### ASA 126th Meeting Denver 1993 October 4-8

## 4aMU2. Transient behavior of time-domain wind instrument models.

**Peter L. Hoekje
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*Dept. of Phys., Univ. of Northern Iowa, Cedar Falls, IA 50614-0150
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An important playing characteristic of a musical wind instrument is its
transient response, which is well suited for calculation by time-domain models.
Typically, the instrument air column is described by a time-domain response
(either impulse response or reflection function), and a reed valve by a flow
control equation and harmonic oscillator dynamics. Since important musical
effects have been observed for changes in harmonicity of instrument resonances
on the order of 10 cents (0.6%), calculations intended to show such effects
need to specify the instrument response with appropriate resolution. In one
calculational experiment, the air column resonance frequencies are adjusted in
the frequency domain, then the corresponding time-domain response is calculated
and the dynamical model run. The results show significant changes in transient
response due to minor changes in air column response or in reed resonance. In
addition to FFT methods, the transient behavior of spectrum partials may be
tracked by applying the Hilbert transform to individually filtered harmonics
and finding their instantaneous frequencies and amplitudes. Alternatively, a
system of nearly harmonic oscillators with varying phases, frequencies, and
amplitudes may be fit to the transient waveform. Each of these methods has
unique benefits and difficulties.