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This paper presents and compares two methods of tracking the beat in musical performances, one based on a Bayesian decision framework and the other a gradient strategy. The techniques can be applied directly to a digitized performance (i.e., a soundfile) and do not require a musical score or a MIDI transcription. In both cases, the raw audio is first processed into a collection of "rhythm tracks" which represent the time evolution of various low-level features. The Bayesian approach chooses a set of parameters that represent the beat by modeling the rhythm tracks as a concatenation of random variables with a patterned structure of variances. The output of the estimator is a trio of parameters that represent the interval between beats, its change (derivative), and the position of the starting beat. Recursive (and potentially real time) approximations to the method are derived using particle filters, and their behavior is investigated via simulation on a variety of musical sources. The simpler method, which performs a gradient descent over a window of beats, tends to converge more slowly and to undulate about the desired answer. Several examples are presented that highlight both the strengths and weaknesses of the approaches.