Maximum a posteriori estimation of piecewise arcs in tempo time-series

TL;DR

This paper introduces a probabilistic model and an efficient inference method for estimating piecewise tempo arcs in expressive musical performances, enabling real-time analysis and prediction of tempo variations.

Contribution

It presents a novel probabilistic framework and a Viterbi-like inference algorithm for modeling and estimating tempo arcs in musical performances.

Findings

Efficient Viterbi-like MAP inference algorithm for tempo arcs

Score-agnostic and suitable for online performance analysis

Ability to predict immediate future tempo trajectories

Abstract

In musical performances with expressive tempo modulation, the tempo variation can be modelled as a sequence of tempo arcs. Previous authors have used this idea to estimate series of piecewise arc segments from data. In this paper we describe a probabilistic model for a time-series process of this nature, and use this to perform inference of single- and multi-level arc processes from data. We describe an efficient Viterbi-like process for MAP inference of arcs. Our approach is score-agnostic, and together with efficient inference allows for online analysis of performances including improvisations, and can predict immediate future tempo trajectories.