Bayesian harmonic models for musical pitch estimation and analysis

Estimating the pitch of musical signals is complicated by the presence of partials in addition to the fundamental frequency. In this paper, we propose developments to an earlier Bayesian model which describes each component signal in terms of fundamental frequency, partials (‘harmonics’), and amplitude. This basic model is modified for greater realism to include non-white residual spectrum, time-varying amplitudes and partials ‘detuned’ from the natural linear relationship. The unknown parameters of the new model are simulated using a reversible jump MCMC algorithm, leading to a highly accurate pitch estimator. The models and algorithms can be applied for feature extraction, polyphonic music transcription, source separation and restoration of musical sources.