Bayesian computational models for inharmonicity in musical instruments

In this paper we describe recent advances in harmonic models for musical signal analysis. In particular we consider cases where inharmonic musical instruments are present. A particular model corresponding to a plucked string instrument is adopted and its parameters are automatically estimated from the data. In addition we describe new Bayesian prior distributions for musical pitch, which allow automatic adjustment to the pitch of the instruments, adaptive modelling of harmonic decay across frequency and automatic selection of the basis function window length. The methods are implemented using sophisticated MCMC algorithms and results demonstrated on a small set of examples, including harpsichord and guitar. The methods are readily adapted to polyphonic settings for pitch transcription and can be expected to lead to improvements in that setting.