Nonlinear characteristics of single-reed instruments: Quasistatic volume flow and reed opening measurements

Abstract

A wind instrument can be described as a closed feedback loop made up of a linear passive element—the resonator—and a lumped nonlinear element—the mouthpiece. A method for measuring the nonlinear characteristics of the mouthpiece—nonlinear flow relationship—in static condition is given. An artificial mouth is used in which the volume flow is deduced from the pressure difference between both sides of a constriction (orifice) which takes place in the resonator. The orifice also plays the role of a nonlinear absorber, thwarting possible reed oscillations. This allows the measurement of the complete characteristics. In addition, the reed opening is measured using an optical device. Results are compared to a model in which the reed is reduced to its stiffness and the flow is governed by the Bernoulli equation. It is shown that the reed stiffness and the ratio of the effective surface of the jet and the reed opening are constant in a large range of openings. Standard range values of embouchure parameters are given.