From music to mathematics and backwards: introducing algebra, topology and category theory into computational musicology

International audienceDespite a long historical relationship between mathematics and music, the interest of mathematicians is a recent phenomenon. In contrast to statistical methods and signal-based approaches currently employed in MIR (Music Information Research), the research project described in this paper stresses the necessity of introducing a structural multidisciplinary approach into computational musicology making use of advanced mathematics. It is based on the interplay between three main mathematical disciplines: algebra, topology and category theory. It therefore opens promising perspectives on important prevailing challenges, such as the automatic classification of musical styles or the solution of open mathematical conjectures, asking for new collaborations between mathematicians, computer scientists, musicologists, and composers. Music can in fact occupy a strategic place in the development of mathematics since music-theoretical constructions can be used to solve open mathematical problems. The SMIR project also differs from traditional applications of mathematics to music in aiming to build bridges between different musical genres, ranging from contemporary art music to popular music, including rock, pop, jazz and chanson. Beyond its academic ambition, the project carries an important societal dimension stressing the cultural component of 'mathemusical' research, that naturally resonates with the underlying philosophy of the “Imagine Maths”conference series. The article describes for a general public some of the most promising interdisciplinary research lines of this project

The Tonnetz Environment: A Web Platform for Computer-aided “Mathemusical” Learning and Research (versión preprint)

We describe the Tonnetz web environment and some of the possible applications we have developed within a pedagogical workshop on mathematics and music that has been conceived for high-school students. This web environment makes use of two geometrical representations that constitute intuitive ways of accessing some theoretical concepts underlying the equal tempered system and their possible mathematical formalizations. The environment is aimed at enhancing “mathemusical” learning processes by enabling the user to interactively manipulate these representations. Finally, we show how Tonnetz is currently being adapted in order to lead computer-based experiences in music perception and cognition that will be mainly carried at universities. These experiences will explore the way in which geometrical models could be implicitly encoded during the listening process. Their outcome may reinforce educational strategies for learning mathematics through music

Spatial Transformations in Simplicial Chord Spaces

cote interne IRCAM: Bigo14bInternational audienceIn this article, we present a set of musical transformations based on chord spaces representations derived from the Tonnetz. These chord spaces are formalized as simplicial complexes. A piece is represented in such a space by a trajectory. Spatial transformations are applied on these trajectories and induce a transformation of the original piece. These concepts are implemented in two applications, the software HexaChord and the Max object bach.tonnetz, respectively dedicated to music analysis and composition