Electroacousticmusic of Xenakis

8/2/2019 Electroacousticmusic of Xenakis

1/26

The Electroacoustic Music of Iannis XenakisAuthor(s): James HarleySource: Computer Music Journal, Vol. 26, No. 1, In Memoriam Iannis Xenakis (Spring, 2002),pp. 33-57Published by: The MIT PressStable URL: http://www.jstor.org/stable/3681399 .

Accessed: 27/10/2011 04:13

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

The MIT Press is collaborating with JSTOR to digitize, preserve and extend access to Computer Music

Journal.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=mitpresshttp://www.jstor.org/stable/3681399?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/3681399?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=mitpress


2/26

JamesHarleyMinnesota State University Moorhead1104 7th Avenue SouthMoorhead,Minnesota 56563, [email protected]

T h e ElectroacousticM u s i c o f l a n n i s X e n a k i s

Of the close to 150 compositions that lannis Xe-nakis created, only a handful involve electroacous-tics (sounds directly producedby electronic, digital,or other studio means). Those works, however, areinfluential beyond their number.Any history ofelectronic music must place Xenakis as a centralfigure,both for his innovations and for the impacthis music has had on successive generations. Hisinvolvement in the creation of multimedia "specta-cles" broughthim wide exposure, although his un-compromising aesthetic vision precludedfame andfortune on a popularscale.Nonetheless, throughhis work, Xenakis (see Fig-ure 1)presenteda bold, charismaticpersona:he wasa revolutionary,both in politics and in art. The res-tive students of the 1960s, in particular,were drawnto him, to his peculiarmixture of forward-reachingmodernismandnoisy, pounding primitivism.Therearemany parallelsbetween Xenakis'swork and ex-perimental elements of popularmusic, particularlyin the embracingof technology andhigh-density/high-amplitudesound set offby disorienting,hallu-cinatory light-shows.The electroacousticmusic ofXenakis, ConcretPH in particular,provideda linkbetween the "academic"components of the 2000 In-ternationalComputerMusic Conferencein Berlinandthe club-oriented"off-ICMC" elebration,heldconcurrently.Additionally,a new Asphodel releaseof his massive electroacousticwork, Persepolis,isaccompaniedby "re-mixes"by, among others,Japa-nese techno artists.It is my aim to present here a brief overview ofXenakis's electroacoustic music in the manner of atutorial. Certain aspects or selected works fromthis areaof his compositional output have been ex-amined in some detail (Di Scipio 1998, 2001; Hoff-mann 2000a; Solomos 1993),and a more detailedstudy of these works within the context of the restof his output is found in Harley (forthcoming).While there is a strong unity of aesthetic and com-positional technique running throughhis entireoeuvre, five stages in the trajectoryof his studioComputerMusic Journal,26:1,pp.33-57, Spring2002? 2002 MassachusettsInstitute of Technology.

output can be distinguished (see Table 1).In each,the technical means change somewhat, as do theaesthetic concerns. There are connections tothe instrumental music he was writing aroundthe same time, and there are also connectionsto the electroacoustic music being written by oth-ers (thoughsurprisinglyfew). Throughouthis life,as clearly exemplified in his electroacoustic works,Xenakis sought to "extend the limits of musicalthought" (Robindor61996).

StageOne:MusiqueConcreteXenakis arrived n Paris as a 25-year-oldrefugee inNovember 1947. He decided,having barelyescapedGreece (asa condemned insurgent)with his life, todevote himself to music, a dreamhe had guardedwithin himself but which had been sidelined byturmoil, both political andpersonal (see Matossian1986 for fuller details of Xenakis's early life). As atrained civil engineer,Xenakis found himself work-ing in the architectural studio of Le Corbusier,where he was able to earn a living while pursuingmusic in his sparetime. He would have known vir-tually nothing of contemporarymusic, but the mi-lieu he worked in was certainly cultured (LeCorbusier was acquaintedwith EdgardVarese,forexample), and he would no doubt have heard vari-ous broadcasts on Radio-France.He very likely lis-tened to the earlybroadcastsof PierreSchaeffer,who, in 1948, presentedhis first experiments inmusique concrete on the radio and in concert.Xenakis met Olivier Messiaen in 1951 andbeganattending his classes that year, a habit he wouldcontinue more or less regularlyfor the next twoyears. Messiaen was a central figure in the Parisiannew music world;PierreHenry, who began work-ing closely with Schaeffer n 1949, had been hisstudent between 1944 and 1948 (Boivin 1995).Dur-ing this period (1951-1952), Messiaen himself vis-ited Schaeffer'sstudio, producinga short piece,Timbres-durees.KarlheinzStockhausen,who satwith Xenakis in Messiaen's class during 1951-1952, also created a tape study during that time.Harley 33


3/26

Table 1. Xenakis's electroacoustic musicYear Title Medium Duration Studio RecordingStage I:Musique concrete1957 Diamorphoses Tape 6:53 GRM EMFCD 0031958 ConcretPH Tape, 2:42 Philips/GRM EMFCD 003, Caipirinhamultimedia CAI.2027.2,Bvhaast CD06/07011959 Analogique B Tape 1:30 Gravesano/GRM VandenburgVAN 0031960 Orient-Occident Tape 10:56 GRM EMFCD 003(soundtrack)1960 Vasarely Soundtrack GRM Withdrawn1961 Formesrouges Soundtrack GRM Withdrawn1962 Bohor Tape (8-channel) 21:36 GRM EMFCD 003StageII:Mixed1967 Polytope de Montreal Orchestra(pre- c. 6 min Radio-France LPrecorded)1969 Kraanerg Orchestra and 75:00 Radio-France Etcetera KTC 1075,tape (4- Asphodel0975channel)1970 Hibiki-Hana-Ma Tape (12- 17:39 NHK Tokyo EMFCD 003channel)StageIII:Multimedia1971 Persepolis Tape (8-channel), 55:06 FractalOX,Asphodelmultimedia forthcoming1972 Polytope de Cluny Tape (7-channel), c. 25 min CEMAMu Mode 98/99multimedia1977 La Ligende d'Eer(Le Tape (7-channel), 46:00 WDR Cologne/CEMAMu MontaigneMO 782058Diatope) multimediaStageIV: UPIC1978 Mycenae Alpha Tape (2-channel), 9:36 CEMAMu Neuma Records450-74,(Polytopede multimedia Mode 98/99Myc ne)1981 Pourla Paix Voices and tape, c. 27 min CEMAMu/Radio-France noneradiophonic1987 Taurhiphanie Tape (2-channel), 10:46 CEMAMu Neuma Records450-86multimedia1989 VoyageAbsolu des Tape (2-channel) 15:25 CEMAMu Perspectivesof New MusicUnari vers PNM 28Andrombde1997 Erod Tape (2-channel) c. 5 min Ateliers UPIC WithdrawnStageV: Stochastic Synthesis1991 GENDY301 Tape (2-channel) 14:15 CEMAMu Withdrawn1991 GENDY3 Tape (2-channel) 18:45 CEMAMu Neuma Records450-861994 S.709 Tape (2-channel) 7:03 CEMAMu EMFCD 003

34 Computer Music Journal


4/26

Figure1. Xenakis at themixing console, Le Dia-tope. (Photographby Mali;used by kind permission ofthe Xenakis family, alongwith all subsequent sketchand score examples.)

It was a few years later, in 1954, that Xenakiswas accepted as one of the first members of theGroupe de recherches de musique concrete (re-named Groupe de recherches musicales in 1958,now commonly called GRM).His assimilation ofthe concerns of contemporarymusical culture hadproceededrapidly.That same year, he completedhis first majororchestral score, Metastaseis, a workthat explores novel sonorities built from complexconfigurationsof stringglissandi (see Figure 2); itprovokeda majorscandal at its premiere in Don-aueschingenthe following year. Drawn to the newpossibilities of the studio, Xenakis expressed his in-tention to "study the evolution of timbres, dynam-ics, and register . .. to make chromosomes ofattacks" (Matossian 1986).DiamorphosesXenakis completed his first electroacoustic compo-sition in 1957. Diamorphoses (Greekfor "continu-ity-discontinuity," "two aspects of being")is a

relatively briefwork, but sonically intense andquite unlike other music being producedat GRMat that time (such as Orphie, the operaby Schaef-fer and Henry, or even Deserts, by Varese).Therewas a strong concern among many of the compos-ers working in the studio to create sounds fromrelatively discrete instrumental or real-worldsounds. Xenakis, on the other hand, sought to cre-ate dense, noisy textures that bore little direct re-semblance to the world aroundhim. Instead,hissounds derived from the same imagination thatwas creating complex clouds and masses in the or-chestra-an imagination, it should also be pointedout, strongly affected by the chaotic, traumaticsounds of war. (One might also speculate that thehearing loss, particularlyin the higher frequencies,Xenakis suffered from his injuries duringthat timewould have shaped,to some extent, his attractionto "noisy" sounds and to high-decibelplayback lev-els.)Indicative of the dichotomy describedby the ti-tle, Diamorphoses combines noisy, primarilylow-frequencysounds-derived from an earthquake,ajet engine, and a train-with more sharplydefined,high-registerbell sounds. The naturalglissando ef-fect of the jet engine winding up is combined withglissandi of other sounds, producedin the studio bymeans of tape manipulations. Often, the compositesonority produces something quite new, thesources being submerged.The formal organization is quite clear:the twoouter sections of more-or-less sustained sounds(layerednoises, glissandi)arecontrasted with a cen-tral, more discontinuous passage, filled with manyshifts of sonority (startingwith the bell sounds,then adding others).Xenakis worked in particularto create shifts and continuities of density throughlayeredvariations of sound objects (Delalande1997). For the discrete sonorities, he used probabili-ties to calculate attack points, layeringthe tracksin the studio to achieve a perceivablerangeor scaleof activity.Concret PHXenakis carried these concerns to his next electro-acoustic piece, Concret PH, produced in 1958. (Ac-cording to Delalande, it was revised in 1961 to

Harley 35


5/26

Figure2. ExcerptfromMetastaseis, eats309-314.

.40 312 32ll2first iolinsV1 12 secondviolinsVII 8 violasA8 cellosVC 6 doublebassesCBVVt,

4 vz554 e r

Me9- --UntI IN I

~'r-- -~ 9e .u.w-.aa~

3--W4 VI

_1 -K--E

CS~

create a stereo version, then re-mixed in 1969 ontofour channels.)This 2-min miniature was producedas an introduction to the Poeme electronique of LeCorbusierandVarese for the Philips Pavilion inBrussels. Xenakis had been heavily involved in thedesign and construction of the Pavilion (see Figure3), often standingin for Le Corbusierwho was alsoworking on a majorprojectin India(Treib1996).His music was intended to fill the gapbetween pre-sentations of the 8-min performancesof the mainmultimedia work, which occurred at 10-min inter-vals. In other words, it was intended to fill in thetime as the audience filed into and out of the pavil-ion. Nonetheless, fora young, relatively unknowncomposer, the opportunityto create a work forpre-sentation at a majorinternationalexposition that

would be heardby many thousands of peoplewould have been enticing. In addition, the facilitiesthat Philips had developedin orderto projectsound, light, and images were among the most ad-vanced in the world.

Unfortunately, Le Corbusier,who was operatingunder enormous pressureand seriously behindschedule, would not grantXenakis leave to work atthe Philips studio in Eindhoven,Holland. Heneeded him to supervise the construction of the pa-vilion, and seemed to consider the composition ofthe little interlude of secondaryimportance. Va-rese, on the other hand, was able to take advantageof Philips's technology, including special equip-ment for the projection of sounds over multipleloudspeakers. (Thepavilion endedup housing over



6/26

Figure3. Philips Pavilion,Brussels WorldFair, 1958.(Used by kind permissionof the Getty ResearchInstitute. ? 2002 ArtistsRights Society (ARS),NewYork/ADAGP,Paris/FondationLe Corbusier.)

400 loudspeakers.)Xenakis, in his sparetime, wasinstead forcedto work in the ratherprimitive fa-cilities of the Philips offices in Paris. He producedamonophonic version there, and then completely re-composed the piece later at GRM. (Xenakispro-ducedmultiple versions of all his tape pieces, up toLaLigende d'Eer,mixing for different numbers ofchannels, accounting for differentplaybacksitua-tions, and so forth.)The only sound source used in Concret PH is thecracklingandhissing of burningcharcoal. Thestudy of density and the application of stochasticfunctions to the calculation of articulationpointsforeach layer of sound were the main concerns.The cracklingtexture evolves in a continuous fash-ion, much like the centralportion of Pithopraktra,his second orchestralscore, completed in 1956. Thesense of spatialmovement as the music movedalong the trajectoriesthroughthe loudspeakersofthe pavilion in Brussels would have been particu-larlyeffective using these primarilymid- to high-registergrainsof sound. Certainly, it was utterlyunlike any other electroacoustic music of the time,and remains a gem of the tape music idiom.Analogique BXenakisfirst met the renowned Swiss conductorandresearcherHermann Scherchen in 1954. Theeldermusician became something of a mentor to

the fledgling composer, encouraginghim in partic-ular to work out his ideas of combining mathemat-ics and music so that they could be expressedcogently. Scherchenheld a "retreat"every year athis estate in Gravesano, to which he invited lead-ing thinkers of the time to discuss a rangeof top-ics. (Guests included WernerMeyer-Eppler,LejarenHiller, Max Mathews, and others.) The proceedingswere published in the Gravesaner Blatter.Scherchen's interests rangedto acoustics and newtechnology, and he had actually developed a rudi-mentary studio for carryingout experiments andproducingelectroacoustic music.By 1958, Xenakis had become interested in thetheory of acoustical quanta (Gabor 1947), the pre-cursor to granularsynthesis (Roads,2002). He haddeveloped a propositionfor composing on the basisof "screens,"a representation of clouds of quantafor each "slice of time" (Xenakis 1992).The pro-gression from one screen to the next is governed byMarkov chains, whereby the settings for one screenexert an influence on the calculations for the next,building a form of "memory"into the temporalorganization of the music.That year, Xenakis composed Analogique A, ashort work for strings in which there arenothingbut discrete notes (no held pitches, glissandi, tre-moli, etc.). The music proceeds as a succession ofchanging densities, registers, ranges,and intensities(alongwith timbral changes from plucked notes tostruck or short bowed ones). In the summer of1959, duringhis stay with Scherchenin Gravesano,Xenakis produceda complementary composition,Analogique B, for discrete electronic sounds, pro-duced in this case by oscillators. The procedurewas the same, though the particular parametricalconstraints are of course different.The composerworked out an interlocking scheme whereby thetwo pieces can be performedas a unit, the stringsalternatingwith the pre-recordedelectronic sounds,with some moments of simultaneity.Analogique A + B was premiered in Paris in 1960along with the first Frenchperformanceof Pitho-prakta, conducted by Scherchen. From that point,Xenakis's music began to receive more dedicatedattention in his adopted land. A final break with LeCorbusier provided him with the opportunity toHarley 37


7/26

quit his day job (forthe most part)and devote him-self at last professionallyto music.

Orient-OccidentOne of the first commissions Xenakis receivedthroughhis association with GRMwas for a sound-track to a documentary film by EnricoFulchignonifor UNESCO. The film, Orient-Occident (1960),tried to expressby visual and sonic means the rela-tions and resonances of artistic relics from variousancient cultures. The film was basedupon an exhi-bition at the CernuschiMuseum in Paris,wherethe director spent three months shooting. Xenakiswas not broughtinto the projectuntil that phasewas complete. Mr.Fulchignoni intentionally gaveno instructions or "interpretation" o the com-poser, preferring o allow him the liberty of work-ing from his own reactions and analyses(Fulchignoni 1981).The film links disparateerasand cultures primarilythroughvisual resemblancesrather than any sort of chronological or culturalnarrative.In effect, this more abstractapproachen-abledXenakis to construct his own "narrative" ounderscore the images.The original 22-min soundtrackis not wellknown. What is available is the concert work ofhalf that length extracted from it. A 4-channel ver-sion was apparentlyproducedat GRM in 1969 (De-lalande 1997), and availablerecordingsshow someslight discrepanciesof detail. (Forexample, the ver-sion released on a compact disc from the ElectronicMusic Foundationstops 16 sec before the versionthat had been released on vinyl by Nonesuch.)Comparedto Diamorphoses or Bohor, the soundsof Orient-Occident aremuch clearer(i.e., lessnoisy). A bow drawnover various objects is thesource of many of the sustained sonorities. Thepercussive sounds are often presentedas regularpulsations or perceptiblepatternsratherthan sta-tistical "clouds."The music is dramatic,with themore reflective sounds being surprised by sharp at-tacks or "ethnic" drumming-like patterns. Thereare some silences, unusual in Xenakis's electro-acoustic output, but also grating metallic soundsthat resemble sonorities from other pieces. The

granulartexture of burningcharcoalfrom ConcretPH makes an appearance n the latter part of thework, this time mixed with water dropletsandother sounds.The formal outline of Orient-Occident is lesssharplydefinedthan is usually the case in Xe-nakis's music, no doubt due to its original concep-tion as a soundtrack.The music proceeds from onesection to another by shifts of sonority, effected attimes by gradualtransition and at other times bysharpdivisions. The liner notes of the NonesuchLPstate that "Xenakislooks upon this work as asolution to the problemof finding many differentmeans of transition from one kind of material toanother" (Brody1970).In drawingupon a relativelywide rangeof sonorities, none recognizably linkedto any particularculture but relatedto each otherby various means of transition or juxtaposition,Xe-nakis enables the listeners (andpresumablytheviewers, originally)to create their own associationsbetween the sounds and images from ancient cul-tures.

Vasarely andFormesrougesIn the period 1960-1961, Xenakis producedtwomore soundtracksin addition to Orient-Occident.Never againwould he work in this domain. (Holly-wood decidedly did not beckon!) Vasarely (1960)was a similar projectto the previous, more well-known piece, a short film by Peter Kassovitz and E.Szabobasedon an exhibition of Op Art paintingsby Victor Vasarely(see Figure4). The composerwas quite taken with this artist, andhe endedupworking with him a few years later on his ballet,Kraanerg.Formesrouges (1961)was a short animated filmby PiotrKamler.Little is known of the music forthese films, as they were both quickly withdrawnfrom the composer's catalog. Produced at GRM,which is the reason fornoting them here, thesepieces were primarilyinstrumental ratherthanelectroacoustic, apparently.Regardless,the soundswould have been assembled in the studio.During this same period,however, Xenakis wasbecoming more and more drawninto completing a

38 ComputerMusic Journal


8/26

Figure4. Vega image byVictorVasarely.

stochastic algorithmfor composing music usingcomputers. These mathematical, abstract concernsconflicted both with the dictates of producingmu-sic for film and with the general aesthetic directionof the GRM studio as directedby PierreSchaeffer.

BohorIn 1962, Xenakis completed his most ambitiouselectroacoustic work to date, and subsequentlywithdrew from being an associate of GRM. Bohorwas one of the first 8-channel works created atGRM(JohnCage and Earle Brown had created 8-channel works back in 1952/1953). The piece con-

stitutes a radicalexposition of the issues of densityand transition that Xenakis had been concernedwith throughoutthis period.It is conceived as asingle, slowly evolving gesture lasting close to 22min. The composer describes it as being "monisticwith internal plurality, converging and contractingfinally into the piercing angle of the end" (Brody1970).There are two basic textures in Bohor:one, aconcentrated, teeming sonority, constantly in mo-tion, rangingin timbre from bell-like sounds (fil-tered to muffle the resonance) to metallic rattlings,finer-grainedmetallic sounds closely resemblingthe charcoal crackles of Concret PH, and noisy,clashing and crashingsounds; the other is a low,Harley 39


9/26

sustained sonority adaptedfrom a Laotianmouthorgan,the characteristiccrescendo-decrescendoandbreakingoff for breathbeing preserved.The lowsounds are heardtwice, primarily,beginning at the5'30" mark, and lasting about 8 min, and reappear-ing after the 17'00"mark and lasting 1-2 min. Theother texture continues throughout,adding layersto itself one by one until there are several going onat the same time. On the 8-channel version, thesewould be distributed aroundthe differentchannels.Each layer builds and subsides independently, pro-ducing an opaque,constantly-evolving texture thatat the same time seems to have no clear linear tra-jectory. When the low sustained sound dropsoutthe first time, there is a noticeable loss of intensityand tension, but the metallic sounds build upagain, leading at the end to a sublimation of all theother layers by the noisiest, crashing sonority,which sharplyboosts its mass and dynamic levelover the final three minutes. (Aswith Orient-Occident, the version presentedon the ElectronicMusic Foundationcompact disc stops 20 sec soonerthan the Nonesuch LPrecording.This is regret-table, as this last segment consists of a greatlyheightened culmination of the crescendo of dynam-ics and density-the "piercingangle" Xenakismentions.)Bohor is, perhaps ironically, dedicated to PierreSchaeffer. The elder director,who had in fact beenquite supportiveof Xenakis throughouthis sevenyears of "apprenticeship"at GRM,was horrifiedbythe piece. Part of his reaction was to the extremelevel of amplification at the Radio-Francepremiere,intensified by the distribution of loudspeakerssur-roundingthe audience. As he put it, "this was nolonger tiny embers, each with its own allure, thiswas an enormous burst of explosions, an offensiveaccumulation of lancet jabsto the earat maximumvolume level" (Schaeffer1981).Xenakis's "war"aesthetic was obviously still present, but also para-mount was the formal concern for sustaining ten-sion for a long period of time through the layeringand variation of density and other sonic parame-ters. Later electroacoustic pieces would carry thisapproach much further.Xenakis left GRM, but he did not cut himself offfrom the studio definitively, nor did Schaeffer de-

mand it. His works continued to be performedthere and issued on recordings,and he visited anumber of times in subsequentyears to producenew mixes of his pieces and to make other uses ofthe facilities (Delalande 1997).One of the sources of conflict was Xenakis'sgrowing conviction that digital technology was vi-tal to the future of music. His growingstatureas acomposer addedweight to his argumentthat GRMshould be the first French institution to equip itselffor carryingout researchin computer music. Thisorientation was anathema to Schaeffer,and Xe-nakis realized that he would be better off workingto establish such a facility elsewhere.A rift had also developed between Xenakis andsome of the other GRMcomposer-associates. A"collective concert" had been plannedfor 1962 in-volving nine composers, the others being ClaudeBallif,FrancoisBayle, EdgardoCanton, LucFerrari,Frangois-BernardMache, Ivo Malec, BernardParme-giani, and Michel Philippot. Xenakis took chargeoforganizingthe event, andput forwardthe idea thatthe succession of electroacoustic fragmentsbe de-termined accordingto a probabilitymatrix. Hisproposalwas rejectedby the others, who preferredto work more intuitively. Xenakis withdrew fromthe project,and there was evidently a certainamount of ill feeling (Schaeffer1981).

StageTwo:MixedHaving made the decision to distance himself fromGRM,Xenakis became preoccupiedwith other con-cerns. He wrote music for the stage (Hiketides, Or-esteia, Medea),began lecturing, finished writing hisbook Musiques Formelles, composed various in-strumental and vocal pieces, did a residency in Ber-lin, and, in 1967, took up a position at IndianaUniversity.One of his concerns through this period (andthroughouthis career)was the spatializedpresenta-tion of his music. He had worked with Philips onthe elaboratesound projection system for the Phil-ips Pavilion in 1958, and had produced Bohor withthe 8-channel "surround" diffusion in mind. Xe-nakis extended this thinking into his instrumental



10/26

Figure . Sketch orPolytopedeMontrealinstallation.

............... - .--i: -.: -::.... .................... .. ............. ........'i::i:::i?:::iN .4 ..:.: :.:::I--:::.:::..,::.::::::- N'::::.:..::;:...::"'N.... I:I-.-N."l: :::X:. :VX;;I;i:: N-:7.N. h:%:.M.1i%-::%-:::-.:. I- 1 IN:1:-:.:..X.-:~;:i~ii:;-ii~2Ni:LN... ........-::--X-1::-%::-%X :::.N............... ................ NIN :--X::X :-X:--:X::%. % - ..:::-4::--:--:X-: . . ...... :-:::.; ? :11;??.... ::..:::::M.. 21: X:IN OMWELS:!;,AMI... ... ..NX: N x .. - , :X:-%:..:--.-...................... : .-X-4.. I-: ......... ........... N N?isi:8-NNIN ...........i il~:I "N:XN:-NIN.X: s U:N1INN A::':ir;-.:-::.:-::-:1-r::::::'i:i?::(:i.Xi::*.ri: I"N.."N(Dii::il?':.ii?.it.:;~li:;~i:.:::::;~:!:i'::?;:::: ;:?:?;?: i: i~iiiilliiliiii*:Pi~ci'jiiii.?ii?.:i':.iiL'i:..:;:::i!.ii IX.N. ..........................1 --X: A:N :.4ijjWi:ii:li''i.:ii:1!iii~iH:X. ...... . .................. ................ . ......................... ::Z.???I??I::xN ........... s IN:cj%~lj~llliiii fi~iiiiiiiiiiiii::'N. N N!:::::.::4:li~j::ji~iii~ii!ii~~iKiit"";'::::?ili'ii'i': -fl:;:-::::li'ri'iiiilli::::.ii~::.. ::::. : %..::..-~::%:::::-!: .A -.X-N t- :: :Ni.:N-A.:-%:: W?X:M. N N ::-A:M: 1: iiiiNipiR.:S Z N 4 :X .: -::t :j:i:cmili8!~i'esei::bii~sP~w ul-thj:Nii::1.............:;::.......::::.. N N - ............ii:i:?i;::? i~l~?:: ::ii:,i ii~............... ..... N:.: JV :%::%!: ?. 'N .... N, .: .. ....... . . ....... :x:zx4: :,::':X-?X............................... .::?X: .................... ... N." 14MTX~~i~i~~~I~~~~a~~~ p?.stsie~eiiN-%:.. . INX;,?r:tir:iiiiii"ilsai~iilii;':.i' iiil:.:?:;i~i?:i?i ijiii~lj~~i~iBiiisL!iiiii~i~fii..... ... . ... ..... . ....:::''::iliiii~ : NN.N- R?%!.:..:XX:Mt.... . .... ... ..........4 S:F..... . ..N -:mN,B~ii~i.::iil:iiiiiili.;:iil.:':::':''::":'::;:''"':RX4''' : :!::::%:: ?::l-:M!:M.-INNN-4.:: INN.-'i. . . ?l:!Uri;:si;,.Nlsmji?4 R W510~iiiUfiic:ii~li~c~H~...........:gs'fn&xV&iv.ii M ?i?M .. .......... ...... ..:: IN::~Qrl'iiiii!. .......... .............:.:iiiiii~ -1-"-?:I'.. .il:?I.II~??:Biliiij~~lijiii~aiiillldl iliic ii~iai~X-:X?--:::X:::X. 4- %f: :X-4!-XX- ::A -4. 4:-- :;::..t.%:;.?t : : mU.N.;g .S;:.N..............N?.............. . ..... N;:M:.. -X%::--A-: ....... . 4 X: rn t .Ii::::: MXi;m-;....""N;-i~.ijiiii.;.;N.-N-N :X4::l.:X.-::-XXN:::-:X.C-IN M;Ns-2:t:::?::.i: 1N%1 IN: X:-::X--:...., :N-1 N?.......... . ........... ?iisW Mi .:t 4- 5;..:.. .... ...... .......ii~li~........ 0::::::.4:X Nbii~iiiiiiii~iii~ r iniiri..................... 31i:.:iili~s~~l~l~i~il~~~~iii iiiiiiiiiiiiiisiiiiii'iiiii~li:.?ii~5!!i:!BPHiii:?ii.:~lsaip~ii'iii.iii:i : :15r:r::;8`8l?30i-ji:Liir8:li~ilili.. .................................isg: !8lalliiirii IiiliXiil:XPX:i:iiH*iIV 1N1 iVZUTMiiU%::.?::ii?::-?,.,o"i!ii~s':'':''::'i;ij~i~ji;ii~!;:%::-:X-1:XN P 7 4, , ': N NXiir~n:!iiiiii:.iiii;gii~iiiliiiiPlilir~iii........ X:-:PS,:-X4NX-::?a~iriiiiiidiii'i 1Bi.BSe~iii'iQiirals,IN:1 VXi1:i i~iriiN.... ::.:x::::`: H,.Q- ....... ......~j.. .... . ...? : .- X :..........................ii~iiijifi ef~isiai"NI :::-::XAX%:::-VXiiriiiNN ...........1 N4MON40"'::"":"H ..........riiis:iva iii~ii. ... .. .... .. . ... .... i:;im-tt.??.I::.I::::::lil:X--:::--:`:i:i,-.:..:-IN.":`:ii.-4iiilii::iil:iiliiilX-l-:::f----X:-%i-;iI.:::-:IXi.:I ?:x88i::YN".:N.-NN I~ iii................... .....:!1 :.::::...?:::%::,..:::,%::..?::..:?.j.?:.:,I;::iiiiii::: ':,:i? tiiN. Ng?;imi..X ?s 2x,8:M::4 4siil?:,i?::lNii :-4N -:iilPi-t iXiM.tN. N.--:.:::j:..:: 6sliti.:sssitu NiliiilX4liINX-Xtl.iiaXis4sN . ..... . . ... .4: N-:-N ...... 2~tc?NisN ''"F smN N 11:p:1 N:~~I"'.:%-:-X:-:.X-X4-.:--:!:X............................. no:101~i liZ~t~............................... .... .... . .. . . .. .. . .... ..... .. .. ... .. . ... .. .. ... .. .k . ....IN: ......... ... ....... . .... .. ..Aii4l'l:X:x W.N N:I-.!::M .I.................... iii::C::: .. ... .. . ...... IXN. t M:-:- 42 isii~i~i'~ii~ii::I N R:::m?m..lXMXin? XX4:?: ..:::: : :--:--. ..:q:: - :0:-M :1 X l:X :-l:AX4n X-::,.............................. .... .... . - MNO, r :W. X- 4 2. ............ .. ..... . I-g g"I-:M:I:::g?!? . . ....N! .:-4:lM;A,Xiif'--XN r .............. iiii'ii;iij'i;i-l;:l r?:ile?:XXei: '44;i.I X:%ai.il-jiX-iiIN-NiX-Nii... .... .. .. - .. .. . .. . ............ .......... . ... ...... INN,............ A..x liil?i~ii:ii~i ?s;?ii8iiiii:40ZX~i~i~ii'iiiiirii ai~iiili~islli~ilii::: ii ~ ii:i'ii!ii!iii'::iii~iiPii:iiiiiiiil~lil~isi%5i;... .. .. ... ....liliiiiii::i

and stage music as well. Eonta (1963), for brassquintet andpiano, requiresthe brassplayers tomove around the stage, point the bells of their in-struments in differentdirections, and so forth. InOresteia (1966), the chorus members are asked tocreate "clouds" of stochastic sounds by playingsmall percussion instruments and sirens whilemoving around the stage. Terretektorh(1966),fororchestra,distributes the individual musiciansamong the audience, so that each listener has aunique experience of the piece.Polytope de MontrialIn 1966, Xenakis received a prestigious commis-sion: to create a multimedia work for the FrenchPavilion at the 1967 Montreal WorldExpo.Hewould have preferred o design the pavilion itself,but that jobwas awarded to architect JeanFaugeron

(who won the GrandPrix de Rome for this work).In fact, the pavilion is still standing, presentlyhousing the Casino de Montreal.For the largecentral space of the pavilion, whichrises throughseveral floors and is accessible fromall of them, Xenakis constructed five networks ofintersecting steel cables, each outlining curved geo-metrical shapes (see Figure5). Onto these cableswere attached 1,200 flash bulbs (800 white, 400colored),which were triggeredby a control systeminvolving a perforated ape andphotosensitivecells. This Poeme de lumibre comprised a succes-sion of visual configurations,the aim being to "cre-ate a luminous flow analogous to that of music"(Fleuret1988).Xenakis used interconnected tech-niques to compose the music and the "poem oflights," but for him, "the link is not between thembut beyond or behind them" (Varga1996).The music for Polytope de Montreal is scored forfour identical instrumental ensembles, each to beHarley 41


11/26

placed along one of the four cardinaldirectionswith the audience placed in the intervening quad-rants. The score, however, has apparentlyneverbeen performed ive. It was recordedat Radio-Francepriorto the presentationsin Montreal, andthe music was playedby means of loudspeakers.The use of a recording,even broadcastfrom fourspaced loudspeakers,would obviously not be thesame as performingthe music live, but Xenakis de-signed the piece very much in terms of layers of so-norities, much as he had composed Bohor.Thus,while not strictly electroacoustic, Polytope deMontreal exhibits similar concerns.Instrumental sonorities produced by similar in-struments in each ensemble arefused primarilythrough register,and dynamic swelling effects areused throughout to producethe sensation of move-ment as the auralspotlight shifts from one ensem-ble (orchannel) to another.The layers are treatedindependently, so that the overall spatializationisquite complex.The architecture of the music, though, is clear,being constructed from three contrastingsections,each containing a number of distinct sonic ele-ments. While the music is intense, concentratingon registralextremes andbeing filled with dynamicgestures, it does seem to leave perceptual space forthe visual elements that were intended to occuralongside.There are no programmatic inks be-tween the design of the cables, the succession offlash bulbs, and the music. But, as Xenakis stated,"We arecapableof speaking two languagesat thesame time. One is addressed to the eyes, the otherto the ears. The content of the communication isdifferent but sometimes there's a link between thetwo" (Varga1996).KraanergThe Polytope de Montreal made quite an impact inMontreal duringits run there in 1967. So, it wasperhapsnot surprisingthat Xenakis's name cameup a year later when officials at the National Balletof Canadawere seeking to commission a new,modernist dance work for the gala inaugurationofthe National Arts Centre in Ottawa, the nation'scapital (HarleyandHarley 1997).

The choreographerwas RolandPetit, fromFrance.Xenakis was given complete freedombythe choreographerand the commissioners to createhis music, aside from the proviso that it be at least75 min in length, and that it incorporate, f possi-ble, an electronic element, along with the chamberorchestra, to highlight the sophisticatedplaybacksystem installed in the new facility (with loud-speakers all aroundthe hall). It was the composerwho recommendedthat Victor Vasarelybe engagedto create the set (see Figure6).Kraanerg Greekfor "to perfect,accomplish; [ce-rebral]energy") s concerned, accordingto the com-poser, with "the overwhelming fight of man's brainand the [un]endingobstacles that exist or that hehimself creates" (Xenakis 1969).Xenakis was alsothinking, apparently,of the student demonstrationsgoing on in Paris and elsewhere throughthe periodhe was working on this piece, extending those so-cial conflicts to global concerns:In barelythree generations, the population ofthe globe will have passed24 billion. 80% willbe agedunder25. The result will be fantastictransformations n every domain. A biologicalstruggle between generations unfurlingall overthe planet, destroying existing political, social,urban, scientific, artistic and ideological frame-works on a scale never before attemptedby hu-manity andunforeseeable. This extraordinarymultiplication of conflict is prefiguredby thecurrentyouth movements throughouttheworld. (quotedin Toop 1989)

The music of Kraanerg s primarilyinstrumentalin conception, similar in its textures to the orches-tral score, Nomos gamma, completed that sameyear. The tape part, originally conceived in fourchannels, is built from processed instrumentalsounds, apparentlybased on recordingsdone withthe same 23-member chamberorchestraas the liveparts. The music needed to be written, produced,andrecordedwithin about six months, in time tobe readyfor the rehearsals with the dancers.Itseems likely that the orchestrapartswere recordedand then sections of that used to create the electro-acoustic part.

The piece is built from blocks of material alter-42 ComputerMusic Journal


12/26

Figure6. Photo of stage de-sign by Vasarelyand per-formanceof Kraanerg.(Photo by Anthony Crick-

man. Used by kind per-mission of the NationalBallet of CanadaArchives.)

nating between tape and live ensemble. The obvi-ous reference is EdgardVarese's Deserts (1954),butKraanerg s much more elaboratein the structuringof the mosaic-like form. The tape often overlapsthe live parts, to create more of a sense of continu-ity than is found in Deserts. The overlapping maybe slight or may be more extended. The continuityis enhancedby the similarity of material betweenthe recordedsounds and the instrumental ensem-ble. There is never any confusing them, though, asthe producedsounds are always processed, some-times quite heavily (primarilythrough filtering, of-ten to obtain degrees of distortion).Silence is alsotreatedas an importantstructuralelement, and

there are 21 such passages of stillness, ranginginduration from 2 sec to 28 sec. These occur primar-ily in the middle portion of the work, so are not in-tended to delineate large-scale formal divisions.The proportionalrelationshipbetween tape and en-semble does shift at certain points, and thesechanges create a tripartiteform. The first sectionpresents the two entities with more or less equalattention (eightblocks each);the second, beginningat 23'00", shifts the focus to the live ensemble; thethird,beginning at 52'00", settles on the tape, pri-marily. The final 6 min, for example, are entirelyfor tape.Within these blocks of sound, Xenakis plays off

Harley 43


13/26


14/26

Figure7. Archeologicalsite of Persepolis,Iran.

projectsfor which he alone, finally, would be re-sponsible.

StageThree:MultimediaIn 1969, Xenakis had traveled to the ancient site ofPersepolis,Iran,for the premiere of his ambitiouswork for six percussionists, Persephassa. The Shi-raz Festival was organizedunder the patronageofthe Empressof Iran,and Xenakis and his musiccreatedquite a sensation (Matossian 1986). He wasapparentlyengagedon the spot to create an evenmore ambitious work for the 1971 festival. Thistime, the composer was to create a multimediaevent, with all the resources of IranianRadio andTelevision placed at his disposal.

PersepolisThe one limitation Xenakis was faced with in plan-ning his first real "polytope" was that the locationwithin the ruins of such an importanthistorical

site necessitated a ban on construction or renova-tion (see Figure 7). All loudspeakers (59), lights (92spotlights), and lasers (2)needed to be installed inas non-invasive a way as possible (see Figure8).The lasers and spotlights were ranged throughoutthe site and projectedto create "luminous patternsevoking the Zoroastriansymbolism of light as eter-nal life" (M.A. Harley 1998). From the central por-tion of the site, where the 59 loudspeakersprojectedthe eight channels of sound throughoutthe audience area, the lights swept upwardand outtoward the hillside tombs of Darius and Artaxer-xes. There, in the distance, bonfires were burning,andparadesof children carrying ighted torcheswended their way up the hillsides, creating ever-changing linear patterns.The music, with its noisy sonorities and overlap-ping waves of intensity, looks back to Bohor. Per-sepolis, though, is 55 minutes in length, a verylong span for a continuously evolving form. Ac-cordingto his sketches, Xenakis constructed thetape from 11 sonic entities distributedamong theeight channels (see Figure9). The sketch showngives precise timings for the first reel of the origi-Harley 45


15/26

Figure8. Composer'ssketch for distribution ofloudspeakers and lights forPersepolis.

AO0 0 c00'.41*

00oaA'

4; do

4040 o01is,?C0*N

1 0 1 "

nal tape, which ends at 31'30". The performancewould have requiredtwo 8-track machines so thatthe piece could be performedwith no breaks. Mul-tiple layers of similar material create overall tex-tural "zones" which serve to delineate the form,though the shifts from one to another arerarelyeasy to distinguish.The sonic entities rangefrom clarinet multi-phonics (3, as numberedin the sketch), to complex,high sustained sounds derived from stringharmon-ics (2), to low, sliding distortions of timpani rolls(9),to gongs (7)and ceramic wind-chimes (11).Oth-ers areharder to identify, but one is derivedfromrecordingsof cardboardbeing handled (6),and an-other sounds as if a strong, buffeting wind had beenfed througha distortion module (8).The remainingentities can be identified as metallic, noisy sonori-ties. Entities 1 and 4 are not used at all in the firstpart,occurringonly in the final moments of thepiece.None of these entities are simple or "pure"so-norities, by any means, and the sonic intensity of-ten seems overwhelming. All of the material isdeveloped rather than just being repeated,so thatthe music evolves, while remainingunified, overthe course of its journeythroughthis violent,shroudedsoundscape. Hearingthe music in the set-ting forwhich it was intended, the darkruins of

Persepolis within the desolate beauty of the Iraniandesert,with spotlights sweeping the sky and firesburningin the distance, would have been an awe-some experience.Polytope de ClunyPolytope de Cluny (1972),Xenakis'snext multime-dia creation,followed fast on the heels of Persepo-lis. It was commissioned for the Festivald'Automne in Paris,and was set in the historic Ro-man Baths of Cluny, just off the BoulevardSaint-Germain-des-Pres. t premieredin October 1972,and ran for 16 months, four times daily, with thecumulative audience reaching over 200,000. Theexperience was popularamong young people, who,in their radicalpolitical and social orientation,sought "music that transcendedthe limits of tradi-tion and nationalism" andrejectedthe "formalap-pareland conventions" of the concert ritual.Underground n Cluny, they "sat on the floor, sur-roundedby strangesonorities and subjectingthem-selves to perceptual and aestheticexperimentation" (M.A. Harley 1998).The T-shapedchambers of Cluny were, like thehistoric site in Iran,not to be altered, so Xenakis'sinstallation was erected within the walls by means



16/26

Figure . Composer'ssketch orthe 8-channeltapepiece,Persepolis, pto 31'30".

t * & 7? iV -rw- ---).._

__? ..

4,1

"'"

WW 2, - -

Lbr U A..4

..,,,e ' ...

.jv,.. ....?.

?IN A

g?

"N:' . 1 --,J

a cl . .

" mp

Al 16 AA ;. i 3

IPA.:Ail AL1'.

,, ,l-Ap m

I

. ..v , i - -.. . 'a ' ,40

..... 77....43. , , ,, .:. .

of scaffoldingand cables. Along with the flashbulbs reminiscent of Polytope de Montreal (600 innumber)were three lasers (coloredred, green, andblue) projectedalong pathways determined by 400adjustablemirrors. Xenakis was able to control theoperationsof the lights, lasers, and mirrorsthroughdigitalmeans. All of the calculations were pro-grammedon a computer, and the output data wasthen converted to electromagnetic signals.This implementation of digital technologybroughtto fruition one of Xenakis's long-helddreams.In 1966, he had established an organiza-tion, EMAMu(l'tquipe de math6matique et auto-matique musicales), which in 1972 became

CEMAMu(Centred'Etudes de math6matique etautomatique musicales), with the goal of pursuingcomputer music and related research. He had ap-parently attempted to set up a paralleloperation atIndianaUniversity duringhis tenure there, but hewas unsuccessful, and he resignedhis position in1972, the same year of Polytope de Cluny and theconsolidation of CEMAMu.One of his interestswas the refutation of Fourieranalysis as the basisfor sound synthesis. As he put it in his chapteron"New Proposalsin Microsound Structure:"

[S]pectralanalysis of even the simplest orches-tral sounds.., presents variations of spectralHarley 47


17/26

lines in frequencyas well as in amplitude...These tiny variations. . . would certainly re-quire new theories of approach,using anotherfunctional basis and a harmonic analysis on ahigher level, e.g., stochastic processes, Markovchains, correleated or autocorrelatedrelations,or theses of patternand form recognition. (Xe-nakis 1992)The electroacoustic music for the Cluny instal-lation was producedon seven channels of the 8-

channel tape, with the last track reservedforelectromagnetic control signals for the lights, la-sers, and mirrors.Timing between the various ele-ments, including the music, could thus be preciselycontrolled-although, as before, Xenakis soughtparallelsrather than unions: "I wanted to establisha contrast: the lights area multitude of points,with stops, starts, etc., and the music is continu-ous, for although the sound changes it does notstop" (Fleuret1972).The music was presented through 12 loudspeak-ers distributedaroundthe site. The event, whichransome 25 min, falls in between the 6-min dura-tion of the Polytope de Montreal and the hour-longlength of Persepolis.The music bears some resem-blance to the Iranianpiece, even borrowingsonicmaterial. There is much that is new, as well, in-cluding a wild, brassy sound that is treated exten-sively throughout. There is a greaterprominencegiven to textures of percussive sounds, such as ce-ramic wind-chimes from the previous piece, butothers as well, including a plucked African thumb-piano. There is a striking moment at the end, whenthe focus suddenly turns to the thumb-piano,anexposed single note being plucked slowly andevenly, the earzooming in on the rich, rattling,res-onances of this distinctive sound.As one would expect, the various sounds are gen-erally layeredand distributed across the sevenchannels, though the density is not as high as theearlierpieces, possibly in deferenceto the vaulted,reverberant performance space. Particularly notablein Polytope de Cluny are the synthesized sounds,created using stochastic algorithms. Xenakis wasproud to have been the first in France to producecomputer-generated sounds, even if he lagged be-

hind Bell Labs,where digital synthesis had beenlaunched by Max Mathews in 1957.

Le Diatope; La Legende d'EerAt first glance, Le Diatope (the title of the installa-tion) would appear o be a variation of Polytope deCluny. The electroacoustic music is recordedonseven channels, with the final channel reserved forcontrol signals. The multimedia performance n-volves 1,680 flash bulb lights, 4 colored lasers, and400 programmablemirrors. This was a far moreambitious project,however. It was commissionedfor the inaugurationof the acclaimed CentreGeorges Pompidouin Paris,and it also included anoriginal architectural component. At long last, Xe-nakis was able to design the free-standingshellwithin which the spectacle would take place (seeFigure 10).It was also, at 46 min, about twice thelength, an ambitious durationfor lighting effectsthat requiredupdating25 times per second.

In addition, the music was commissioned sepa-rately, and was clearly conceived to stand as an in-dependentpiece. WestDeutscher Rundfunk(WDR)invited Xenakis to producethe piece using the fa-cilities in Cologne, and it was in fact premieredthere in February1978, months priorto the open-ing of Le Diatope outside of the Centre Pompidouin Paris. Its North American premiere took place atthe 1978 InternationalComputer Music Confer-ence in Evanston,Illinois (to much acclaim, andsome controversy).Xenakis, almost uniquely in his entire output,expended much effort on the programnotes for LeDiatope, presentinghis own thoughts andgather-ing inspirational texts which, while not forming anarrative,resonate in multiple ways with the cos-mic, apocalypticscope of the sounds and lights.The title of the music, La Ligende d'Eer, s takenfrom the concluding passageof Plato's Republic, inwhich a soldier is killed in battle then broughtback to life full of images of the afterlife, includingthe famous "music of the spheres." The medievalera is represented by Hermes Trismegistus, an al-chemist, who, in a similar way, is given a vision ofthe boundless darkness and light of immortality.



18/26

Figure 10. Design ofLe Diatope.

. .......

"WIV ?"T .

Le 'b;0,4/7

The passagefrom Blaise Pascal's Pensees contem-plates the insignificant place of humanity withinthe infinity of nature, and Jean-PaulRichter carriesthe vision further,writing of the terror of beingalone in the universe. The final text is a scientificdescriptionof a supernova, presenting its awesomesize and energywith detached precision. It is al-ways easier to interpretwords than music, andclearly, these texts all share a vision of the vastnessof the universe, with differentimages of light andlife within that infinity. The composer, in discuss-ing LeDiatope and his other polytopes, confessed:"Iwant to bringthe stars down and move themaround.Don't you have this kind of dream?"(Ma-tossian 1981).Even if less protracted n durationthan Persepo-lis, LaLigende d'Eeris vast in scope, with a more

concentrated, directed formal outline. The overalltrajectory,which proceeds without break,is one ofa gradualdescent, returningat the end to the highwhistling sounds of the opening. The multi-channel projection of the sounds aids perception ofthe different,often overlapping,entities, and alsoallows rather subtle shifts in emphasis to be ef-fected.There are eight basic sonic entities used in LaLigende d'Eer,present or dominant at differenttimes (see Figure11). Each is treated to a great dealof studio manipulation, including transposition, fil-tering, and reverberation.Each is also varied interms of density. These techniques serve, on onelevel, to create links between the differententities.Forexample, the high whistling tones of the open-ing, smooth at first, arevaried with tremolo/Harley 49


19/26

Figure11. Chartshowingprogressionof sonic out-lines and sectional divi-sions of LaL6gende 'Eer.

0:00 6:35 7:35 8:33 9:23 10:2717:13 17:5818&26 9:2121:0623:47 25'0 26'032730 29'13 3155 322? 32563213whistllngones in- - - - - - - - - outnoise: ndulatnggranuldted in out in-----outSrustling(cardboard) in- - - - - - --.electricdonkey/guitar) in---out in--------out (in)-y: noisyonset in -.. -main out inplucked.thumbiano' in outermic,atled in outpercussive,umi' iut

puleangv 'wavow (n1st 2nd 3rd 4th 5th 6th

3512 3535 36'46 37'273W1039'314001 4168 4028 41*0541'33 42'57 45high, hisingones in outnoise: ndulating,ranulatad in -ou tnoise:rnatlngcardboeard) out in. - -- - -outm r:lscc (donkeylguiar) - in - - - ------ --out:noisyonset out in --outuced.ub piano' out in ou,rttledout

Percussive,uNumi'lc: pusating *Wes' _ _

amplitude-modulationeffects to create a morestriated variant. This developedsonority resembleshigh transpositions of the rattling ceramic sonority,itself narrowly filtered to producea recognizableidentity of pitch. These two entities in turn resem-ble the high, narrow-bandversion of the granulatedundulating noise, and even the drum (tsuzumi) ele-ment, transposedand mixed to create a texture ofhigh density. Thus, while the entities arerelativelydistinct, they can also be related along differentparametricalcontinua.La Ligende d'Eer can be divided into eight sec-tions. The first is the clearest, containing only thehigh, whistling sounds that Xenakis calls "sonicshooting stars." Over 6 min, this layer alternatesbetween the smooth sound and the striated variant.The second section begins when other sounds be-gin to enter and the high sonority starts to fade out.This is a transitional passage, as five different enti-ties are introducedone afteranother, none of themdominating the sound-field.A rustling noise alter-nates with a brassy synthetic sonority, until, at17'13", this entity begins to layera number oftracks upon itself, commanding most of the atten-tion. With the abruptarrestof the brassvoices, thefourth section begins with percussive sounds alone,

a mixture of the plucked mbira(Africanthumb pi-ano), the rattlingceramics, and the tsuzumi. At25'00", a rich electronic entity enters and graduallysaturates the texture. The pulsating, wave-like con-tours of this sonority strongly resemble the pound-ing undulations of the second section of Jonchaies,the orchestral score Xenakis completed around thesame time (Xenakis 1977).After close to 8 min,this entity begins to fade out, and the brassy sonor-ity takes over again. A number of other sounds en-ter too, and the brassis less dominant. A wildmetallic sonority, sounding like a cross betweenthe amplified and distortedbrayingof a donkey andan electric guitar, is prominent throughout thispassage. Up to that point, the generalrangeof thesounds had been descending.The lowest transposi-tions of the brass and metallic entities carrythemusic through to the final section, where they fadeout over some 3 min as the high tones of the open-ing enter and carryon to the end.The pavilion that was designedto house thispiece, together with the light show that went alongwith it, was constructed from redvinyl stretchedover a metal frame. The design somewhat resem-bles the Philips Pavilion, although the point of de-parturewas to create a form that would have the



20/26

maximum volume for the minimum surfaceofouter shell. Rejectingthe obvious solution-thesphere-as being acoustically andvisually poor,Xenakis created a more complex form. As he put it,"the effect of the architectural formhas a quasi-tactile influence on the quality of the music orspectacle presented within it. This is beyond anyconsiderationsof optimal acoustics or proportions"(Xenakis 1978).There is an aesthetic character thatthe structureimposed on the performanceswithinit. In the case of Le Diatope, the point of departurewas the sphere,but with the design's double curva-ture, its "flights,"it is an architecture "opento theworld."StageFour:UPICThroughout 1972-1978, duringwhich Xenakis washeavily involved in overseeing the multifacetedproductionof Polytope de Cluny and Le Diatope,he was also working with his engineers atCEMAMu on the development of a novel approachto digital sound synthesis. The UPIC (Unite Poly-gogiqueInformatiquede CEMAMu) s a computermusic system enabling the user to create sounds bymeans of a graphicinterface (Lohner1986).All theelements of the sound are designed with an electro-magnetic pen on a large electromagnetic drawingboard.(Recentversions have replacedthe pen anddrawingboard with a mouse.) These elements in-clude the waveforms, the dynamic envelopes of thesounds, and the "arcs,"or notes. Interestingsoundscan be obtained by designingnoisy waveforms andcomplex envelopes, and also by layeringas many asseveral hundrednotes (Marinoet al. 1993). Xenakishad always sketched much of his music on graphpaper,so such an approachto sonic compositionwas perfectlynatural. It has also proven to be anengagingmedium for young children (and manyothers, of course) to approachcreatingsounds onthe computer.Polytope de Mychnes;Mycenae AlphaMycenae Alpha, Xenakis's first piece createdonthe UPIC,was completed in the summer of 1978,not long afterthe opening of Le Diatope. It was,

like La Legended'Eer,producedfor a multimediaperformance,though also conceived to be an inde-pendent concert piece. The Polytope de Myceneswas an outdoor spectacle mounted at the historicsite of Mycenae in Greece. Similarin style to Per-sepolis, this event included torches on the moun-tainsides, searchlights crossing the sky, and alsoincorporatedseveral of Xenakis's "Greek" nstru-mental and choral works. Mycenae Alpha, under10 min in length, served as an electronic interludebetween the other pieces.The music is noisy and dense, made up primarilyof massive clusters designed so that the scorewould also be visually compelling (see Figure12).The basic impetus is to move from complex tex-tures to more stable ones and back again (orto anew complex sound). Interspersedaremoments ofmore focused, simpler sonorities. The main limita-tion of that first version of the UPIC was that itwas not possible to mix the different"pages"of thegraphicscore. Xenakis's piece, then, is a successionof differentgestures, one following on the other. Inaddition, each of these "pages"could be no longerthan one minute in duration.Mycenae Alpha isbuilt from 12 such graphic/sonicentities, two be-ing repeated,to make a total of 14.In this piece, a structural distinction can bedrawnbetween complex sonorities createdbymeans of masses of relatively stable note-segments,and others created from dynamic arcs. It is easy todesign intricate glissandi on the UPIC merely bypicking up the electromagnetic pen andtracingthem onto the design board-held notes, in fact, aretreated as a sub-class of the more generalized"arc."The design of the waveforms (ahand-drawnwave-form is written into a look-up table) is also criticalto the sonorities created. The timbres tend to benoisy, but also static. Variationis achieved throughthe layering of the notes and the dynamic enve-lopes.Mycenae Alpha is remarkablefor demonstratingthe innovations of the UPIC system. Clearly,though, this piece is far more limited in its soniccontent than La Ligende d'Eer. But, for the poly-tope at Mycenae, the harsh sonorities would havematched the savage magic of the landscape, so per-meated with ancient myths.Harley 51


21/26

Figure12.PageofgraphicUPIC core romMycenaeAlpha.

hAwl__ '14W

-- __- ___ _ _

_ I.-_-

-i- -A.,L

-mama--= ...AAMi*

Pour la PaixIn 1981, Xenakis was commissioned by Radio-France to producea radiophonicwork for the PrixItalia (althoughapparently t was never enteredinthe competition). In response, he put together aratherstrange, collage-like work for reciters, choir,and electronic sounds created on the UPIC. Thetexts are taken from two works by the composer'swife (acelebrated author in her own right),Frango-ise Xenakis:Ecoute and Les morts pleureront.Partof this same selection of texts was used in thework composed just priorto this, Nekuia, for choirand orchestra.Pour la Paix exists in four forms. The full versionlasts over 26 min, and includes all three elements:the spoken text, the sung parts,and the electronicfragments. There is an abridgedversion comprisingthe ten choral sequences on their own. The othertwo versions present the work in pre-recordedform, either completely on tape or with just the re-citers speaking their texts live. The spoken textsconstitute roughlyhalf the work, there are ten sungpassages, and there are numerous sequences ofUPIC material.The electronic sounds heardin Pour la Paixcover a much wider timbral rangethan those inMycenae Alpha. Some are cinematic, evoking thesounds of war, for example, in response to a pas-

sage of text. Others are more abstract,and the re-maining fragments aresupportive,to accompanyeither the choir or the recited parts.The choir partsrangefrom straightforward hanting on a restrictedset of notes, as in the first sequence, to more com-plex sonorities-a compendium, really, of elementsfrom Serment, an a cappellachoral work from ear-lier that same year.In spite of the intensity of the texts, poetic rail-ings on war and death,Pour la Paix is ratherdisap-pointing as a radiophoniccreation. The sequencesof material mostly succeed each other with littleoverlap,with the exception of the electronicsounds which sometimes appear n conjunctionboth with the spoken and sung parts.The produc-tion lacks sonic depth and spatialorganization, apuzzling weakness consideringthe level of sophis-tication common in all kinds of broadcasts,not tomention Xenakis's other electroacoustic works.This would be his only forayinto the medium ofradioart, in any case.

TaurhiphanieIn 1987, Xenakis was given his last opportunitytoproducea multimedia event. The Festival de Mont-pellier commissioned him to create a work for theancient Roman arena in the Provengaltown of



22/26

Arles. Bull fights were still held in that same arena,so the focus of the event became the incorporationof bulls into the proceedings (alongwith the fa-mous white stallions of the nearby Camarguere-gion). The plan was to wire the bulls with radiomicrophones to capturetheir snortingbreaths.These sounds would then be processed in real-timeusing the new version of the UPIC system, whichwould be installed in a tower in the middle of thering. Spotlights were to projectpatternsof lightonto the floor of the arena and the animals wouldcreate dynamic stochastic patternsas they movedaround the ring.To top it all off, twelve percus-sionists were stationed around the upperseats ofthe roundarena,and they performedselectionsfrom Xenakis'spercussion music (Idmen B, Pleia-des, and Psappha).In the end, a lack of time and resources forcedXenakis to dropthe amplification of the bulls. In-stead, he incorporatedbrief samples from this un-usual source into a tape work created at CEMAMuon the UPIC.This piece, Taurhiphanie,was pro-jected in the arenaalong with some live manipula-tion of fragments of the sonic material using theUPIC. The animals did not cooperate in creatinginteresting stochastic patterns;they tended to hud-dle at one end of the ring or another, apparentlytraumatized by the pounding of the amplified per-cussion and the extreme dynamic rangeof the elec-tronic sounds. The performancewas not anunqualified success.Taurhiphanie,though, remains as perhapsXe-nakis's most successful piece createdusing theUPIC. At just under 11 min in duration,it isslightly more substantial than Mycenae Alpha,and, given the technological improvements of theUPIC, it is clearly conceived as an organicwholeratherthan a succession of parts, as in the earliertwo pieces.The first 5 min form a continuous gesture, thelayers of sustained sounds gradually rising until ahigh point is reached at 4'22". At that point, thesounds begin to descend again, but are interruptedat 5'28". After a series of shorter, disruptive ges-tures, a sustained sonority takes over at 5'57" fea-turing some stable intervals-a "still point." By6'45", fractures appear in the texture, with a vari-

ety of sonorities making brief entrances. The rangeof timbres is relatively wide for a synthesizedscore, though still not as rich as pre-UPICworkssuch as La Legended'Eer.A breakat 8'00" preparesfor a return to the bands of sliding sounds from theopening section, this time interrupted by dramaticinterjections of more concentrated, sweepingsounds that heighten the intensity of the passage.As the music nears its conclusion, the sustainedsounds begin to diverge, some migratinghigher,some lower. The piece ends abruptly,as if cut off.Most of Xenakis's electroacoustic works end insimilar fashion.While there is a certain roughnessto Taurhi-phanie that might indicate a lack of finesse in theshaping of certain details, there is also a strongsense of assurance and cohesion. As with the otherpieces that had their sources in multimedia crea-tions, this music stands on its own and carries on avitality that long-past spectacles cannot retainthrough mere documentation.

Voyage absolu des Unari vers AndromedeIn 1989, Xenakis producedhis most ambitiousUPIC work, a commission for the inaugurationofan InternationalExposition of PaperKites in Japan.Voyage absolu des Unari vers Andromede extendsthe image of a kite soaringthroughthe air to a cos-mic voyage throughspace in the direction of theAndromedagalaxy. While the music is not exces-sively programmatic,one may quite easily imaginetraveling throughspace while listening, with vari-ous "episodes"occurring along the way.The formal outline of Voyage absolu is con-ceived on a broadscale, though the 15-min, 25-secdurationis still nowhere nearthe breadth of Per-sepolis or La Ligende d'Eer. The piece is structuredin two parts.The first, lasting until 8'40", is themore turbulent,with numerous sonic scrabblingsand short dramaticgestures surroundingmore on-going layers of archingcontours. One striking tex-ture occurs at 4'48", where a percussive noisepulsation briefly sets up a regular beat that mightgo over well at a techno club. The second part ismuch more serene, as the sustained sounds undu-Harley 53


23/26

late more slowly. In this section, the added sonori-ties are less prominent in the mix, though there aremany discrete gestures heardin the background.The sonic arcs evolve both higher and lower, andthere arewell-defined episodes where timbres anddensities clearly shift. The music at 10'38", for ex-ample, is quite sparse, though by 11'30" it starts tobuild up again. The final few minutes encompass agradualascent into the high register,decoratedwith aliasing effects that producelow buzzingsounds.

ErodBy the time he reached the 1990s, Xenakis wasclearly not well. In addition,he was preoccupiedwith developinghis stochastic synthesis algo-rithms. He did, however, returnto the studio toproduceone last UPICpiece. Erod was created atLes Ateliers UPIC in 1997 for a commission fromthe Bath Festival in England.Xenakis workedclosely with Brigitte Robindor6,and they evidentlyexperimented with derivingnew sounds from re-cordings of earlierscores, both electroacoustic andinstrumental. The piece lasts less than 5 min, andit was withdrawn soon after its premiere. (The con-tribution of Ms. Robindor6to the productionof thepiece was so integral that Xenakis could not ingood faith put his name on it.)

StageFive:StochasticSynthesisAs early as the late 1950s and early 1960s, Xenakisspeculated about the possibility of synthesizingnew sonic waveforms on the same basis as his STalgorithmfor stochastic composition. He carriedout some experiments to that end at IndianaUni-versity, and continued at CEMAMu n Paris.Hisfirst results were appliedto electronic sounds pro-duced forPolytope de Cluny and La Ligende d'Eer.Until the mid 1980s, though, the main preoccupa-tion at his researchcenter was the developmentand promotion of the UPIC system. In 1986, withthe loan of a minicomputer from Hewlett Packard,Xenakis was at last able to return to this project.

By 1991, his team had succeeded in developingacomputer program hat would not only synthesizesounds stochastically, but would also implementmacro-compositional proceduressimilar to thosedefined for the algorithmimplemented in 1962(Serra1993).On the synthesis level, the aim was to generate awaveform that could be varied continuously ac-cordingto some stochastic function. In searchingfor the most efficient way to do this, Xenakis andhis assistants eventually adopteda waveform cycleas the basic unit (rather han, say, a sample), sim-plified as a series of line segments ratherthan acurve (see Figure 13).The degreeof change, bothvertical and horizontal, from one point in a cycle tothe correspondingone in the next, is calculatedonthe basis of a probabilityformula. The cycle is var-ied both in its amplitude (verticalextent) and fre-quency (horizontalextent). If each cycle of a sonicwaveform varies radically, the resulting sound willbe very unstable, or noisy. In orderto obtain arangeof timbres, a second-orderprocess needed tobe set in place to control the boundaries,or degreeof possible change, for each operation. This processcould of course be dynamic, effecting gradualshiftsin the rates of change. On the higher level, pro-cesses were implemented in order to select thenumber of "voices" (waveforms)activated at anyone time, their points of entry in the time-line ofthe piece, and the durationof each of these seg-ments for each voice. With these basic tools it be-came possible to input control data so as togenerate an entire piece digitally on the basis ofstochastic functions.

GENDY301;GENDY3Xenakis's first compositional productfrom thisGENDYN (GENeralDYNamic stochastic synthe-sis) algorithmwas GENDY301,presentedat the1991 InternationalComputerMusic Conference inMontreal, Canada.A newly-generated work derivedfrom similar control datawas producedlater thatsame year for the Joum6es de Musique Contempo-raine in Metz, France.This work, titled GENDY3,is the version that has become known throughsub-



24/26

Figure13. Segmentedwaveform cycle subjectto time and amplitudevariation.

0

sequent performancesand release on compact disc.In spite of the close relation of the two pieces interms of their genesis, they in fact sound com-pletely different.GENDY301is the shorterof the two, at 14 min15 sec in duration. It also exhibits a wider dynamicrangethan the other better-knownpiece, with ex-tremely loud textures entering suddenly on top ofnarrower-range onorities. In addition, it containsmore breaks of silence. Xenakis never stated hisdissatisfaction with the piece, but he may have de-cided not to release a "family" of works as he hadproducedin 1962 with the data fromhis ST pro-gram. (Thosepieces include ST10 for mixed ensem-ble, ST/4 for string quartet, ST/48 for orchestra,Amorsima-Morsima for mixed quartet, Morsima-Amorsima for mixed ensemble [withdrawn],andAtries, for mixed ensemble.)At 18 min 45 sec in duration,GENDY3is clearlymore substantial than the earlier version. Upon lis-tening, it is apparentthat, as in the ST scores,clearly defined sections areintegral to the algo-rithm. The piece is structured,from the listener'sperspective, as a succession of eleven short sec-tions, each lasting from one to two minutes, theoverall progression expandingthese durationsslightly. The sections aredistinguished by registralplacement and scope, and degreeof instability ineither frequencyor timbre. Each sound is relativelyconsistent in its settings throughout a section,though there are always mixtures of types, and theindividual layers are often laced with a great deal ofsilence, to avoid oversaturation.

What is surprisingabout GENDY3is the degreeof harmonicity present. Everysection containssome number of sustained voices, cutting in andout in stochastic fashion, and there are most oftenconsonant relationshipsbetween the stable pitches.In some sections, there arealso less stable voices,either in terms of frequency (creatingglissandi)ortimbre, resulting in noisy or rapidly fluctuating so-norities. There are some surprisinglylifelike tim-bres at certain points, including vocal-soundingandbrassy (thoughmore like organstops than realbrassinstruments) sounds. In fact, there is a greatdeal of organ-liketone to the held sonorities. It isalso true that the unstable sonorities, because oftheir novelty, stand out from the other sounds inthe sections where they occur.

S.709After producingthe two GENDY works in 1991,Xenakis continued tweaking the GENDYN algo-rithm (Hoffmann 2000b). For a monographconcertat Radio-France n December 1994, a new piecewas generated. S.709 focuses more on unstable, dy-namic sonorities. These areproducedby allowingthe vertical and horizontal points of the waveformsegments to vary more widely andrapidly.With aduration of just 7 min, this is a much shorterpiecethan GENDY3,but the degreeof sonic activity-the acoustical intensity-justifies the truncatedar-chitecture.

There are no clear sections in S.709 by which aHarley 55


25/26

formal outline can be perceived. Instead,the musicis highly fragmented.The harmonic, sustainedtones of GENDY3areentirely absent. By contrast,each of what seem to be no more than three or four"voices" arein constant fluctuation in terms ofpitch, timbre, or both. Amplitudes, too, arehighlymodulated.While there are some consistencies-certain characteristicsonorities-each voice under-goes considerabletransformation,both graduallyand in sudden shifts. The density of sonic informa-tion within each voice surely dictated the reduc-tion in the number of layers. In fact, for much ofthe time, there is only one layer sounding at atime.Taken together, the GENDY pieces and S.709demonstrate the wide rangeof possibilities inher-ent in the GeneralDynamic Stochastic Synthesisalgorithm.

ConclusionOnce he developeda workable compositional algo-rithm in 1962, Xenakis integratedhis creative pro-cesses and experimental approachwith computertechnology throughout the remainder of his career.It is worth noting, though, that some of the proce-dures he developed priorto 1962 could also havebeen programmed,had Xenakis had access to com-puting facilities. He appliedhis stochastic (andother) functions to his instrumental andvocal mu-sic, and worked at CEMAMuto generate newsounds digitally. Toward the end of his career,heat last found a way to reconcile his higher-ordercompositional concerns with the generation of thesounds (waveforms)themselves. Even so, Xenakisdidn't drop everything else in order to work withthese long-awaited tools. The acoustical richness oflive instruments and voices remainedcompelling,as the vitality of his late orchestralscores such asDammerschein (1994) or Ioolkos (1996) attests.In the domain of electroacoustics, Xenakis's mu-sic evolved a great deal, from origins in the mu-sique concrete style through more abstractnoise-based sonorities that were fashioned intocontinuously evolving waves of intensity, to the in-corporation of transformed instrumental sounds,

to, finally, digital synthesis. A detailed assessmentof his achievements in this domain in relation toother work in the field remains to be undertaken. Itis safe to say, however, that lannis Xenakis fol-lowed a singularpath, guided by his unique charac-ter as a Greek revolutionary, trained inengineering,influenced by architecture,self-taughtin music. The seeds he sowed, his works, and histechnical or conceptual innovations, have proven,and will continue to be, fruitful for succeeding gen-erations.

AcknowledgmentsI am grateful to Radu Stan of Editions Salabertforsupplyingme with archivalrecordingsof the elec-troacoustic works of Xenakis otherwise unavailableat the time of my research.I am also gratefultoBrigitteRobindord or detailing the productionofErod,Xenakis's last computer piece, and for allow-ing me to hear it. Others who have been helpful invarious ways in my research include: CorneliaCo-lyer, Cort Lippe,GerardPape,Jean-MichelRaczin-ski, Curtis Roads, and Malcolm Smith. Thanks alsogo to Doug Keislarfor his help in editing the arti-cle. I would also like to acknowledge the supportoflannis Xenakis himself, who permittedme to workwith the UPIC system at CEMAMuduring 1985-1987, and who was generous in many other ways.ReferencesBoivin, J. 1995. La classe de Messiaen. Paris:Christian

Bourgois.Brody,J.M. 1970. "IannisXenakisElectro-acousticMu-sic." Liner notes. Nonesuch RecordsH-71246.Delalande, F. 1997. "Ilfaut etre constamment un immi-gr6."Entretiensavec Xenakis. Paris:Buchet/Chastel &INA/GRM.Di Scipio, A. 1998. "CompositionalModels in Xenakis'Electroacoustic Music." Perspectives of New Music36(2):201-243.Di Scipio,A. 2001. "Clarificationof Xenakis: TheCyberneticsof Stochastic Music." In M. Solomos,ed. Presencesof/Presencesde Iannis Xenakis. Paris:Centre de documentation de la musique contempo-

raine,pp. 71-84.56 Computer Music Journal


26/26

Fleuret,M. 1972. "Une musique a voir." L'Arc 51:32-35.Fleuret,M. 1988. "Il teatro di Xenakis."In E. Restagno,ed. Xenakis. Torino: Edizioni di Torino,pp. 159-187.Fulchignoni,E. 1981. "SurOrient-Occident."In H. Ger-hards,ed. RegardssurIannis Xenakis. Paris:Stock, pp.257-263.Gabor,D. 1947. "Acoustical Quantaand the Theory ofHearing."Nature 159(4044):591-594.Harley,J.Forthcoming.The Music of lannis Xenakis.London:Harwood Academic Publishers.Harley,J.and M. A. Harley. 1997. "Triumphsof Moder-nity: Xenakis'Kraanergat Canada'sNational ArtsCentre."Musicworks67(Winter):24-31.Harley,M. A. 1998. "Music of Sound and Light:Xenakis'Polytopes."Leonardo31(1):55-65.Hoffmann,P. 2000a. "Analysis through Resynthesis:Gendy3 by lannis Xenakis."In M. Solomos, ed. Pres-ences of/Presences de lannis Xenakis. Paris:Centre dedocumentation de la musique contemporaine, pp. 185-194.Hoffmann,P. 2000b. "The New GENDYN Program."ComputerMusic Journal24(2):31-38.Lohner,H. 1986. "Xenakisand the UPIC."ComputerMusic Journal10(4):42-47.Marino, G., M.-H. Serra,andJ.-M.Raczinski. 1993. "TheUPIC System: Originsand Innovations."Perspectivesof New Music 31(1):258-269.Matossian, N. 1981. "L'artisande la nature." In H. Ger-hards,ed. RegardssurIannis Xenakis. Paris:Stock, pp.44-51.Matossian, N. 1986. Xenakis. London:Kahn & Averill.

Roads,C. 2002. Microsound.Cambridge,Massachusetts:The MITPress.Robindor6,B. 1996. "Eskhat6Ereuna:Extendingthe Lim-its of Musical Thought-Comments On andBy lannisXenakis."ComputerMusic Journal20(4):11-16.Schaeffer,P. 1981. "Chroniquesx6nakiennes."In H. Ger-hards,ed. Regardssur lannis Xenakis.Paris:Stock, pp.79-88.Serra,M.-H. 1993. "Stochastic Composition and Stochas-tic Timbre:GENDY3by lannis Xenakis."Perspectivesof New Music 31(1):236-257.Solomos, M. 1993. Apropos des premieresoeuvres(1953-69) de I. Xenakis. Pour une approchehistoriquede l'emergence du phenomene du son. Doctoral disser-tation. Paris:Universit6 de Paris IV.Toop, R. 1989. "The Music of Iannis Xenakis." Linernotes. Etcetera Records KTC 1075.Treib,M. 1996. Space Calculated in Seconds:The Phil-ips Pavilion, Le Corbusier,EdgardVardse.Princeton:PrincetonUniversity Press.Varga,B.A. 1996. Conversations with Iannis Xenakis.London:Faberand Faber.Xenakis, I. 1969. Letter to WallaceRussell, Administra-tor of the National Ballet of Canada,6 March 1969.Toronto:Archives, National Ballet of Canada.Xenakis, I. 1977. Foreword o Jonchaies.Paris:EditionsSalabert.Xenakis, I. 1978. Le diatope: geste de lumikre et de son[ProgramBook].Paris:CentreGeorges Pompidou.Xenakis, I. 1992. FormalizedMusic: Thoughtand Mathe-matics in Music, revised edition. Stuyvesant, NewYork:PendragonPress.

Documents

Electroacousticmusic of Xenakis