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RE: you've never heard of "cupped hands" distortion?

Not sure where to begin, there are several misunderstandings here.
First, "non-flat" amplitude response is not distortion, it is non-flat amplitude response.

Distortion in the first order is sound the speaker adds not present in the input signal and normally 2,3,4, 5 etc times the input frequency and is caused by non-linearity.

A horns response is governed by the drivers acoustic power response AND it's directivity both are a function of frequency.

Due to issues I outlined in the loudspeaker chapter in "Handbook for Sound Engineers 5th edition" horn drivers do not have a flat power response and can only measure flat driven directly when on a horn who's radiation pattern narrows with increasing frequency.

For a horn that has the same pattern angles up high, a CD or EQ slope is applied yielding flat response and at the same time as correcting the amplitude, it also corrects the phase being a mostly minimum phase device.

Another issue with horns is they are too large to coherently combine with the lower device and I have only found one approach in 20+ years that allows making a multidriver / multi way horn radiate as if it only had one driver and no crossover phase shift.
When you do that, there is no cupped hand horn sound at all.
Best,
Tom

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