Prime Decomposition Encoding: An Analytical Tool by the Use of Arithmetic Mapping of Drum-Set Timelines

Abstract

This paper introduces an original proposal intended to encode timelines as univocal integers, by the use of arithmetic mapping, exploring inherent properties of prime numbers. A group of algorithms were developed in order to encode drum-set timelines (as well as to retrieve the original rhythms from the codes), either individually or taken together, forming grooves. Additional parameters (dynamic levels and timbre) are also included in the encoding process. Geometrical representation of the grooves, adopting terminology and methodology proposed by Gottfried Toussaint [19], is also provided. Some practical application, addressing analysis and composition, are suggested at the last section of the study.

Music and Mathematics in Latin America: Major Developments in the Last 25 Years

“…1 relies on building mathematical structures for rhythmic representation and the use of these very structures on computational generation of rhythms. Recent efforts on the latter approach have been recently made in partnership with Carlos Almada, with whom Mathias recently wrote an article proposing an encoding system for drum set's rhythms based on Gödel numbering [104].…”