Simulation of the nonlinear characteristic of the clarinet exciter and of the side holes

Pierre-André Taillard and Jean-Pierre Dalmont

LAUM, Le Mans

Sunday, September 15, 2019 from 13:40 to 14:00

in Summer Theater

Abstract :
At the last ISMA, a method for measuring the nonlinear characteristic and the static mechanical behaviour of the clarinet exciter (reed + mouthpiece + lip of the player) was presented. Here, we show how this measured behaviour can be integrated in a real time simulation using a waveguide clarinet model, including nonlinear losses at the toneholes. The clear separation of the aeraulic (nonlinear characteristic) and mechanical (static bending of the reed against the mouthpiece lay, like a stiffening spring) aspects allows a straightforward, piecewise simulation of the dynamic behaviour, apparently without any numerical stability problem. For the simulation of the instrument, at a low sound level, the proposed empirical tonehole model tends towards the linear radiation impedance, whereas at high level, nonlinear losses dominate. They are modelled by Bernoulli's law with turbulent flow (as for the exciter). Taking nonlinear losses into account is crucial for a credible simulation of the instrument, especially in the second regime. The model allows to realistically predict the playing frequency and the timbre of the instrument according to the two main objective factors characterizing clarinet reeds: stiffness and opening at rest (without lip pressure). This allows a virtual prototyping of the clarinet exciter and resonator.

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