Théorie des cribles

Dimitris Exarchos A sieve is an abstract generalization of the concept of the scale. In Xenakis’s own words, a sieve is “every well-ordered set [that] can be represented as points on a line, as long as a reference point is given for the origin and a length u for the unit distance” (1992, 268). As […]

Montage

Benoît Gibson Iannis Xenakis is a composer who is well–known (and often criticized) for his use of mathematics and abstract calculations in his works. To refer to montage when describing these works may come as a surprise to the reader. And yet, in some way, the formalization of music attempted by Xenakis encouraged the practice […]

Théorie des jeux

James Harley In Chapter 4 of Formalized Music (1992), “Musical Strategy—Strategy, linear programming, and musical composition,” Xenakis explores musical applications of game theory. First developed by computer science pioneer John von Neumann (1903-57), game theory was presented in pure mathematics first, then applied to economic behavior theory, among other fields. In essence, game theory is “the study of […]

UPIC

Au milieu des années 1970, Xenakis a commencé à développer le système UPIC, un système informatique musical utilisant une surface de dessin comme dispositif d’entrée numérique : les dessins réalisés sur une tablette de type CAO (conception assistée par ordinateur) pouvaient être transformés en sons grâce à une interface logicielle, un processeur dédié et un […]

Pans de verre ondulatoires

Elisavet Kiourtsoglou Undulating glass panes consist in an assemblage of glass panes of various lengths; they were used for the first time for the Monastery of Sainte Marie de la Tourette (1953-1961). The project was assigned to Le Corbusier (1889-1967) by the Dominican Friars’ Community of Lyon, in an attempt to modernize the architecture of […]

Synthèses stochastiques

Peter Hoffmann This technique refers to a method of computer sound synthesis. The original conception dates back to 1962, when Xenakis was working with his ST algorithm, resulting in the stochastic compositions ST/x (see Stochastic Music). Stochastic synthesis rejects Fourier analysis or pure electronic sounds and favors applying stochastic processes directly to the sound pressure […]

Musique stochastique

Benoît Gibson While avant-garde composers such as Boulez or Stockhausen developed their compositional methods on the basis of serial techniques, Xenakis followed criteria other than those stemming from any musical tradition. By approaching the musical phenomena globally, he opened up a new sound world that included textures comparable to natural phenomena governed by the law […]

Sonorité

Makis Solomos translation from the French: Jennifer Higgins Possibly the most important musical revolution of the 20th and 21st centuries has been the emergence of sound, and the ever-greater importance accorded to it (see Solomos 2019). Xenakis occupies a special place in this development, whereby, to put it simply, composition of sound has tended to […]

Surfaces réglées

Elisavet Kiourtsoglou In geometry, a surface is ruled if a straight line (skew line) passes through each one of its points. The cylinder, the cone, the helicoid, the hyperbolic paraboloid, the conoid and many other three-dimensional shapes follow the above mathematical definition. Xenakis (1958) first referred to the properties of ruled surfaces during his collaboration […]

Marche aléatoire

James Harley In mathematics, a random walk is a process that describes a path that consists of a succession of random steps on some mathematical space (e.g., 2-dimensional space: amplitude-time, or pitch-time). It was first introduced by Karl Pearson in 1905. An elementary example of a random walk is on the integer number line which […]