Geddes research on horns led him to focus on High Order Modes or hom's. I believe his findings are published somewhere...
Higher Order Modes (HOMs) are reflection and/or diffraction paths within a horn. They are not predicted by Webster's horn equation but are predicted by Earl Geddes' more modern waveguide theory.
The proportion of HOMs produced by a horn does not change with level, so it is a linear distortion. But HOMS become increasingly audible and objectionable as the sound pressure level increases. This because the ear actually has a non-linear perception of this type of distortion; that is, it sounds like the distortion increases disproportionately as the sound pressure level goes up. Because of the time delay caused by the HOMs travelling a slightly longer path before reaching the ear, they are not effectively "masked" by the original undistorted signal, and so as the volume level goes up the HOMs become more audible and therefore more objectionable. HOMs tend to sound like edginess or harshness (which increases with SPL), which is probably why they can be mistaken for driver or horn throat being over-driven.
Abrupt angular changes within a horn, like diffraction slots, are strong sources of HOMs. Gentle curvatures are more benign. The curvature which generates the weakest HOMs is the Oblate Spheroid, according to Geddes, though apparently some of Jean-Michael L'Cleach's horns also generate very low HOMs. The junction between compression driver and horn can be a major source of HOMs if there is a significant angular mis-match there.
Imo taking steps to minimizing the generation of Higher Order Modes pays dividends in reducing "horn sound".