Filtration of Pitch-Class Sets Complexes
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.
KeywordsPitch-class sets Harmonic similarity Simplicial complexes Pitch-class set complexes Filtration Persistent homology
We would like to thank friends and colleagues for fruitful discussions and careful proofreading including Mattia Bergomi, Paul Ladyman, members of the spatial computing project and the Algomus team. We also thank Antoine Lafrance for his contribution on the online visualization application.
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