Eigentriads and Eigenprogressions on the Tonnetz

TL;DR

The paper introduces the eigenprogression transform, a deep, multiscale, convolutional representation for Western tonal harmony that is invariant to time shifts and pitch transpositions, achieving state-of-the-art results in composer recognition.

Contribution

It presents a novel multidimensional transform combining spectral graph theory and wavelet methods, without requiring prior training, for music information retrieval tasks.

Findings

Achieved state-of-the-art accuracy in composer recognition.

Demonstrated invariance to time shifts and pitch transpositions.

Provided a new framework for analyzing Western tonal harmony.

Abstract

We introduce a new multidimensional representation, named eigenprogression transform, that characterizes some essential patterns of Western tonal harmony while being equivariant to time shifts and pitch transpositions. This representation is deep, multiscale, and convolutional in the piano-roll domain, yet incurs no prior training, and is thus suited to both supervised and unsupervised MIR tasks. The eigenprogression transform combines ideas from the spiral scattering transform, spectral graph theory, and wavelet shrinkage denoising. We report state-of-the-art results on a task of supervised composer recognition (Haydn vs. Mozart) from polyphonic music pieces in MIDI format.