Sensitivity of the inharmonicity h to small changes in L ₁, R _h , and L _h (in cents per mm). Rows correspond to the parameter varied. Left column: upstream hole. Right column: downstream hole. Thin black (y ≈ 0): sensitivity of first-register notes. Thin colored: second-register notes. Thick colored: difference between second- and first-register sensitivities. The thin and thick colored lines almost completely overlap, reflecting the fact that changes to a closed register hole have minimal impact on the resonator’s resonance frequencies.