### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 4pMU5. Computer modal analysis of percussion sounds: A preliminary study.

**James W. Beauchamp
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**
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*School of Music and Dept. of Elec. Eng., Univ. of Illinois at
Urbana-Champaign, Urbana, IL 61801
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Short time Fourier transform methods can be applied to the problem of modal
analysis of percussion sounds, which are well known to contain inharmonic
partials. One problem is that the Fourier transform is equivalent to a
harmonically spaced filter bank, so it is not possible to position filter
centers at arbitrary positions. Another problem is that, typically, percussion
modes are closely spaced while their amplitudes change rapidly, which plays
havoc with frequency versus time resolution limitations. For widely spaced
modes, the first problem is solved by choosing the base analysis frequency to be
an integral common divisor of the modal frequencies, so that each mode
corresponds to a unique equivalent filter. When modes become too dense, they
cannot be resolved, and bands of modes must be treated as indivisible entities
in order to conserve the temporal behavior. For example, if a 20-ms time
resolution is desired, modes no closer than 50 Hz can be resolved. Results and
ramifications of these limitations for analysis of percussion instruments such
as tubular bells, timpani, and cymbals will be presented and discussed.