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RE: Are there horn profiles or geometries that work better than others?

Hi
There are (at least) two things going on, if you want / need constant directivity (where the highs extend to the edges of the lower frequency pattern), then you need to use a horn who's walls are more or less straight and obeys some other horn related guide lines.
The reason is for both the acoustic transformation and pattern control, the locations inside the horn that are in control all change with frequency, moving towards the throat with increasing frequency so a curved wall horn becomes narrower as the frequency climbs.

With the right driver and horn, this can have flat or pretty flat response. However, the power response of all hf horn drivers falls off around -6dB /oct 2 to 4Khz and if you have a CD horn, you get the shape of the power response which needs eq to be flat.
In a room, these two sound very different when off axis.

So far as two or more drivers combining into one source either inside (or outside) of a horn, they must be less than 1/4 wavelength apart at the highest frequency they interact.

This IS part of the stereo image. With separate sources, there is some distance one must be before the sources combine subjectively into one. However, "sounds like" isn't the whole story. With your eyes closed, listening to one speaker it's easy to point at where it is BUT you can also triangulate how far away it is thanks in part to the still separate radiations.
A single small source at significant distance has no distance clues to triangulate on, what reaches the right and left ears is identical. All you have to go on is the hf roll off and reflections as clues, It is the difference from one ear to another that allow triangulation in depth.

The cool / unexpected part developing these horns, about a single simple radiation is there is much less information radiated by the speaker about how far away it is and so with a good recording, the sources are not part of the stereo image.
This is something anyone can hear too.

Obtain and mount a pair of these drivers on a flat baffle at least 18 in square.

https://faitalpro.com/en/products/LF_Loudspeakers/product_details/index.php?id=401000160



Cover the baffle with 1/2 inch foam (super77), front mount the driver through the foam. Figure out a small sealed back box and set these up about 6 or 8 feet away pointed at you in normal stereo.

These drivers are an amazing little full range driver, small enough to radiate simply up to pretty high, no crossover phase and while they can't do low bass, they do a good job fading behind a phantom stereo image.

WE can hear things how sound is radiated in 3d, we measure in 1d even with the Klipple machine.
Tom


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