# Monte Carlo Methods For Tempo Tracking And Rhythm Quantization

## Ali Taylan Cemgil Bert Kappen

CEMGIL QS NN K UN N L
BERT Q S N N  K U N  N L
SNN, Geert Grooteplein 21 cpk1 - 231, University of Nijmegen NL 6525 EZ Nimegen, The Netherlands

## Abstract

We present a probabilistic generative model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note locations as in a musical ssss music recognition problems, namely tempo tracking and automatic transcription (rhythm quantization) as filtering and maximum a posteriori (MAP) state estimation tasks. Exact computation of posterior features such as the MAP state is intractable in this model class, so we introduce Monte Carlo methods for integration and optimization. We compare Markov Chain Monte Carlo (MCMC) methods (such as Gibbs sampling, simulated annealing and iterative improvement) and sequential Monte Carlo methods (particle filters). Our simulation results suggest better results with sequential methods. The methods can be applied in both online and batch scenarios such as tempo tracking and transcription and are thus potentially useful in a number of music applications such as adaptive automatic accompaniment, score typesetting and music information retrieval.

## 1. Introduction

Automatic music transcription refers to extraction of a human readable and interpretable description from a recording of a musical performance. Traditional music notation is such a description that lists the pitch levels (notes) and corresponding timestamps.

Ideally, one would like to recover a score directly from the audio signal.  Such a representation of the surface structure of music would be very useful in music information retrieval
(Music-IR) and content description of musical material in large audio databases. However, when operating on sampled audio data from polyphonic acoustical signals, extraction of a score-like description is a very challenging auditory scene analysis task (Vercoe, Gardner,
& Scheirer, 1998).

In this paper, we focus on a subproblem in music-ir, where we assume that exact timing information of notes is available, for example as a stream of MIDI 1 events from a digital ky board.

A model for tempo tracking and transcription from a MIDI-like music representation is useful in a broad spectrum of applications. One example is automatic score typesetting,