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In this study, an acoustic resonator -- a bass brass instrument -- withmultiple resonances coupled to an exciter -- the player's lips -- with oneresonance is modelled by a multidimensional dynamical system, and studied usinga continuation and bifurcation software. Bifurcation diagrams are explored withrespect to the blowing pressure, in particular with focus on the minimalblowing pressure allowing stable periodic oscillations and the associatedfrequency.The behaviour of the instrument is first studied close to a (nonoscillating) equilibrium using linear stability analysis. This allows todetermine the conditions at which an equilibrium destabilises and as such whereoscillating regimes can emerge (corresponding to a sound production). Thisapproach is useful to characterise the ease of playing of a brass instrument,which is assumed here to be related -- as a first approximation -- to thelinear threshold pressure. In particular, the lower the threshold pressure, thelower the physical effort the player has to make to play a note [Campbell etal., 2021].Cases are highlighted where periodic solutions in the bifurcationdiagrams are reached for blowing pressures below the value given by the linearstability analysis. Thus, bifurcation diagrams allow a more in-depth analysis.Particular attention is devoted to the first playing regime of bass brassinstruments (the pedal note and the ghost note of a tuba in particular), whosebehaviour qualitatively differs from a trombone to a euphonium for instance.

Minimal blowing pressure allowing periodic oscillations in a model of bass brass instruments