14

I 3

(D

QC

oS

w O

82

Fl. on Sol

pp

=F(F = = F (DO =

=E(E =

= CO(GO =

Pierre Boukz--LE MARTEAU SANS MArTRE ? Copyright 1954 by Umniversal Edition (London) Ltd., London. Final Verion ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. All Rights Rscrved. Used by permission of European American Music Distributors Corporation, sole U.S. agent for Universal Edition.

EXAMPLE 14: PDA CLUSTER NUMBER 1 (MM. 33-34 AND 83-84)

w 0

-o CD

-z: CD

cD

0

n C*-

z FD

C 0, r)

~RP

I ,' s ' '5 PDA = G (E = 10)ni I

^ E (

s - ̂ - -- -- -

-PD A = F (A = 5) t

*%,_ _ pr 7PDA= F (GO =4)

PDA = E (A =6) 7 |

.1 8 : ^::^

^ PDA = E (GO = 5) 'rnn' r - ,

PDA = D (D =12 8 2

UJ^ , ''- I 8 Cf ^PDA = D (F =3) Gi t.

, T

'? 'I [ ^

^ ^

^ u rIt )

r ' rff^^ ': A -0

Pierre Boulz-LE MARTEAU SANS MAITRE E C ? Copyight 1954 by Univcrsal Edition (London) Ltd., London. p Final Verion ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. All Rights Rserved. Used by permission of European American Music Distributors Corporation, sok U.S. agent for Univrsal Edition.


Lw

3g o

n. 1^J2i^T^rAu t U' /I on WI

Fl. Xyl. en Sol

~~~X~~~~~~ ~~~yl~~~~ ~~ ~~~. 4+\~~~~~~~ \~ A ;P~Xyl.

\ ' PDA = A (D =5 V

PDA = F# (G =2) /

PDA = F (A# =5) / PDA = F (C =8) \ 5 ?

8 C)

AWcSOU. TePDA = D (GO =6) - I ,^^4 I ur PDA = D (A =8)

rr3e~f ~PDA = C (C = 1) -

n

Picrrem Bouklz-LE MARTEAU SANS MAITRE Alto S I ? Copyright 1954 by Universal Edition (London) Ltd., London. avee - Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. All Rights Rtserved. Used by permission of Europan American Music Distributors Corporation, sole U.S. agent for Universal Edition.


36

Xyl. PDA = BB =

-PDA = B (G# =

DA = B (A# =

PDA=G(C = DA = G (C =

2 4

46..~4 ^ h Gull.

p

Alto L . NwC sourd. 6t

MaP

I p

Pierre Boulez-LE MARTEAU SANS MAITRE ? Copyright 1954 by Universal Edition (London) Ltd., London. Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. Al Rights Raeserved. Used by permission ofEuropan American Music Distributors Corporation, sole U.S. agent fr Universal Edition.

EXAMPLE 17: PDA CLUSTERNUMBER4 (MM. 37-39 AND 53-55) 0 CD, c_n

0 C

N

cD

CD :;'Z

CD A m C) Q

VD

Q1 Z

r-f:

a

It /1 A

kc I - 1 ^T l -

l-,

g?$ ̂ r 1 ^ 1-

~~~~ ~~~ ti -.Pl- f~~~~~~~~~~~~~

I I

1'

7- ,. 'w

-4 _ i P I Im I

I;, no Ii, I -

I I

LJO O 59

./A Fl.

PDA = DO (DO= 1) an.ol

PDA = DO (B =9) xy,.

,PDA = D# (C = 10)

PDA = G (A# = 4) vIb

~~~~~~~~\ \ \ ~ Mrc. ~~~~~~~~~\ \ \ (sonnJ

\ \ \ Gult.

ntcecl

t \ Voix

Alto \ w e ourd

t M

_ \

C L T

F

CD

cD n

CD

o

z

c_ L4 n"

Xyl.

Vibr. . '1i1 in-.

s mp)

Pierr Boukz-LE MARTEAU SANS MAITRE ? Copyright 1954 by Universal Edition (London) Ltd., London. Final Venion ? Copyright 1957 by Universal Edition (London) Ltd., London.

Copyright renewed. All Rights Reserved. Used by permission of European Amcrican Music Distributors Corporation, sole U.S. agent for Universal Edition.


Boulez' Le Marteau sans maltre

0z 1

1

... 's

. ..I 'a,M

307

11 11 11 11 11

111

00

Ln

'I r-4 d4 4 ED z 34 ;4

dD Wj

63

P--

W4

1.

s SiY X

42 V - , i.

--- - ? L

w V ir.^

I I Picrc Boukz-LE MARTEAU SANS MAITRE Vibr. Copyright 1954 by UnivcrsEdition (London) Ltd., London

J L L. t~ 44?~ ' ^ Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. All Rights Reserved. Used by permission of European American Music Distributors Corportion, sok U.S. agent for Universal Edition.

^ s^!^ T,,,.. ^ ^4 -f df r ?4

G uit. i-E ^

(f'= 132) Ancora meno lento (J6 132) \ / / ~ ~79 ( = 66)

Fl(

Cf

PDA=E (A=7) ^

-PDA= E (C =9) / vibr. T '

-V b'

\\\\ PDA = E (CO = 10)( on. (sonn.)

I


= C (F Vl*br tX2 C - r -C I f / PDA = E (Alt =7# vlhr '7< "I . ''<

( Bon.) -r PDA F (B =7) ; ,onn)

3 -p

/jr~s~~~~? ^-PDA=B (C =2)

- d d,0l . ,, . . , t...... / 0 D

UrdboErop ~i~~ n .u- Db. . o 8ta CD

0

PierreBoukz-LEMABTEAUSANS MAITRE Vibr. -

? Copyright 1954 by Univrsa2l Edition (London) Ltd., London. 7 Final Vrasion 0 Copyright 1957 by Universal Edition (London) Ltd., London. ^P /o Copyright renewd. All Rights Rmeserved. Used by pcnission ofEuropcan Amrincan Music Distributors Corpornon, -,

sole U.S. agen for Univeral Edition.

PDA = CQ(F = 5) is missing from mm. 77-79.

" fIF

o LO 0Z

EXAMPLE 21: PDA CLUSTER NUMBER 8 (MM. 46-48, 77-79, AND 87-88)

Tempo

Picrre Boulez-LE MARTEAU SANS MAITRE ? Copyright 1954 by Universal Edition (London) Ltd., London. Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. agent for Universal Edition.

EXAMPLE 22: PDA CLUSTER NUMBER 9 (MM. 47-48, 61-62 AND 68-70)

Fl. en Sol

Xyl.

Vibr.

Fl. Xn yol

Xyl.

uJ

5

-o (D

CD CD

0

_C

CD

z C^

Gult.

Voix

Fl. en sol

= GO

= A

Alto

= D# (GO

= GO (A

= GO (E

= A (D

-cee sa_ - char - - ge de_

Pierre Boulez-LE MARTEAU SANS MAITRE ? Copyright 1954 by Universal Edition (London) Ltd., London. Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. agent for Universal Edition.


co 0 C_ cD N

(-

D (e)

Q CD

(0

C)

C I

_, Q

4.n..l wT T II1r

-D

n. ,, . ? I ~'r ,'r/ I Yr -r I /

l 4 8 - " 4 . / 2

Gwt,I~~~~~~~~~. lyq~4 CD

71' '

"

-, . ,, 4 8 4 2

Picrr Boulz-LE MARTEAUSANSMAITRE ; /1f f ?Copyright 1954 by Universal Edition (London) Ltd., London. / ppl v _ / f'f 4 _/ ,' Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Voix Ii LI Copyright renewed. All Rights Reserved. J J \ I 1,-

' " Used by permision ofEuropean American Music Distributors Corpoation, ce sa char . ge de_ sole U.S. agent for Universal Edition.

EXAMPLE 24: PDA CLUSTERNUMBER 11 (MM. 51-53 AND 63-65)


II II II I ti II I

II II II II II II II

C

?.I

- <o oo _ _ 00

t . xia. .r v

tY - m^ - - l

L

IL?

"t^ " 3. N _ i i

_ S 3

.r: , <

i| 5I

B%:4n

a?

i -a1

313

5 5

4 /I, 14 12 , 12

m.34 36 38 40 42 44 46 48 50 52 54 56 58 6Q 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90

I t123 I I I --- I I I I 6 7 I I I i t1 I 83I I 8 1 2 3 6 7 8 0' 11 6 1/l 9 8 ,6 3\ I8

t ,

f% 1 0 II

J 1/ 1*I 7'

cD -c

o

z

n

The numbers 1-12 correspond to Examples 14-25 (Le Marteau, movement VI, mm. 33-89).

EXAMPLE 26: SYMMETRY OF PDA CLUSTERS

Flite en sol

Voix Pierre Bouz-LE MATEAU SANS MAITRE ? Copyright 1954 by Univeal Editon (Ldon) Ltd., London. Final Vion ? Copyright 1957 by UnivCrl Edition (London) Ltd., London. Coright enewed. All Righ Rcved. Used by pmnt ofEuropean Amrican Mui Distributors Cp n, soe U.S. agnt for Univenal Edition.

EXAMPLE 27: MELODIC STRUCTURE IN MOVEMENT III, MM. 9-15

Picm Boulez-LE MARTEAU SANS MAITR ? Copyright 1954 by Univeal Edition (London) Ltd., L Final Vrion Copyright 1957 by Universal Edition (Lo Copyrght rnwed. All Rights Rrved. Used by pemmni of Europn Amcan Music Dismi sole U.S. agent for Univenal Edition.

m.7 8 9

co 0

(D N

r- cD

C3 Vr)

c) _, E

If

10 4 6 4

8 8 8 C1aves : A A _ AAA .! A A 8 Claves: , , i, c r [ L i 6 : C6m ' ;C c r r r ' ' 7

ondon| I I ndon) Ltd., London. I

ton Corporation,

EXAMPLE 28: RHYTHMICAL SYMMETRY, MOVEMENT VIII, CLAVES PART

UA

Cn

Plus Vif(J = ca 88100t144) , A 5V

4LJ LJ 16A A8 g 41

4n? 1g.* 1 & II

PO &D' lF iJ: I ** I jp

4 t *t rI - - Cs SP

4 <-

4 1T6 b,=. )p 4 L_ U U L1%A A

4 _ I - '11 t ^o:

' I It

Picre Boukz-LE MARTEAU SANS MAITRE ? Copyright 1954 by Univesal Edition (London) Ltd., London. Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. agent for Universal Edition.

EXAMPLE 29: SYMMETRICAL VERTICAL SONORITIES IN MOVEMENT IX, MM. 56-57

Xyl.

Vlbr.

Gull.

Alto

57 \N rth.

Xyl.

Vlbr.

LUJ W\

Gult.

Voix

Alio

.s I _ m/ pp

-o (D r

0

rD

c~

I

6r

Xyl.

Vibr. e T r I I Vibr. y "- ,

7 2 9 9 _' 0 16U h' 2Y`916

vo:,'( I - 1 -?**?<"?** ^

Guit. y e Gult. I 'N_

r5 V? C opyright 1954 by Uvrsal Edition (LSndon) Ltd., London.o

Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London Copyright renewed. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. agent for Universal Edition.

EXAMPLE 30: SYMMETRICAL VERTICAL SONORITIES IN MOVEMENT IX, MM. 74-75

mm. 128-33

2 ' //3,3,/ --==

7 2 5 '

Z 3. PPm/ / 1/ (-o 14) CD

2 ///

2 4 8 4 4 8 2 inm. 134-40

Pierre Boulz-LE MARTEAU SANS MAITRE Copyright 1954 by Univrsal Editon (London) Ltd., London.

Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. All Rights Reserved. Used by permission of European Arnrican Music Distributors Corporation, sok U.S. agent for Universal Edition.

EXAMPLE 31: MOVEMENT IX, FLUTE IN G, PITCH REPETITION

I

Bourwaux de solitude

Le pas s'est eloigne le marcheur s'< Sur le cadran de l'Imitation Le Balancier lance sa charge de gra

Picrre Boulcz-LE MARTEAU SANS MAITRE ? Copyright 1954 by Universal Edition (London) Ltd., London. Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewed. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. agent for Univrsal Edition.

est tu

nit reflexe.

:n

THamgen ofsolitud

The step has receded the walker has killed himself On the dial of Imitation The Pendulum thrusts its load of reflex granite.

Fn81

42 'Flzg

| en sol i . I

P

Xyl. - $

f

Vibr. |

- t IC Ar - / Mrc.

' .'

(Bonn.) 7r 3 ... . '

,,y,is? , J i ,,,yF ' Guit. ' 1 Pr*- cu .$ |t '? t-;f f af

Voix 1- I - I - (L

Alto u li |fl 4' Y nvcn .lr - I

W 0D

EXAMPLE 32

0

N

(S 0

(S 0 0

(S

z

:3 L/)

E3 C)> ac

------- -f

320 Perspectives of New Music

EXAMPLE 32 (CONT.)

Boulez' Le Marteau sans maltre 321

Pierrc Boukz-LE MARTEAU SANS MAITRE ? Copyright 1954 by Universal Edition (London) Ltd., London. Final Version ? Copyright 1957 by Universal Edition (London) Ltd., London. Copyright renewcd. All Rights Reserved. Used by permission of European American Music Distributors Corporation, sole U.S. agent for Universal Edition.

EXAMPLE 32 (CONT.)

symmetry and pitch-duration associations in boulez' le

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