TubeLab: Interactive inverse design of wind instrument bores with hard spectral constraints

Abstract

We present TubeLab, a browser-based acoustic simulator and inverse design tool for wind instrument bores without tone holes. The direct problem is solved by a Transfer Matrix Method. Inverse design - finding a bore correction that shifts selected resonance frequencies toward specified musical targets - is formulated as a Tikhonov-regularized least-squares problem whose Jacobian is computed by a single adjoint backward pass per mode. Modes whose frequencies must be preserved are handled by a saddle-point formulation that enforces hard equality constraints regardless of the regularization strength. Resonance frequencies agree with state-of-the-art finite-element calculations to within 1.21 cent over eleven geometries and 132 mode pairs. Experimental validation against tap-tone measurements of 16 numerical control-machined didgeridoos spanning six distinct bore designs yields 9.6 cent RMS deviation over 189 matched mode pairs. Replicate specimens of the same nominal bore disagree with each other by 4.5 cent RMS, so about 36% of the residual variance is fabrication scatter.