This paper presents a statistical method for use in music transcription that can estimate score times of note onsets and offsets from polyphonic MIDI performance signals. Because performed note durations can deviate largely from score-indicated values, previous methods had the problem of not being able to accurately estimate offset score times (or note values) and, thus, could only output incomplete musical scores. Based on observations that the pitch context and onset score times are influential on the configuration of note values, we construct a context-tree model that provides prior distributions of note values using these features and combine it with a performance model in the framework of Markov random fields. Evaluation results show that our method reduces the average error rate by around 40 percent compared to existing simple methods. We also confirmed that, in our model, the score model plays a more important role than the performance model, and it automatically captures the voice structure by unsupervised learning.
In a recent conference paper, we have reported a rhythm transcription method based on a merged-output hidden Markov model HMM that explicitly describes the multiple-voice structure of polyphonic music. This model solves a major problem of conventional methods that could not properly describe the nature of multiple voices as in polyrhythmic scores or in the phenomenon of loose synchrony between voices. In this paper, we present a complete description of the proposed model and develop an inference technique, which is valid for any merged-output HMMs, for which output probabilities depend on past events. We also examine the influence of the architecture and parameters of the method in terms of accuracies of rhythm transcription and voice separation and perform comparative evaluations with six other algorithms. Using MIDI recordings of classical piano pieces, we found that the proposed model outperformed other methods by more than 12 points in the accuracy for polyrhythmic performances and performed almost as good as the best one for non-polyrhythmic performances. This reveals the state-of-the-art methods of rhythm transcription for the first time in the literature. Publicly available source codes are also provided for future comparisons.