Filtration of pitch-class sets complexes. (English) Zbl 1456.00060

Bigo, Louis; Andreatta, Moreno

Montiel, Mariana (ed.) et al., Mathematics and computation in music. 7th international conference, MCM 2019, Madrid, Spain, June 18–21, 2019, Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11502, 213-226 (2019).

Summary: A pitch-class set complex is a multidimensional object that spatially represents a collection of pitch-class sets and the intersections between them. If we consider the pitch classes within short time slices a piece can be divided into, we can evaluate for how long some combinations of pitch-classes sound simultaneously and then filter the piece according to the most relevant ones. This filtration process is performed by considering the superlevel sets of the function that computes the cumulative duration of pitch-class sets during the piece. Experiments show that musical sequences in the same style can exhibit similar sub-complexes in the filtration of their pitch-class set complexes. Filtered pitch-class set complexes also provide original informations on the use of the tonality and on the notion of centricity within a piece.
For the entire collection see [Zbl 1425.00082].

MSC:

00A65

Mathematics and music

Keywords:

pitch-class sets; harmonic similarity; simplicial complexes; pitch-class set complexes; filtration; persistent homology

Software:

HexaChord

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