Effect of the shape of mouth pressure variation on dynamic oscillation threshold of a clarinet model

TL;DR

This paper investigates how different mouth pressure variation shapes affect the dynamic oscillation threshold of a clarinet model, extending analytical predictions from linear to exponential pressure increase scenarios.

Contribution

It extends the analytical prediction of the dynamic oscillation threshold to exponential mouth pressure profiles, improving understanding of bifurcation delay in clarinet models.

Findings

Analytical predictions align well with simulations for exponential pressure profiles.

The shape of mouth pressure variation significantly influences the dynamic oscillation threshold.

Extended model accounts for realistic pressure stabilization during note attack.

Abstract

Simple models of clarinet instruments based on iterated maps have been used in the past to successfully estimate the threshold of oscillation of this instrument as a function of a constant blowing pressure. However, when the blowing pressure gradually increases through time, the oscillations appear at a much higher value, called dynamic oscillation threshold, than what is predicted in the static case. This is known as bifurcation delay, a phenomenon studied in [1,2] for a clarinet model. In particular the dynamic oscillation threshold is predicted analytically when the blowing pressure is linearly increased. However, the mouth pressure cannot grow indefinitely. During a note attack, after an increasing phase, the musician stabilizes the mouth pressure. In the present work, the analytical prediction of the dynamic oscillation threshold is extended to a situations in which the mouth pressure approaches a steady state pressure according to an exponential time profile. The predictions still show a good agreement with simulation of the simple clarinet-model. This situation is compared in terms of dynamic oscillation bifurcation.