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Simple models of clarinet instruments based on iterated maps have been usedin the past to successfully estimate the threshold of oscillation of thisinstrument as a function of a constant blowing pressure. However, when theblowing pressure gradually increases through time, the oscillations appear at amuch higher value, called dynamic oscillation threshold, than what is predictedin 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 ispredicted 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 thepresent work, the analytical prediction of the dynamic oscillation threshold isextended to a situations in which the mouth pressure approaches a steady statepressure according to an exponential time profile. The predictions still show agood agreement with simulation of the simple clarinet-model. This situation iscompared in terms of dynamic oscillation bifurcation.

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