Abstract
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.
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Bigo, L., Andreatta, M., Giavitto, JL., Michel, O., Spicher, A. (2013). Computation and Visualization of Musical Structures in Chord-Based Simplicial Complexes. In: Yust, J., Wild, J., Burgoyne, J.A. (eds) Mathematics and Computation in Music. MCM 2013. Lecture Notes in Computer Science(), vol 7937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39357-0_3
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DOI: https://doi.org/10.1007/978-3-642-39357-0_3
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