Monument und Monopoly. György Ligetis erstes Stück für zwei Klaviere und Spieltheorie

Abstract

Motivated by the exchange of ideas with the biologist and chaos researcher Manfred Eigen and Douglas R. Hofstadter’s Gödel, Escher, Bach (1979), György Ligeti’s later compositions refer explicitly to mathematical phenomena (e.g., in the Piano Etudes since 1985). Ligeti himself recognized scientific models also in his works that were composed before this period. One of the significant pieces during the transition to his late works is Monument (the first movement of the Three Pieces for two Pianos from 1976) which points clearly in the direction of the late compositional style. Monument does not follow rigid mathematical rules, but rather a flexible set of game rules. A simple starting point and a clear goal cause continuously ramifying rules. Their complexity forces the composer to exert a maximum of control over the conception and the compositional process. Monument starts with six layers of tones, played in different dynamics, different cycles of varying durations and different “instrumentations”, i. e., the distribution of pitches over the octaves. Several processes like lowering the notes and dynamics, diminishing the duration cycles and changing the “instrumentation” interact with ideas of game-like fluctuations, ramifications and the aesthetic idea of wellformedness. There are several points during the course of the composition where the composer has to decide how he wants to change the rules. Whereas the over-all formal plan obviously was conceived graphically or spatially (thus being connected to Ligeti’s synaesthesia), the developmental character of the music stands somewhere between architectonic form and process form. This article develops an analysis in relation to game theory that tries to synchronize the conception with the creative process as far as it can be reconstructed from the score. Even though at first glance Ligeti’s compositional method seems to be axiomatic and mathematic, it contains many playful elements including “trial and error”. “I do not have a computer, not even a pocket calculator”, was one of his catch phrases – another one, as a consequence: “I always had to start anew because it didn’t work.” This way of working with game-like rules is significant and shows that Ligeti’s music cannot be thoroughly understood in the tradition of serial or process-like music; an important connection leads to Béla Bartók whose conceptions often lead in similar directions.