Iterative method of construction of good rhythms

TL;DR

This paper introduces an iterative method to transform any rhythm into a maximally even rhythm, demonstrating convergence through a self-map on the space of rhythms with fixed onsets.

Contribution

It presents a novel iterative approach using a self-map to systematically construct maximally even rhythms from arbitrary initial rhythms.

Findings

Any rhythm converges to a maximally even rhythm after finite iterations

The method applies to rhythms of any length with fixed onsets

Provides a new mathematical framework for rhythm optimization

Abstract

On the space of rhythms of arbitrary length with a fixed number of onsets, a self map $F$ is constructed. It is shown that for any rhythm $\mathbf{r}$ of the space there exists a nonnegative integer $k$ such that $F^k(\mathbf{r})$ falls into the category of "maximally even rhythms" investigated in [1].