  This paper focuses on the oscillation threshold of single reed instruments.
Several characteristics such as blowing pressure at threshold, regime
selection, and playing frequency are known to change radically when taking into
account the reed dynamics and the flow induced by the reed motion. Previous
works have shown interesting tendencies, using analytical expressions with
simplified models. In the present study, a more elaborated physical model is
considered. The influence of several parameters, depending on the reed
properties, the design of the instrument or the control operated by the player,
are studied. Previous results on the influence of the reed resonance frequency
are confirmed. New results concerning the simultaneous influence of two model
parameters on oscillation threshold, regime selection and playing frequency are
presented and discussed. The authors use a numerical continuation approach.
Numerical continuation consists in following a given solution of a set of
equations when a parameter varies. Considering the instrument as a dynamical
system, the oscillation threshold problem is formulated as a path following of
Hopf bifurcations, generalizing the usual approach of the characteristic
equation, as used in previous works. The proposed numerical approach proves to
be useful for the study of musical instruments. It is complementary to
analytical analysis and direct time-domain or frequency-domain simulations
since it allows to derive information that is hardly reachable through
simulation, without the approximations needed for analytical approach.

Classical Physics