Symmetry and Pitch-Duration Associations in Boulez' Le Marteau Sans Maître Author(S): Steven D

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

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http://www.jstor.org SYMMEIRY AND PITCH-URATION ASSOCIATIONSIN BOUTE7,' LE MARTEA U SANS MAITRE

STEVEND. WINICK

e Marteausans maitre is one of Boulez' most widely known compositions and yet it remainsone of his most enigmatic. In contrastto PolyphonieX (1951), the two Etudes(1951-52), and Structures,book one (1951-52) which immediatelypreceded Le Marteau (1953-54, revised1957) and whose pitch, duration, dynamics, and modes of attackare strictly serializedand relatively easily analyzed, the compositional processes in Le Marteau are obscured by transformedserialization, veiled relationships,and speed and complexity of texture. One aspect of Le Marteau which has been generallyoverlooked is that of pitch-duration association. This technique usually associates pitches of an ascendingchromatic scale with durationswhich increasearithmeticlly by small increments,such as a sixteenthnote. For example,C = , C = , D = , Boulez'Le Marteau sans maitre 281

DO = J, etc. I will referto this as a pitch-durationassociation based on C, or a PDA = C. What I will attempthere is to sharea few discoveriesand observations of my own concerningthe use of PDA's and theirinfluence on the overallstruc- ture of movement VI ofLe Marteau. Le Marteau's glassy, ethereal sound of pulverized, constantly changing pitches, dynamics,timbres, and rhythms mirrorsthe surrealistpoetry of Rene Char upon which the composition is based. This kaleidoscopicsoundscape seems as fragmentedas the text, and both transmutethe irrationalchaos of our age into music. It is well known that Boulez is reluctantto explain his own compositions. When askedto supplyprogram notes for the firstperformance ofLe Marteauin 1955 at the Baden-Baden International Society for Contemporary Music, Boulez laconicallywrote, as quoted by FriederichSaathen: "Le Marteausans Maitre, after a text by Rene Char, written for alto, flute, viola, guitar, vibraphone, and percussion. The text is partiallysung, partiallyinterpreted through purelyinstrumental passages."' In a fashiontypical of manywriters on this subject,Saathen commented that it was unlikelythat anythingmore could be said and that his own article would provide random reflections and impressions. In his recent book on Boulez' music, Paul Griffithsnotes that Le Marteau "resistsany kind of conventionalserial analysis"2 and accordingto Joan Peyser, "the machineryoftwelve-note organization[in LeMarteau] is so complexthat it is impossibleto tracethe steps which leadfrom one pitch to the next."3 Boulez himselfhas saidthat an analysisofLe Marteauwould be very difficult because

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

Yetreportedly, Boulez is annoyedat suggestionsthat LeMarteau's success is due

merelyto the factthat he had greatlyrelaxed the rigorof his serialism.On the contrary,he says,it was preciselythe serialexperience of "Structures" that enabledhim to turn at once to the compositionof 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 becausethe texturesand harmoniesare absolutelycon- trolled," he explains."Serialism provided me with a syntax.In 'Le Mar- teau,' I used it to formulatethoughts. "5 282 Perspectivesof New Music

The analytic literature is replete with accounts of the development of the serializationof note duration (termed variously as "chromatic rows," chiffrge siriel orgrillesd'enchainement), tracing its use from WladimirVogel's Varitudes(1939-40) to Babbitt'sThree Copositionsfr Piano (1948), and Mes- siaen's Mode de valeurset d'intensites(1949) to Boulez' Structures,book one (1951-52). However, only a few analysesofLeMarteau discussthe use of pitch- durationassociations and they do so only briefly,noting occasionaland appar- ently unrelatedexamples.6 Boulez usespitch-duration associations with varyingdegrees of consistencyin movementsII, VIV,VIII, and IX ofLeMarteau. The techniqueis used in a most interestingfashion 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 measureseach. (Due to the pitchlessnature of the maracaspart it is necessarily omitted from the pitch-duration association analysis.) Analyticexamination begins easily,with PDA's on D, GO,At, CO,A, and E beingquite discernible(measures 1-13: see Example1, pp. 288-89). In measures 1-2 PDA = D. All twelve chromaticpitches and all twelve durationsin sixteenth note incrementsfrom D = 1 through C# = 12)s areutilized. From measure2, last quarternote through the firstpart of measure4 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'sD has eight insteadof seven sixteenths. In the last part of measure3 in the flute, xylorimba,and viola (D) through measure5 the PDA = A#. As in measures1-2, all twelve chromaticpitches and all twelve durationsfrom A# = 1l throughA = 12)s areemployed. In measures6-8, eight of the twelve notes of PDA = C# are "disguised"by using irrationaldurational values which do not exactlyfollow the system of sixteenth note increments.The following chartwas constructedin an attempt to discoverwhether or not Boulez used anyapparent method in his employmentof these tripletrhythms. The left column lists the durationalvalues as actuallyused in measures6-8 while the rightcolumn shows the valuesas they should be notatedto conformto the normalprogression of sixteenth-noteincrements. The centercolumn indi- catesthe fractionof a quarternote by which the left column differsfrom the right and which of these two durationsis the larger.It can be observedthat thereis no apparentpattern or method by which the durationsare altered,yet they con- form basicallyto the PDA = CO.Since this is also the case in a numberof other instancesit was decided that notes written under tripletsigns would be consid- ered as though they were not written under tripletsigns, even though a small degreeof inaccuracymight occur in the analysis. Boulez'Le Marteau sans maitre 283

PITCH-DURATIONASSOCIATION 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

' 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 4lJ.) 224/12 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, pitchesin measures10-14 conformto the PDA = E if the notes written under triplet signs are consideredas though they are not under triplet signs.7Thus, in measures9-12, the vibraphone's B-D Ab -C 284 Perspectivesof New Music

printedin the scoreas '3. crttFr;` areconsidered as being written as

_r P? __ t P t 6' G with sixteenthnote durationalvalues of 8 -11 12-9. Similarly, in measure/s: the: pitch/es: printedin is/areconsidered as withsixteenth- the score as: beingwritten: note durational valuesof:

11 xylorimba's E 6 1

18-19 vibraphone'sCO ~ , 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'sE r t r r11 F 4 40-41 guitar's A-G-EbI i tt 5-5-1

40-43 viola's F-F4D [.t3Jola'sri Lp_f_ . fr r^-12 9 9 12

Beginningwith measure13, at the first entry of the voice, mattersbecome complicatedand the clean-cut scheme disintegrates:PDA's are only partially used while, at the same time, new PDA's are introduced. Furtherinspection shows that Boulez utilizes all twelve possiblePDA's simultaneouslythroughout the rest of the movement. At this point, no structuralplans or relationshipsare readilyapparent. Quite startling relationships are revealed, however, by dissecting the movement into its twelve individualpitch-duration associations and examining the pitch orderof each. In Examples2 through 13, pitch names in each pitch- Boulez'Le Marteau sans maitre 285

durationassociation are listed under the measurenumbers in which the pitches begin. Pitchesplaced vertically are attacked at the same time. Palindromic,symmetrical, and otherwiseordered arrangements of pitchesin most PDA's are now made evident in surprisingquantities. In Examples 2 through 13, symmetricalarrangement 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 symmetricaltendencies and no apparent symmetryexists for PDA = D, the instancesof strongsymmetry are far too pre- ponderantand orderedfor them to be consideredmerely coincidental. What is discoveredwhen the twelve individualPDA's are consideredsimul- taneously, as presentedin the music itself?Certain pitches from variousPDA's synthesize or cluster to form new, symmetricalrelationships on a "macro- level." The effectis somewhatanalogous to twelve gearsin a machinerotating at differentrates, some of whose cyclessynchronize from time to time. Twelve points of synchronizationor clustersof PDA's have been identified and areillustrated below as Examples14 through25. These twelve PDA clustersimpart a camouflaged,symmetrical structure to the arrayof pitches, durations, and resultant harmonic and intervallicrela- tionships inherent in the music. A linear presentationof the PDA clusters, (Example26), allowsthe symmetricalstructure to be readilyobserved. RecallingWeber's influenceon Boulez, this structureis a logicalextension of other symmetricalrelationships which permeateLe Marteauin variousways. Some representative instances of symmetry are presented in Examples 27 through 31. As may be seen from the examplesabove, Boulez' cerebralcompositional style employs complex structuresnot immediately(if ever) perceivableto most listeners.In this musicalcontext, the occasionaluse of imitationis all the more noticeableand remarkable.I would suggestthat the numerouspitch repetitions in movement VI are subtle examplesof text paintingon the part of the com- poser. It is interestingto note the relationshipbetween the text of "Surle cadran de l'Imitation" (On the dial of Imitation)and the conspicuouspreponderance of pitch imitationin the section beginningwith measure44 (Example32). The "D" in the guitarin measure44 is imitatedby the voice in measure45, reinforcedby the "D" in the xylorimba.In measure46 the voice's "B" is dou- bled by the vibraphone.The flute's "B-flat"in measures46-47 is transferredto the voice in measure47. The guitar's"E-flat" in measure47 is echoed in the viola. The vibraphone's"E" in measures46-48 is repeatedafter a sixteenthrest by the guitar. In measure49 the "D" in the vibraphone is imitated by the viola, etc. If one is immediatelyattracted by the unique beauty ofLe Martau's shim- meringsonorities, one must also be intriguedby the reali7ationthat, beyond the firstor second hearing,there is much more comprehensionto "master"in this music. 286 Perspectivesof New Music

NOTES

1. FriederichSaathen, "Le Marteausans Maitre," SchweizerischeMusikzeitung, 97 (July15, 1957): 290. Translationby the author. 2. Paul Griffiths,Boulez (London: OxfordUniversity Press, 1978): 37. 3. Joan Peyser,Boulez (New York:Schirmer Books, 1976): 102. 4. Pierre Boulez, Conversationswith CelestinDeliege, English translation (London:Ernst Eulenburg Ltd., 1976), 66. Firstpublished in Frenchunder the title Par Volonmtetpar Hasamd:Entretiens avec Cilestin Delige (Paris:Les Editionsdu Seuil, 1975). 5. Peter Heyworth, "Profiles:Taking Leave of Predecessors-I," New Yorker (March24, 1973): 64. 6. Susan Bradshawand RichardRodney Bennett, "In Search of Boulez," Musicand Musicians, 11 (Aug., 1963): 17-18. The authorsstate that "the second and sixth movements employ various techniques of 'chiffrage sriel ' " but quote an examplefrom movement IX (measures79-81). 7. In measures10 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 printedin the score. This is printedincorrectly 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-engravedPhilhar- monia score printed in Austria (front cover marked "No. 398," page 1 marked"UE 12.450 LW W. Ph. V. 398," succeedingpages marked "UE 12450-12652 LW"). While we have our correctingpencils handy, we should also correctthe mistakein measure78 in the viola. The London edition score printsthis as

p m

Obviously, these two notes are too long in durationto be containedin a 3 measure.The re-engravedAustrian score attempts to correctthe mistakeby changing the double-dotted half note to a double-dotted quarter, thus I neatlycompleting the measure:

- >

p mf Boulez'Le Marteau sans moftre 287

However, a carefullistening to the recordingmade with Boulez conducting (TurnaboutTV 34081S/TV 4081) revealsthat the last note in this measure should be a naturalharmonic sounding B, a twelfth higher. Probablyit was written originallyas

p rmf but printed mistakenlyas a double-dotted half note ratherthan as a harmonic with a durationof a double-dottedquarter note. 288 Perspectivesof New Music

5) Assez lent(;- )Temporigoureux IG"=, IAD=J - Fin. Flfte en sol I~~g.-~??-?-- . 7 ,mp J - 11 I L _suilvantooooto les dynamiques, employerhi baguettc douces ou dures f Xylorimba .-y I< ^ P?F -1-. =- - -f I ,,da 1P T,T _ II. - Vibraphone I.. I - vi P07 I .h I 6- ff "m , sFi -E, Maracas I ' r- 8~r & r Y r r I i r r r Y I I .'r t- rloi (ou sonnailles) I I I. 1 ' 3 pp empre - sans nuances I' 4 ? a - - !q-e22 -1 -r, Pr I ~d I f -d Guitare 7 - ? r I If ly L. pp 4tfPP Voix d' alto - I (kI TI (sul. D). - -- arco-60 hl. _ .-- . Y, J -, Alto r |. -, v V '~H I I - avec sourdinel' f !- | ~ I P l.f

' n To -d ~e n l .r wE ~4? Alf=>g ' I 'l i ' - ff ' ' * '

4 pp 1 4 6Li1A Gt,,. i 7,I i IJ r i MPJT -"6r - ]~.; avttcsourd~~~~~~~~~~~~~~~~~~~~~~~' p jij~~~~~~~,=AAlto *) 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 Boulez'Le Marteau sans maitre 289

cedez - - - Fl. en sol

B C CO D D E F FM G GO A AS 12 Vibr. Al B C CO D DO E F FM G G A 11

A AM B C CO D D E F FM G GM 10 Mrc. (sonn.) 9 GO A AM B C CO D DM E F FM G 9

8 G GM A At B C CM D DO E F FM 8

7 FM G GM A AM B C CM D DM E F 7 Gutll. 6 F FM G GO A AM B C CO D D E 6

5 E F Fl G GM A AM B C CO D DM 5

Voix 4 DO E F FM G GM A AM B C C D 4

3 D D E F FM G G A AM B C CO 3

2 CO D DM E F FM G GO A AM B C 2

1 C CO D DM E F FM G GM A AM B 1

PimurBoulez-LE MARTEAUSANS MAITRE ? Copyright1954 by UniversalEdition (London) Ltd., London. FinalVersion ? Copyright1957 by UniversalEdition (London) Ltd., London. Copyrightrenewed. AU Rights Reaved. Used by permiion of EuropeanAmerican Music Distributors Cotporation, sole U.S. agentfor Universal Edition.

EXAMPLE 1 (CONT.) .- 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

C#cc Xyl. C# c c E c 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'0I'D N-J Nx measure no. 1 ..16..18..26..34..36..38..41..45..49..65..67 68..71..74 ..77..79..81..84 85 86 87..92..94 Fl. E G F# A A E en sol

Xyl. D E)# D# D

Vibr. AX C# B C# E G# B C F#E F# A E F C

Mrc. CD

Guit. G A A# F D# A F F A CD

CD ~t, Voix F D# A D D# D

CD Alto A#C

EXAMPLE 4: PITCH-DURATION ASSOCIATION BASED ON D = 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

I I Fl. DA AG# A# G# G# G# en sol

Xyl. E F /D# D#F. F D# B-- 03 C Vibr. (F G# F C# A# G# A# C F# F# F# 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 measure no. NO -p 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

Fl. G# A# E B en sol

Xyl. F#F E F F# E F

Vibr. B D B G A#- G# C F

Mrc. -o CD

CD Guit. D# A G GG# A D C- A B A#

CD Voix A B C' n CD Alto C#G G D E

A-'

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

Fl. en sol

Xyl.

cG Vibr. 0 C cD Mrc. N r- rD>

Guit. 0CD 0Qj C Voix 0

Alto F ?5(0

\0 EXAMPLE 7: PITCH-DURATION ASSOCIATION BASED ON F = 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

k Ij

Fl. D D# F1 D en sol

Xyl. G# G G G G G G CD 0

Vibr. C* G#F D A D E N_ CD Mrc. CDA

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

CD Voix

Alto A# A E C# C F C#c G

EXAMPLE 9: PITCH-DURATION ASSOCIATION BASEDoN G =

-4 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. A# A

0 Vibr. D 0 \ (D N Mrc. I- CD

Guit. A# Q

Voix C, :3 50(A 9 Alto (( A

\D EXAMPLE 11: PITCH-DURATION ASSOCIATION BASED ON A = ',D measure no. C ...3 4 ..32..37..41..44..48 49 50..53..56..62..66 67..75 76..79..81..85 86 87 88 89 90 91 92 C)

Fl. A D C# B D DC# en sol

Xyl. A# C B A# B A#

Vibr. IFE

Mrc.

-o(D Guit. C # D#F# G 0-rD

Voix CD

Alto D G# D

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 B C C C G# F BC C# B

Co 0OD Vibr. F c_ CD 0 I-- Mrc. (D) C Q Guit. E C#D F 014 C (D I Voix A#DE C# G F#B D#C 3 oS QC Alto D F

EXAMPLE 13: PITCH-DURATION ASSOCIATION BASED ON B = P w O 82 w Fl. 0 on Sol pp

=F(F = = F (DO = =E(E = = CO(GO= -o CD

-z: CD n C*-cD

0 z FD

PierreBoukz--LE MARTEAU SANS MArTRE ~RP ? Copyright1954 by UmniversalEdition (London) Ltd., London. C FinalVerion ? Copyright1957 by UniversalEdition (London) Ltd., London. 0, Copyrightrenewed. All RightsRscrved. r) Used by permissionof EuropeanAmerican Music Distributors Corporation, soleU.S. agentfor Universal Edition.

EXAMPLE 14: PDA CLUSTER NUMBER 1 (MM. 33-34 AND 83-84) ,'I s ' I '5 PDA = G (E = 10)ni ( - ^ E- -- -- t s -PD A ^=- F (A = 5) *%,_pr_ 7PDA= F (GO=4)

PDA = E (A =6) 7 | ^ : PDA = E = 5) 'rnn' , - .1 8 ^::^ (GO r PDA = D (D =12 8 2 Cf UJ^ ''- I , ^PDA8 = D (F =3) Gi t.

r ' ': ^ rff^^ -0 A T [ ^ , '? 'I ^ u ^ rIt )

PierreBoulz-LE MARTEAUSANS MAITRE E C ? Copyight 1954by UnivcrsalEdition (London) Ltd., London. p FinalVerion ? Copyright1957 by UniversalEdition (London) Ltd., London. Copyrightrenewed. All RightsRserved. Used by permissionof EuropeanAmerican Music Distributors Corporation, sok U.S. agentfor Univrsal Edition.

EXAMPLE 15: PDA CLUSTERNUMBER 2 (MM. 34-36 AND 82-84)

Lw 3g o t /I onn. WI 1^J2i^T^rAu U'

Fl. Xyl.Sol en

~~~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 ur = ,^^4 I PDA D (A =8) - rr3e~f ~PDA = C(C = 1) n

PicrremBouklz-LE MARTEAU SANS MAITRE Alto S I ? Copyright1954 by UniversalEdition (London) Ltd., London. avee - FinalVersion ? Copyright1957 by UniversalEdition (London) Ltd., London. Copyrightrenewed. All RightsRtserved. Used by permissionof Europan AmericanMusic Distributors Corporation, sole U.S. agentfor UniversalEdition.

EXAMPLE 16: PDA CLUSTER NUMBER 3 (MM. 36-39 AND 81-82) 36

Xyl. PDA = BB =

-PDA = B (G# =

DA = B (A# =

PDA=G(C = DA = G (C = 0 C 2 N 4 cD h 46..~4 ^ :;'Z Gull. CD I p A CDm C)Q Alto L . VD A NwCsourd. 6tp Z It /1 Q1 r-f: MaP a

PierreBoulez-LE MARTEAUSANS MAITRE ? Copyright1954 by UniversalEdition (London) Ltd., London. FinalVersion ? Copyright1957 by UniversalEdition (London) Ltd., London. Copyrightrenewed. Al RightsRaeserved. Used by permissionofEuropan AmericanMusic Distributors Corporation, soleU.S. agentfr UniversalEdition.

EXAMPLE 17: PDA CLUSTERNUMBER4 (MM. 37-39 AND 53-55) 0 CD,c_n LJO 59 O ./A Fl. - PDA = DO(DO= 1) an.ol ^T l l-, kc I - 1 PDA = DO (B =9) xy,. tg?$ ^ r ^ 1 M ,PDA = D# = 1- (C 10) _\ vIb PDA = G (A#= 4) ~~~~ ~~~ti -.Pl- f~~~~~~~~~~~~~ \ \ Mrc. ~~~~~~~~\ ~ I T I ~~~~~~~~~\\ \ (sonnJ C L F 1'

\Gult. \ \ Xyl. ntcecl 7- ,. 'w ncD t \ CD Voix P Im _-4 Ii I o z Vibr. . '1i1 in-. Alto no - \ w e ourd I;, s Ii, I mp) L4c_ n" I I 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.

EXAMPLE 18: PDA CLUSTERNUMBER 5 (MM. 38-39 AND 60-61) Boulez' Le Marteau sans maltre 307

0z 1 ... 's

. ..I 'a,M 111 00

11 11 11 11 11 'I r-4 d4 4 ED z 34 ;4 dD Wj

63 P--

SiY X s 42 - --- L i.V , ? - w I PicrcBoukz-LE MARTEAU SANS MAITRE ir.^ I V Vibr.Copyright 1954 by UnivcrsEdition (London)Ltd., London J L L. t~ 44?~ ' ^ FinalVersion ? Copyright1957 by Universal Edition (London) Ltd., London. Copyrightrenewed. All Rights Reserved. Usedby permission ofEuropean American Music Distributors Corportion, sokU.S. agent for Universal Edition.

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

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

Cf PDA=E (A=7) ^ ' b' -PDA= E (C =9) / vibr.-V T PDA = E (CO= 10)( \\\\ on. I (sonn.)

EXAMPLE20: PDA CLUSTERNUMBER 7 (MM. 42-45 AND 79-80) = C (F Vl*br I- r vlhr ''< tX2 C -Cf / PDA= E (Alt=7# '7< "I . (Bon.) -r PDA F (B =7) ; ,onn) 3 -p /jr~s~~~~? ^-PDA=B (C =2)

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

UrdboErop~i~~n .u- Db. . 8ta o CD 0

- PierreBoukz-LEMABTEAUSANSMAITRE Vibr. ? Copyright1954 by Univrsa2lEdition (London) Ltd., London. 7 FinalVrasion 0 Copyright1957 by UniversalEdition (London) Ltd., London. ^P /o Copyrightrenewd. All RightsRmeserved. Used by pcnission ofEuropcanAmrincan Music Distributors Corpornon, -, sole U.S. agen forUniveral Edition.

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

" fIF

LO o0Z

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

uJ Fl. en sol 5

Fl. en Sol = GO

Xyl. = A

Vibr.

-o (D

CD CD _C Fl. CD Xnyol 0 C^ Xyl. z

Gult.

Voix PicrreBoulez-LE MARTEAUSANS MAITRE ? Copyright1954 by UniversalEdition (London) Ltd., London. FinalVersion ? Copyright1957 by UniversalEdition (London) Ltd., London. Copyrightrenewed. All RightsReserved. Alto Used by permissionof EuropeanAmerican Music Distributors Corporation, sole U.S. agentfor UniversalEdition.

EXAMPLE22: PDA CLUSTER NUMBER 9 (MM. 47-48, 61-62 AND 68-70) = D# (GO = GO(A = GO(E = A (D

0co C_ cD N

(e)(- D CDQ (0

C I C)

Q_,

-cee sa_ - char - - ge de_ PierreBoulez-LE MARTEAUSANS MAITRE ? Copyright1954 by UniversalEdition (London) Ltd., London. FinalVersion ? Copyright1957 by UniversalEdition (London) Ltd., London. Copyrightrenewed. All RightsReserved. Used by permissionof EuropeanAmerican Music Distributors Corporation, sole U.S. agentfor UniversalEdition.

EXAMPLE23: PDA CLUSTER NUMBER 10 (MM. 48-50 AND 63-66) ,, . -r I 4.n..ln. I ? ,'r/~'r wTYr I T II1r /

-D

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

" 71' ' . . l 8 -, ,, 44 - 8 " 4 . / 2

Picrr Boulz-LE MARTEAUSANSMAITRE ; /1f f v _ ?Copyright 1954 by Universal Edition (London) Ltd., London. / ppl _/ / f'f ,' 4 FinalVersion ? Copyright1957 by UniversalEdition (London) Ltd., London. Voix 'Ii " LI Copyrightrenewed. All RightsReserved. \ J J I 1,- Used by permision ofEuropean American Music Distributors Corpoation, ce sa char . ge de_ sole U.S. agentfor Universal Edition.

EXAMPLE24: PDA CLUSTERNUMBER 11 (MM. 51-53 AND 63-65) Boulez'Le Marteau sans maitre 313

. .r v t xia. L

IL?

tY - m^ - - l IIII II I ti II I "t^ " N 3._ i i

II II II II II II II

.r: , <

_ 3 S

C 5I i| a? ?.I B%:4n i -a1 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

t123I I 6 7 I I --- I I I I t1 I I I i I 83I I 8 1 2 3 6 7 8 0' 11 6 9 8 ,6 3\ I8 , 1/l0 J t f% 1 II 1/ 1*I 7'

cD -c

o z

The numbers 1-12 correspondto Examples14-25 (LeMarteau, movement VI, mm. 33-89).

EXAMPLE 26: SYMMETRY OF PDA CLUSTERS Flite en sol

0co (D Voix N PierreBouz-LE MATEAU SANS MAITRE r- ? Copyright1954 by Univeal Editon (Ldon) Ltd., London. cD FinalVion ? Copyright1957 by UnivCrl Edition (London) Ltd., London. Coright enewed. All Righ Rcved. Used by pmnt ofEuropean Amrican Mui DistributorsCp n, soe U.S. agnt for Univenal Edition. Vr) C3

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

m.7 8 9 10 4 6 4 A A 8 A A 8 8 C1aves: _ AAA .! Claves:, , c r i : ' c r r r '7 ' Picm Boulez-LE MARTEAU SANS MAITR i, L[ 6 C6m ;C ? Copyright1954 by Univeal Edition (London) Ltd., London| I I FinalVrion Copyright1957 by UniversalEdition (London) Ltd., London. I Copyrght rnwed. All RightsRrved. Used by pemmni of Europn Amcan Music Dismi ton Corporation, sole U.S. agent for Univenal Edition.

UA Cn

EXAMPLE28: RHYTHMICAL SYMMETRY,MOVEMENT VIII, CLAVESPART LUJ 57 \N rth. Plus Vif(J = ca88100t144) 4 - W\ Xyl. t *t rI - , A 5V Cs SP Xyl.

Vlbr. 4 Vlbr. <- 4 L_1T6 U L1%AU A 16A I )p b,=. 4LJ LJ 41 gA8 Gult. Gull. 1 4n? 1g.* II & Voix 4 _ I - '11 Alto ** PO&D' I I (D-o lF iJ:6r Alio 'It r jp t ^o: I .s I _ m/ pp Picre Boukz-LE MARTEAUSANS MAITRE 0 ? Copyright1954 by Univesal Edition(London) Ltd., London. FinalVersion ? Copyright1957 by UniversalEdition (London) Ltd., London. Copyrightrenewed. All RightsReserved. rD Usedby permissionof EuropeanAmerican Music Distributors Corporation, soleU.S. agentfor Universal Edition.

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

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

2 9 7 9 _' 0 16U2Y`916 h' Guit.e y I Gult. 'N_

I - 1 -?**?<"?** ^ opyrightV?1954 by Uvrsal C vo:,'( Edition (LSndon) Ltd., London.o r5

? London FinalVersion Copyright 1957 by Universal Edition(London) Ltd., Copyrightrenewed. All Rights Reserved. Usedby permission ofEuropean American Music Distributors Corporation, soleU.S. agent for Universal Edition.

EXAMPLE 30: SYMMETRICALVERTICAL SONORITIES IN MOVEMENT IX, MM. 74-75 mm. 128-33

--== ' 2 ' //3,3,/ 7 / 2 5 1/ Z 3. PPm/ (-o 14) CD 2 ///

2 4 8 4 4 8 2 Iinm. 134-40

PierreBoulz-LE MARTEAUSANS MAITRE Copyright1954 by Univrsal Editon (London)Ltd., London. FinalVersion ? Copyright1957 by UniversalEdition (London) Ltd., London. Copyrightrenewed. All RightsReserved. Used by permissionof EuropeanArnrican Music Distributors Corporation, sok U.S. agentfor Universal Edition.

EXAMPLE31: MOVEMENT IX, FLUTE IN G, PITCH REPETITION Bourwaux de solitude THamgen ofsolitud Le pas s'est eloignele marcheurs'< est tu The step has recededthe walkerhas killedhimself Surle cadrande l'Imitation On the dial of Imitation Le Balancierlance sa chargede granit reflexe. The Pendulum thrustsits load of reflexgranite.

:n 42 'Flzg Fn81 | I . 0 en sol i P

N Xyl. - $ (S f 0

- (S Vibr. - 0 | t ICAr / 0z ' Mrc. .' ' :3 (Bonn.) . 3 L/) 7r ... (SE3 C)> Guit. ' Pr*- ' ac 1 ,,y,is? , J i,,,yF '? cu .$ |t t-;ff af Voix - - 1- I I (L PicrreBoulcz-LE MARTEAUSANS MAITRE ? Copyright1954 by UniversalEdition (London) Ltd., London. FinalVersion ? Copyright1957 by UniversalEdition (London) Ltd., London. renewed.All Copyright RightsReserved. u li |fl Used by permissionof EuropeanAmerican Music Distributors Corporation, Alto 4' Y nvcn .lr - sole U.S. agentfor Univrsal Edition. I ------f

W 0D EXAMPLE32 320 Perspectivesof New Music

EXAMPLE32 (CONT.) Boulez'Le Marteau sans maltre 321

PierrcBoukz-LE MARTEAUSANS MAITRE ? Copyright1954 by UniversalEdition (London) Ltd., London. FinalVersion ? Copyright1957 by UniversalEdition (London) Ltd., London. Copyrightrenewcd. All RightsReserved. Used by permissionof EuropeanAmerican Music Distributors Corporation, sole U.S. agentfor Universal Edition.

EXAMPLE32 (CONT.)