Peter L. Hoekje
Dept. of Phys., Univ. of Northern Iowa, Cedar Falls, IA 50614-0150
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.