Building Topological Spaces for Musical Objects

Louis Bigo (1) , Jean-Louis Giavitto (1) , Antoine Spicher (1)

1 Repmus - Représentations musicales

The development of spatial representations of musical ob- jects allows for a reformulation of algorithmic problems arising in musi- cal theory, fosters novel classifications and provides new computational tools. In this paper, we show how a topological representation for n-note chords associated with the degrees of the diatonic scale and for the All- Interval Series (AIS) can be automatically built using MGS, a rule-based spatial programming language. Then, we suggest a new categorization for AIS based on their spatial construction.

Mots clés: Spatial computing; algebraic topology; All-Interval Series; n-chords and diatonic scale; self-assembly; n-Hamiltonian path

Mots clés: Informatique musicale

Domaines: Langage de programmation [cs.PL]; Son [cs.SD]; Traitement du signal et de l'image [eess.SP]; Machine Learning [stat.ML]; Intelligence artificielle [cs.AI]; Théorie et langage formel [cs.FL]; Musique, musicologie et arts de la scène

Louis Bigo, Jean-Louis Giavitto, Antoine Spicher. Building Topological Spaces for Musical Objects. Mathematics and Computation in Music, Jun 2011, Paris, France. pp.1-1. ⟨hal-01161290⟩