On Xenakis’s Games of Musical Strategy

Abstract

In this article, Xenakis's trilogy of pieces based on zero-sum games is investigated, revealing axiomatic inconsistencies between game-theoretical models and their musical translations implemented according to the aesthetic preferences of the composer. The problematic elements regard 1) the formal definition of the games and 2) the limits of objective utility functions in the music domain. After introducing these games of musical strategy and the few existing practical implementations found in the literature, a detailed comparison between the mathematical models and Xenakis's renditions is presented to highlight their divergence. Then, the feasibility from a musical perspective of the rational decision-making required by the models is explored through a computational simulation of game dynamics using Reinforcement Learning. Lastly, the article concludes by contextualising the findings to the increasingly ubiquitous role of the machine in the creative processes of musical composition and generation. In doing so, Xenakis's original works offer themselves as a springboard for (re-)imagining and developing novel approaches integrating human-machine decision processes with musical design and interaction.