From Music to Mathematics and Backwards: Introducing Algebra, Topology and Category Theory into Computational Musicology

Moreno Andreatta
CRNS Director of research on mathematics and music at IRMA – Institut de Recherche Mathématique Avancée, University of Strasbourg / IRCAM – Institute for Research and Coordination in Acoustics/Music, Paris, France

This lecture will provide an overview of the most active research axes of the SMIR Project at the University of Strasbourg (led by leader Moreno Andreatta). 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 musicologists of GREAM (Groupe de recherche expérimentale sur l’acte musical) and computer science researchers from the IRCAM Music Representation Team. 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, Moreno Andreatta will offer several music-theoretical examples showing how to approach interesting mathematical problems starting from music representations and computer-aided modelling. The focus will be in particular on some computational models of harmonic spaces that have been implemented in the web environment The Tonnetz, which enables an interactive exploration of a panoply of geometric spaces for music-theoretical, analytical and compositional purposes. Furthermore, a current research project supported by CNRS which constitutes the cognitive component of the SMIR project will be presented. This project – entitled ProAppMaMu (Processes and Learning Techniques of Mathemusical Knowledge) – aims to investigate the link between geometric representations and cognitive neurosciences by following some previous work by researchers in neurosciences and experimental psychology and by focusing on the interplay between structural mathematics and computational models.

Moreno Andreatta holds diplomas in mathematics (University of Pavia, IT), piano performance (Conservatory of Novara, IT) and computational musicology (IRCAM/EHESS, FR). He is currently the principal investigator of the SMIR Project devoted to Structural Music Information Research, which aims to investigate the power of algebraic, topological and categorical formalization in the field of computational musicology. Moreno Andreatta is a founding member of the Journal of Mathematics and Music (Taylor & Francis).

Dieser Vortrag findet im Rahmen der neuen Reihe Musik & Mathematik statt, die sich sich mit den interdisziplinären Ansätzen und Perspektiven zwischen Musik und Mathematik beschäftigt . Die Durchführung und Gestaltung erfolgt gemeinsam mit internationalen Expertinnen und Experten aus den Bereichen Mathematik, Statistik, Computerwissenschaften, Komposition und Musikforschung und eröffnet Einblicke in die aktuellen Forschungen und Entwicklungen in den Grenzbereichen zwischen den Wissenschaftssparten. Die jeweiligen Vorträge sind auch Teil einer disziplinübergreifenden Lehrveranstaltung, in der an den Schnittstellen der Disziplinen jeweils Themen aus dem Forschungsumfeld der eingeladenen Vortragenden diskutiert werden.

Idee und Leitung Reihe „Musik & Mathematik“:

• Arne Bathke (Statistiker, Data Scientist, Leiter PB (Inter)Mediation | FB Mathematik & SciTecHub Itzling, Universität Salzburg)
• Katarzyna Grebosz-Haring (Systematische Musikwissenschafterin| Department Musikpädagogik, PB (Inter)Mediation | Mozarteum Salzburg)
• Martin Losert (Musikpädagoge, Saxophonist, Leiter Department Musikpädagogik, Leiter PB (Inter)Mediation | Mozarteum Salzburg)

Eine Zusammenarbeit von (Inter)Mediation mit dem Fachbereich Mathematik der Universität Salzburg

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