Notations as Models: Music and Mathematics

Abstract In this paper we argue for a surprising similarity between the kinds of roles notation plays in music and in mathematics. We argue that in both cases the notation is doing more than merely documenting something that we have an independent grip on – either a musical performance/composition or a mathematical structure. In both instances, the notation can lead to new innovations, it can help in abstracting away from distracting details and it can facilitate explanations. In light of these functions, we argue that both musical and mathematical notations serve as models of the intended targets: musical and mathematical structures. Seen in this light, developing, and reflecting upon, notation is central to both musical and mathematical practice and is deserving of greater philosophical attention.