Automatic music transcription is a unique problem to which Monte Carlo methods can be applied. It is sometimes desirable to extract human-readable music scores from a performance by musicians, but it is not a simple task. The basic difficulties of extracting the information are, perhaps, somewhat obvious, but there also lie more subtle issues. For example, music is usually performed in such a manner that the tempo is not constant throughout the piece. Even more troublesome are the instances where only one or two notes are drawn out for musical impact.

This process of extracting all this information starts with a probabilistic model for timing deviations and uses tempo tracking algorithms for quantization. Then, the Monte Carlo methods are used to approximate the probabilities of note placement. The paper cited followed a Bayesian modeling approach for the tempo tracking and transcription. This paper then goes on to specifically explore the Markov Chain Monte Carlo (MCMC) and the sequential Monte Carlo (SMC) methods using both fake data and real data. It was found that the SMC method outperformed the MCMC method in terms of the quality of the results. This is reasonable, as SMC is well suited for applications in which observations arrive sequentially.

Monte Carlo Methods for Tempo Tracking
and Rhythm Quantization