Physical modelling of trombone mutes, the pedal note issue

International audienceBrass players use a variety of mutes to change the sound of their instrument for artistic expression. However, mutes can also modify the intonation and the playability of the muted instrument. An example is the use of a straight mute on a trombone, which makes it very difficult to play stable pedal notes.Previous studies have shown that using a straight mute establishes a parasitic acoustic resonance in the trombone. To cancel this modification, an active control device was developed and integrated into a mute, with satisfying experimental results [Meurisse et al., 2015]. With this device, the perturbed pedal notes can easily be played again.This paper investigates the ability of a physical model of brass instrument to reproduce the behaviour of the trombone pedal Bb without mute, or with an "active" or a "passive" straight mute. Linear stability analysis and time-domain simulations are used to analyse the behaviour of the model in the parameter range corresponding to the pedal note. Numerical results are compared for different models of instruments: a trombone, a trombone with a straight (passive) mute, an a trombone with an active mute. It is shown that the simple physical model considered behaves similarly to what is experienced with real instruments: the playing of the pedal note is perturbed with a passive mute, whereas the model of trombone with the experimental active mute gives results very similar to those obtained with an open trombone