A parametric model and estimation techniques for the inharmonicity and tuning of the piano.

Inharmonicity of piano tones is an essential property of their timbre that strongly influences the tuning, leading to the so-called octave stretching. It is proposed in this paper to jointly model the inharmonicity and tuning of pianos on the whole compass. While using a small number of parameters, these models are able to reflect both the specificities of instrument design and tuner's practice. An estimation algorithm is derived that can run either on a set of isolated note recordings, but also on chord recordings, assuming that the played notes are known. It is applied to extract parameters highlighting some tuner's choices on different piano types and to propose tuning curves for out-of-tune pianos or piano synthesizers.