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Clarification on Xenakis: The Cybernetics of Stochastic Music

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Agostino Di Scipio
Clarification on Xenakis: the Cybernetics of Stochastic Music
Symposium "Présences de Iannis Xenakis"
Paris / Centre de Documentation de la Musique Contemporaine et Radio France
January 29th and 30th, 1998
Initially published in the volume
Présences de Xenakis (Makis Solomos, ed.), CDMC, Paris, 2001, pp.71-84.
(note: some of the pictures included in the original, have been dropped from this copy)
(note: tiny portions of the original text have been slightly changed or amended, they are included here with grey background)
Premise
In their approach on the analysis and the aesthetic discussion of contemporary music repertoires,
musicologists ultimately seek to tell why a composer does what s/he does. Composers, instead, are often
more interested in how other composers do what they do, as in principle they already have (or presume to
have, or are having in their work) reasons that urge them to compose. When focussing on electroacoustic
music, a composer's interest in understanding how another composer does what s/he does sometime turns
into a commitment to music analysis while being peculiarly oriented towards music resynthesis, i.e.
individual compositional work.
In this spirit I, as a composer having a particular interest in electroacoustic and computer music
technology, and in issues of contemporary music-theory, would like to focus here on an important issue
in Xenakis' electroacoustic works, one that I often deal with in my own composing. I refer to the
emergence of "sonorities of second order" (Xenakis' own words, Formalized Music, p.103).1 In dealing
with this issue, in the following I also touch on broader questions concerning the aesthetic of Xenakis'
electroacoustic works (a more extended discussion is in (Di Scipio, 1995a)).
The notion of "2nd-order sonorities" in Xenakis' early works
In the late '50s Xenakis formulated "the basic abstract hypothesis" of "the granular construction
of all possible sounds" (FM, p.47). He followed Dennis Gabor's (1947) representation of acoustic signals,
which was based on time-finite functions - grains - rather than purely sinusoidal (infinite, harmonic)
functions.2
With Analogique A, for string ensemble, Xenakis set out to use stochastic processes to compose
"clouds of sound grains". The term sound grains means, here, short sound events played by the
traditional string instruments. Therefore, a clear-cut distinction can be made between the process of
music composition (formalized stochastic processes) and the modalities of sound production (several, but
limited, ways of string playing). In Analogique B, Xenakis replaced instrumental sound grains with short
chunks of electronically generated sinusoidal waves, with the help of "several magnetic tapes or
synchronous recorders, filters and sine-wave generators" (FM, p.103). In this case, the distinction can
hardly be made between a model of musical articulation and a model of sound design, insofar as the
composer's action is meant to let the musical (macro-level) structure emerge from sound itself and its
1 for brevity, in the following sections I refer to Formalized Music as FM, and to Musique. Architecture as MA.
2 in one occasion, namely in his preface to the 1992 edition of FM, Xenakis seemed to take a distance from Gabor, and
preferred to mention Albert Einstein's idea of "phonon" as the relevant precedent to his quanta of sound (FM, p.xiii).
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internal organization (micro-level). This may be called microcomposition, or micro-time sonic design (Di
Scipio, 1994a).3
The effort behind Analogique B followed in particular from the observation that using pre-
existing, instrumental sounds as basic grains (as in Analogique A) was not suitable to validate "the
hypothesis of a sonority of a second order" (FM, p.103). By addressing himself towards the
electroacoustic production of entire clouds of grains, Xenakis in actuality was connecting the medium of
microcomposition with the possibility of composing timbre. (At the time, other composers in Europe
were exploring methods of microcomposition, including Stockhausen, Henri Pousseur and Herbert Brün,
though in ways different among themselves). He wrote: "[...] using all sorts of manipulations with these
grain clusters, we can hope to produce not only the sound of classical instruments and elastic bodies, and
those sounds generally preferred in concrete music, but also sonic perturbations with evolutions,
unparalleled and unimaginable until now. The basis of timbre structures and transformations will have
nothing in common with what has been known until now" (FM, p.47). He continued: "Suppose each
point of these clusters represents not only a pure frequency [...] but an already present structure of
elementary grains [...] We believe that in this way a sonority of a second, third, or higher order can be
produced" (ibidem).
Today cognitive scientists and epistemologists would probably describe the hypothesis of 2nd-
order sonorities as a question of emergent properties of sound structure. According to this view, the task
of microcomposition can be understood as the task of making a meta-level organization or system emerge
from a ground-level organization or system (Di Scipio, 1994b). Sound design becomes then a question of
modelling a phenomenon of emergence, perhaps in the shape of a causal but nonlinear process. The
problem facing the composer (and music-theorist) becomes: how (or what kind of) microtemporal
relationships among acoustic quanta may bring forth a macrostructure, an audible object or process of
certain characteristics? In a sense, any answer would require from the composer an ability to implement
his/her own theory of sonological emergence.
The issue is not unique to compositional work with granular synthesis/processing methods. It
comes out in a variety of cases ranging from algorithmic composition at the level of digital samples (or
non-standard synthesis methods) to unusual signal processing of recorded natural sounds. However
different, all such lines of work share the fundamental fact that the composer has to make decisions that
apply at smallest scales of time, where things happen that result in the larger-scale, perceivable attributes
we may want to call timbre and texture.
At the time of Analogique B, Xenakis certainly knew he could find help in the field of
psychoacoustics.4 He wrote: "Recent work on hearing has given satisfactory answers to certain problems
of perception" (FM, p.47), and asked questions of psychophysiology, such as "What is the minimum
perceptible duration [...] of a sinusoidal sound, as a function of its frequency and its intensity? What are
the minumum values of intensities [...]? What are the minumum melodic interval thresholds [...]?"
(ibidem). He then added that the Fletcher-Munson diagram of equal loudness contours answered those
questions with "good approximation" (ibidem).
As it seems, then, Xenakis was factoring the question of 2nd-order sonorities in two distinct
dimensions: on one side there was the question concerning the formalizations aimed at composing the
grains together; on the other, there was the question of the properties of the grain itself. Accordingly,
"1st-order sonority" would refer to the perceptual attributes of the grain itself, the perceptual
characteristics of the most basic element of the musical construction. On the other hand, "2nd-order
sonority" would correspond to perceptual properties of a whole sound texture composed of myriads of
these grains. The two Gestalts are such that the emergence of the one implies the disappearence of the
other. Albert Bregman, in a quite different context of investigation (namely in a passage of his Auditory
Scene Analysis, 1990, pp.118-119) points out that granular representations are specially useful in the
analysis and perceptual modelling of dynamical events of peculiar complexity (transient phenomena,
3 throughout this paper, I try to use terms such as microstructure and macrostructure (or micro-level and macro-level,
microcomposition and macrocomposition, etc.) in conformity to the correspondent scales of time as described in Xenakis' own
theoretical work (FM, p.266), where micro- is put in direct relationship with "timbre", and macro- with "global evolution in the order
of some tens of minutes".
4 Gabor himself had felt the need that a quantum approach to acoustic representations should somehow take into
consideration our perceptual experience of them. Indeed he spoke of a "theory of hearing" (Gabor, 1947) - not of a "theory of
sound".
turbulence, sound textures rich in noise components and made of innumerable microscopic events). He
adds that this modelling (he refers to actual experimental work carried out by other researchers) requires
two distinct descriptions: one concerning the grain itself (shape, duration, time-scale, etc.), and one
concerning how grains succeed and overlap each other (time-location, density, etc.). This very precisely
mirrors the way Xenakis factored the problem. In short: the possibility of 2nd-order sonorities stems from
the composition of minimal sonic units which are made to cohalesce in a holistic audible image. Bregman
also refers to the pioneering work of Bela Julesz with his notion of texton, i.e. the basic perceptual unit of
sound textures. (More on the perception of musical sound textures is found in (MacKay, 1984); an
application of Julesz's theory in the field of music analysis, is found in (Gabel, 1993)).
The making of Analogique B (the birth of granular sound synthesis)
In the making of Analogique B (in part realized at Pierre Shaeffer's GRM in Paris, in part realized
at Hermann Scherchen's studio, in Gravesano, 1959) the possibility was explored of composing sound by
innumerable overlapping sinusoidal grains. This can be expressed as a Gabor series expansion:
s(t) = Σn,k an,k g(t-kT) ejnΩt
The elementary signal is represented by g(t) having a real and an imaginary part:
ejnΩt = exp - a2(t - t0)2 exp i2pf0t
where a is the parameter allowing for the determination of both grain duration and bandwidth. For Gabor
"...elementary signals are harmonic oscillations of any frequency fo, modulated by a probabilistic pulse"
(1947). A Gaussian curve should be utilized to envelope the pulse, as in fact such a curve allows for
elementary signals precisely located in both the time and frequency domain, with minimal spectral
dispersion.
Xenakis' grains were different, as they had no envelope curve (or, if you want, a perfectly squared
envelope). Their duration was 0.04", amplitude and frequency values were determined by composed
grids (or "screens") broken into cells of area ΔgΔf. For dynamical sounds, entire books of such screens
had to be used, spaced between themselves of a (rather large) time lag (Δt = 0.5").
The density of grains in ΔgΔfΔt was a function of a stochastic process: changes in the sound
texture depended on the probability that at a certain time t the screen parameters were modified with
respect to time t-Δt. Probabilities were determined by transition probability matrices (TPM). A simple
TPM would be:
X Y
X 0.2 0.8
Y 0.8 0.2
representing the probability that symbol X will be followed by another X (20%); that X will be followed
by Y (80%); that Y will be followed by X (80%) and that Y will be followed by another Y (20%). Two
TPMs were utilized as a Markov process determining amplitude, density and frequency values.5 Decision
as to whether one or the other should be used was made on the basis of other formalizable rules (not
described here). X and Y correspond to two sets of values selected from among 16 regions of frequency
(one octave each), two different sets selected from among four regions of amplitude (in phones) and two
different sets selected from among seven regions of grain density (arranged along a logarithmic scale).
Once a set was selected, the particular values could be chosen randomly (flat probability function).
Following the mathematics of stochastic processes, Xenakis could approximately predict whether
some init values would orient the process towards a "stationary state" or a longer "perturbation" state
(FM, p.85-86). As a macroscopic control over these two global options, he devised a "protocol of
exchange" commuting the overall process from one end state to the other, selecting different TPM values
for each section of the piece. In short, the exchange protocol was like a series of switches between states
of growing entropy and equilibrium points, or viceversa. Each following section in the piece (total
5 Xenakis usually refers to the mathematics of Markov processes (or Markov chains, first presented 1905) following its
reworking by later scientists, especially Meurice Frechet (FM, p.79; MA, p.29)
duration of 2’35”) stems from a different setting of these macrolevel control parameters. We can
summarize the compositional model at work here in this way:
(1) the elementary units of musical structure are implemented through a granular representation of
sound;(2) actual sound results from the arrangement (composition) of those elementary units;
(3) the concept of "screen" is the interface allowing for particular arrangements of grains to be
determined, and for the short-term articulation of sound textures (the passage from a screen to the next, at
a rate of half a second);
(4) the higher-level determination screen parameters allows of the long-term articulation (screen
parameters are a function of the exchange protocol, at a rate of tens of seconds).
The model may be seen as an instance of algorithmic composition consolidating into a mechanism let to
"manifest itself" (FM, p.94) for a while, and then re-triggered by the composer (via the exchange
protocol).
Two annotations on Analogique B
For many listeners, the sound of Analogique B is rather disappointing compared with the
theoretical implications in play. Xenakis has never said to what extent he was happy with the actual
results (his annotations (FM, pp.103-109) are more prescriptive than descriptive, they were made at the
outset and in the course of the composition). We should remember, however, that this work was initially
conceived as an experiment aimed at the verification (or falsification) of the hypothesis he had put forth
while composing Analogique A. We should also remember that in the end Xenakis decided that the two
works had to be pasted together to form Analogique A-B. This may lead us to argue that he was not
particularly satisfied with Analogique B in itself. In the coupling, Analogique A-B, we do not experience
each component piece per se, but "a sensorial and structural confrontation" (MA, p.31) of two distinct
projections of the one and the same creative process in different media.6 Indeed, the same exchange
protocol was applied in the making of both pieces (FM, p.105), all lower level details being arranged ad
hoc for the two different sound generating media.
The partial failure behind Analogique B was anyway a success of experimental science and art. It
can be explained with the poverty of the music technology available at the time, especially for such a
heavy task as granular composing. Xenakis himself observed that things would have improved by using
computers and digital-analog converters (FM, p.13). Later, indeed, Curtis Roads (1978, 1991), Barry
Truax (1988, 1990) and many others, have implemented digital granular synthesis, with more convincing
results. I think a less obvious explanation should be added, possibly more fruitful on both the theoretical
and the practical level. The question is whether the strategies pursued by Xenakis - namely, the stochastic
laws he was implementing in his compositional mechanisms - may be seen as not particularly suitable in
determining the emergence of 2nd-order sonorities. Just as the string pizzicatos of Analogique A could
not but remain string pizzicatos, however dense their articulation, the electronic grains in Analogique B
remain just grains and do not build up into a more global auditory image. One may ask whether the
stochastics does really provide as good a means for higher-order sonorities to emerge from a ground-level
patterning of minimal sonic units.
I shall focus on this question later. For the moment, it is important to stress an other relevant issue
cocnerning Analogique B. I refer to the fact that, in composing this piece, Xenakis for the first time
merged together an attitude of "algorithmic composition" with one of "timbre composition". This was an
attempt (one of the earliest of the kind) to generate both complex timbral entities and the unfolding of the
musical form by one and the same creative gesture, thus "rendering the passage between micro- and
macro-structure continuous" (Orcalli, 1993). Not unlike Concret PH, a piece on which I will focus on in
a moment, this was also a significant effort to bring together the two paths Xenakis had been, and still
was, following in those years: "formalized music" (Pithoprakta, Achorripsis) and "electroacoustic music"
(he had already worked in this medium at GRM since 1957). I think any attempt at unifying timbre and
musical form through microstructural composing, should be considered of the utmost significance for the
history and the aesthetics of art music in the 20th century (Di Scipio, 1994b; 1995b).
6 a similar case, in those years, was Sonoriferous Loops, a work for ensemble and tape by Herbert Brün, composed in
1963
The making of Concret PH (the birth of granular sound processing)
At the time of Analogique B (1959) Xenakis had just finished composing Concret PH (1958). This
short tape piece, lasting 2'45", served as "interlude sonore"7 for Le Courbusier's Philips Pavillon, at the
Brussells World Fair in 1958 (it is well-known that the internal of the Pavillon included Edgar Varèse's
only tape piece, Poéme Electronique).
The composition of Concret PH followed three steps. As a first step, the sound of hot coals and
burning material was recorded on tape. Then, as a second step, separate tape chunks were isolated – each
including a number of noise bursts of duration no longer than few hundredths (sometimes few
thousandths) of a second. Necessarily, sounds such as these have very large spectra and unclear pitch. It
is impossible for human ears to integrate differences of pitch and amplitude in such brief moments.
Indeed, in Concret PH frequency and its perceptual attribute, pitch, can hardly be considered significant
to enfolding of the musical process and the articulation of musical form. Attention shifts towards other
(less determinable, statistic) parameters, such as "density" (number of random events per time unit).
As a third step, these short bursts were re-assembled together to create denser or sparser sound
textures. This was made by piecing together several scraps of tape. A number of textures was obtained,
each one featuring its own density dn = kn/Δt. Such textures were submitted to two simple methods of
densification: (1) layering of m copies of one and the same texture, with overall density D = mdn; (2)
layering of textures of different particular density: D = ndn. Both methods resulted in a qualitative
enrichment of the sound texture, ultimately heard as the fluctuating timbre of a rough sonorous dust,
completely devoid of periodic patterns, rid of apparent causality.
Fig.1 shows a sonogram of the entire piece. Two types of texture are distinguishable. One is made
of very short noise bursts (wide frequency bands, energy peaks at 6000-9000 Hz). The other is made of
slightly longer bursts (narrower frequency bands, energy peaks at 4000-5000 Hz). Often the two types
overlap each other, e.g. in fragments 40”-50” (fig.2) and 110”-120”. Occasionally, either one or the other
gets more in evidence - e.g., the one at 30”-40” (fig.3) and the other at 80.9”-86.6” (fig.4), and 100”-
110”. The overall visible shape of these long-term sonograms, is also found at smaller time-scales. The
sonogram in fig.3 (30”-40”), for example, looks quite similar not only to the sonogram of the entire piece
(fig.1) but also to that of a tiny particular of just 0.3" (fig.5, 37.7”-38”). Fig.6 illlustrates this
phenomenon at 90”-100” and in smaller particulars, 94.5”-96” and 94.8”-95.2”. In short, this "zooming
in" reveals the properties of a self-similar object, a sort of surface in relief with a fractal dimension -
something halfway between a plane and a solid. An object of this kind, with dimension H = 2.6666667,
can be observed in fig.7 (reprinted from Benoit Mandelbrot's Fractals. Form, chance, dimension, 1977).
This feature of self-similarity in Concret PH, though hidden to the ear, is very meaningful to our
considerations here, as it reflects the composer's need to establish a structured link between compositional
strategies bearing on the microstructure (sound) and those bearing on musical macrostructure (form). In
this respect, Concret PH represents an important precedent to the questions raised with Analogique A-B,
although the two seem to proceed from different perspectives.
Down to the sample level (nonstandard sound synthesis)
In the first English edition of FM (1971), Xenakis described a sound synthesis method
independent of the Fourier paradigm (summation of harmonic functions)8 or any other standard method.
The description followed from experiments made at CEMAMu, in Paris, and at Indiana University, in
Bloomington. Later this approach was taken even further, for the composition of (parts of) La Légend
d'Eer (1977). Later again the approach developed into what eventually came to be known as dynamic
stochastic synthesis (FM, p.289-295; Serra, 1993, Hoffmann, 1996).
The level of sound representation in this new approach is the discrete time-domain of the acoustic
waveform itself. The sound is obtained by directly calculating the sample values along the linear bi-
7 such was the description of Concret PH in the credits for the Philips Pavillion
8 the notion that any signal whatsoever can be reduced to the superimposition of (infinite) partial harmonic components
(in Jean-Baptiste Fourier's case: cosines and sines) is found in earlier work than Fourier's (1822), namely in the work of D.Bernoulli
(1755) and L.Euler (1753).
dimensional space ΔtΔg (time-amplitude). The idea is to synthesize the sound directly with probabilistic
functions. The sound signal is seen as the path of a point animated by incessant Brownian motion.
This method belongs to a class which we can simply generalize as follows:
s(i) = f(s(i-k))
where f establishes the relationship between the amplitude value at time i and the amplitude value at time
i-k. If f does not implement any consistent acoustic model (this is the case with Xenakis' experiments),
then we have a non-standard synthesis technique. In computer music, methods of non-standard synthesis
have been invented by other composers, either belonging to Xenakis' generation (Gottfried M.Koenig,
Herbert Brün and others) or younger (e.g. Paul Berg, Arun Chandra, Jonathas Manzolli, Michael
Hamman). I myself worked in this area and implemented iterated function synthesis (Di Scipio &
Prignano, 1996).
Xenakis' commitment to sound synthesis by probabilistic functions, followed from two basic
observations: (1) the complexity of natural sound phenomena cannot be reduced in terms of the Fourier’s
harmonic paradigm; (2) in electroacoustic music, sound design should be regarded as an act of creative
imagination, not reducible to the simulation of known sounds (see FM, p.246).
The latter point is extremely important. If carefully pondered, it can shed light in retrospect over
Xenakis' early experiments with granular sound. It is well-known that in the history of modern art music
the notion of musical form has been gradually freed from the imperative to match pre-established
structural frames. Now, the potential in a music of electronically produced sounds ultimately is to extend
that freedom to the realm of the sound material itself. Simulation of pre-existing sounds (e.g. musical
instruments), although crucial for learning about sound in general and auditory perception in particular, is
excluded by Xenakis on the basis of this (ethical, not just aesthetic) position.
With non-standard synthesis methods, often frequency and timbre become the unpredictable result
of an arbitrary sample patterning of the composer's own invention. This turns the synthesis process into
an open, explorative process across unknown territories of possible sounds. Properties of sound such as
timbre or pitch, become as epiphenomena of a process running at the lowest technically feasible time-
scale. Hence, the question of 2nd-order sonorities moves under an even more radical perspective. While
granular representations allow to factor the sound design problem-domain in two (grain parameters and
the criteria of grain patterning), nonstandard synthesis methods usually force the composer to work in a
single dimension - the linear space of the sample sequence. In this medium a model of sound design
(composing-the-sound) in principle becomes identical with a model of musical structuration (composing-
with-sounds) (Di Scipio, 1995b).
Gendy3 and S709 (the birth of dynamic stochastic synthesis)
Approximately twenty years after his first experiments in this area, Xenakis took up this research
line again and created a computer program, GENDY (GENeration DYnamique) that implements dynamic
stochastic synthesis. The program is itself a child procedure called upon by an other program, PARAG3,
the latter having the role of a higher level control process. Gendy301 (1991) was the first work composed
with GENDY. It was premiered in Montreal the same year of its composition. A slightly different
version, Gendy3, was premiered the same year in Metz. A second piece, S709, was composed by Xenakis
in 1994, premiered in Paris the same year of composition (in 1997 this was presented in Italy as a
component piece of the Tetractys concert-installation I have myself created with the help of Manilio and
Ignazio Prignano).
Dynamic stochastic synthesis entails transforming an initial waveform in time and amplitude,
calculating the amount of transformation through stochastic variations. The sound signal is seen as a
series of waveforms J, each consisting in I linear segments (fig.8). The end coordinates of the i-th
segment in the j-th waveform are xi,j, yi,j. Phase continuity between waveforms j and j+1 is assured by
establishing
xo,j + 1, yo,j +1 = xi-1,j, yi-1,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+1 = xi,j + fx(z)
yi,j+1 = yi,j + fy(z)
where fx(z) and fy(z) return positive or negative values, given an argument z (itself a random number).
Samples are computed by linear interpolation between the init and the end point in each segment:
s(t) = s(t) + [(yi+1,j-yi,j) / ni,j]
where ni,j is the number of samples in the i-th segment. The segment duration is:
di,j = (ni,j-1) / SamplingRate
Therefore the j-th waveform will have a total duration (a period) of:
Dj= i di,j
There are three possibilities:
(1) transformation of the ordinates only
yi,j+1 = yi,j + fy(z)
xi,j+1 = xi,j
(only amplitude values are modified, causing a change in timbre);
(2) transformation of the abscissae only
yi,j+1 = yi,j
xi,j+1 = xi,j + fx(z)
(changes in Dj, causing glissando and other frequency modulation effects);
(3) transformation of both coordinates
xi,j+1 = xi,j + fx(z)
yi,j+1 = yi,j + fy(z)
(changes in both timbre and pitch; fig.8 shows a transformation of this type).
As the sound signal is represented with 2's complement 16-bit integers, values of yi,j must be kept
within the interval [+-32767] to avoid saturation. Moreover, too extremely aleatoric variations of xi,j can
lead to wild frequency modulations, so they too must be kept within a given range. To deal with this
technical detail, Xenakis applies so-called "elastic barriers", a control process with three arguments:
fx(z) <- MIR [fx(z), fxmin, fxmax]
fy(z) <- MIR [fy(z), fymin, fymax]
ni,j+1 <- MIR [ni,j+1, Nmin, Nmax]
yi,j+1 <- MIR [yi,j+1, Ymin, Ymax]
wherein fxmin and fxmax determine the margins of stochastic variations for the abscissae, fymin and fymax
determine the margins of the ordinates, Nmin and Nmax determine the range of samples per segment (the
duration range for di,j) and lastly Ymin and Ymax equal to -32767 and +32767 (or lower amplitude values).
The effect is a mirror-like reflection of exceeding values within the allowed ranges.
PARAG3 feeds GENDY with the following parameters: number of I segments per waveform;
duration of the synthesis process; type of stochastic function fx; type of stochastic function fy; arguments
of the elastic barriers. Functions fx and fy can be selected from among various probability density
functions (exponential, Cauchy, Lehmer, logistic, etc.). Parameter values supplied by PARAG3 are
themselves dependent on stochastic functions of the same type as those adopted at the synthesis level.
Again we find, here, a unifying link of micro- and macro-structural features.
Gendy3 and S709 stem from this compositional model. Upon listening, both show an interplay
between sounds with harmonic spectrum and recognizable pitch (often in glissando), and sounds heard as
very articulated textures of nearly white noise. Yet the two pieces have a somewhat different character.
The former divides in 11 sections of variable duration (total 19'40"), where sustained strias of pitched
tones (fixed drone sounds and glissandos) alternate with noisy textures (see in fig.9 a sample sonogram
illustrating the transition from section 3, with its glissandoing harmonic spectra, to section 4, with its wall
of noise). S709, instead, features a more rhythmical character. A peculiar rhythmical figure is presented at
the beginning and then at other times during the piece. This figure and its variations overlap with (often
repetitive) step-wise glissandos. The overall construction is rather simple and linear in its shape, and
anyway shorter (7'00") than Gendy3.
In both pieces we hear sounds that are somehow new and, at the same time, ancient in the context
of electroacoustic and computer music. This music reflects the classical opposition of harmonic spectra to
noise spectra, between order and disorder, but at the same time, being the outcome of an indeterministic
and largely unpredictable model of sonic design, at the outset they present us (and the composer) with
unheard-of sonorities. At times, the sound fabric reaches quite deafening extremes, sometimes (in
Gendy3) contrasting with sudden silent pauses, in a rather dramatic effect. Once the synthesis process
stops leading to interesting results, Xenakis (or his alter ego, here, the PARAG3 program) resets the
synthesis mechanism, causing a new orientation in the musical flow. This is close to the process of
Analogique A-B, for also in that case, too, each following section followed from a re-initialization of
high-level parameters (remember the protocol of exchanges between perturbations and equilibrium).
Theoretical relevance of algorithmic microcomposition
In Analogique B and Concret PH, just as in Gendy3 and S709, Xenakis aims at creating a
"mechanism" that, once started, manifests itself in time and makes auditorily explorable the knowledge it
captures. I think this is a key-notion that can be discussed from two distinct perspectives.
On one hand, it is precisely through such a mechanism that Xenakis makes the particular medium
of electroacoustic music technology a vehicle for a theory of sound at the level of his more general theory
of music. That is to say that in his mechanism, controlled indeterminacy and stochastic rules are made not
only a means for generating musical structure, but also for composing sound in a musically coherent
manner. In principle, at least, timbre and form come to be inseparable notions (this notio may be
considered as the terminem ad quem proper to electroacoustic music theory (Di Scipio, 1995b)).
On the other hand, the mechanism is such that the composing process begins with a network of
structural relations which hardly can be properly considered (and by no means perceived) as a kind of
musical syntax. Things happening at this microscopic time-scale apparently do not determine phenomena
of cause and effect at the level of the audible musical flow, as they happen within sound, at a pre-
syntactic level - before sound can be heard as such. The properties of the musical surface are a nonlinear
function of the micro-level organization. Music comes to life by means of operations that take place
before any syntactic norm can be recognized as such by the listener. With the terms of cognitive theories,
music here is composed at a subsymbolic - rather than symbolic - level of human information processing.
The composer's decisions are primarily addressed towards elements per se insignificant to perception
(grains, samples, chunks of waveform segments). These elements are relevant only insofar they cohalesce
into an overall sound image, which emerges as a complex function of their composition.
The latter observations are crucial when we consider both the question of 2nd-order sonorities,
and the notion that the composer creates both sound and music by one and the same process, thereby
breaking with the traditional distinction between them. A fruitful discussion here would ultimately
require an analysis of the nature and operation of Xenakis' "mechanism": it's there - within the
mechanism - that we may possibly approach both the problem of the 2nd-order sonorities, and that of an
"automatic art, without any human interference except at the start" (FM, p.295).
Accordingly, the discussion can lean to a view of cybernetics, where the compositional mechanism
is adequately characterized as a system (συστ###μα, συν−στ###ναι = reunion, assembly) of certain
characteristics. By taking such a perspective, we shall see that Xenakis' mechanism has inherent
limitations as to the possibility of bringing forth 2nd-order sonorities dynamically evolving through time.
A twofold problem with the cybernetics of Xenakis' mechanism
"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 quote from Edgar Morin (1972, p.31) can help us fixing the conceptual coordinates to
discuss the cybernetics of Xenakis' compositional mechanism. In an attempt at generating the sound
material and the musical form by one and the same process, his mechanism tends to establish itself a self-
organizing system - a dynamical system which is virtually capable, once starded, of controlling and
feeding its own life, and eventually change itself upon particular occurrences.
The effort is in part successful, when we consider the notion (drawn from the mathematical
theory of deterministic chaos) of "sensitiveness to the initial conditions": the mechanism behaves
differently, but consistently, upon different initial settings.
However, the effort is not successful insofar self-organization remains incomplete: the
mechanism is event-insensitive, i.e. incapable of changing its behavior upon the occurrence of particular
states or events provoked by its own functionality. Overall, it implements a "stochastic" process, and that
is an asymptotic process oriented "towards a stable state, towards a kind of goal, of stochos, whence
comes the adjective stochastic" (FM, p.4). The composer moulds musical form by exploring its "nooks
and crannies [...] while modifying the values of the input data" (FM, p.144; MA, p.28); each time he does
so, he is "provoking" the "natural process" of the mechanism, introducing an element of perturbation
which makes the mechanism itself advance "towards its goal, its stationary state, once the perturbation
has ceased its action" (FM. p.94). Musical form appears then as the by-product of "a whole series of these
perturbations" which force the mechanism "towards exceptional regions at odds with its behaviour at
equilibrium" (ibidem).
Before Gendy3, where the macro-level controls are no more determined directly by the
composer but by a "composing" program that triggers and initializes lower-level synthesis processes,
Xenakis' mechanism can hardly be seen as an actual instance of "automatic art" freed of human
interference. However, even in the case of Gendy3 or S709, the stochastics laws anyway prevents the
mechanism itself from establishing a truly self-organizational dynamics.
Self-organization means that the system observes itself and changes itself upon particular
occurrences in his life. Stochastic laws are by their very definition indifferent to any occurrence, and
blind to the unexpected. In the world of stochastics, singular events, the fortuitous and unexpected, are
not a source of information and transformation, in favor of a levelling-off tendency reflecting the
relentless increase of entropic disorder (in agreement with the traditional interpretation of the Second
Principle of thermodynamics). Being memoryless (as from Xenakis' own decision),9 the mechanism does
not learn from the history of its previous states. It captures no self-regulating adaptive dynamics. It is
blind to the external and to its own history. In a sense, by no means purely metaphorical, Xenakis' system
is not an eco-system - it lives in no context, not even that of its own history. Self-organizing systems, as
described in the cybernetics followed from Heinz Von Foerster's early work, as well as described in the
mathematics of dynamical physical (and biological, and social) systems, are defined as such insofar they
are capable of interacting with a contextual situation (history and ambiance) and to shape themselves
upon contact with events occurring in that context. In short, they must include feedback. To preserve
themselves, self-organizing systems transform themselves and their behavior.
In Xenakis' formalized music, instead, the event is forced by the composer from the external. In
Analogique A-B, this is the case with the series of values provided in the exchange protocol (alias the
composer himself) in order to re-initialize and re-activate the mechanism. In Gendy3 and S709, we have a
higher-level, automated computer program which determines the init values in each successive synthesis
process. In neither cases changes of relevance for the building up of the musical form are determined as a
function of the mechanism's present or previous states. A kind of temporal suspension ensues, moment by
moment, section by section, in the flow of time experienced by the listeners.10 Unforeseeable sound
9 in the chapter Free Stochastic Music, Xenakis describes the composition of sound events "obeying an aleatory law
without memory" (FM, p.23). Markov processes (like in Analogique B), on their part, do have memory, but (at least in the form
utilized by Xenakis) limited to a single memory cell: event n+1 is an aleatory function of event n.
10 I believe in the methodological necessity, here, of skipping over Xenakis' own reductionistic definition of time as "a
blackboard on which one writes events and structures" - a definition which anyway fits well only with his work on the UPIC system
(e.g. Mycenae Alpha, 1978). I would concentrate here on how he actually works and what he actually works upon, rather than his
events open no temporal horizons, leaving no traces of themselves in time. Coherently with the
assumptions of the stochastics, the particular is soon forgotten in favor of the global tendency of the
mass. The very nature of stochastic laws, their potential and their limitations, may provide an
analytically and compositionally useful explanation for Xenakis' difficulties with 2nd-order sonorities. In
all systemic situations, emergent properties seem to require more a lively chaotic order than a statically
organized disorder - the two are not the same and, anyway, there exists "many kinds of disorder" (Morin,
1983, p.63).11 Though conceived as a thoroughly formalized system, Xenakis' compositional mechanism
has to be reset and retriggered in order that the contrasts and transformations that nourish musical form
are finally instilled in the flow of sounds. The former and the latter question (that of emergent sonorities,
and that of thoroughly automated composition) are two, interconnected aspects of the phenomenology of
Xenakis' stochastic mechanism.
At the interface between the explicable and the inexplicable
In making the above argument, I have considered a link between the question of 2nd-order
sonorities and the question (of relevance for contemporary music aesthetics) of the identity of sound
materials and musical form. I have tried, too, to show that the link has to be analyzed by addressing
ourselves to the composer's implementation of generative systems or mechanisms aimed at producing
sound and music together. The interplay of causality and breakdown that animates musical time is not
comprised in the criteria of the mechanism itself, and remains largely at the mercy of a transcendental
demiurge which repeatedly intervenes to orient his mechanism's behavior. The compositional system
needs to be repeatedly "provoked" in order "to manifest itself, be".
Now I have to add: it is precisely at that point that Xenakis' music stops being formalized music
and lets other criteria enter the picture. It is at that point that it becomes a particularly rich experience
where the scientific and the humanistic element meet and confront each other. What I have called a
"twofold problem", in actuality is the very frontier where Xenakis stops formalizing and geometrizing,
and make decisions according to non-explicable (at least, not formally explicable) criteria. By addressing
ourselves to the technicalities of the composer's mechanism, we finally get at the interface where
technology - i.e. the composer's knowledge captured into workable tools of his own design -
communicates with other modes of human understanding. In other words, here comes in the humanistic
side of Xenakis.12
Conclusion. Towards a shift from "disorder" to "chaos"
The cybernetics of Xenakis' mechanism reflects an interesting epistemological position. Xenakis
merges the algorithimic and the stochastic, determinism and indeterminism, and in this way present us
with a correct picture, I think, of the complexity of human existence. Formalized works like Analogique
B or Gendy3, where both sound and music are the object of invention, reflect a world no longer
describable in terms of the order-from-order principle - with which Erwin Schrödinger described a
purely deterministic rationalism of Laplacean stamp - but a world that has to be described in terms of the
order-from-disorder principle, a world where things are being incessantly put in order, warding off the
ever-deeper abyss of entropic disorder (Von Foerster, 1960).13 Xenakis seems to point to - and yet not to
make - a further step, a step possibly leading to the order-from-noise principle, i.e. to a view according to
which our world is neither strictly coherent (algorithmic order) nor strictly incoherent (statistic order), but
in a dynamical condition of chaos (invisible order that manifests itself only on a meta-level, as emergent
shapes, suddenly appearing, individual epiphenomena).
Stochastic processes can hardly account for the richness of chaos. Indeed, the latter would entail
an incessant interplay of construction and destruction, where things would find their own unstable,
temporary order by themselves. The world of the order-from-noise principle takes form, and then
declarations. Most composers' declarations of intent are to be distinguished from their practical compositional process, as also
observed in (Solomos, 1997).
11 Morin mentions some 15 kinds of disorder (1983, p.63).
12 see the Addendum, at the end of this paper.
13 in his Berlin lecture, in 1964, Xenakis asked "how can one organize such a statistic disorder?" The answer was to be
found in the kinetic theory of gaz, going back to Maxwell and Boltzmann (MA, p.23).
transforms, by reacting to the event, through creative singularities, through interactions with the
unforeseen. A positive meaning of the Second Principle advances here: in the theory of self-organizing
dynamical systems, an increase in entropy is regarded as a creative force, a bearer of isles of temporary
order in the on-going flow of transformation (Von Foerster, 1960). This view also mirrors the process of
very particular self-organizing systems, systems having a special relevance for all of us, i.e. living (auto-
poietic, self-regenerating) systems (see Maturana & Varela, 1980).
The technology of the stochastics keeps Xenakis within the margins of statistic order, before a
chance for structured disorder may arise from within the sound matter. What we, as listeners, experience
as form in this music is inevitably linked to a series of coherent reactions of the mechanism following
from the composer's changes in the init data. However, by raising (in a very radical way) the question of
2nd-order sonorities and that of automated composing, the music of Concret PH, Analogique A-B,
Gendy3 and S709 is an unprecedented contribution to an utopic art where the dialectics of materials and
form appears ideally resolved. The intelligence of these works of organized sound testifies to a kind of
human understanding for which chance and necessity are perfectly integrated.
(September 1997)
Addendum
It is my conviction that, when we deal with the work of Iannis Xenakis, we can hardly separate
the humanistic from the scientific element, the one and the other being just two faces of the same coin,
two inseparable aspects of the same cultural potential. I think we could hardly try to describe the
humanistic element in his work if we disregard the technicalities of the various scientific theories he
creatively exploited (many more than those mentioned in the above!). Conversely, we could hardly
characterize the scientific aspects in his work if we don't look at them within the cultural context they
reflect, thereby reflecting a historically determined world-view.
Somehow, we should strive with the particulars of the composer's constructive process, before
we get ourselves at the point where - finally - we are entitled to speak of the overall relief to be
recognized in Xenakis' work. In order to see what, in the end, is left out of formalization in his music, we
must first see what is not left out. We should first bring ourselves at the interface where the explicit and
the implicit in this art communicate one to the other. To orient ourselves towards the one, we have to
stand up well rooted into the other. Today for me this is perhaps the deepest, subtle influence that
Xenakis' art had on me, as a composer and as an individual. (January 1998)
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Figure 1 : sonogram of Concret PH (up 0’00” – 1’20”, down 1’20”- 2’40”)
Figure 2 (40”-50”)
Figure 3 (30”-40”)
Figure 4 (80.6”-86.9”)
Figure 5 (37.7”-38”)
Figure 6 : (up) 90”-100”), (mid) 94.5”-96”, (down) 94.8”-95.2”.
Figure 7
Figure 8 : waveform segments in Gendy3
Figure 9 : sonogram of passage from section 3 to section 4 in Gendy3
... ' [9] Concerning Analogique B, even if it may not be considered a particularly successful application of the theory, it is very significant since it is regarded as the first work of granular sound synthesis [10]. In the basis of Xenakis' application of his hypothesis, as he describes, there is a mechanism, 'the " analogue " of a stochastic process' [7]. ...
... Di Scipio claims that the stochastic laws, which Xenakis is using to apply his hypothesis, are not capable of determining the emergence of second order sonorities [10]. He explains: 'Just as the pizzicatos of Analogique A could not but remain string pizzicatos, however dense their articulation, the electronic grains in Analogique B remain just grains and do not build up into more global auditory image.' ...
... He explains: 'Just as the pizzicatos of Analogique A could not but remain string pizzicatos, however dense their articulation, the electronic grains in Analogique B remain just grains and do not build up into more global auditory image.' Summarizing the conclusions of Di Scipio, Xenakis' mechanism: 1) is sensitive only to initial conditions, 2) its process is oriented towards a goal 3) the goal changes upon different initial conditions [10]. I have to add here that all of the above clearly show the characteristics of a 'closed system'. ...
Conference Paper
Full-text available
The present paper discusses an alternative approach to electroacoustic composition based on principles of the interdisciplinary scientific field of Systemics. In this approach, the setting of the electronic device is prepared in such a way to be able to organise its own function, according to the conditions of the sonic environment. We discuss the approaches of Xenakis and of Di Scipio in relation to Systemics, demonstrating the applications in their compositional models. In my critique on Di Scipio's approach, I argue that the composer is giving away a major part of his control over the work and therefore the notion of macro-structural form is abandoned. Based on my work Ephemeron, I show that it is possible to conduct emerging situations applying the systemic principle of 'equifinality'. Moreover, I argue that it is possible to acquire control over these situations and their properties over time so as to develop formal structure.
... Entre les considérations diverses liées à la notion de pluralité, passages entre niveaux et temporalités multiples, la possibilité de prendre en compte la dynamique des systèmes complexes (grâce à des processus numériques itératifs) et le chaos13 , représente pour le compositeur Agostino Di Scipio 14 une manière de composer « des petites unités sonores de telle sorte qu'une sonorité d'ordre supérieur puisse se manifester d'elle-même durant le processus »(Di Scipio 2001). Dans son exploration de la synthèse granulaire avec des systèmes dynamiques15 non linéaires (ayant « un comportement adaptatif » et en lui permettant d'exploiter divers types de textures, grains et comportements variés) Di Scipio assimile la macro-forme à un second niveau qui émergerait du niveau élémentaire (c'est le processus qui doit être composé, et non le résultat). ...
... Les théories du chaos qui ont fasciné les musiciens vers le milieu des années 1980 introduisent une espèce de continuité entre les deux extrêmes du dualisme ordre/désordre. 14 « Dans toute situation systémique, les propriétés émergentes semblent exiger plus un ordre chaotique vivant qu'un désordre statiquement organisé »(Di Scipio 2001).15 Un système dynamique est un système dont l'état présent dépend des états précédents et d'un certain nombre d'autres paramètres qui peuvent, ou non, aussi varier avec le temps(Tiberghien 2002).23 comme « émergence » 16 est à la base de la « théorie de l'émergence sonologique », élaborée dans un de ses premiers articles -Theory of sonological emergence (Di Scipio 1994) -, où la proposition d'une conception de la forme décrite comme « formation du timbre » 17 ouvre une connexion intéressante entre ces deux constituants principaux du langage musical.À partir des différentes observations, notamment sur des positions relevant la séparation dans la musique électroacoustique entre la musique algorithmique et la composition de timbre, Di Scipio décrit des phénomènes, proches des systèmes vivants, de morphostase (conservation de l'identité, donc cohérence) ou morphogenèse (changement et comportement dynamique), des processus, des pratiques de causalité circulaire (dans une idée de récursivité élargissant ainsi le concept de feedback), des interactions composées, la prise en compte d'un espace concret (et pas virtuel), qui est le lieu de la performance (imaginé soit comme excitateur soit comme caisse de résonance), ayant le pouvoir, avec ses qualités acoustiques, de se répercuter sur le timbre et le son de l'oeuvre.Nonobstant des différences musicales et esthétiques avec ses réalisations musicales, notamment sur la question de l'interaction, l'étude de la pensée de Di Scipio a représenté pour moi un stimulant point de vue, en même temps qu'un moyen de confrontation critique obligeant à m'interroger sur les nécessités profondes sous-jacentes à mon idée de la forme comme résultante de relations à plusieurs niveaux entre objets, processus et typologies différenciés. ...
Thesis
Cette recherche vise à étudier l’intégration contemporaine, dans la composition et la performance, des outils technologiques et artistiques correspondant à l’état de l’art en matière d’interaction temps-réel entre production instrumentale, production numérique du son et production de formes spatio-temporelles dans le lieu d’écoute. On souhaite notamment étudier comment cette intégration pourra constituer en retour une nouvelle modalité de l’écriture où fusionnent en cohérence une écriture du son, une écriture du temps et une écriture de l’espace informées par la technologie.Les paradigmes informatiques pour la gestion du temps et de l'interaction, les outils de synchronisation de processus, l'analyse de flux sonores et gestuels, le contrôle des paramètres à partir du son instrumental, la recherche sur la question du timbre instrumental et de ses descripteurs numériques et l’interaction interprète-ordinateur forment les éléments clefs de cette recherche.L’idée principale de ce travail est centrée sur l’interaction en temps réel avec des dispositifs informatiques avancés, dans le cadre d’une écriture particulièrement virtuose, avec des aspects spécifiques de construction temporelle et spatiale, cette situation hybride influençant en retour la nature de l’écriture elle-même. Les différents thèmes relatifs à cette exploration, tels que l’écriture du son, du temps et de l’espace, sont le point de départ pour décliner et développer, selon la nature des diverses productions envisagées, les liens possibles avec d’autres disciplines artistiques.
... Analysing Xenakis's hypothesis (Xenakis, 1992: 103) of an (auto-)creation of " higher order sonorities " in Analogique A et B (1958–1959, for nine strings and tape), a composition that uses the granular paradigm, Di Scipio makes a small shift in Xenakis's concept: " Today cognitive scientists and epistemologists would probably describe the hypothesis of 2nd-order sonorities as a question of emergent properties of sound structure " (Di Scipio, 2001: 72). The question of emergent structures can be formulated as follows: " In this case [concerning Analogique B], the distinction can hardly be made between a model of musical articulation and a model of sound design, insofar as the composer's action is meant to let the musical (macro-level) structure emerge from sound itself and its internal organization (micro-level) " (Di Scipio, 1997: 165). ...
... The question of emergent structures can be formulated as follows: " In this case [concerning Analogique B], the distinction can hardly be made between a model of musical articulation and a model of sound design, insofar as the composer's action is meant to let the musical (macro-level) structure emerge from sound itself and its internal organization (micro-level) " (Di Scipio, 1997: 165). Whereas the " failure " of Analogique to create second-order sonorities is probably viewed by Xenakis as a failure of the grain's fusion, Di Scipio views this failure as one of emergence and attributes it to the limits of Xenakis's mathematical tools: " One may ask whether the stochastic does really provide as good a means for higher-order sonorities to emerge from a ground-level pattern of minimal sonic units " (Di Scipio, 2001: 73, 79). And, in fact, in his own music, Di Scipio opted for complex dynamic systems: " Chaos and the dynamics of complex systems, as accessible with iterated numerical processes, represented for me a way to compose small sonic units such that a higher-level sonority would manifest itself in the process " (Di Scipio in Anderson, 2005). ...
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This paper discusses the possibility of analysing (in the musical sense of the word) Agostino Di Scipio's ‘audible ecosystems’. The first part is focused on the notion of the audible ecosystem and its theoretical counterpart, the idea of emergent sound structures. With this last idea, higher levels of a musical work (for instance, the macroform itself) appear as an emergence from lower levels. As for the notion of the audible ecosystem—analyzed here through the live electronics solos named Audible Ecosystemics—this is achieved through interaction between the performer, the electronics and the environment. In its second part, the paper tries to define an analytic image of the resultant sounds of the audible ecosystems. To do so, we use the concept of imprint (empreinte in French) as it is analyzed by Georges Didi-Huberman. Then, we go back to musical analysis and argue that a musical analysis of Agostino Di Scipio's audible ecosystems involves an analysis of the relationships between what we have listened to, what we can only imagine and the compositional techniques themselves. Before concluding, the article shows an example of this way of analyzing by taking a sample at random from the piece Audible Ecosystemics 3b.
... cf. Solomos, 2004] 29 For more details on Xenakis, cf.: -the articles of Di Scipio: 1995Scipio: , 1997Scipio: , 2001 hal-00770088, version 1 -7 Jan 2013 sonorities have to do with granularity, as for instance Ionisation's third sonority 30 (cf. figure 6) 31 . ...
Article
This paper examines: 1) the way Xenakis introduced the granular paradigm; 2) some elements for the history of the granular paradigm (especially the work of Horacio Vaggione and Agostino Di Scipio). NB. The English version of this article has not been revised (except 2.2) Many ways start from or go through Xenakis. One of these ways is the granular paradigm 1 . In this paper, I will start from Xenakis, suggesting that, in his aesthetic, this approach is a "theory" in the ancient meaning of the word, and searching for the constituent elements of this "vision". Then, I will try to incorporate the granular paradigm into a musical historicity, searching for his becoming inside other aesthetics, in particular with Horacio Vaggione's and Agostino Di Scipio's music.
... According to Di Scipio, Xenakis' use of stochastic laws in the application of his hypothesis are unable to determine the emergence of second order sonorities: 'Just as the pizzicatos of Analogique A could not but remain string pizzicatos, however dense their articulation, the electronic grains in Analogique B remain just grains and do not build up into more global auditory image' (Di Scipio, 2001). Furthermore, Di Scipio states that Xenakis' mechanism although it is sensitive to initial conditions it is unable to be influenced by the events of his own function. ...
Conference Paper
Full-text available
Systems thinking' includes a number of interdisciplinary theories based on organizational approach to problems, in other words considering everything as systems. The paper discusses the connection of Iannis Xenakis and Agostino Di Scipio with 'systems thinking' and proposes an experimental compositional model related to this line of thinking. Xenakis, in order to formulate and explain what he called 'Stochastic Music' he used the methodology of 'cybernetics', one of the most important theories of 'systems thinking'. Also, based on the same approach, he formulated the hypothesis of 'second order sonorities'. After this historical point Di Scipio comes to add his objection to Xenakis's approach. Di Scipio doubts that the stochastic laws are capable of determining the emergence of 'second order sonorities'. Resulting from this problematics on Xenakis, his criticism of the conventional model of interactive music and the application of notions found in 'systems thinking', Di Scipio is suggesting a 'self-organized' interactive model. According to this model, the sound system is able to observe itself and regulate its own processes. It can be considered as a self-organized system, an organism, placed in his environment, the space of the concert hall. Based on this line of music evolution connected with 'systems thinking', we have attempted to develop a systemic model of symbolic music, an experimental compositional model mainly used for instrumental writing. The term 'symbolic' refers to the focus on the information's flow through symbolic means, i.e. through music notation. In addition, the approach treats 'systemically' the compositional work, applying notions found in 'systems thinking' through the cognitive sciences. We have abstracted the 'live interactive music model' used in live electronics, from a systemic viewpoint, using it as the basis of what we call the Creative System of Symbolic Music. Using simple examples, the structural design and the functional performance of the model will be presented.
... Di Scipio doubts that the stochastic laws Xenakis is using are able to achieve the emergence of second order sonorities. Summarising the conclusions of Di Scipio for Xenakis mechanism (Di Scipio 2001), as I have already pointed out (Kollias 2009b), we can identify the characteristics of a closed system. 8 In addition, Di Scipio interprets the mechanism within the systems thinking framework, having to suggest the application of a more advanced systemic notion, that of the self-organising system. ...
Conference Paper
Full-text available
This paper focuses on the link between the musical thought of Iannis Xenakis and theories of systems thinking. It will be demonstrated how the composer interprets in his musical thought, concepts of systems thinking, such as markovian stochastic music, or in the formulation of second order sonorities, which resulted in the formation of a new music paradigm. Finally, we shall examine how these lines of thought evolved, as for instance in the music of Agostino Di Scipio or in my own music.
Chapter
Full-text available
Meta-Xenakis offers readers a comprehensive collection of insights into the history, works and legacy of Iannis Xenakis, one of the twentieth century’s most significant creative figures. It presents a transcontinental engagement with his life and output, focusing as much on the impact of the questions he posed as on the accomplishments of his body of work. This volume evolved out of the multi-modal, international Meta-Xenakis Consortium’s artistic and scholarly events commemorating his centenary. Informative and comprehensive, contributions span subjects including music composition, creative pedagogy, aesthetics, game theory, architecture, and the social and political contexts in which Xenakis operated. The book is organized in eight sections, centered on different facets of Xenakis’s work and reception. It includes a digital archive of audio and visual media from the events staged throughout 2022, as well as computer software. Bringing into conversation the diverse perspectives and insights of researchers, musicians and artists, this volume serves as a foundational resource for future research on the life and work of Xenakis. It will be of interest to students, scholars, and practitioners across a range of disciplines including music, architecture, cybernetics and computation, and the digital arts.
Article
Cellular automata are developed since some decades, belonging to the field of abstract automata. In the beginning of the 1980s, they were popularized in relationship with the study of dynamic systems and chaos theories. They were also applied for modelling the evolution of natural systems (for instance biological ones), especially in relationship with the idea of auto-organization. From the end of the 1980s since nowadays, several composers begin to use cellular automata. Xenakis must have been one of the first (or the first), as he used them, probably for the first time, in Horos (1986), so as to produce harmonic progressions and new timbre combinations. His use of cellular automata seems to be limited. This paper has three aims: 1. To try to understand the reasons why Xenakis used cellular automata. This will mean a discussion of the idea of "automaton", characterized as a model of autonomy (as opposed to the model of the "command"); 2. To analyze three instances of musical implementations of cellular automata in Horos; 3. To discuss the notion of "theory" specific to Xenakis. Based on the analysis of scores and of sketches (Archives Xenakis, Bibliothèque nationale de France), the analysis of musical implementations of cellular automata in Horos will show that Xenakis acts as he is always acting when he is appealing to one or another form of formalization: he uses them to produce a result, allowing himself bricolage (either in the construction of the tool itself, either in the results produced by the tool). In other terms, his use of cellular automata is mediated through manual interventions.
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This article outlines a particular mode of composition wherein timbre emerges from micro-level processes of sonic design, on the basis of discrete-time microstructural representations of sound. This approach is characterised in terms of models of detailed sonic design and is described as a unique instance of an indeterministic style of creative thinking in electroacoustic music composition.The discussion includes examples drawn from early electroacoustic music works (Pousseur, Xenakis, Brün, Stockhausen) and more recent work in computer music, including the author's own experience with methods of granular synthesis. Finally, we examine the notion of timbre as conceived in the approach under observation, and suggest that timbre composition fosters a profound changes of compositional paradigm; indeed, it can challenge a clear-cut dualism between materials and form, and transform the conception itself of musical form into one of processes of timbre formation through time.
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A mixture of sounds, though distinct in the environment, arrives in the form of a single pressure wave at each ear. From it, listeners must extract the signals coming from individual sources of sound, a process called auditory scene analysis (ASA). ASA first characterizes the incoming waveform by its frequency components and other features, then creates subsets (auditory streams) that extend over time, each representing a single environmental sound source. ASA exploits regularities in the signal to determine how to parse it. ASA is present at birth in humans and has been found in other animals.
Article
Granular synthesis is a unique method of achieving complex sounds by the generation of high densities of small grains on the order of magnitude of 10-20 msec duration. Current digital signal processing (DSP) hardware offers the potential for real-time implementation of this technique by dividing the responsibility for calculation between the DSP and various levels of controllers. This type of implementation can be regarded as an instance of real-time composition, and therefore it is suggestive of a trend towards systems that combine the complexity associated with studio composition with the spontaneity of live performance. This article describes a real-time implementation of granular synthesis and signal processing.
Article
GENDY3 by Iannis Xenakis is a stochastic music work entirely produced by a computer program written in 1991 by the composer himself at CEMAMu. The work GENDY3 is the continuation of the series of stochastic music works that Xenakis inaugurated in 1955 with Metastasis. In GENDY3, the use of stochastic rules is more deeply systematic, as the composer says in his recent publication (Xenakis 1991b). Not only is the musical structure of GENDY3 stochastic, but the sound synthesis is also based on a stochastic algorithm that Xenakis invented and called "dynamic stochastic synthesis." In this paper, we describe the whole process of the computation of GENDY3, from the low-level sound production to the high-level global architecture. We also take up aspects which GENDY3 has in common with earlier stochastic works which Xenakis composed and described in Formalized Music (Xenakis 1971). The stochastic program that was used for the composition of GENDY3 is partly listed in the new edition of Formalized Music (Xenakis 1991a).
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