We propose a novel method to model hierarchical metrical structures for both symbolic music and audio signals in a self-supervised manner with minimal domain knowledge. The model trains and inferences on beat-aligned music signals and predicts an 8-layer hierarchical metrical tree from beat, measure to the section level. The training procedure does not require any hierarchical metrical labeling except for beats, purely relying on the nature of metrical regularity and inter-voice consistency as inductive biases. We show in experiments that the method achieves comparable performance with supervised baselines on multiple metrical structure analysis tasks on both symbolic music and audio signals. All demos, source code and pre-trained models are publicly available on GitHub.

It models the structure as an automata and derives its complexity. It also solves the complexity for the L-system. This complexity can resolve the similarity between trees. This complexity serves as a measure of psychological complexity for rhythms.

We have attempted to discover formal rules for transcribing into musical notation the fugue subjects of the Well-Tempered Clavier, as this might be done by an amanuensis listening to a'deadpan' performance on the keyboard. In this endeavour two kinds of problem arise: what are the harmonic relations between the notes, and what are the metrical units into which they are grouped? The harmonic problem is that the number of keyboard semitones between two notes does not define-- their harmonic relation, and we further develop an earlier theory of such relations, arriving at an algorithm which assigns every fugue to the right key and correctly notates every accidental in its subject.