Quantization revisited: a mathematical and computational model
Declan Murphy · Journal of Mathematics and Music · 2011
A nascent theory of near division is presented, from which an efficient quantization algorithm for rhythm intervals is derived. Based on a number theoretic analysis of the uniqueness and convergence of this first algorithm, a generalized 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.