Constructing geometrical spaces from acoustical representations

Özgür İzmirli

pp. 245-256

in: Tom Collins, David Mérédith, Anja Volk (eds), Mathematics and computation in music, Berlin, Springer, 2015

Abstract

This paper presents several models for constructing geometrical spaces from acoustical representations. Through specific spectral representations and associated distance measures each model is designed to highlight or ignore certain types of relationships within the given pitch sets. Dimensionality reduction is employed to obtain low dimensional embeddings from spectral representations. The viability of these models is demonstrated for the resulting low dimensional embeddings with respect to a number of group actions including octave shifts, permutation, transposition and inversion.