On Mathematical Modelling of Time-Related Musical Structures

In this article, the first steps towards mathematical modelling of time-related musical structures are taken, and the algebraic structure of musical time relations is elaborated starting from a perceptive point of view. A basic characterization of fundamental properties of perceived time relations and their interpretations regarding musical context are given, and some mathematical properties of the proposed definitions are examined. Stemming from musical motivation, a category is found whose objects are finite strict (partially) ordered sets and whose morphisms are weakly monotone and reflect the strict order of the codomain. The category is found to have initial and terminal objects, equalizers, and coequalizers but fails to have binary products or coproducts.