An Analytical Prediction of the Bifurcation Scheme of a Clarinet-Like Instrument: Effects of Resonator Losses

TL;DR

This paper analytically studies how resonator losses affect the bifurcation and oscillation regimes of a clarinet-like instrument, providing insights into sound extinction and playing ease.

Contribution

It extends previous models by analytically analyzing the effects of resonator losses on bifurcation schemes in clarinet-like instruments.

Findings

Resonator losses can invert bifurcation behavior at high loss levels.

Analytical expressions relate parameters to oscillation regimes.

Loss effects influence the ease of sound production and extinction.

Abstract

The understanding of the relationship between excitation parameters andoscillation regimes is a classical topic concerning bowed stringinstruments. The paper aims to study the case of reed woodwinds and attemptsto find consequences on the ease of playing.In the minimum model of clarinet-like instruments, three parameters areconsidered: i) the mouth pressure, ii) the reed opening at rest, iii) thelength of the resonator \ assumed to be cylindrical. Recently asupplementary parameter was added: the loss parameter of the resonator(using the \textquotedblleft Raman model\textquotedblright, that considersresonator losses to be independent of frequency). This allowed explainingthe extinction of sound when the mouth pressure becomes very large. Thepresent paper presents an extension of the paper by Dalmont et al (JASA,2005), searching for a diagram of oscillation regimes with respect to thereed opening and the loss parameter. An alternative method is used, whichallows easier generalization and simplifies the calculation. The emphasis is done on the emergencebifurcation: for very strong losses, it can be inverse, similarly to theextinction one for weak losses. The main part of the calculations areanalytical, giving clear dependence of the parameters. An attempt to deducemusical consequences for the player is given.