Reed instruments, from small to large periodic oscillations

Abstract

Reed instruments are physical systems which can be considered as self-sustained oscillators. The ‘‘normal operation’’ of the instrument corresponds to the establishment of a permanent periodic regime. On the one hand, the behavior of the small periodic oscillations in the fixed point (threshold) vicinity is well known: the bifurcation’s nature and the oscillation’s characteristics depend on both the excitator and the resonator. On the other hand, a theory has been developed for lossless resonators coupled with the excitator: compared to experimental results, this theory is relevant for large amplitude oscillations. The matching between the analytical solutions of the two theories is not instantaneous. The matching is studied using the harmonic balance technique with the continuation method coming from known analytical results near the threshold. The bifurcation graphs are constructed for different resonators. The particular resonator with two harmonic resonances is discussed in detail. The role of the octave regime is unexpected: the octave is matched to some of the fundamental regimes. Some resonators (cylinder, lattice of cylinders, cone) are arranged on an artificial mouth designed for single-reed woodwinds. Measurements of periodic regimes are compared to the theoretical results. A movie will be shown.