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.
Email:
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.
Email:
davide.rocchesso@univr.it. Web:
www.sci.univr.it/~rocchess
The paper discusses numerical issues related to discretetime
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.

 kHz,
rad/s,
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.

 kHz,
rad/s,
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).

 kHz,
rad/s,
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.