Stochastic Music

What is Stochastic music?

-In the mathematics of probability, a stochastic process is a random function. In the most common applications, the domain over which the function is defined is a time interval or a region of space.

-A stochastic process operates on a family of random variables which is indexed by another set of variables with compatible probability of distribution. A stochastic process particularly appropriate to music is Markov process. In this profanities at any one point depend on the occurrences of events so far; the process thus contains a high degree of uncertainty in its initial stages, an increasing certainty as events unfold, and a high degree of determinacy on its closing stage.

How it works?

Stochastic music is a mathematics probability: stochastic process is a random function. In the most common applications, the domain over which the function is defined is a time interval. it also called time series or a region of space. Stochastic time series, it is include stock market and exchange rate fluctuations, there are three types: signals such as speech, audio and video, medical data such as a blood pressure or temperature and random movement such as Brownian motion or random walks.

Stochastic music composer - Iannis Xenakis :

He was born in Romanian. In 1932 his family returned to Greece, and he was educated on Spetsai and at the Athens Polytechnic where he studied engineering. In 1947 he arrived in Paris, where he became a member of Le Corbusier's architectural team, producing his first musical work, Metastasis, 1954, he based on the design for the surfaces of the Philips pavilion to be built for the Brussels Exposition.

1962 Iannis Xenakis interested in electronic music and composed amount of piece for the orchestral and instrumental pieces for piano, drama or cello. From the mid-1970s he strikes back from modernist complexity to ostinato and modes suggestive of folk music. 2001: he died on 4th of feb.

First piece “Metastasis”

This piece is Iannis Xenakis first major work written in 1953-54. It is an orchestral work for 65 musicians including 12 winds, 7 percussion and 46 strings with no two performers playing the same part. It was written using a sound mass technique in which each player is responsible for completing glissandi at different pitch levels and times. The piece is dominated by the strings, which open the piece in unison before their split into 46 separate parts.

Where is the idea from?

Metastasis was inspired by the combination of an Einsteinian view of time and Xenakis' memory of the sounds of warfare, and structured on mathematical ideas by Le Corbusier. Music usually consists of a set of sounds ordered in time; music played backwards is hardly recognizable, as a listener does not perceive the music as existing backwards and forwards the way one can look at a building from different angles and have it appear to be still the same work. In warfare, as Xenakis knew it through his musical ear, no individual bullet being fired could be distinguished among the cacophony, but taken as a whole the sound of "gunfire" was clearly identifiable. The particular sequence of shots was unimportant: the individual guns could have fired in a completely different pattern from the way they actually did, but the sound produced would still have been the same. Einsteinian views show it as a function of matter and energy; change one of those quantities and time too is changed. Xenakis attempted to make this distinction in his music. While most traditional compositions depend on strictly measured time for the progress of the line, using an unvarying tempo, time signature, or phrase length, Metastasis changes intensity, register, and density of scoring, as the musical analogues of mass and energy.

Combine with Architecture

The architect Le Corbusier's influence and architectural work was prominently realized in "Metastasis" as the original plotting of the massed glissandi were done on the same graph paper that was used for plotting building structures. This reflects Xenakis' idea of a musical 'space-time', where pitch is represented on the y-axis and time on the x-axis. "A two-dimensional space is created where potentially time-independent musical structures can be contained in a temporal setting." He later used plotting of string glissandi in "Metastasis" as the curvature for the walls in the Philips Pavilion (constructed for the 1958 Brussels World Fair).

Reference

Wikipedia. Stachastic music. http://zh.wikipedia.org/w/index.php?title=%E9%A6%96%E9%A1%B5&variant=zh-tw

Grove music. Stachastic music. Grove entry

Iannis Xenakis.http://www.iannis-xenakis/org/english.htm

Music link (Metastasis):

http://www.uoguelph.ca/~digimus/xenakis/pages/fig5.html

Music example:

McCallum, Stephanie.Notations. track 20: Herma for solo piano.

Pleiades; Concertante, op. 79. track 4: Peaux for percussion