  The piano soundboard transforms the string vibration into sound and
therefore, its vibrations are of primary importance for the sound
characteristics of the instrument. An original vibro-acoustical method is
presented to isolate the soundboard nonlinearity from that of the exciting
device (here: a loudspeaker) and to measure it. The nonlinear part of the
soundboard response to an external excitation is quantitatively estimated for
the first time, at \approx -40 dB below the linear part at the ff nuance. Given
this essentially linear response, a modal identification is performed up to 3
kHz by means of a novel high resolution modal analysis technique (Ege et al.,
High-resolution modal analysis, JSV, 325(4-5), 2009). Modal dampings (which, so
far, were unknown for the piano in this frequency range) are determined in the
midfrequency domain where FFT-based methods fail to evaluate them with an
acceptable precision. They turn out to be close to those imposed by wood. A
finite-element modelling of the soundboard is also presented. The low-order
modal shapes and the comparison between the corresponding experimental and
numerical modal frequencies suggest that the boundary conditions can be
considered as blocked, except at very low frequencies. The frequency-dependency
of the modal density and the observation of modal shapes reveal two
well-separated regimes. Below \approx 1 kHz, the soundboard vibrates more or
less like a homogeneous plate. Above that limit, the structural waves are
confined by ribs, as already noticed by several authors, and localised in
restricted areas (one or a few inter-rib spaces), presumably due to a slightly
irregular spacing of the ribs across the soundboard.
