# 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.