The basic techniques of Iannis Xenakis
Iannis Xenakis is a French/Greek composer who developed his own style of music based on mathematics. He used various mathematical concepts in his compositions, including stochastic processes, spectralism and dynamic stochastic synthesis. This article will teach you about these different techniques that Xenakis uses in his work, and you can discover some of Iannis Xenakis sheet music with the video at the end of the article..
Markov processes are a type of stochastic process. They are based on the Markov property, which states that future states of a system only depend on the current state and not on the past states. In other words, Markov chains generate random numbers that have some distribution but do not depend on previously generated random numbers.
Markov processes can be used to simulate probability distributions, for example by generating random numbers following a uniform distribution or Gaussian distribution (or any other distribution with which you might be familiar). That’s exactly what Xenakis does in Stochastic Synthesis: he uses them to generate samples from various probability distributions (Gaussians, Poissons) in order to create his masterpieces.
A stochastic process is a collection of values which are called random variables. A stochastic process can represent any situation where it is possible to observe or measure different outcomes, with each outcome having a probabilistic distribution
The Xenakis technique of composing using stochastic processes has been adopted by others including John Zorn and Karlheinz Stockhausen. The idea of generating music from random events was first proposed by Xenakis in his 1972 article Metastasis Music (later reprinted in Formalized Music: Thought and Mathematics in Composition). In this article he described the use of “metastases” as being a generalization for probability measures based on complex numbers; he then used metastases to produce computer-generated music. This method was further developed by Dragan Espenschied at Stanford University who created software that generated pieces based on user-specified constraints such as desired tempo, time signature, number of instruments, etc..
Brownian motion is a type of random movement that occurs when particles are suspended in a fluid. It’s named after Robert Brown, who first observed this phenomenon in 1827.
Brownian motion is not an example of chaotic or non-linear dynamics; it’s just random movement caused by random collisions between the particles and other molecules in the fluid. The average velocity of these tiny particles can vary over time, but it’s always proportional to their temperature (since they’re moving around due to thermal agitation).
Granular synthesis is a sound synthesis technique based on the concept of grains. The term granular refers to the nature of the sounds produced, which are short samples (typically between 1 and 100 milliseconds) that can be played back at any pitch. The grain size is usually between 4 and 8 milliseconds, but can be as large as 40 milliseconds or small as 100 Hz.
A granular synthesis system consists of three main components: an input sound source (e.g., a wave file), a random generator that creates grains from this source, and an output module where grains are processed into new sounds according to various algorithms (including filtering).
Spectralism (as a technique, and not as a musical movement like the Musique spectrale in Paris with Tristan Murail and Gérard Grisey) is a technique used by Xenakis to compose music. It is based on the idea that sound can be broken down into its component parts, or “spectra”. Spectralism is closely related to serialism, and it was developed as an alternative to it when Xenakis found serialism too restrictive for his compositions.
Xenakis used spectralism in his compositions such as Metastasis (1957), Music for Onomatopoeia (1960), and Poèmes pour Mi (1963).
Dynamic stochastic synthesis
Xenakis was inspired by stochastic processes. Stochastic processes are random, but they can be mathematically manipulated. He used this mathematical approach to create his music, which he called Dynamic Stochastic Synthesis.
Stochastic processes are used in mathematical set theory and group theory, among other fields of study.
His music has been described as “an ever-expanding universe where nothing is clear nor obvious”, with a great deal of unpredictability.
Xenakis uses mathematics in his compositions.
You’ll find that Xenakis’s music is characterised by the extensive use of mathematics, especially mathematical set theory, but also group theory and analysis of geometric figures. He often used special graphical techniques to explore complex sounds, such as in his “Metastasis,” for example.
Xenakis was known for his mathematical approach to composition. In his words:
“The composer must be able to think with numbers and convert them into tones.”
Xenakis is one of the most influential composers of the 20th century. His work has influenced many contemporary composers, including John Adams and Brian Ferneyhough. Xenakis’s compositions often make use of stochastic processes, which are mathematical models describing phenomena in nature that are random but not completely chaotic; they also often use granular synthesis techniques.
Now it’s time to look at some Iannis Xenakis sheet music with this video.