Influence of hammer velocity in piano sound

Abstract

Recent models of piano string excitation suggest that string motion is proportional to hammer velocity. Preliminary to measuring dynamics in piano performance, the relationship between radiated piano sound and hammer velocities was studied. A computer‐monitored piano allowed reproduction of a range of hammer velocities, and a microphone placed near a pianist's head location recorded radiated sound. The first eperiment indicated that peak amplitude of the waveform was directly proportional to the hammer velocity of individual notes for a wide range of frequencies and hammer velocities. A second experiment investigated the waveforms of notes struck simultaneously and compared these with the waveforms of the individual component notes. The peak amplitude of the dyads was directly proportional (with proportionality close to 1) to the sum of the individual peak amplitudes. A third experiment extended these findings to a wider range of dyadic pitch intervals. These findings suggest linear relationships between hammer velocity, amplitude of string motion, bridge motion, and amplitude of the soundboard vibration for single notes. The additivity of dyads indicates that the principle of superposition is obeyed with a small energy loss. [Work supported by MIT Media Lab, Ohio State University Small Research Grant, and a Wellesley College Brachman Hoffman Fellowship.]