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Pithoprakta

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Title: Pithoprakta  
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Subject: Aleatoric music, Iannis Xenakis, 1956 in music, 1955 in music, Stochastic, Sound mass, Metastaseis (Xenakis), Indeterminacy (music), Metastaseis and Pithoprakta
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Pithoprakta

Pithoprakta (1956) is a piece by Iannis Xenakis for 46 string instruments, two trombones, xylophone, and woodblock. Premiered by conductor Hermann Scherchen in Munich on March 1957, the piece was made into a ballet by George Balanchine, Metastaseis and Pithoprakta, along with the earlier Metastaseis.

The title translates as "actions through probability",[1] and 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]

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 = one 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 ("a situation impossible in [the] reality [of the model]").[4] Each part gets nowhere,[4] but as a whole the mass's pitch is freely modulated and its speed determined "temperature" varies.[3]

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