Linear-acoustic effects of asymmetrical undercutting of toneholes of woodwind instruments.

The influence of the presence and magnitude of asymmetrical undercutting of the toneholes of woodwind instruments on the change in their effective radius and the corresponding shift of the eigenfrequencies of the air duct is considered. Within the framework of the electro-acoustic analogy, a tonehole with an asymmetrical undercutting along the axis of the main bore is presented as a cascade connection of two holes with different radii (undercutting and not undercutting parts of the hole), and with a sideway undercutting-in the form of a parallel connection. Formulas for numerical calculations are given that make it possible to determine the effective radius of such holes for the open state in the low-frequency approximation.