Quantisation revisited: a mathematical and computational model

Source: https://www.maths.tcd.ie/report_series/abstracts/tcdm1110.html Parent: https://www.maths.tcd.ie/research/papers/

A nascent theory of near division is presented, from which an efficient quantisation algorithm for rhythm intervals is derived. Based on a number theoretic analysis of the uniqueness and convergence of this first algorithm, a generalised algorithm is presented. An empirical study of the algorithm's performance reveals a readily computable criterion within which the perceived ratio may reliably be produced on real performance data. Distribution properties are shown to be reasonable for computation.