An Analytical Prediction of the Bifurcation Scheme of a Clarinet-Like Instrument: Effects of Resonator Losses
Résumé
The understanding of the relationship between excitation parameters and
oscillation regimes is a classical topic concerning bowed string
instruments. The paper aims to study the case of reed woodwinds and attempts
to find consequences on the ease of playing.
In the minimum model of clarinet-like instruments, three parameters are
considered: i) the mouth pressure, ii) the reed opening at rest, iii) the
length of the resonator \ assumed to be cylindrical. Recently a
supplementary parameter was added: the loss parameter of the resonator
(using the \textquotedblleft Raman model\textquotedblright , that considers
resonator losses to be independent of frequency). This allowed explaining
the extinction of sound when the mouth pressure becomes very large. The
present paper presents an extension of the paper by Dalmont et al (JASA,
2005), searching for a diagram of oscillation regimes with respect to the
reed opening and the loss parameter. An alternative method is used, which
allows easier generalization and simplifies the calculation. The emphasis is done on the emergence
bifurcation: for very strong losses, it can be inverse, similarly to the
extinction one for weak losses. The main part of the calculations are
analytical, giving clear dependence of the parameters. An attempt to deduce
musical consequences for the player is given.
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