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Pithoprakta (1955–56) is a piece by Iannis Xenakis for two trombones, 46 string instruments, xylophone, and woodblock, premièred by conductor Hermann Scherchen in Munich on March 1957.

The title translates as "actions through probability".[1] In the case of "Pithoprakta," this relates to Jacob Bernoulli's law of large numbers which states that as the number of occurrences of a chance event increases, the more the average outcome approaches a determinate end. The piece is based on the statistical mechanics of gases,[2] Gauss's law,[3] or Brownian motion.[4] Each instrument is conceived as a molecule obeying the Maxwell–Boltzmann distribution law,[5] with Gaussian distribution of temperature fluctuation.[3] This theory states that "the temperature of a gas derives from the independent movement of its molecules." Xenakis drew an analogy between the movement of a gas molecule through space and that of a string instrument through its pitch range. To construct the seething movement of the piece, he governed the 'molecules' according to a coherent sequence of imaginary temperatures and pressures. Brownian motion is a four-dimensional phenomenon (three-dimensions and time), and Xenakis created the score by first creating a two-dimensional graph, necessitating some simplifications.[4] The abscissa (x) represents time at 5 cm = 26 MM, while the ordinates (y) represent pitch at 1 semitone = .25 cm.[3] When transcribed into musical notation 5 cm = 1 measure.[4] This length is subdivided into three, four, and five equal parts, allowing for fine differences in duration,[3] but also creating a steady pulse in each instrument part, reducing the rhythm of the random walk to steady footsteps; composer Simon Emmerson notes that this regularity is "impossible in reality and fails to use his ‘stochastic’ approach in this instance."[4] Each part gets nowhere, but as a whole the mass's pitch is freely modulated and its speed determined "temperature" varies.[3]

This piece was made into a ballet by George Balanchine, Metastaseis and Pithoprakta, along with the earlier Metastaseis.


  1. ^ Harley, James (2004). Xenakis: His Life in Music, p.13. Routledge. ISBN 0-415-97145-4.
  2. ^ Ilias Chrissochoidis, Stavros Houliaras, and Christos Mitsakis, "Set theory in Xenakis' EONTA", in International Symposium Iannis Xenakis, ed. Anastasia Georgaki and Makis Solomos (Athens: The National and Kapodistrian University, 2005), 241–249.
  3. ^ a b c d e Xenakis, Iannis (1992). Formalized Music: Thought and Mathematics in Composition, p.15. ISBN 9781576470794.
  4. ^ a b c d Emmerson, Simon (2007). Living Electronic Music, p.48. ISBN 9780754655480.
  5. ^ Randel, Don Michael (1996). The Harvard Biographical Dictionary of Music, p.999. ISBN 9780674372993.