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A Topological Approach of Musical Relationships


The notion of space is often summoned in music theory, both for the analysis of existing pieces and for the composition of new ones. The use of space as a metaphor is instrumental in conveying musical insights but it is also a very effective heuristic for developing new computer tools to assist musicians in their creative processes. This chapter offers some applications of spatial representations of musical notions based on elementary concepts in algebraic topology: the representation by cell spaces of the melodic and harmonic content for the classification or the generation of musical phrases. The basic idea is to represent classes of simple musical objects (e.g., pitches, chords or intervals) as elementary spatial domains and to represent 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 cell space that represents the chord structure; the form of that path reveals some information concerning the musical strategies used by the composer.
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hal-01377659 , version 1 (07-10-2016)


  • HAL Id : hal-01377659 , version 1


Jean-Louis Giavitto, Antoine Spicher. A Topological Approach of Musical Relationships. Jordan B L Smith (National Institute for Advanced Industrial Research and Technology (AIST) Japan); Elaine Chew (Queen Mary University of London, UK); Gérard Assayag (IRCAM - UMPC - CNRS, Science and Technology of Music and Sound Lab, France). Mathemusical Conversations - Mathematics and Computation in Music Performance and Composition, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore (32), World Scientific, pp.283--298, 2016, 978-981-3140-09-7. ⟨hal-01377659⟩
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