The paper introduces a probabilistic model for the analysis of line spectra – defined here as a set of frequencies of spectral peaks with significant energy. This model is detailed in a general polyphonic audio framework and assumes that, for a time-frame of signal, the observations have been generated by a mixture of notes composed by partial and noise components. Observations corresponding to partial frequencies can provide some information on the musical instrument that generated them. In the case of piano music, the fundamental frequency and the inharmonicity coefficient are introduced as parameters for each note, and can be estimated from the line spectra parameters by means of an Expectation-Maximization algorithm. This technique is finally applied for the unsupervised estimation of the tuning and inharmonicity along the whole compass of a piano, from the recording of a musical piece.