compositionalModels Xenakis

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Compositional Models in Xenakis's Electroacoustic Music Author(s): Agostino Di Scipio Source: Perspectives of New Music, Vol. 36, No. 2 (Summer, 1998), pp. 201-243Published by: Perspectives of New MusicStable URL: http://www.jstor.org/stable/833529Accessed: 05-05-2015 21:11 UTC

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COMPOSITIONAL MODELS IN XENAKIS'S

ELECTROACOUSTIC MUSIC

AGOSTINO DI SCIPIO

N IANNIS XENAKIS'S OUTPUT, electroacoustic music plays a role that is quantitatively marginal but quite meaningful in its content. In the fol-

lowing observations, my aim is to demonstrate that highly relevant aspects of Xenakis's contribution to today's musical thinking are found in electroacoustic works like Concret PH (1958), Analogique A-B (1958- 59), and Bohor (1962), up to La Legend d'Eer (1977), Mycenae-Alpha (1978), and Voyage absolu des Unari vers Andromede (1989), and most recently Gendy301 (1991) and S709(1994).

PRELIMINARY OBSERVATIONS

In electroacoustic music, compositional strategies are mediated by tools of work and thought-i.e., by a TxXvql (tekhne), an entire world of


Perspectives of New Music

techniques and technologies-often considered foreign to the field of the musicological discourse. However, this z?xvi( represents an essential expression of the knowledge which converges in the compositional process. As Pierre Schaeffer wrote, ". .. les idees musicales sont prisonnitres, et plus qu'on ne le croit, de l'appareillage musicale...."' The elabora- tion of the sound material and the strategies of musical design are captured in actions, procedures, and tools which actually permit us to "record" and study the compositional process and to observe how the composer's ideas are transformed into audible musical objects.

My analyses below lean on the notions of model of sound material, model of musical articulation, and control structure:

* A model of sound material is the operative description of "composing the sound." The analysis of electroacoustic music cannot waive the study of this aspect so essential to, and distinctive of, this type of compositional praxis. Characterizing a model of sound material shows the features of sound (microstructures) that are cognitively available to the development of musical form (macrostructures), and may illustrate the theory of sound implicit in the way in which the composer represents, conceives of, and works on and within the sound material.

* A model of musical design is the operative description of "composing with sounds." It illustrates the strategies of articulation of musical form, i.e., the way in which the material is worked on and the way by which the overall form is developed out of smaller units and components.

* A control structure represents the conceptual interface, as well as the operative link, between microstructures and macrostructures. It implements the relationship between the conception of material and the conception of musical form, and thus illustrates the features of material actually used (from among those available) in a certain musical construction.

This approach helps us, I believe, to tackle questions that are funda- mental in music analysis: what is the material of the musical work under observation? By what methods was the material worked on? How did this way of working finally bring forth the perceived musical structure? What relationship is there between sound and music? Thus, it becomes possible to grasp meaningful features of the music theory and the aesthetic hypoth- eses underlying the work in question. Music analysis is understood here as a question of characterizing and evaluating the musical knowledge

202


Xenakis's Electroacoustic Music 203

mediated by the z-XvTI in the process of composing, and the way in which such a mediation is accomplished.2 This is crucial as long as the particular tools for such a mediation are consciously chosen or even spe- cially designed by the composer-as in Xenakis's case.

* * *

Xenakis's work with electroacoustics has developed in two main phases: first, at Pierre Schaeffer's Groupe de Recherches Musicales, in Paris, from 1957 to the middle of the sixties; later, at the Centre Etudes Mathema- tique Automation Musique (CEMAMu), founded near Paris in 1966 by the composer himself together with mathematicians and researchers in computer science.

Except for Analogique B (for tape, eventually superimposed on Analogique A, for strings), Xenakis's work at the GRM resulted mostly in pieces of musique concrete. I use the term here in its oldest sense (1948), pointing to a transformation of the compositional process: "... une inversion dans le sens du travail musical ... il s'agissait de recueillir le concret sonore, d'oui qu'il vienne, et d'en abstraire les valeurs musicales qu'il contenait en puissance."3 Bohor (eight-track tape) is an outstanding example of such an attitude, a powerful, compact, sonorous fresco more than twenty-three minutes long, delirious and violent in its materic magma. A relevant characteristic here is that this music is void of appar- ent phrase-like articulation, void of recognizable logical progression.4 This is perhaps explained by Xenakis's decision to focus on the potential for articulation in -rather than with-the sound material itself. I would like to illustrate this potential as explored in the composition of Concret PH and Analogique B-two works which, in rather different ways, both represent a mediation between the noisy violence of Bohor and the constructive, mathematico-philosophical approach in Xenakis's instrumental works of the same period, such as Achorripsis (1956-57) and the computer-generated ST/10-1 (1956-62).

FROM CONCRET PH . . .

Concret PH (1958) is a 2'45"-long textural composition, a "cloud" filled with splinters of sound only vaguely differentiated among themselves. As is well known, this piece was conceived as an introductory event in Le Corbusier's Philips Pavilion, presented at the Brussels World's Fair in 1958 (the Pavilion also included Varese's only tape work, Poeme Electro- nique).



Sound design for Concret PH followed three steps. As a first step, the sounds of hot coals and burning material were recorded on tape. As a second step, very short chunks were extracted from the recording and isolated from their original context. Each chunk here corresponds to a single crackle, to a single creak of the coal in consumption-noise bursts lasting no more than a few hundredths (sometimes even a few thou- sandths) of a second. As is expected, such sounds have a very large spectrum (see Example 1). Indeed, at this level the determination of frequency becomes dependent on the duration: the shorter the sound impulse, the wider the frequency band. (In other words, following Heisenberg's "uncertainty principle," a precise localization in the time domain causes indeterminacy in the frequency domain.) As a conse- quence, frequency and its perceptual attribute, pitch, are hardly control- lable here, as it is impossible for human ears to integrate differences of pitch and amplitude in such brief moments.5

As a third step, the short noise bursts were assembled to create a longer texture, by piecing together innumerable scraps of tape. A series of such textures was obtained, each having a particular temporal density dn = kn/At. Textures were then submitted to two distinct strategies of densification:

1. layering of m copies of the same texture: D = mdn (density of microevents controlled by means of a geometric series)

2. layering of different textures each with its own density: D = 2ndn.

In both cases, the result of layering is a qualitative enrichment of the sound texture, heard as the fluctuating timbre of a rough dust of sound, with rare periodic patterns.

In Example 2 readers can see a sonogram of the entire recording of Concret PH.6 Two types of texture can be distinguished, one made of very short noise bursts (wide frequency bands, with peaks at around 6000-9000 Hz), the other made of slightly longer bursts (narrower frequency bands, with peaks at 4000-5000 Hz). Often the two types overlap, e.g., in fragments 40"-50" (Example 3a) and 110"-120" (Example 3b). Occasionally, one of the two is more in evidence-the first in fragment 30"-40" (Example 3c) and the second in the brief excerpt 80.9"- 86.6" (Example 3d) and later in fragment 100"-110" (Example 3e).7

Features found in large-scale spectral analysis are also found at smaller scales. For instance, Example 3c (fragment 30"-40") shows a sonographic snapshot which is quite similar not only to that of the entire piece (Example 2) but also to that of a very short detail only 0.3" long

204


Xenakis's Etectroacoustic Music20

(Example 4, 37.7"-38"). Example 5 illustrates this phenomenon in fragment 90"-100" (Example 5a), and in its ever-smaller particulars (Example 5b, 94.5"-96"; Example 5c, 94.8"-95.2"). In short, this "4zooming in" reveals the properties of a self-similar object, a surface in relief that is fractal in dimension: something halfwvay between a plane and a solid. An object of this kind, of dimension H = 2.6666667, is illustrated in Example 6.8

a ii . .11 I sh l J 0.11i l ik lI Ii I i ,LL L - It

1S4.467 '111.3?0 '200272 '203 17S '206O77 '208,980 '211-882 1214.785 '217.682iw

.0 dB8

-10

-20

-30.

-40 -

A 50-

-s0

EXAMPLE 1: CONCRET PH IS ENTIRELY MADE OF EXTREMELY SHORT NOISE BURSTS. SHOWN HERE IS THE WAVEFORM OF ONE SUCH SOUND (APPROXIMATELY 0.1" IN DURATION) AND ITS FREQUENCY SPECTRUM

HZ:

205



0'-80"

EXAMPLE 2A: SONOGRAPHIC REPRESENTATION OF CONCRET PH00"--80"

* . . ..

I : . : . . D . . . ' j:"

*- '^!:''-! .": :.., ; ? ,i :, ,'

'

:'

...

.. : :.

'

. ' ' ','' :

_ t , -- ...... ';, I : ' '

:t' i - ; :

EXAMPLE 2B: CONCRETPH-808:~'"- I60"

. j;EXAMPLE 2B' CONCRT ;

i: PH-80"-160"

EXAM PLE 2B: CONCRET PH-80-1 60

206


Xenakis's Electroacoustic Music

n,

i:: o, ?i ? i:: ? :?:' ? : - :-I.:I

: ? i ' ' ' a, (

:j: i ? i ir::::.?:':'-?;??? : :? ?'? ?:::' ,, -:

?, f: i:: ? ? ,. " :.i t,l r ?,r:? It %? ?, .? I ::

: : I i ?:- sC ?rri ?f. ;F?

-fair ?1 ??? ? i '? ?':

ix:?tt: ilai : :i: : i

hi .. :i. ' ?? - ? ; *r k ." t" ,ir? 'I .r? :? re .?( :1: 1

t: r t ": 1??::I?: 'I' I i ii i ? ?I,:, :. . Z... -?.? I;:I ir;- I ?i: i.; ?::p:L ??'

:$ a ?* : i: t:''I

:1:I '??? ??I/ : :

::1 i '." i? 'f I' I"?' i ' ' :i: I' i (b :? ' ai : r?:r i :i?f? r L I:i ?1 ?? ::: L:: :O Cia :i': (-il I I? Er '. r f i:.-:? ?:L i +. f :?

r 1 Y I ?; .r! i? ?L: 1: i t I r ii ?i I- ?1 r

ii. 1 .?I ?;L?r? r?.: IO LI U U

EXAMPLE 3A: PARTICULARS OF CONCRET PH-OVERLAPPING OF TWO TYPES OF SOUND TEXTURE, FRAGMENT 40"-50"

EXAMPLE 3B: CONCRET PH-OVERLAPPING OF TWO TYPES OF SOUND TEXTURE, FRAGMENT 110"-120"

207



EXAMPLE 3C: CONCRET PH-FIRST TYPE OF SOUND TEXTURE (NOISE BURSTS OF WIDE SPECTRUM IN EVIDENCE), FRAGMENT 30"-40"

n,

r,

r- .

w,

s : I?: o_

1(, - ? . ?' . ? I : 1 ;

*-? 1 i ?: :. ::: / ::.?: :?I?.: :?? i,?i? h:: j??: i :?:?i: 1 ?I t j?;? " ii. j ;I: ::i:? , , F "'' ,? ?t I:, - I.i ?? ?:t:?' i : i: i?

: .;? r ? i????:.t .r i . i r- tI? i? ?? C r?: r. s :I PI :Icl L?

asidclki ?-; ?I it- I ?..I:li t : I ?:Ilj.I TF:i :::i::iC " :;?:! ' ??i ?, -L? ii: ti. ?? ?1, .ii?. ??;-? "'i .1.' I? i.?l ;.?

?'": r,l r: i).'. "' i s"t?l:::II i''l.t' 1: i , ,t u:r? ?e ;I B?: c;? i : ffi':, '' CI:C i .I:i "! ' c ?'?. t ?' :: " 'I' C? ? ri, .1 ; 1

'i? ? ?: i'E

O I) LP * w r lvr,n r u* -rxln*e sra*n?-,?-- I--------?r*nlrurm

g0'524- 26'613

EXAMPLE 3D: CONCRET PH-SECOND TYPE OF SOUND TEXTURE

(NOISE BURSTS OF NARROWER SPECTRUM) IN EVIDENCE, FRAGMENT 80.9"-86.6"

208



R

?, ?, *,

6 r . O ir: ? . ?

(( ?i : ?:: ?i .:.:::: ? : . . : . . ??.'. . .... : : : : ?. '. : . '? : : : ?':1- ?:l..:l::::::i " ii::

:;?:? ;;t ,1 . I

,Ir; iT: ?:I ':d : ' ? ???i ?:?/ ?i?: .i.- ;?: ri -:r 7-k?'': ? i ii( *- i

.:.i :?;f 1 ?: ? ,? :! I-: ::

E t: ???. I ...,. I!; rl ,j?

.?lI?: ; r i:: 1: "?'YY : '' *.. i: ?( ?:?? i? i:b i i Y?i i

? ji .. f:i, iiO iii.;F-; :p;l i:r it ?r rS" 1I.i I '1

.i'JI:i .i i. 'r:::: ?. ?.!:?'

.1. I: ii : : li? .: r ;: :?:

i .?). c. ?r?i?::,-?. i?

j'?2i ?tr C 1":'''? ? ' oo tl to

-?? r* "'C""' ?:::: ;??::

EXAMPLE 3E: CONCRET PH-SECOND TYPE OF SOUND TEXTURE

(NOISE BURSTS OF NARROWER SPECTRUM) IN EVIDENCE, FRAGMENT 100"-110"

EXAMPLE 4: A SMALL DETAIL OF CONCRET PH, 37.7"-38"

209



So"- Ioo'

EXAMPLE 5A: CONCRET PH, FRAGMENT 90"-100"

I_

'i& '^ ::1:.::*:M J|^ ~~~~~~~~~~ ? :1I

-.

f

* "i!~ -.~i':: - *~ ":.: : . .... ':^ ' - r ^ . - ~/ ". : :i . ' *: . " * ".* - ' : ^ . *^ * . ;: :-: ' **^ .

*,~~~~~~~~~~~~~~~~

?-;... .. :

- ::t'".; -..' - : ? ' .'. * : : :.' . ..:::*! : : !.*/:.. : .':'. . . ..

^ ***.~~~~~ ':

-* *:'"* '"

;' ?''''"(":""''' '

'- '. h ' '"""

r~~~~~~~?

:_ ?.l.:'i: '.: : : .

~

. :

* ^ t.4 '^ '.^t "-^4'a '-.?*-? ,(:*!...* to '^ ^ li . :/ .* * *"**


?; ~ ~ ~ ~ ~ ~ '3

?, ~ ~ ~ 4 ~

if? re,?

EXAMPLE 5C: CONCRET PH, A SMALLER PARTICULAR, 94.8"-95.2"

..

rd . . J ; W0

.

I i &

EXAMPLE 6: A FRACTAL SURFACE, OF DIMENSION 2.666667 (REPRINTED FROM B. MANDELBROT, FRACTALS: FORM, CHANCE,

AND DIMENSION. SAN FRANCISCO, 1977)

21 1



The overall piece presents a rather simple macroscopic shape, going from the sonorities of the first type of texture, in evidence at the beginning of the piece (Example 7a, 15"-20"), to the slightly less fragmented ones of the second type, in evidence towards the end (Example 7b, 140"-145").

~~~~~~~~~~?- i....

* - . :. : . ? ?

_

'

*-'~~~. . ': . *

.

. .

, . . . . . ?

' .*

' . '* * * **

-

?._, .. .. . *. '

. .; ?

- '.i ''

.

0~~~~~~~ ~ ~" " : * " ..A.f.....; i,...'" ~ " i:.,:/:^.? l^ e >;* *; ,-:?:^; .: .>.-...: :.' ..;:: . ....t-.',::; ^'.i^*,?;.:^ '. ;.^^;...^^ ' ..*: .^. ,' -i.'. ~:,,X-;

'"~" ' ' !~ :. i~ .i!~;..ii~; ' i~.. ~: ': :~'~ Ji~ :' ,.i? zib :""? ? :i: i . !~ :'. .. ~ ~:".. :~ :!i? ~..~ i :..~ . i '

,-.~. ::: :.' : 'r..i~" 16 ::' .. :':

if~ ~ ~ ~~ ~ i" . ':, :;i ::I : :'

EXAMPLE 7A: DETAIL OF THE SONOGRAM OF CONCRETPH-THE FIRST TYPE OF TEXTURE IS PREDOMINANT AT THE BEGINNING OF THE PIECE,

AS IN FRAGMENT 15"-20"

* ..-

=6"-;!. i . '

' ' ': '*:4-:.- ::;:! : .

X::A

"' ....1^',;~~~~ ^~' -l^' '^ ':~~ "' ^140' 1:465..'

EXAMPLE DETAIL OF THE SONOGRAM OF CONCRETPHTHE SECOND TYPE OF EXAMPLE 7B: PREDOMETAIL OF WARDS THE CONCRE T PH- THE SECOND TYPE OF

TEXTURE IS PREDOMINANT TOWARDS THE END, AS IN FRAGMENT 140"--145"

212



* * *

Xenakis's interest in particular acoustic phenomena-such as the shrill sound of cicadas, the drumming of rain, the human noises of crowd scenes, the thunder of battle9-is well known. However, I would rather avoid speculation here as to the possible implications behind the sound of burning materials. The material of Concret PH, as we have seen, does not so much lie in this acoustic phenomenon as in the audible result of the dissection, selection, and composition of innumerable noise impulses. That is the material handled by the composer, something which is itself designed, and largely devoid of perceptual qualities revealing its actual phenomenal origin (indeed, listeners tend to perceive these sounds as the sound of breaking glasses). That material is then manipulated, as we have seen, by means of simplistic statistical principles, which in the end lead to the rather simple form of the whole piece.

It is to be emphasized that each fleeting creak of sound in Concret PH is a point of catastrophe and discontinuity; it represents a tiny explosion which transforms a bit of matter into energy. Not by chance, then, is the overall form of the piece so simple and static: simplicity at the macro-level allows the listener-and the composer himselfl-to turn his/her attention to the morphology of the scraps of sound this music is made of, to the shortest processes by which matter is transformed into energy. The listener's attention, then, is turned towards the form of each of these sonic events.

In line with the musique-concrete approach, here the model of sound material is a mixture of manipulative procedures through which-with a definition found in the system-theory literature-"noise is transformed by learning into a sign."'l In this annotation, "learning" is perhaps the most important thing: it means interior accretion and awareness of the auditory experience, which finally becomes a project of art through choice and isolation of particular features of the acoustic phenomenon. These are the features of the very material in the composition of Concret PH: every single component of the whole is marked by a creative intention, by an intentional act that changes its nature and meaning. What we call material here, then, tends to lose its connotation of something natural and becomes a designed object itself-an artifact.

In spite of the simple cloud-like structure, the unfolding of Concret PH is rather extraneous to explicit figurative criteria and devoid of mimetic or narrative references. Despite Xenakis's debt to Schaefferian aesthetics, there is something here that sets Xenakis at the margins of musique concrete. I refer to an attitude that renders the musical work a definitive artificium, the resultant of a project of art addressing many

213



time scales in the structure of music. Incidentally, this is mirrored- though hidden from the ear-by the self-similarity of the time-frequency representation of the piece as a whole.

... TO ANALOGIQUE B

Analogique B (1958-59) marks a departure from the concretist approach of pieces like Concret PH and Bohor (this latter, however, was composed later, in 1962). Brought to conclusion partly at the GRM and partly in Hermann Scherchen's studios in Gravesano, Analogique B represents the very first attempt at welding musical invention to a conception of sound freed from classical acoustics.

This "electro-magnetic music for sinusoidal sounds"" is made up of many brief sinusoidal signals recorded on tape. Here Xenakis's conception of sound lies close to that put forth by physicist Dennis Gabor (as well as by Norbert Wiener). The possibility is explored of composing sound by innumerable overlapping elementary signals-sinusoidal sound grains. Such a possibility is expressed by Gabor's series expansion:

s(t) = Zn,k an,kg(t-kT)ejnn The elementary signal is represented by g(t). It has a real and an imagi- nary part-i.e., in Gabor's own description:

enQt = p-2(-texp-a i2Tfol

where a is the parameter allowing us to establish both the duration of the grain and its band width. For Gabor, therefore, "elementary signals are harmonic oscillations of any frequency fo, modulated by a probabilistic pulse."'2 A Gaussian curve is utilized for the pulse's envelope, as in fact it allows one to locate the elementary signal in both time and frequency with minimal spectral dispersion. Example 8 shows Gabor's "grid," where the time/frequency continuum is quantized into its smallest cells-called by him logons-of area AtAf An elementary signal is represented by a corresponding logon in the grid. The three graphs in Example 8 show the intuitive notion that the frequency spectrum depends on the temporal pattern of elementary signals, while the density in the particular time span remains the same.

Xenakis's approach is different with regard to the envelope curve of the grain. He leaves it constant-a rectangular envelope. Shown in

214



F

Af I

u -> T

t

A

F

F IIms F

III -> T

A

iF

II -> T

A

F

EXAMPLE 8: THE NUMBER OF SINUSOIDAL GRAINS REPRESENTED IN THE TIME/FREQUENCY GRID (TOP), IS THE SAME IN ALL THREE EXAMPLES,

BUT THEIR TEMPORAL PATTERN IS DIFFERENT, THUS CAUSING THE SOUND TO CHANGE SPECTRUM (BOTTOM)

Example 9 are a Gaussian grain and a rectangular grain, with their relative frequency spectra. As can be imagined, the latter is perceived as a brief explosion of noise in a frequency range centered on the frequency of the elementary signal.

The rectangular grains in Analogique B have a fixed duration of 0"04; amplitude and frequency values are localized on a plane broken down into tiny cells with an area of AgAf-Xenakis calls it a "screen." In order to obtain dynamical sounds, a "book" of such "screens" is used, at a distance of At = 0"5 (see Example 10).

The global characteristics of a "screen" are (1) the density of grains in the volume AgAJAtC, (2) the shape of grain distribution; (3) the degree of order/disorder in such a distribution. The strategy employed for Analogique B deals only with the first of them. It consists in a Markovian process implemented as a transition probability matrix (TPM): the evolution of the sound texture is traced by the probability that at a certain time t the screen's parameters will be modified with respect to t - At.

215



\\ a

I

t

/ [N

a

A f f EXAMPLE 9: A GAUSSIAN GRAIN AS DESCRIBED BY DENNIS GABOR IN 1944, AND A RECTANGULAR GRAIN AS UTILIZED BY XENAKIS IN ANALOGIQUE B

Ag n

hf

At

EXAMPLE 10: A "BOOK OF SCREENS," AS UTILIZED BY XENAKIS AT THE MICROCOMPOSITIONAL LEVEL IN ANALOGIQUE B. REPRESENTED ARE DIS-

CRETE VALUES OF FREQUENCY (AF), AMPLITUDE (AG), AND TIME (AT). DE- SCRIBED HERE ARE TWO IDEALLY SINUSOIDAL TONES OF EQUAL AMPLITUDE,

ONE AT FIXED FREQUENCY, THE OTHER SWEEPING DOWN IN FREQUENCY

- I

216

\

I

t

k)

-



A simple TPM looks like the following:13

X Y X 0.2 0.8 Y 0.8 0.2

It represents the probability

* that symbol Xwill be followed by another X (20%); * that Xwill be followed by Y(80%); * that Twill be followed by X(80%) and * that Ywill be followed by another Y(20%).

In Analogique B, two TPMs were utilized in the determination of amplitude, density, and frequency values:

x Y X Y X 0.2 0.8 X 0.85 0.4 Y 0.8 0.2 Y 0.15 0.6

The decision as to whether the former or the latter should be used was made at any given time on the basis of several rules which, for brevity's sake, are not described here. X and Tare associated with two sets of values selected from among sixteen regions of frequency (each corresponding to an octave), two sets selected from among four regions of amplitude (in phones), and two sets selected from among seven regions of density (in logarithmic units). Once the set has been selected, the particular values in that set are chosen on a purely random basis.

To successfully predict the evolution of the parameters, it is necessary to answer this question: what is the system's general tendency during a certain number of transitions? In the case of our first example matrix, we have the following relationships:

X' = 0.2X+0.8T T = 0.8X+0.2r

Thus, after only eight transitions, a stationary state is reached. Probability levels in the stationary state are X = 0.5 and Y = 0.5; for the second matrix, X = 0.73 and T = 0.27. It is possible to calculate the mean entropy of each TPM in a stationary state as

H = (HX) + (Hr)

217



in which Hx represents entropy for X states of the TPM and Xy represents entropy for the Ystates, calculated as

H = --pilogpi

(pi are the transition probabilities established by the matrix). A further macroscopic control utilized by Xenakis is called the

exchange protocol between perturbation states and stationary states. It is employed to determine TPM internal parameter values for each section of the piece-eight in all, for a total of only 2'35". The exchange protocol thus establishes the alternation between sound behaviors of growing entropy, or perturbations P, and more static behaviors, or equilibrium points E.14

These details give us a pretty clear picture of the various levels in the compositional process: (1) the granular representation of sound provides the composer with minimum discrete elements; (2) manipulating these elements (microcomposition) results in the actual sound material for the entire work; (3) the concept of "screen" represents the control device connecting microcomposition with criteria of short-term (TPM) and long-term musical design (exchange protocol P and E).

As in Concret PH, here we see again a continuity of micro- and macro- levels. However, this time such continuity is caught in a rather formalized system, whose states in time finally shape the resultant sound object. As with later examples of algorithmic composition, the compositional approach here seems to consolidate in a "mechanism" that the composer lets manifest itself.'5 The perturbations that temporarily disrupt the system's stability actually prove to be anything but an ulterior means for manifesting the mechanism's functionality and consistency.

In short, the composition of Analogique B reflects the quantistic approach that Xenakis borrowed from Gabor16 as well as the statistical methods that Xenakis utilized in instrumental works during the late fifties.

* * *

In the composition of Analogique B, the quantization of the sound continuum down to the finest time scale enables the composer to instantiate programmable, formalizable compositional processes within the sound itself. More recently, this has become typical of granular approaches to digital sound synthesis. In general, while sound synthesis based on Fourier's paradigm-a summation of perfectly harmonic sine functions, which are impossible to locate in time-leads us to thinking of and

218



working out the sound material in terms of spectral characteristics, i.e., in the frequency domain only, granular representations lead us to working it out in its micro-time structure. "Composing the sound," then, requires the determination of time relationships among innumerable finite elements. In Analogique B, the conceptual tool to accomplish this is the transition-probability matrix. More recently, composers have employed other techniques, such as random distribution within either static or dynamic boundaries (as used by Curtis Roads and Barry Truax),17 and mathematical models of nonlinear, chaotic systems (as used in my own compositional work).18 In most approaches of this kind, the morpholog- ical and perceptual properties of sound and music are to some extent dependent on the coherence of micro-level processes, whose functionality, then, is to bring forth the overall form of a sound object or texture.

Albert Bregman, renowned scholar in the field of auditory perception, has pointed out that granular representations can be pertinent in model- ing dynamical sound events of particular complexity (transient phenomena, turbulence, auditory images rich in noise components and compounded of innumerable microscopic events). He adds, however, that this is only possible if an adequate description of the way in which grains succeed and overlap each other is developed.19 That is, if the composition of grains is adequately achieved.

For many, the sonority of Analogique B is rather disappointing in comparison with the theoretical implications in play. This is not explained simply by the poverty of the technical means available at the time of its composition. Indeed, it can be explained, as we shall see later, also by the strategies themselves pursued by Xenakis: stochastic laws seem to prevent the emergence of a higher structural level; they seem not to be capable of bringing forth those "sonorities of second order" Xenakis expected to achieve.20 The reason for this may be that his formalized system is not an ecosystem, i.e., it is not nourished by retroaction and "environmental" conditioning; it does not change itself with the changing context. It has no (nor does it desire) memory. The relevance of this point is hardly tri- fling-and I will come back to the issue in my final discussion.

Still, emblematic in this music is Xenakis's gesture aimed at generating, by one and the same process, both complex timbral entities and the overall form of the work, so that the passage between micro- and macro- structure is rendered continuous.21 As is well known, a similar compositional attitude was shared by many composers at the time of the realization of Analogique B. Xenakis's contribution with respect to these matters, rarely understood, represents a position of a profoundly different nature compared with that of Stockhausen, who, however, has been

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the most famous supporter of temporal and structural unity in electroacoustic music.22

MYCENAE -ALPHA

Mycenae-Alpha (1977) was the first music realized by means of the UPIC computer system-the "polyagogic" computer unit of the CEMAMu. It was recorded on monophonic tape although its public performance calls for either two or four loudspeakers.23 On the UPIC, composing is car- ried out by tracing lines on a graphic pad connected to the computer. The graphs are stored and then utilized either as audio waveforms or as amplitude envelopes. They can also be utilized as pitch envelopes (glissandi) or tempo curves.24

The sound is generated by table look-up synthesis, the most straightfor- ward standard synthesis method known in computer music. The sound- sample amplitudes are looked up from a short array (wavetable) where the waveform samples are stored, stepping through the array by a step o proportional to the desired frequency:

a = NpSt(l/p) wherein Np is the number of points in the wavetable, St is the sampling period and p is the period of the signal to be generated. The method can be formulated in this way:

s(i) = Ag(,) wherein g(O) is the sample read from the array location X, namely

O = [0+ + o(i)]modNp As we can see, o varies with the index of discrete time, i. In the UPIC system, o is controlled by the curves the composer intends to use as pitch profiles.

The "score" of Mycenae-Alpha (Example 11) consists of a diagram illustrating the temporal progression (horizontal axis) of a values (vertical axis). It gives no information as to the actual pitches heard (except in case the wavetable utilized stores the samples of a single-period sinusoid). Nor does it give information about the particular wavetable selected for the synthesis. However, it shows that the piece is made up of thirteen sections, each having a characteristic graphic outline. The shortest section is section 4, only 5" in duration; the longest is section 13, lasting 1'01".

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1 2 3

C., -_ I

C,.

5. i

5 A'\ 6

4

.,

a'

I

11 _ _

12 13

i I I I

EXAMPLE 11: THE SCORE OF MYCENAE-ALPHA

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Section 7 and 13 have an identical shape but a different duration (1'01" and 24"). The low, fine weave in section 3 is almost perfectly mirrored in section 6, but the latter ends with different pitch profiles. There is also a strong similarity between section 11 and 12. Many sections feature tree- like shapes (like section 5, where each line follows an independent path). Only the transition from section 9 to 10 is rather smooth; in all other cases the beginning of a new section is marked by abrupt changes in the music.

From the point of view of computer music system design, UPIC cer- tainly represents one of the earliest examples of a uniform and coherent music interface. However, there are also strongly constrictive aspects. I shall mention two of these from among those which, in my opinion, betray an involution in comparison with earlier works:

* The notion of timbre appears reduced here to one "parameter" among others, understood as the set of harmonics of a periodic waveform (as is typical of table look-up synthesis); in earlier works, as we have seen, timbre tended to be understood as dynamic form, the epiphenomenon of microcomposition;

* The distinction between "musical structure" and "sound structure" has been reinstated (the fact that the same profiles could be used as either audio waveforms or pitch functions, does not prove the con- trary). That distinction was implicitly put into question in the earlier works, which reflected a notion of composition that shares little with instrumental and vocal music.

Similar observations also apply for Voyage absolu des Unari vers Andromede (for two-track tape), realized with an updated version of UPIC.25 Despite the different formal reach (Mycenae-Alpha lasts 9'36" and Voyage more than 15'), Voyage, too, is divided into sharply contrast- ing sections. Both works feature extensive glissando textures26 contrast- ing with constant-pitch structures. Overall, differentiated sonorities alternate between the following oppositions:

* sounds having wide-band spectra * continuous spectrum: noise strias (at times rhythmically ani-

mated); * discrete spectrum: pulse trains.

* sounds having limited-band spectra * harmonic spectrum: smoothed pulse trains; * almost-pure sounds: one single spectral line.

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Introducing the UPIC system,27 Xenakis insists on the impact of computer graphics on musical didactics, and on the potential of compositional design laid out graphically. Using the UPIC, composition takes place first of all within the flat world of the time-o plane; auditory experience takes place only after this drawing of lines. Although it has raised the interest of many,28 I find this approach a debatable one in that it implies an a posteriori association of a sound pattern with a visual pattern. In a sense, the sound is conceived almost as if it were the by-product of gestures removed from the flow of time-which, instead, is the essential dimension in the experience of all acoustic phenomena, including music. (Notice in section 8 of the Mycenae-Alpha score that some pitch profiles move back in time!)

In this sense, Xenakis's work with the UPIC seems to conform literally to his well known statement that "time could be considered as a blank blackboard, on which symbols and relationships, architectures and abstract organisms are inscribed."29 I shall return later to the issue of time in Xenakis's music, as I do not believe it can be reduced to such a thoroughly reductionist position.

SOUND AS A STOCHASTIC PHENOMENON. FROM LA LEGEND D'EER ...

In the first English edition of his book Formalized Music, Xenakis described an approach to sound synthesis that is completely independent of the Fourier paradigm. The approach was based on initial experiments Xenakis pursued at CEMAMu and at Indiana University (Bloomington), and which he further pursued in the realization of La Legend d'Eer (1977), worked out at CEMAMu and at Cologne WDR, and later in the realization of Gendy301 (1991) and S709 (1994).

La Legend d'Eer is a long continuum of sound lasting about forty-six minutes, recorded on a seven-track tape.30 It is made up of both computer-synthesized sounds and recorded samples. The latter include the sounds of African and Japanese instruments, eventually processed at the Cologne studio. (Listening to the piece, I find that these sounds seem to resonate from earlier electroacoustic works, especially Diamor- phoses and Orient/Occident.) The computer sounds were obtained in part with the UPIC system and in part with stochastic methods.31 At first, the music is a rather fine thread of high-pitched synthetic sounds. Later it gets denser and denser until it becomes a massive texture mixing up several distinct sources. Processed instrumental samples are present in an ever increasing manner as the piece unfolds. Except for the initial pitched

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sounds, most synthetic sounds in the piece are quite noisy. In my observations below, I focus on the stochastic synthesis methods through which these sounds were achieved. I will then discuss the detail of the musical application of these methods in Gendy301.

* * *

The sound-representation domain addressed by Xenakis is the time domain of the acoustic waveform. The idea is to directly generate the sound signal by using probabilistic functions. The signal is seen as the path traced by a point animated by incessant Brownian motion, capable of ranging continuously from more or less stable periodic patterns to rather irregular curves devoid of periodicity. The mathematical constructs Xenakis used to this end unite in a group of eight methods of sound gen- eration, all of which, despite some differences, share the same strategy: to establish a condition of initial disorder and introduce means by which it can either be reduced or increased. The reasoning behind this approach stems from two considerations:

* the complexity of natural sound phenomena cannot be reduced to the terms of the Fourier paradigm because its limitations heavily condition the sonological applications (both with analog and digital technology);

* sound design should be regarded as an act of creative imagination; it cannot be relegated, therefore, to the simulation of known sounds.32

The latter consideration is extremely important. In the twentieth century, musical forms have gradually been freed from the reproduction of pre- established frames. The inspiration behind a music of electronically pro- duced sounds springs from extending this freedom to the realm of the sound material itself. Therefore, simulation of pre-established sonic materials (e.g., the sound of musical instruments) is excluded on the basis of this position.

As mentioned above, in the direct-synthesis approach developed by Xenakis the instantaneous signal amplitude can be thought of as an alea- tory variable and can be defined in terms of the probability of the occurrence of allowable values. The whole of such probabilities can be expressed by relating x value of variable X to the probability P of its occurrence. Thus, by means of

f(x) = P[Xsx]

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Xenakis's Electroacoustic Music25

we show that P is the probability that X will assume a value included in the interval [oo, x]. We can also characterize the probability density function expressing the probabilities of a continuous random phenomenon:

F(x) =f xf(t) dt.

The functions most often used by Xenakis are the following (see Example 12):

e Uniform: f(x) I 1, withO0< x < * Cauchy: f(x) / (a2+ +x2) * Gauss: f(x) = [1/( F2-na)]e_(X _t)2 / (2a2) * exponential: f(x) = l/2keXli-i

These can rather easily be simulated on the computer using simple Algo- rithms. 33

f lxi ix i x

I I K

-a + 'tI

f (xj f([XI

EXAMPLE 12: AN APPROXIMATE GRAPHICAL RENDITION OF PROBABILITY DENSITY FUNCTIONS (TOP LEFT: CAUCHY; TOP RIGHT: EXPONENTIAL;

BOTTOM LEFT: GAUSS; BOTTOM RIGHT: UNIFORM)

225

.-O.



There is a connection in the way Xenakis conceived of sound material in Analogique B and Concret PH and this digital sound synthesis approach. The quantistic hypothesis he followed during the late fifties is taken here to extreme consequences. Earlier the quantization of the time continuum reached the granularity of elementary signals as short as a few hundredths of a second. It is now even finer: the entity subjected to compositional decisions is the digital sample itself, the instantaneous pulse necessary for a digital computer to generate sounds. In Xenakis's experiments, samples succeeded each other with a lapse of about At = 0.00002" (sampling rate = 50 KHz). The signal was obtained by directly calculating the sample values in discrete time, i.e., operating in a bidimensional space AtAg. Frequency and timbre characteristics, therefore, become the resultant of particular sample patterns; they are to be regarded as emer- gent properties, i.e., epiphenomena of a process that occurs in the lowest technically available scale of time.

Broadly speaking, Xenakis's stochastic synthesis belongs to a class of methods that can be formulated quite simply as

s(i) = f(s(i- k))

in which function festablishes the relation between the amplitude of the signal at time i and its amplitude at time i - k. Iffdoes not implement any consistent acoustic model, then we may call this a nonstandard synthesis approach.

In computer music, nonstandard synthesis has been used not only by Xenakis but also by composers like Herbert Briin (in his compositions realized with the SAWDUST program) and Gottfried Michael Koenig (SSP program). More recently it has been utilized by younger composers (e.g., Paul Berg, Arun Chandra, Jonathas Manzolli, Michael Hamman). The important point shared by all nonstandard methods is that the sound-generating process depends on the composer's arbitrary invention. Sound material shifts into the realm of the possible-paradoxically appearing dematerialized, virtual, i.e., not preexistent to an act of cre- ation and design. The composer becomes integrally responsible for the musical artifact, by means of a thorough continuity of the compositional approach. He composes sound and music at once. A perfect instance of this is Xenakis's recent Gendy301.

... TO GENDT301

In 1991, twenty years after his first experiments with direct synthesis, Xenakis took up this research line once again. He marked his return by

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writing a computer program called GENDY (GtNeration DYnamique), which he wrote himself in BASIC and which was later translated into C by his colleagues at CEMAMu. The program implements an algorithm of sound synthesis called dynamic stochastic synthesis,34 and is called up by another program, PARAG3, which has the role of a higher-level control structure. Gendy301, a tape piece lasting 18'45", is the first work using dynamic stochastic synthesis. The world premiere took place at the Mon- treal International Computer Music Conference (October 1991). The piece is now available on CD (Neuma 450-86), but there it bears the slightly different title of Gendy3. The two recodings being perfectly identical, I think the title was changed because of editorial aspects, which are, of course, completely irrelevant to us here (in the files available at Xenakis's Paris publisher, Salabert, Gendy3 is officially claimed to have been premiered in Metz, France, in November 1991).

Dynamic stochastic synthesis entails distorting a waveform in time and amplitude, calculating the amount of transformation through stochastic variations. It assumes that the sound signal is traced by a series of waveforms J, each consisting of I linear segments (Example 13a). The end coordinates of the i-th segment in the j-th waveform are xij, Yij. Phase continuity between waveforms j and j + 1 is assured by establishing

Xo, j+ 1, 0,j+ = Xi- i,j,Yi- I,j- The method can be described by saying that the end coordinates of segment i in the j-th waveform are stochastic variations applied to the end coordinates of the segment i in waveform j- 1. That is,

Xi,j+ = Xi,i+fx(z)

Yij, = Yi,j+fy(z)

where fx(z) and fy(z) return positive or negative values, given an argu- ment z (itself a random number with uniform distribution, i.e., white noise). Samples are computed by linear interpolation between the initial and end points in each segment:

s(t) = s(t) + [i + , j-Yi, /ni,j] where nij is the number of samples in the i-th segment. The segment duration is

dij = (nij- 1)/Sampling rate.

227



Therefore the j-th waveform will have a total duration (period) of

Dj = Yidi,. We have three possibilities:

* transformation of the ordinates only

Yi,j+ = Yi,+fy(z) i,j+ 1 = Xi,j

(which means only the amplitude values are modified, thereby causing a change in the spectrum);

* transformation of the abscissae only

Yi, j+ 1 = Yi,j xi,j+1 = Xi,+fx(z)

(which means alterations of Dj, which cause changes of funda- mental frequency of the sound, and, therefore, of pitch; eventually this also causes audio rate frequency modulation, with related spectral enrichment);

* transformation of both coordinates

Xi,j+ = Xi,j+fx(z) Yi,j+l = Yi,j+fY(z)

(which means alterations of both spectrum and pitch; Example 13a and Example 13b show a transformation of this type).

As the width of the signal is represented by sixteen-bit integers, the values of yij must be kept within the interval [+-32767] to avoid satura- tion. Moreover, too-extreme aleatoric variations of xij can lead to wild frequency modulations; so they, too, must be kept within a given range. To deal with these problems, Xenakis resorts to the notion of an elastic barrier, a control process with three arguments

fx(z) MIR[fc(z), fXmin, fXmax] fy(z) - MIR[fy( z),fYmin,fYmax] nij+ MIR[n ,j+ 1, Nmin, Nmax]

Yij+ 1 MIR[yi, + 1, Ymin, max]

228


Xenakis's Electroacoustic Music22

whereinAfrin andAfXax determine the margins of stochastic variations for the abscissae, fY'min and J5tma. determine the margins of the ordinates, Nm..in and N,,, determine t-he range of samples per segment (the duration range for dij), and lastly Ymin and Ymax are equal to -32767 and +32767 (or lower amplitude values) respectively. This causes a mirror-like reflection of excess values within allowable limits.

2.j

x x x x 5. O.j 1.1 2,j 3.j 4,j X8.j 9.j

FDj

y 5,j y6, EXAMPLE 13A: POLYGONAL WAVEFORM GENERATED

WITH DYNAMIC STOCHASTIC SYNTHESIS

y 5Si V6j+

j+V'%OJ I

O .j+1

Y7,j+l

EXAMPLE 13B: POLYGONAL WAVEFORM GENERATED WITH DYNAMIC STOCHASTIC SYNTHESIS; SEGMENT END POINTS HAVE BEEN

CALCULATED AS STOCHASTIC VARIATIONS OF SEGMENT END POINTS IN THE PREVIOUS WAVEFORM

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The PARAG3 program supplies the GENDY program with the following parameters:

* number of I segments per waveform; * duration of the synthesis process; * type of stochastic function fx; * type of stochastic function fvy; * arguments of the elastic barriers;

For fx and f, one can select among stochastic functions of the type already illustrated (uniform, exponential, normal, Cauchy). In Gendy301, these functions are also used at the level of the macro-structure. The PARAG3 program assigns a "time-field" to sixteen different voices-or simultaneous synthesis processes; a field may be passive (silence) or active (synthesis triggered) and its duration is calculated by exponential law, based on a mean value D:

d = (-1/D)log(l - z)

(as usual, z is a random number of the interval [0, 1]). Overall, this formalization closely resembles the approach taken for

Achorripsis and ST/10,35 except that the musical parameters for the instrumental lines are now replaced with initialization parameters for the stochastic synthesis. Like Achorripsis, the large-scale framework of Gendy301 can be represented by a matrix (voices x time-fields) with a certain density of active cells, as, for instance, in Example 14.

Some of the eleven sections in Gendy301 show a predominance of harmonic spectra, with much or little glissando activity. This is the case in section 1; Example 15 shows the sonogram of its first thirty seconds, where very wide harmonic spectra (partials up to 8000-9000 Hz.) and the parallel striations of the harmonic glissandi can be seen.36 Wide noise bands are found in other sections; in Example 16 we see the sonogram of a seven-second fragment corresponding to the passage between section 3 and 4 (ca. 5'10" from the beginning). In section 4 (Example 17a), acoustic energy is statistically spread over a very wide frequency range, up to 17 KHz (notice, however, the strange "hole" between 10 and 11 KHz). By observing Example 17a, we can also understand how dense the temporal articulation is at very high frequencies; we can also glimpse a harmonic structure which appears three times behind the wall of noise. In Example 17b the first of these three interruptions in the noise band is

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Xenakis's Electroacoustic Music 23

SOt:S352;ysp/- 7;psi7; 8;Pge: 3;,ur.iin:Sec: 2:13; tot,Hin: Sec 2:13 128 139 149 159 169 197 180sec

,. . .... ,

.... ....*, ....*I,.... , ....,I .... **....** *... I *..*. * **.* I*-.*-11 I.. . . , . . . . ... I.. . . . .. . . . . . ." * . . . . *. . . . . . . . * . . . . 1 . 2 3 .5. .... ....I ...., ...., ....,I .... ...., ....2 ....t , ...., .... 3

.. .. . .... .... .... .... .... . . .... .... .... .... ....

.... ,

.... .... .... ...., ...., ...., ...., .... .... .... I .... ,5 ....

, .., ..... .... I.. .... .... I .. I ? . .. . ....

, ....

. .. .. , .... , .... , .. .. . .. .. , .. .. . . ... , .... , .... , .. ..I,? ,.. . . . .... .... .... .... .... ........ . . ...., n

I ... ....... .... I .... I .... .... .... .... I .... I .... .... ....I 11 .... * .... . . .... ,, . .. . .... .... ... . .. .... , * * ...1 , .... , ...., .... I ...., ...., ...., ...., ...., .... i ...., .... , .... ,14 , .... ...., ..... .. . -... ...., . *... .... .... .... . 11 , .. .. .... .. .... , .. .. .. .. .. .. .. .. .. .. .... ' .. ..1

E XA.M .. . T PA. .E .O. T ... .... ... O... . T1 LI NS 2

.. ; , ... I , .... . ............. ... , 4.. ,3

enlarged, wi in Em . 7 w. e se the7 s o a s frag-

tra i a.c....co ur. Th e .a ace isf as the reflect

. .... .... .... I.... I.... I.... I.... I.... i.... a .... .... 11

St:S352;sp. ?;Psi;- 8 Pge= 2; du,,in Sec= 2 ,13 tot,in Sec- 2:13 69 79 89 99 199 119 12.M

I... .. , .. I .. . . . . .. .. . .. .... I ....*14

I 113

-I- I.... .... .... I ..I . .. I .... .. .... .... 1

I, I , I ..... .... I .. . . . .... I .... I it ' I 15

I ..I .... .. . .. .. I I .. .. I..... .. ,6 I 114

I- . . 1 . .. ..,... ..I . . ..?I ...., .... .... I I.I ...

EXAMPLE 14: TWO PAGES OF THE GENDT301 SCORE. THICK LINES

INDICATE ACTIVE TIME FIELDS (ACTIVATION OF THE SYNTHESIS

PROCESS). THE ONLY PARAMETERS REPRESENTED HERE ARE START TIME AND DURATION FOR EACH OF THE SIXTEEN LAYERS AVAILABLE

enlarged, while in Example 17c we see the sonogram of a sound fragment of only 0"5-nearly white noise.

Sounds in Gendy301 are both new and ancient in the context of electroacoustic and computer music. They are ancient insofar as they reflect the classical opposition between harmonic spectrum and noise spectrum,



as well as the proliferation of glissandi so peculiar to Xenakis's orchestral works. And yet, they are new each time inasmuch as they result from a microcompositional process based on an indeterministic model-and also because they are absolutely mobile, so varied in their dynamics as to reach quite deafening extremes.

. Mj '

: ~ ; ..'.. f-. . .:.. ~'.. ',.' 5' . ''

:.

v e t "s

EXAMPLE 15: SONOGRAM OF THE BEGINNING OF GENDY301, 0"-30"

EXAMPLE 16: SONOGRAM OF A SEVEN-SECOND PASSAGE IN GENDY301 (TRANSITION FROM SECTION 3 TO SECTION 4)

232



EXAMPLE 17A: SONOGRAM OF THE ENTIRE SECTION 11, 94" IN DURATION

EXAMPLE 17B: A PARTICULAR OF SECTION 11, 4" IN DURATION

233



EXAMPLE 17C: A PARTICULAR OF SECTION 11, 0.5" IN DURATION

DISCUSSION

There is a thread uniting pieces like Analogique B and Concret PH to Gendy301 (and S709, not described here): Xenakis tends to create a mechanism that, once started, exhibits itself in time, rendering auditorily explorable the potential of knowledge captured in the theoretical pre- mises and assumptions behind the model mechanism. Xenakis makes electroacoustic music a vehicle for a theory of sound of a level adequate to his theory of music. In this medium he seems to circumscribe the compositional techniques of his instrumental music. Xenakis's art then becomes an utterly cultural fact-a creative gesture which no longer leans on materials existing prior to the artistic concept. This represents a most important challenge in contemporary music, one which is both highly influential and yet very poorly understood. Also, the approach implies the possibility of interpreting music technology in the special sense of an integral poiesis, as a cognitive disposition for exploring possible results (sound and music) rather than as a powerful means for the realization of musical ideas too often highhandedly considered independent from the technical substratum. That represents, in a sense, a condition sine qua non towards the reconciliation of music theory and music praxis in our time.

Even in the work of composers reputed to be highly sensitive to the sound materials' inner vitality, the ontological status of sound appears as

234



something preexistent, an external natural object subjected to human channeling and transformation. Technology then plays the role of a microscope revealing the sound matter's most intimate details. And still this matter is given before the act of composing, as a natural, preexisting process in which the composer grasps details of musical form. Gerard Grisey writes: "the object allows us to understand the process in its Gestalt, and to effect a system of combinations."37 So it happened that some have used the computer to analyze preexisting sounds and to use the analysis data as a compositional structure. Tristan Murail's orchestral writing, for example, "simule (...) des spectres naturels donnant a entendre la metamorphose d'un son inharmonique de cloche en un son harmonique de trompette."38 Here, the technological medium is important for its instrumental function-its computational "power" and preci- sion. In a way not foreign to widespread platitudes and beliefs, T?;XvT is still an instrument for the control of Nature: tools are exploited to put sound to use. In contrast, Xenakis seems to conceive of technological means as a concrete way for the sonic matter to become the very result of invention. The sound object is the result of composition, and therefore is wholly comprised in the world of the artificial-it represents no preexisting nature to be contemplated in its perfection, nor does it represent an aim that results from an exploitation of natural forces.

What the sound material "materializes" is the creative intent from which it takes origin and form. Musical form, then, begins with a network of relationships in which it is difficult to glimpse a "syntax," since this network does not determine relations of cause and effect at the level of the elements (or symbols) of the musical flow, but at the level of the minimal time units within sound. By acting "within" the sound rather than "on" it, Xenakis's mechanism aims at creating a network of relations on a presyntactic (or subsymbolic) level, allowing perceptually relevant data to emerge at a time scale relevant to the listener. The music comes to life by means of operations that take place before any syntactic norm can be recognized as such by the listener.

This leads to a paradigm shift that I have tried to summarize in the following way:

It is possible to reconcile and combine "composing the sound" with "composing with sounds," following a line of musical research uniting formalized approaches (algorithmic composition) and qualitative exploration of sound and music as perceived. This includes a blur- ring the opposition of form vs. matter-the quantitative vs. the qualitative, the conceptual vs. the perceptual-and is to be seen as a realm of artistic expression peculiar to electroacoustic music and computer music, as it is only accessible through these media.39

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In a similar vein, Hugues Dufort writes: "Si tout le concret percu par l'oreille est sous-tendu par des relations abstraites, on ne voit plus la rai- son de maintenir une distinction entre une composition musicale qui porterait les sons et une composition musicale qui porterait sur le formes."40 In Xenakis's electroacoustic music, composing means letting the form of sound and music emerge from lower-level processes-be it the level of sound grains (Analogique B) or the digital samples themselves (Gendy301).

* * *

It must be pointed out, however, that Xenakis's methods fail to develop an evolutionary flow in sound matter. I shall conclude this discussion by examining this theoretical knot, which has quite strong repercussions on the issue of musical time.

Even though a statistic process may have a direction, it is always moving towards the mean-and this is exactly what evolution is not.

This statement-quoted from Edgar Morin41-helps us define the epistemological and conceptual coordinates in order to discuss the experience of musical time in Xenakis's electroacoustic works. By starting from here, I also mean to affirm the methodological necessity of skipping over Xenakis's own reductionistic definition of time as "a blackboard on which one writes events and structures." I would rather concentrate on how he works and what he works on-than on his declarations concerning the subject matter. Declarations of intent sometimes are to be distinguished from actual experience. The notion of a perfectly spatialized time seems well suited only to works like Mycenae-Alpha which, as has been said above, are not at all entirely representative of Xenakis's electroacoustic works.

The preceding sections of this essay suggest that Xenakis, in his electroacoustic music, is aiming but perhaps not succeeding at setting up a self- organizing system or mechanism. That his mechanism does tend toward self-organizing behavior is revealed by its being sensitive to the initial conditions set up by the composer: the system behaves differently, though consistently, upon different initial settings. That self-organization, however, does remain purely potential is revealed by the fact that his mechanism is event-insensitive, i.e., unable to change its behavior upon the occurrence of unpredicted states or events provoked by its own functionality.

This notion-that stochastic processes are event-insensitive-means that the unexpected, the singularity of events, does not become a source

236



of information and transformation, but rather favors a levelling-off tendency reflecting the relentless increase of entropic disorder (this is coherent with the world view proper to the classical interpretation of the Second Principle of thermodynamics). Being memoryless, Xenakis's mechanism does not learn from the history of its previous states; it cannot interact with the external, nor can it interact with its own history. As stated above, it is not an eco-system-it has no context.

Paradoxical as it may appear, this state of affairs represents a deficit in "technological efficiency," a problem brought in by the theoretical- cognitive limitations of stochastic laws-which in fact the composer adopted in order to deliberately break down causality, i.e., the symmetry of before and after. Hence there derives the need for very simple overall formal shapes, with separate sections for each of which the mechanism is reset with new input data. We might say that in this utterly formalized music the event is forced by the external: all changes having some relevance for the shaping of the musical form are fed in by an intention that ulti- mately transcends formalization and stems, therefore, from intuitions left out of formalized processes.

For Xenakis's mechanism cannot avoid being uprooted from its context. Particular occurrences in the sonic matter leave no promises and open no temporal horizons; they leave no traces of themselves in time. Singularity does not become catastrophe, in the sense that it does not cause a change of behavior by altering, even without annulling, the laws governing the functioning of the mechanism. A state of suspension ensues, moment by moment, in the flow of time as experienced by the listener.

If time, here, really were dynamic evolution, the mechanism's laws would then require that the occurrence of unforeseen (unforeheard) events cause the activation of self-organizational dynamics. In reality, the occurrence of particular patterns and textures of sound is not capable, in Xenakis's mechanism, of reorienting the flow of time. The occurrence is soon forgotten: the composer's mechanism denies time the power of endowing the elements of the musical flow with a coefficient of creativity.

Xenakis's radical gestures reflect an epistemological need to combine algorithmic and stochastic, determinism and indeterminism,42 and finally lead to an essential nonlinearity and fragmentation in the experience of time. His work reflects a world no longer describable in terms of the order-from-order principle-with which Schrodinger had identified a purely deterministic rationalism of Laplacean stamp-but a world animated by the order-from-disorder principle, a world where things are incessantly put in order, warding off the ever-deeper abyss of entropic disorder. Yet, Xenakis does not manage to take a further step, toward the order-from-noise principle, i.e., toward a world neither strictly coherent

237



(algorithmic order) nor strictly incoherent (statistic order) but, if anything, in a dynamic condition of chaos.43 There things would find their (unstable) order, and the world would take form through the event, through singularity. As is proposed by a positive interpretation of the Sec- ond Principle: in self-organizing systems, an increase in entropy is a creative force, the bearer of isles of temporary order in the incessant flow of transformation.

Xenakis's compositional models leave the sound matter in a condition of statistic order, lacking any theory of the event capable of describing the constructive and destructive dynamics of the experienced musical form.

CONCLUSION

From Concret PH to Gendy301, Xenakis is approaching an aesthetic- cognitive paradigm that pushes his art right into the sphere of noise, as the reflection of the violent Nature that is free will-not unlike Lucre- tius's description in his De Rerum Natura. The technology of the stochastic laws constrains him within the margins of disorder and statistic order, before any chance for true evolution can arise from the sound. The events and discontinuities that nourish the musical form remain largely at the mercy of a demiurge, not comprised by the criteria of the mechanism itself.

This music incarnates the utopia of an art which aims at resolving the dialectic between material and form-between Nature and Culture-by means of an integrally constructivist disposition. This I call an instance of integral subjectivity, resulting in works of art which are thoroughly arti- facts: nothing in the work exists prior to the artist's action. Constructiv- ism, here, takes the form of the objective, "natural" manifestation of the mechanism; but the latter is designed and built up by the subject itself. The S6val.;t (dynamis)-the living force-which in principle could let the mechanism reveal itself remains largely left to the incursion, from the external, of the subject. The techno-logy (knowledge in use) behind this music testifies to the intelligence of an art in which chance and necessity are perfectly integrated.

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NOTES

This paper revises and expands a previous essay published in Italian in 1995. The author wishes to thank the editors of Sonus-Materiali per la Musica Contemporanea (Potenza) for permitting translation of the unre- vised parts.

1. Pierre Schaeffer, Traite des objects musicaux. Essais interdisciplines (Paris: Le Seuil, 1966), 16-17.

2. On this issue, see my paper "On the Centrality of Techne for an Aes- thetic Approach on Electroacoustic and Computer Music," Journal of New Music Research 24, no. 4 (1995): 369-83.

3. Schaeffer, Traite, 23.

4. At the time, Bohor was one of the most radical attempts at annulling linear articulation in Western music. Another tape piece that was just as radical at the time was Fabricfor Che (1968) by James Tenney.

5. See Brian Moore, The Psychology of Hearing (London: Academic Press, 1982), 50-52.

6. The sonograms in these pages were made using a NeXT computer at the Centro di Calcolo, Padua University. All other graphics were realized on an IBM486 at the Laboratorio Musica & Sonologia in L'Aquila. At the time of the making of this analysis (1994), the only recording of Concret PH at my disposal was that published on None- such LP H-71246. The work is now also available on the Electronic Music Foundation CD, EMF 003 (together with Diamorphoses, Orient-Occident, Hibiki-Hana-Ma, and S709).

7. In this second type of texture are hidden some sweeping sounds- heard as extremely short chirps; see example, overleaf.

8. Example 6 is drawn from Benoit Mandelbrot's book Fractals: Form, Chance, and Dimension (San Francisco: Freeman, 1977).

9. See Iannis Xenakis, Formalized Music (New York: Pendragon Press, 1992), 9. The 1992 edition of Formalized Music is an updated and augmented version of the 1971 English edition (Bloomington: Uni- versity of Indiana Press, 1971), which, in turn, integrally reprinted and expanded the original French version, Musique Formelles (Paris: La Revue Musicale, 1963).

239


240 Perspectives of New Music

.~

?- ?* - ' : ^

.* ,

; . . . .. .

,

- ll* ;l: j *: l l ,~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~.. . -

.

^: ~i

" " "fi^^h^,^,,- ~~~ ~~~~~..

i. ''^'^ ^

^ ; .. :.- . '*

.

;|-,;, .^

i rc ./

CONCRET PH: TWO EXTREMELY SHORT, BARELY AUDIBLE CHIRPING SOUNDS (SEE NOTE 7); TOP-79.4"; BOTTOM-130.7"



10. Stafford Beer, "Below the Twilight Arch," General Systems no. 5 (1969): 20.

11. Formalized Music, 103; Philips recording 835487.

12. Dennis Gabor, "Acoustical Quanta and the Theory of Hearing," Nature 4044(3) (1947): 592.

13. For an easily readable computer-code implementation of first-order TPMs, see Charles Dodge and Thomas Jerse, Computer Music: Syn- thesis, Composition, Performance (New York: Schirmer Books, 1985), 283-88.

14. The same strategy was utilized in Analogique A (for three violins, three cellos, and three double-basses). The compositional process of Analogique B closely resembles that of Analogique A, the basic elements of which are very short notes; the distance between successive screens is At = 1.111 (MM J, 54). Analogique A-B proposes the neat superimposition of instrumental and electronic sounds; it makes overtly clear that no attempt at timbral integration was made. Musi- cologist Angelo Orcalli describes the sounds of Analogique B as "the buzzing of insects" in his book Fenomenologia della Musica Speri- mentale (Potenza: Sonus Edizioni, 1993), 117.

15. Formalized Music, 94.

16. He borrowed Abraham Moles's as well. However, Gabor had antici- pated most of the relevant psychoacoustical notions discussed in Moles's The'orie de l'Information et Perception Esthetique (Paris: Flammarion, 1958).

17. Barry Truax, "Real-Time Granular Synthesis with a Digital Signal Processing Computer," Computer Music Journal 12, no. 2 (1988): 14-26; Curtis Roads, "Automated Granular Synthesis," Computer MusicJournal 2, no. 2 (1978): 61-62; Curtis Roads, "Asynchronous Granular Synthesis," in Representations of Musical Signals, ed. Gianni De Poli, Aldo Piccialli, and Curtis Roads (Cambridge: MIT Press, 1991), 143-86.

18. Agostino Di Scipio, "Composition by Exploration of Nonlinear Dynamical Systems," Proceedings of the International Computer Music Conference (Glasgow, 1990), 324-27; "Caos deterministico, composizione e sintesi del suono," Atti del IX Colloquio di Informa- tica Musicale (Genoa, 1991), 337-50; "Micro-Time Sonic Design and the Formation of Timbre," Contemporary Music Review 10, no. 2 (1994): 135-48.

241



19. Albert Bregman, Auditory Scene Analysis (Cambridge: MIT Press, 1990), 118-19.

20. Formalized Music, 103. For a more extended discussion on this point, see my paper "The Problem of Second-Order Sonorities in Xenakis's Electroacoustic Music," Organised Sound 2, no. 3 (1997): 165-78.

21. Orcalli, Fenomenologia, 120.

22. "Die Einheit der musikalischen Zeit" was written in 1961 for broad- cast on the WDR, Cologne. It was first published in English translation as "The Concept of Unity in Electronic Music," trans. Elaine Barkin, Perspectives of New Music 1, no. 1 (Fall 1962), 39-48. The original German text was published with some revisions in Zeugnisse (Frankfurt: Europaische Verlagsanstalt, 1963), and in Karlheinz Stockhausen, Texte 1 (Cologne: Verlag M. DuMont Schauberg, 1963), 211-21. For a discussion of microcomposition in the fifties and sixties, see Henri Pousseur's book Fragments Theoriques: I-Sur la musique experimentale (Universite Libre de Bruxelles, 1970), in particular the section "De la microstructure absolu."

23. Neuma CD 450-74. Perspectives of New Music cassette PNM 25.

24. In a later release of UPIC on the AT386 computer, these curves were called arches, see G. Marino, J. M. Raczinsky, and Marie- Helene Serra, "The New UPIC System," Proceedings of the Interna- tional Computer Music Conference (Glasgow, 1990), 249-52.

25. Perspectives of New Music CD PNM 28.

26. Though Xenakis's orchestral scores are liberally supplied with glissandi, that is not the case with his earlier tape works, with the excep- tion of Diamorphoses.

27. See, for example, Iannis Xenakis, "Music Composition Treks," Com- posers and the Computer, ed. Curtis Roads (Los Altos, Calif.: Kauf- mann, 1985), 171-91.

28. On graphical methods of sound synthesis, see discussion in Curtis Roads, Computer Music Tutorial (Cambridge: MIT Press, 1996), 329-35.


30. A stereo mixdown of the seven tracks is available on CD, Montaigne MO 782058.

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31. See Richard Toop's liner notes for the CD MO 782058; see also Formalized Music, 293.


33. See code examples in Dodge and Jerse, 266-78. 34. Iannis Xenakis, "More Thorough Stochastic Music," Proceedings of

the International Computer Music Conference (Montreal, 1991), 517-18; Marie-Helene Serra, "Stochastic Composition and Stochas- tic Timbre," Perspectives of New Music 31, no. 1 (Winter 1993): 236-57; Peter Hoffman, "Implementing the Dynamic Stochastic Synthesis," offprint from Les Cahiers Groupe de Recherche en Infor- matique Image et Instrumentation 4 (Caen, 1996).

35. Formalized Music, 134. 36. These sonograms have been realized analyzing a monophonic copy

of the tape, so as to provide an image of the total spectral structure.

37. Gerard Grisey, "Tempus ex machina: A Composer's Reflections on Musical Time," Contemporary Music Review 2, no. 1 (1987): 269.

38. Hugues Dufourt, Musique, pouvoir, ecriture (Paris: Bourgois, 1991), 335.

39. Agostino Di Scipio, "Inseparable Models of Material and of Musical Design in Electroacoustic and Computer Music," Journal of New Music Research 24, no. 1 (1995): 34-50.

40. Dufourt, Musique, pouvoir, ecriture, 195. 41. Edgar Morin (ed.), Teorie dell'evento (Milan: Bompiani, 1972), 31

(translation mine). 42. Morin, Teorie dell'evento, 297. 43. H. von Foerster, "On Self-organizing Systems and Their Environ-

ment," in Self-organizing Systems, ed. C. Yovits (New York: Perga- mon Press, 1960), 31-50.

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Article Contentsp.[201]p.202p.203p.204p.205p.206p.207p.208p.209p.210p.211p.212p.213p.214p.215p.216p.217p.218p.219p.220p.221p.222p.223p.224p.225p.226p.227p.228p.229p.230p.231p.232p.233p.234p.235p.236p.237p.238p.239p.240p.241p.242p.243

Issue Table of ContentsPerspectives of New Music, Vol. 36, No. 2, Summer, 1998Front Matter [pp.1-247]A Seventieth-Birthday Festschrift for Karlheinz Stockhausen (Part Two)Guest Editor's Introduction [pp.5-11]Metamorphoses of Invention [pp.13-39]Three Poems [pp.41-52]Leap of Faith: A Personal Biography of Karlheinz Stockhausen's Prozession [pp.53-62]Inori: Microcosm/Macrocosm Relationships and a Logic of Perception [pp.63-90]Stockhausen's Secret Theater: Unfinished Projects from the Sixties and Early Seventies [pp.91-106]

The Interval Angle: A Similarity Measure for Pitch-Class Sets [pp.107-142]The "Continuous Line" and Structural and Semantic Text-Painting in Bernard Rands's Canti D'Amor [pp.143-185]Inner-Views [pp.187-199]Compositional Models in Xenakis's Electroacoustic Music [pp.201-243]Editorial Notes [pp.244-246]Errata: Babbitt-Introduction: A Response [p.248]Back Matter [pp.249-254]

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