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Figure 7


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Top and bottom plots represent respectively the threshold pressures and threshold frequencies given by the locus of the Hopf points (blue) and the locus of the saddle-node bifurcation points (orange and green) with respect to the lips’ resonance frequency in the case of the B♭-contrabass tuba (colors correspond to the ones in Figure 6). The circles identify the local minimum of blowing pressure for each note, namely the pedal note (PN), the ghost note (GN), and the second regime (R2). In the case of the second Hopf bifurcation, the easiest note playable is given by the minimum of the Hopf points’ locus (blue curve), since its minimal threshold mouth pressure is lower than the one given by the saddle-node bifurcation points’ locus (orange curve). On the contrary, in the case of the ghost note it is given by the minimum of the saddle-node bifurcation points’ locus (orange curve).

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