Mathematics and Music

Algebraic Models, Topologies, and Categories in Computational Musicology

The project "Modèles algébriques, topologiques et catégoriels en musicologie  computationnelle  (Algebraic Models, Topologies, and Categories in Computational Musicology)" was selected by the CNRS upon the creation of a director’s position in the Musical Representations team. This project follows the MISA project (Computer Modeling of Algebraic Structures in Music and Musicology), broadening the spectrum of mathematical tools for computational musicology (tools from algebra and also from topology and category theory). At the same time, this project attacks the theoretical and practical articulations between classical and popular music (rock, pop, jazz, song). Four institutions support the project: the Society for Mathematics and Computation in Music (an international society for which the MISA project was a federating force), the GDR ESARS (Esthétique, Art et Science), a collaboration with Sorbonne Universités’ IReMus (during international encounters held at the Centre de Recherche on popular music), and a partnership with université de Strasbourg (in particular with IRMA and Labex GREAM). This project also supports the Mamuphi seminar on mathematics, music, and philosophy organized in collaboration with the école normale supérieure and the book collections: Musique/Sciences (Delatour France) and Computational Music Sciences (Springer).

The spatial program aims to model problems such as movements in a specific space or the transformation of spatial structures. It provides computer tools that enable the development of analyses in line with Set Theory. This work has already made it possible to explore the pertinence of topological tools for the representation and classification of musical objects such as calculating all-interval series, Neo-Reimannian harmonic theory, and the geometric representation of chord progressions.

The result is an experimental environment to assist analysis of musical sequences called HexaChord.                                    
 HexaChord is an environment that makes it possible to build spatial representations associated with a group of chords and analyzes them via several topological notions. The spatial representations proposed include divers Tonnetz and simplical complexes corresponding to groups of chords’ pitches. The software offers 2D and 3D visualizations of the representations produced.

IRCAM's Teams: Music Representations team.

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