We represent chord collections by simplicial complexes. A temporal organization of the chords corresponds to a path in the complex. A set of n-note chords equivalent up to transposition and inversion is represented by a complex related by its 1-skeleton to a generalized Tonnetz. Complexes are computed with MGS, a spatial computing language, and analyzed and visualized in Hexachord, a computer-aided music analysis environment. We introduce the notion of compliance, a measure of the ability of a chord-based simplicial complex to represent a musical object compactly. Some examples illustrate the use of this notion to characterize musical pieces and styles. © 2013 Springer-Verlag.
CITATION STYLE
Bigo, L., Andreatta, M., Giavitto, J. L., Michel, O., & Spicher, A. (2013). Computation and visualization of musical structures in chord-based simplicial complexes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7937 LNAI, pp. 38–51). https://doi.org/10.1007/978-3-642-39357-0_3
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