Prime Decomposition Encoding: An Analytical Tool by the Use of Arithmetic Mapping of Drum-Set Timelines
Carlos Mathias, Carlos de Lemos Almada · MusMat Brazilian Journal of Music and Mathematics · 2021
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.