Mathematical Models for Binarization and Ternarization of Musical Rhythm

Francisco Gómez, Imad Khoury, Jörg Kienzle, Erin McLeish, Andrew Melvin, Rolando Pérez-Fernández, David Rappaport and Godfried Toussaint
Bridges Donostia: Mathematics, Music, Art, Architecture, Culture (2007)
Pages 99–108


The process of mapping a ternary rhythm of, say 12 pulses, to a binary rhythm of 16 pulses, such that musicologically salient properties are preserved is termed binarization. By analogy the converse process of mapping a binary rhythm to a ternary rhythm is referred to as ternarization. New algorithms based on geometric proximity rules are proposed and investigated for the binarization and ternarization of musical rhythms with the goal of understanding the historical evolution of traditional rhythms through inter-cultural contacts.