Testing the Nonlinearity of Piano Hammers Using Residual Shock Spectra

Summary Force pulses and residual shock spectra of voiced, unvoiced (soft), and used (hard) piano hammers are compared. The peak frequency 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, is well above the fundamental frequency which helps to explain the dominance of higher partials in the bass notes. At the treble end, however, 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.