Thanks a lot for your reply!

To be more specific: In my horns the first 3/4 of an inch (the "adapter")is not flared at all, but resembles a "tube" (I hope it is possible to visualize my description!). After that, the circular entry is slowly (over a distance of app. 2 inches) converted to the rectangular form of the exponential horn. This transition piece is fairly smooth, but not perfect.

Given your expertise, do you find it likely that a "transition" as described above would (or could) course harshness in the 6-9 kHz range (in my case, especially too pronounced s-sounds in female voices)?

Thanks again Wayne!

All the best
Peter