The bichromator as the quintessence of a saxophone and the question of harmonicity

Abstract

Reed wind instruments are divided into two families: those with a cylindrical bore (clarinet) and those with a conical bore (saxophone, oboe, bassoon). Apart from the timbre, the main features of the behavior of a clarinet can be obtained with a resonator modeled with a single mode (monochromator), while that of a saxophone can be obtained with a resonator modeled with two modes (bichromator), whose proper frequencies ratio is close to 2. This system has been largely studied by J. Gilbert et al. In particular, it has been demonstrated that when the inharmonicity is small, the oscillation on the fundamental frequency is obtained by an inverse bifurcation. Moreover, perfect harmonicity represents an optimum in terms of threshold pressure. Now a question remains: to what extent does the inharmonicity impact playability? This question is investigated in the present paper using both experiments and advanced numerical modeling.