Choice of algorithms for reed instruments oscillations: how to solve the equation for the nonlinear characteristics?

Jean Kergomard (1) , Philippe Guillemain (1) , Fabrice Silva (1)

1 Sons

For the simplest model of clarinet-like instruments, leading to the iterated map scheme, the solving of the nonlinear characteristic equation involves the inversion of the modified characteristic function linking the incoming wave to the outcoming one. The inversion can be problematic when the reed opening is large, i.e. when the associated dimensionless parameter is larger than unity, the inverse function being multi-valued. The problem was already noticed by Gokhstein (1981) concerning oboes or bassoons. To overcome this difficulty, several discretization schemes can be found, e.g. by modelling a reed as a one degree of freedom oscillator, or by modelling the air in the mouthpiece as a simple spring. The use of these schemes at their limits allows studying how the choice between the solutions can be done when using the classical scheme with the multi-valued function for the incoming/outcoming waves. The case of conical reed instruments is particularly investigated.

Mots clés: musical instruments; wind instruments; self-sustained oscillations

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]

Jean Kergomard, Philippe Guillemain, Fabrice Silva. Choice of algorithms for reed instruments oscillations: how to solve the equation for the nonlinear characteristics?. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810696⟩