The Journal of the Acoustical Society of America
vol. 111(5), May 2002, pp. 2293-2301.


Efficiency, Accuracy, and Stability Issues in Discrete Time Simulations of Single Reed Wind Instruments

Federico Avanzini
Universita' di Padova, Dipartimento di Elettronica e Informatica. Via Gradenigo 6/A, 35131 Padova, Italy.
E-mail: avanzini@dei.unipd.it . Web: www.dei.unipd.it/~avanzini


Davide Rocchesso
Universita' di Verona, Dipartimento di Informatica. Strada Le Grazie 15, 37134 Verona, Italy.
E-mail: davide.rocchesso@univr.it. Web: www.sci.univr.it/~rocchess


The paper discusses numerical issues related to discrete-time simulations of a single reed physical model, and proposes a set of numerical tools for constructing a digital reed that preserves as closely as possible the physical properties of the system. This page provides some sound examples synthesized using the digital instrument.
$F_s=44.1$ kHz, $\omega_r=2\pi \cdot 3700$ rad/s, $g_r=3000$ Hz
Oscillation in the fundamental register can be heard from this example; realistic values for the reed parameters have been chosen (see Table I in the paper). On the one hand, the overall sound quality is clearly not satisfactory; this is mainly due to poor modeling of the resonator (see the paper for details) and can be noticed during steady state oscillations. On the other hand, accurate modeling of the excitation mechanism provides a realistic attack transient.

$F_s=44.1$ kHz, $\omega_r=2\pi \cdot 2020$ rad/s, $g_r=1400$ Hz
This example shows that the second (clarion) register can be played without opening the register hole, if the reed parameters are properly adjusted. Both the resonance and the the damping coefficient are lowered, in particular the reed resonance matches the seventh harmonic of the bore. The transition from the fundamental register to the clarion register (one twelfth above) can be clearly heard in the attack transient, and this behavior from the model is qualitatively in agreement with experimental results on real clarinets (see the paper for a detailed discussion).

$F_s=44.1$ kHz, $\omega_r=2\pi \cdot 3150$ rad/s, $g_r=300$ Hz
A transition to the reed regime ("squeaks") is achieved in this example. This is obtained by giving the damping coefficient a very low value. Again, this behavior is qualitatively in agreement with experimental results (see the paper for a detailed discussion). A similar effect can be produced on a real clarinet if the player presses the reed using his teeth instead of his lip, therefore providing little damping.