A new algorithmic model and simulation of neighboring variants for Désordre, György Ligeti’s first étude for piano

This article discusses a new algorithmic model of Désordre, György Ligeti's first étude for piano. The model is able to accurately reconstruct the original score and automatically simulate neighboring variants. The algorithm is deterministic, that is, each set of parameter values corresponds to one and only one result. The basic strategies used to model the highly entropic aspects of the composition were the formulation of primitive versions of the secondary voices and the decomposition of rhythmic patterns at independent subjacent and explicit levels. The first parameter controls the pitch- set used by the right hand and by way of its left-hand complement. The NSP parameter (the nth sum of different primes) determines the basic rhythmic relationships and ensures the asymmetry of rhythmic patterns. Computer simulations are further controlled by specifying units of time and pitch allowing for other, uncommonly used temperaments and divisions of the whole note. Several neighboring variants of the original piece are discussed, such as simulations of octatonic, whole-tone and chromatic scales being used as a pitch-set of one of the pianist's hands. The piece was also simulated using other asymmetrical rhythmic relationships, as well as a temperament based on quarter-tones.