Slow motion: hammer, string, bridge force
Top: one string of the focused key (height exaggerated), the hammer rising from below, the bridge and its piezo at the right. Bottom: the force on the bridge (what the piezo hears) and the felt's contact force. The kink travels to the bridge and back; each arrival is a step in the force.
Modes of C4
Spectrum
live output · faint lines: harmonics n·f₁ · markers: the stretched partialsSpectrogram
live output · ticks: the spectrum's markersThe upper partials fade first, so each note's stack of lines thins from the top down. The ticks are the stretched partials, a little sharp of the harmonics.
Why the piezo is bright
string displacementbridge force (piezo)soundboard microphone
Level of each partial after the strike, in dB. The force on the bridge is T·∂y/∂x, so partial n is weighted by n(1 + Bn²) relative to its displacement.