When predicting and comparing the acoustical properties of horns it is customary practice to formulate the propagation as a one‐parameter plane wave front problem. However, when particular attention is paid to the rapid flare near the mouth of a horn structure such as the tractrix, it also seems plausible to formulate the propagation on the basis of a one‐parameter spherical wave front theory. By visualizing the surfaces of constant phase as spheres of constant radiiaand the flow lines as tractrixes having a generating arm of lengtha, a one‐parameter wave equation and Ricatti impedance equation may be derived. Solutions to these equations have been obtained by wave perturbation and by analog computer techniques.Axial response and throat impedance measurements are compared with theoretical calculations postulating first a hemispherical and then a plane piston radiation pattern. It appears that the most satisfactory explanation lies somewhere in between these two limiting cases.