Acoustic Horn Design – The Easy Way (Ath4)

This is perhaps the highest reasonably controlled DI I have seen in the set:

Frequencies above ~10 kHz are affected especially by the throat details and that is pretty independent of the rest of the waveguide (different 'k' values). So in these examples the behaviour above 10 kHz may not be directly related to anything below that and could be different with a different value of 'k'.

It seems there's nothing one can do to make the DI lower than about 15 dB at 20 kHz (for a simple open 1" throat, that is). So if it's already that high below that, it makes a "nicer" top end...
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