Keywords: formalisation, algebraic structures, music theory, tools for music analysis, compositional process, computational musicology

Abstract: The application of algebraic methods to music is a relatively new approach in musical research. We analyse the problem of the emergence of algebraic structures in music by looking at three main figures of Twentieth-Century theorists/composers: Milton Babbitt, Iannis Xenakis and Anatol Vieru. Some of their music-theoretic constructions are the starting point for a discussion on the notion of music theory in some analytical as well as compositional applications. This work discusses an algebraic formalisation of Set Theory and its transformational developments from a perspective which includes an analysis of the relationships between American tradition and a formalised European approach. The concepts elaborated in this work lead to a definition of the place of a computational approach in musicology and open several philosophical questions on the relationships between mathematics and music.

Laboratory: Music Representation Team, IRCAM/CNRS (U.M.R 9912)