Numerical simulation of transients in single-reed woodwind instruments
* Presenting author
In this work, we discuss a mathematical model of the sound production in single-reed woodwind instruments focusing on player-instrument interactions. The model consists of an ordinary differential equation, coupled to a system of partial differential equations. The motion of the reed is described by a nonlinear harmonic oscillator, where the nonlinearity stems from the collision of the reed with the mouthpiece lay and the coupling between air flow and pressure. The dynamics of air pressure and air velocity inside the instrument are described by a boundary value problem for the wave equation. We introduce a method to model the interaction between the player's tongue and the reed, which leads to a further nonlinearity in the reed equation. Moreover, we study strategies to estimate the model parameters relevant for the production of realistic tones, as well as for realistic transients in between tones. Finally, using the proposed model, recordings of real players are resynthesised.