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 on the production of second-register notes. First, an experiment is conducted to study the ability of a register hole to produce second register. A cylindrical tube is drilled with holes of increasing diameter. Five are at the same level as the register hole of a B-flat clarinet, and five are at the same level as the thumb hole. Participant clarinetists are then asked to play with constant control parameters. At the beginning of each measurement, all holes are closed. The operator then opens randomly one of the ten holes.The resulting register is noted. The experiment is replicated numerically by time integration of two different models. The first is the state-of-the-art model based on the modal decomposition of the input impedance of the resonator. The second accounts for localized nonlinear losses in the register hole, through the model from Dalmont and Nederveen (2002). These losses are handled through a variable modal coefficients method. For the first model, simulations never produce 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.