Caracterização musical via espectro de grafos

Abstract

This work intends to characterize songs in a consistent way, using graphs and the spectrum of their respective Laplacian matrices. The graphs that represent songs are completely determined by these matrices. The use of eigenvalues of Laplacian matrices to index graphs, and consequently songs, is a recurrent approach in the literature. We also propose the use of the eigenvectors of such matrices for the representation of songs. Eigenvectors express the relationships between notes in music and therefore contain relevant information. We project the eigenvectors onto 12 vectors of R2, which represent the 12 musical notes. From these projections, we make a polygon whose shape reflects the song’s characteristics.