8+8=4: Formalizing Time Units to Handle Symbolic Music Durations

This paper focuses on the nominal durations of musical events (notes and rests) in a symbolic musical score, and on how to conveniently handle these in computer applications. We propose the usage of a temporal unit that is directly related to the graphical symbols in musical scores and pair this with a set of operations that cover typical computations in music applications. We formalize this time unit and the more commonly used approach in a single mathematical framework, as semirings, algebraic structures that enable an abstract description of algorithms/processing pipelines. We then discuss some practical use cases and highlight when our system can improve such pipelines by making them more efficient in terms of data type used and the number of computations.