Maximum Likelihood Method for Estimating Rhythm and Tempo

This paper presents a rhythm recognition technique based on a probabilistic approach by utilizing generative model for timing information in expressive music performance. The problem of rhythm recognition including rhythm parsing and tempo tracking, is to retrieve information of rhythm and tempo from a sequence of observed note durations. Since performed note length deviates in real performance and decomposition of the duration into rhythm and tempo is not unique in general, this problem must be solved in a probabilistic approach. We formulate rhythm recognition as maximum a posteriori (MAP) state sequence estimation among a finite state network of Hidden Markov Models (HMMs). The structure of the proposed stochastic model is almost equivalent to a network model of HMMs used in continuous speech recognition technique. The most likely rhythm and tempo in this probabilistic model are obtained by use of an effective search algorithm, level building. Experimental evaluation using MIDI recordings of a classical music piece is also reported.