Musical Note Estimation for F0 Trajectories of Singing Voices Based on a Bayesian Semi-Beat-Synchronous HMM

This paper presents a statistical method that estimates a sequence of discrete musical notes from a temporal trajectory of vocal F0s. Since considerable effort has been devoted to estimate the frame-level F0s of singing voices from music audio signals, we tackle musical note estimation for those F0s to obtain a symbolic musical score. A naı̈ve approach to musical note estimation is to quantize the vocal F0s at a semitone level in every time unit (e.g., half beat). This approach, however, fails when the vocal F0s are significantly deviated from those specified by a musical score. The onsets of musical notes are often delayed or advanced from beat times and the vocal F0s fluctuate according to singing expressions. To deal with these deviations, we propose a Bayesian hidden Markov model that allows musical notes to change in semi-synchronization with beat times. Both the semitone-level F0s and onset deviations of musical notes are regarded as latent variables and the frequency deviations are modeled by an emission distribution. The musical notes and their onset and frequency deviations are jointly estimated by using Gibbs sampling. Experimental results showed that the proposed method improved the accuracy of musical note estimation against baseline methods.