Ensemble

Art

Math and Science

Technology

Ensemble (Stockhausen)

Ensemble is a group-composition project devised by Karlheinz Stockhausen for the 1967 Darmstädter Ferienkurse. Twelve composers and twelve instrumentalists participated, and the resulting performance lasted four hours. It is not assigned a work number in Stockhausen's catalogue of works.

History

For the 1967 Darmstädter Ferienkurse Stockhausen organised a composition seminar during the two-week period preceding the courses proper, in which twelve composers from various countries each developed a composition which was a dialogue to be performed by an instrumentalist and the composer, using either a previously prepared tape of sound materials or a short-wave receiver (Gehlhaar 1968, 9, 45). This was the first time in the history of the Darmstadt Courses that actual composing was formally undertaken within the framework of the courses themselves (Iddon 2004, 87).

The participating composers were paired with the instrumentalists (eleven members of the Ensemble Hudba Dneska (Bratislava), directed by Ladislav Kupkovič, plus Aloys Kontarsky (Stockhausen 1971, 213; Gehlhaar 1968, 7, 39, 43, 75:

Statistical ensemble (mathematical physics)

In mathematical physics, especially as introduced into statistical mechanics and thermodynamics by J. Willard Gibbs in 1902, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in. In other words, a statistical ensemble is a probability distribution for the state of the system.

A thermodynamic ensemble is a specific variety of statistical ensemble that, among other properties, is in statistical equilibrium (defined below), and is used to derive the properties of thermodynamic systems from the laws of classical or quantum mechanics.

This article treats the notion of ensembles in a mathematically rigorous fashion, although relevant physical aspects will be mentioned.

Physical considerations

The ensemble formalises the notion that an experimenter repeating an experiment again and again under the same macroscopic conditions, but unable to control the microscopic details, may expect to observe a range of different outcomes.