''Pithoprakta'' (1955–56) is a piece by

Iannis Xenakis Giannis Klearchou Xenakis (also spelled for professional purposes as Yannis or Iannis Xenakis; el, Γιάννης "Ιωάννης" Κλέαρχου Ξενάκης, ; 29 May 1922 – 4 February 2001) was a Romanian-born Greek-French avant-garde c ...

for string orchestra (with 46 separate solo parts), two

trombone The trombone (german: Posaune, Italian, French: ''trombone'') is a musical instrument in the brass family. As with all brass instruments, sound is produced when the player's vibrating lips cause the air column inside the instrument to vibrate ...

xylophone The xylophone (; ) is a musical instrument in the percussion family that consists of wooden bars struck by mallets. Like the glockenspiel (which uses metal bars), the xylophone essentially consists of a set of tuned wooden keys arranged in ...

, and wood block, premièred by conductor Hermann Scherchen in Munich in March 1957. A typical performance of the piece lasts about 10 minutes. The word ''Pithoprakta'' translates to "actions through probability". This relates to

Jacob Bernoulli Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Le ...

's law of large numbers which states that as the number of occurrences of a chance event increases, the average outcome approaches a determinate end. The piece is based on the statistical mechanics of gases,

Gauss's law In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it sta ...

,Xenakis, Iannis (1992). ''Formalized Music: Thought and Mathematics in Composition'', p.15. . or

Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position insi ...

.Emmerson, Simon (2007). ''Living Electronic Music'', p.48. . Each instrument is conceived as a molecule obeying the Maxwell–Boltzmann distribution law,Randel, Don Michael (1996). ''The Harvard Biographical Dictionary of Music'', p.999. . with Gaussian distribution of temperature fluctuation. 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 spatial dimensions and time), and Xenakis created the score by first creating a two-dimensional graph, necessitating some simplifications. The

abscissa In common usage, the abscissa refers to the (''x'') coordinate and the ordinate refers to the (''y'') coordinate of a standard two-dimensional graph. The distance of a point from the y-axis, scaled with the x-axis, is called abscissa or x coo ...

() represents time at 5 cm = 26 MM, while the

ordinate In common usage, the abscissa refers to the (''x'') coordinate and the ordinate refers to the (''y'') coordinate of a standard two-dimensional graph. The distance of a point from the y-axis, scaled with the x-axis, is called abscissa or x c ...

s () represent pitch at 1

semitone A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent no ...

= .25 cm, when transcribed into musical notation 5 cm = 1 measure. This length is subdivided into three, four, and five equal parts, allowing for fine differences in duration but also creating a steady pulse in each instrumental part, reducing the rhythm of the random walk to steady footsteps. Composer

Simon Emmerson Simon Emmerson (born 12 February 1956) is an English record producer, guitarist, DJ, musical director at Lush, and founder of the group Afro Celt Sound System. He is also the main organiser of The Imagined Village, a collaborative work from ...

notes that this regularity is "impossible in reality and fails to use his ‘ stochastic’ approach in this instance." Each part gets nowhere, but as a whole the mass's pitch is freely modulated and its speed-determined "temperature" varies. This piece was made into a ballet by George Balanchine, ''

Metastaseis and Pithoprakta ''Metastaseis and Pithoprakta'' is a ballet by New York City Ballet co-founder and ballet master George Balanchine to two orchestral works by Iannis Xenakis: ''Metastaseis (Xenakis), Metastaseis'', written 1953–54, and ''Pithoprakta'', written 1 ...

'', along with the earlier '' Metastaseis''.

References

Sources

Compositions by Iannis Xenakis 1956 compositions Modernist compositions {{composition-stub