A topological approach of musical relationships

Jean-Louis Giavitto 1, 2
1 MuTant - Synchronous Realtime Processing and Programming of Music Signals
Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, IRCAM, CNRS - Centre National de la Recherche Scientifique
2 Repmus - Représentations musicales
STMS - Sciences et Technologies de la Musique et du Son
Abstract : The notion of space is often summoned in music theory, both for the composition of new pieces or for the analysis of existing pieces. The spatial metaphor is instrumental to convey musical insights but it is also a very effective heuristics to develop new computer tools to assist musicians in their creative processes. This presentation explores some spatial representations of musical notions based on elementary concepts in algebraic topology: melodic and harmonic transformations, all-interval series classification or generation, style recognition... The basic idea is to represent simple musical objects (for example pitches, chords or intervals) by elementary spatial domains and their relationships (e.g., their co-occurrence or their succession) as neighborhood relationships. The topological notions of incidence, path, boundary, obstruction, etc., are then used to unravel the musical structure. For instance, a musical sequence can be represented as a path in a cellular complex materializing the chords structure and the look of the path reveals some information concerning the musical strategies used by the composer. Applying geometrical operations on trajectories leads to musical transformations of the initial piece. Etc. We attempt to explain the "Unreasonable Effectiveness” of spatial representations in Music by some profound connections between the organization of percepts and some topological relationships. In particular, we investigate the links between the topological approach sketched and the Formal Concept Analysis developed in symbolic learning.
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https://hal.archives-ouvertes.fr/hal-01257546
Contributeur : Jean-Louis Giavitto <>
Soumis le : dimanche 17 janvier 2016 - 17:13:58
Dernière modification le : vendredi 31 août 2018 - 09:18:09

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  • HAL Id : hal-01257546, version 1

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Jean-Louis Giavitto. A topological approach of musical relationships. Mathemusical Conversations, Feb 2015, Singapour, Singapore. 〈https://sites.google.com/site/mathemusicalconversations/〉. 〈hal-01257546〉

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