ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06
5aMU5. A linear filter approximation to the hammer/string interaction for
use in a commuted synthesis piano model.
Scott A. Van Duyne
Julius O. Smith, III
Ctr. for Comput. Res. in Music and Acoust., Dept. of Music, Stanford
Univ., Stanford, CA 94305
In commuted synthesis of string instruments, the soundboard/body resonator
is commuted to the excitation point and replaced by its own impulse response
[Smith and Van Duyne, elsewhere in this session]. Hence, the highly nonlinear
hammer/string interaction must be replaced by a commutable linear filter. Using
the wave digital hammer computational model of the piano hammer [
3300(A) (1994)], it was observed that the force pulse of a hammer striking an
infinite string was qualitatively similar to the impulse response of a
second-order filter with two real poles. Hence, good second- and higher-order
filter designs based on physical data were possible. However, multiple humps
may appear in the hammer force pulse on a terminated string due to returning
string waves. It was observed that the magnitude spectra of the single hump
spectrum and the multiple hump spectrum were similar in bandwidth, differing
only in a slight ringing in the lower spectrum due to the lowpassed combing
effect of the returning string waves. Therefore, an equalization filter was
designed to summarize this combing effect by fitting a bank of parallel
second-order sections to the complex ratio spectrum. Excellent linear piano
hammer simulations were produced.