Identifying Metrical and Temporal Structure With an Autocorrelation Phase Matrix

Abstract

This article introduces a new method for detecting long-timescale structure in music. We describe a way to compute autocorrelation such that the distribution of energy in phase space is preserved in a matrix. The resulting Autocorrelation Phase Matrix (APM) is useful for several tasks involving metrical structure. In this article we describe the details of calculating the APM. We then show how phase-related regularities from music are stored in the APM and present two ways to recover these regularities. The simpler approach uses variance or entropy calculated on the distribution of information in the APM. The more complex approach explicitly searches through the phase and lag space of the APM to predict meter and tempo in parallel. We compare these approaches against standard autocorrelation for the task of tempo prediction on a relatively large database of annotated digital audio files. We demonstrate that better tempo prediction is achieved by exploiting the phase-related information in the APM.We argue that the APM is an effective data structure for tempo prediction and related applications, such as real-time beat induction and music analysis.