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Energy analysis of structural changes in pianos

Chaigne, Antoine; Chabassier, Juliette and Duruflé, Marc 

The leading idea of this theoretical paper is to examine the effects of structural changes in the piano on the basis of energetic quantities relative to its constitutive parts. These energies are global quantities which characterize the intrinsic properties of the instrument, irrespective of the observation point. The evolution of the various energy terms with time are calculated with a help of a recent piano model which couples together the hammer, the nonlinear strings, the soundboard and the acoustic space. Some parameters, which play a major role in the history of the piano are particularly examined: string tension and diameter, soundboard thickness and rigidity, hammer mass and velocity. The results show that direct links can be established between the energetic quantities and the tonal properties of the piano sounds, in terms of temporal envelope and spectral content. they also shed useful light on the energy exchange between the constitutive parts of the instrument, and on its acoustical efficiency. This study is intended to have potential applications as a theoretical guideline for piano making, restoration and reproduction of historic instruments.