  In this study, an acoustic resonator -- a bass brass instrument -- with
multiple resonances coupled to an exciter -- the player's lips -- with one
resonance is modelled by a multidimensional dynamical system, and studied using
a continuation and bifurcation software. Bifurcation diagrams are explored with
respect to the blowing pressure, in particular with focus on the minimal
blowing pressure allowing stable periodic oscillations and the associated
frequency.The behaviour of the instrument is first studied close to a (non
oscillating) equilibrium using linear stability analysis. This allows to
determine the conditions at which an equilibrium destabilises and as such where
oscillating regimes can emerge (corresponding to a sound production). This
approach is useful to characterise the ease of playing of a brass instrument,
which is assumed here to be related -- as a first approximation -- to the
linear threshold pressure. In particular, the lower the threshold pressure, the
lower the physical effort the player has to make to play a note [Campbell et
al., 2021].Cases are highlighted where periodic solutions in the bifurcation
diagrams are reached for blowing pressures below the value given by the linear
stability analysis. Thus, bifurcation diagrams allow a more in-depth analysis.
Particular attention is devoted to the first playing regime of bass brass
instruments (the pedal note and the ghost note of a tuba in particular), whose
behaviour qualitatively differs from a trombone to a euphonium for instance.
