We present a probabilistic generarive 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 score. The continuous hidden variables denote the tempo. We formulate two well known music recognition problems, namely tempo tracking and automatic transcription (rhythm quantization) as filtering and maximum a posteriori (MAP) state estimation tasks. Ex- act 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.

In this paper we introduce a probabilistic framework for matching different music representations (score, MIDI, audio) by incorporating models of how one musical representation might be rendered from another. We propose a dynamical hidden Markov model for the score pointer as a prior, and two observation models, the first based on matching spectrogram data to a trained template, the second detecting damped sinusoids within a frame of audio by subspace methods. The resulting Bayesian framework is robust to local variations in tempo, and can be used for a wide variety of applications. We evaluate both methods in a score alignment context by inferring the posterior distribution of the current position in the score exactly. The spectrogram method is shown to infer the score position reliably with minimal computation, and the damped sinusoid model is able to pinpoint the positions of score events in the audio with a high level of timing accuracy. 1