Physical principle of pitch bent by cross-fingering

Cross-fingering is a technique of playing woodwind instruments in which one or more tone holes are closed below the first open hole. It usually yields a pitch lower than that played with normal fingering. However, pitch is raised in exceptional cases. Pitch flattening has been traditionally understood using the lattice tone hole theory. On the other hand, pitch sharpening has been scarcely explained except for pointing out the possibility for the open hole to act as a register hole. This talk proposes understanding these pitch bending phenomena in a unified manner with a model of two coupled mechanical oscillators. Bores above and below the open hole interact with each other by sharing the air in the open hole oscillating as a lumped mass. This mechanism is known in physics as avoided crossing or frequency repulsion. With an extended model having three degrees of freedom, pitch bending of the recorder played with cross-fingering in the second register can also be explained.