Second register production on the clarinet: Nonlinear losses in the register hole as a decisive physical phenomenon

This study investigates the role of localized nonlinear losses in the register hole of a clarinet in producing second-register notes. First, an experiment is conducted to study the ability of the opening of a register hole to trigger a jump in oscillatory regime from the first to the second register. A cylindrical tube is drilled with holes of increasing diameter: five at the register hole level and five at the thumb hole level of a B-flat clarinet. Clarinetists are asked to play with constant parameters, blindfolded, beginning with all holes closed. The operator randomly opens one of the ten holes, noting the resulting register. The experiment is replicated numerically by time integration of two different models. The first is the model from Taillard, Silva, Guillemain, and Kergomard [(2018). Appl. Acoust. 141, 271-280] based on the modal decomposition of the input impedance. The second accounts for localized nonlinear losses in the register hole, through the model from Dalmont, Nederveen, Dubos, Ollivier, Méserette, and Sligte [(2002). Acta Acust. united Ac. 88, 567-575]. These losses are handled through variable modal coefficients. For the first model, simulations never produce the second register for any of the open holes. For the second, the proportion of second-register production is close to the experiment for upstream holes, but remains at zero for downstream holes.