Alessandra CapannaLaboratorio Multimediale di Architettura Università di Roma "La Sapienza" Via Antonio Gramsci, 53 - 00197 Rome Italy
I am writing about Iannis Xenakis [1] (Figure 1, to the left), an uncommon man and the kind of composer who embodies the ideal of an 'architect of music'. This characterization has been attributed to many great composers of the past (from Brahms to Schönberg to Bach), but it particularly fits Xenakis, not only because he worked as architect for twelve years in Le Corbusier's Atelier in Paris - during his first experiences as composer of a new musical genre - but mainly because of his tendency to appropriate for himself a demiurgical style through his philosophical speculations on the concepts of symmetry, the masses and space-time. His social and cultural development took place in the 1940s,
the years of the Greek civil war. His restless personality developed
in the impetuous climate of the Polytechnic in Athens, where
he formed a tormented personality for which interest in politics
was not only a necessity, but was fed by the deep-seated sense
of being a Greek. Thus the sometimes tragic events relating to
the cruel and ferocious fighting in the streets fused with a
maniacal reading of Plato's Xenakis was among the components of Le Corbusier's immediately
after the second world war. He is mentioned in At the beginning of 1956, when the Philips firm asked Le Corbusier
to design their pavilion for the Bruxelles World Fair, Xenakis
had experimented with compositions for The most evident quality of Le Corbusier's reflections regarding harmonic proportions is the consciousness that an interest on the occult aspects of the golden mean was not coherent with the scientific uses related to it, in particular its use to construct the grid for the dimensional standards for the prefabricated building "Unités". This rational attitude - more coherent with mathematical thought - appears to bring the famous French architect closer to his pupil, the young as-yet-unknown musician whose unusual and independent ideas were gaining ground in the extremes of contemporary circles of research in which Le Corbusier himself was engaged through of his involvement in several artistic fields. The Philips Pavilion seems to sum up all the the objects "à
réaction poétique" designed in the study of
rue de Sèvres, freed as it was from the rigid stereometry
of right angles and by the Platonism of the pure volumes.[2] The shape
of the pavilion derives from the combination of the initial idea
of a bottle containing the 'nectar' of the show with Xenakis's
mathematical studies on hyperbolic conoids. In October 1956 Le
Corbusier's sketches were entrusted to Iannis Xenakis, who was
charged to
This unique compositional event upholds the thesis that at the basis of some architectural events - perhaps those celebrating most completely the process of transformation of an idea from pure abstraction to factual object - were those concepts whose development is possible through the intervention of the mathematics because:
The innovative logic introduced by Xenakis concerns more than only a new way of facing the problems of constructing the compositional structures, which explicitly returns to an "antique" reasoning, but which presupposes the architect's and musician's knowledge and deep intuition of the new mathematical theories connected to the problem of symmetries. No longer and not only characterized by geometric regularity - sometimes all too evident - but seen as parts of both group theory of the calculus of probabilities; thus it will be easier to understand asymmetry as an extension of symmetry and, more generally, in the field of probabilistic speculation, to affirm that it is impossible to improvise randomness. Thus that total liberty to which assymetry - often used as a substitute for the word 'irregularity' - would seem to allude, would not exist, because nowadays we know that even irregularity doesn't necessarily presuppose the absence of rules. It is sufficient to think of the vast production of aleatory music, deconstructivism and all those compositional phenomena in which chaotic form is the result of a patient and transient research on the actual state of the cosmos. In the fifties, Xenakis was developing these kind of thoughts and was asking himself first of all about rules in composition and whether is possible to produce something in music or in any other field in the total absence of rules, or in other words, in an absolutely free way. Stravinsky insisted that to make music the rules are necessary; Xenakis himself, less than ten years ago, claimed to be convinced that:
Configured in such a way, the cardinal idea of composition
turns out to be a kind of cross between the Pythagoreanism of
numbers and the Parmenidean dialect, if it is analyzed from the
particular point of view of Xenakis of a "future classic":
The operations through which Xenakis transferred formulas,
concepts and mathematical symbols into his compositions were
always dictated by a philosophical option. Immersed in the elusive
climate of his hypotheses about the world and driven by a strong
desire of abstraction, his works impose a passage from the calculation
of probabilities to formal logic, fact that also signals a kind
of retrieval of the mathematical-philosophical matrix of twentieth
century logical neopositivism. The composition, therefore, is
not only a metaphor of logical processes, but a representation
of them projected sometimes into the world of sounds, sometimes
into that of space, or into both in unison through those complicates
structures of light, space and sound called Polytòpes,
which really are sonorous architectures born of the convergence
of the physical image of the Philips Pavilion with the theoretical
speculations on what is a new sonorous plastic art, with the
memory of the bombardment in the campaign of Attica, the nighttime
sky " In these spectacular performances, conceived to involve all the spheres of perception, the related architectural space was designed to contain loudspeakers and light projectors in determined positions so that they could interact with one another. The sound and light thus projected were difused by the internal walls of the space with studied and sometimes variable effects on the spectators and their casual disposition. These were ephemeral architectural installations that wee part of experimentation with architectural continuity, carried out through the rigorous application of a mathematical-formative idea. The same structural principle is adopted for the composition of the music, which sometimes loses its meaning when it is listened to out of its spatial context, and which generally adopt the principle of variation of the density as a ideative constant, the creative potential of which have yet to be exhausted. Further, Xenakis made his own a thesis of minimum rules, from the general law of the entropy that some years ago was studied for its expressive potential which led directly to Xenakis's simple definition of stochastic compositions:
With the aid of a computer, Xenakis was able to explore the
large universe of configurations based on the variation of sonorous
density, in the same way in which the of material or spatial
density are delineated, through the application the formulas
of the calculus of probability. Wha was derived was an extension
of an extension of the concept of entropy and the introduction
of some selective operations within the statistic procedure,
produced from the combination of sequential studies that govern
such modifications. This has to do with the so-called Chain of
Markov, an autoregressive process explored at the beginning of
the twentieth century by the Russian mathematician Andrej Andreievic
Markov, the constitutive mechanism of which was applied by Xenakis
to compositional structures, and vaguely described in in the
chapters "Three poles of condensation" and "Stochastic
and Markovian Music" in Xenakis was interested in a concept of music that was capable
of going beyond the limits of the music, both by crossing over
into other expressive means - as it happened for the transformation
of the graphical-musical sketches of The
return
to text[2] For more about the Philips Pavilion, see A. Capanna,
"Conoids and Hyperbolic Paraboloids in Le Corbusier's Philips
Pavilion" in [3] Iannis Xenakis, [4] Paul Valéry, "Storia di Anfione",
[5] In: AA.VV.
[6] In: Iannis Xenakis, [7] in AA.VV. Xenakis, a cura di E. Restagno, Torino
1988, p. 39. [8] In: Iannis Xenakis,
L'imagination au-dessus par Pascal Dusapin (essay in French) Polytopes par Iannis Xenakis (essay in French) Iannis Xenakis (links to list of works) Groovy composers on the Web (Mp3 clips of some of Xenakis's works) I. Xenakis: Colone/Niuts/Serment/Knephas (Real Audio clips from the album)
Iannis Xenakis. E. Restagno Iannis Xenakis. Mario Bois.
Copyright ©2001 Kim Williams top of
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