A toroidal bend causes tuning changes, which are mode dependent and may amount to 10 cents. This is caused by a change of the inertance in the bend, whereas the compliance is not affected. The inertance change was studied by Nederveen [Acoustical Aspects of Woodwind Instruments (1969)], Rostafinski [J. Acoust. Soc. Am. 52, 1411–1420 (1971)], and Keefe and Benade [J. Acoust. Soc. Am. 74, 320–332 (1983)]. At first sight, the results seem different. However, it can be shown that, at long wavelengths, they are essentially the same: The apparent density equals ρB=ρB2/2[1−(1−B2)1/2], where ρ is the unperturbed air density and B is the ratio of the tube radius and the tore curvature radius. The transition of the torus into the regular cylindrical bore causes a correction which was measured by Keefe and Benade. This was verified by numerical calculations using conformal transformations. The effects of a torus on the tuning can be neutralized by reducing the bore in the torus, for sharp bends of up to some 5%.