Testing the Nonlinearity of Piano Hammers Using Residual Shock Spectra

Force pulses and residual shock spectra of voiced, unvoiced (soft), and used (hard) piano hammers are compared. The peak frequency f_max of the residual shock spectrum is related to the frequency range over which the hammer will be most effective in exciting string modes. Hammer speeds of 1 to 6 m/s, used in these experiments, span the normal dynamic range of the piano. Peak force is related to pulse duration and also to a nonlinearity exponent in the equation relating force to compression of the felt. For lower notes on the piano, f_max is well above the fundamental frequency which helps to explain the dominance of higher partials in the bass notes. At the treble end, however, f_max is comparable to the fundamental frequency, resulting in a strong fundamental and few partials in these notes on a piano. In addition to its usefulness in piano research, the residual shock spectrum could serve as a useful guide in the production and voicing of pianos.