From Music to Mathematics and backwards: introducing algebra, topology and category theory into computational musicology
In this presentation, I will provide an overview of the most active research axes of the SMIR Project I'm leading at the University of Strasbourg. This Project, devoted to Structural Music Information Research (SMIR), is hosted by IRMA (Institut de recherche mathématique avancée) and is carried out in collaboration with computer science researchers from IRCAM Music Representation Team and music-theorists and musicologists from CREAA (Centre de recherche et d’expérimentation sur l’acte artistique) of the University of Strasbourg. Ongoing research axes include Mathematical Morphology, Formal Concept Analysis and computational music analysis; Generalized Tonnetze, Persistent Homology and automatic classification of musical styles; Category theory and transformational music analysis; Tiling musical problems, Homometry and Fuglede Spectral Conjecture. After discussing the "mathemusical" dynamics underlying the SMIR project, I will offer several music-theoretical examples showing how to approach interesting mathematical problems starting from music representations and computer-aided modelling. I will end by shortly discussing some very recent research directions in music cognition we are currently exploring within a subproject entitled ProAppMaMu (Processes and Learning Techniques of Mathemusical Knowledge) which makes use of a web Tonnetz environment we have developed within the SMIR Project and we are adapting to interactive perceptual tasks.