@phusis wrote: " but in any event I find singling out particular horn geometries as "the best" to be more of a marketing ploy to boost business than a marker of the diversity of great sounding horns out there."
My statement about the Oblate Spheroid profile was based on my understanding that it is the mathematical optimum for minimizing detrimental internal reflections within the horn. There are other profiles optimized for other things - minimum phase, wavefront preservation, etc.
Duke