A Musicological Introduction to “Mathemusical” Research: Theoretical Aspects and Epistemological Challenges
This article presents certain theoretical aspects and discusses some epistemological challenges of the author’s research into the links between mathematics and music. After a general introduction on the context of “mathemusical” research at Ircam and the place of the misa project (Computer Modeling of Algebraic Structures in Music and Musicology) in the research activities of the Musical Representations team, we discuss the problem of algebraic formalization in set theory and transformational theory, two analytic paradigms whose theoretical and computational aspects we have studied in the process of constructing an abstract model of musical structures and processes. Musical analysis based on the theory of sets and their transformations raises interesting philosophical questions, notably in their relationships with phenomenology and the cognitive sciences. In particular, relating our musicological perspective with phenomenology, we advance the idea of “phenomenological structuralism” in a reinterpretation of the structural tradition in musical analysis.