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

This article focuses on the influence of asymmetrical undercutting of toneholes on the effective radius and resonant frequencies of woodwind instrument air ducts. Using an electro-acoustic analogy, the study models toneholes with asymmetrical undercutting as combinations of linear quadripoles and provides formulas for numerically calculating their effective radii in the low-frequency approximation. Theoretical results, including shifts in resonance frequencies and displacement of the tonehole's "center of gravity," are validated through finite element method (FEM) simulations using COMSOL Multiphysics. Findings indicate that axial undercutting significantly affects resonance frequency shifts (up to 20–25 cents), while sideway undercutting has a smaller impact, and that these effects are cumulative when multiple holes are undercut. The presented method offers a practical approach for fine-tuning woodwind instruments, especially for small degrees of undercutting commonly used in manufacturing.