Effects of resonator losses on the sound production by clarinet-like instruments

The understanding of the relationship between excitation parameters and oscillation regimes is a classical topic concerning bowed string instruments. For reed instruments, results are less numerous. Nevertheless it is interesting to know the range of parameters for which sound can be produced or not, and if the emergence and extinction bifurcations are direct or not, with consequences on the pianissimo playing and more generally on the ease of playing. In the minimum model of clarinet-like instruments, three parameters are considered: i) the mouth pressure, ii) the reed opening at rest, iii) the length of the resonator assumed to be cylindrical. Recently a supplementary parameter was added: the loss parameter of the resonator (using the “Raman model”, that considers resonator losses to be independent of frequency). This allowed explaining the extinction of sound when the mouth pressure becomes very large. The present paper presents an extension of the paper by Dalmont et al (JASA, 2005), searching for a diagram of oscillation regimes with respect to the reed opening and the loss parameter. An alternative method is used, which allows easier generalization. The emphasis is done on the emergence bifurcation: for very strong losses, it can be inverse, similarly to the extinction one for weak losses. The main part of the calculations are analytical, giving clear dependence of the parameters. An attempt to deduce musical consequences for the player is given.