Quasimusic: tilings and metre

Abstract

In this paper, I try to explain how, by using concepts and ideas from the mathematical theory of tilings, we can approach metre in music through a geometric and algebraic point of view, being pinned down by a subgroup of with the hierarchical structure, leading to an abstract approach to rhythm, tempo and time signatures. I will also describe an algorithmic approach to write down sound using this structure which gives a way in which music can be written in an irrational metre.