This work is concerned with the Bayesian analysis of musical signals. The ultimate aim is to use Bayesian hierarchical structures in order to infer quantities at the highest level, including such things as musical pitch, dynamics, timbre, instrument identity, etc. Analysis of real musical signals is complicated by many things, including the presence of transient sounds, noises and the complex structure of musical pitches in the frequency domain. The problem is truly Bayesian in that there is a wealth of (often subjective) prior knowledge about how musical signals are constructed, which can be exploited in order to achieve more accurate inference about the musical structure. Here we propose developments to an earlier Bayesian model which describes each component `note' at a given time in terms of a fundamental frequency, partials (`harmonics'), and amplitude. This basic model is modified for greater realism to include non-white residuals, time varying amplitudes and partials `detuned' from the natural linear relationship. The unknown parameters of the new model are simulated using a variable dimension MCMC algorithm, leading to a highly sophisticated analysis tool. We discuss how the models and algorithms can be applied for feature extraction, polyphonic music transcription, source separation and restoration of musical sources.

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