Is it possible to cover the whole spectrum, high SPL, low distortion with a 2-way?

"Directivity changes the ration of direct sound to diffuse sound" that is identical to what room treatment does.
Similar, but not identical. With room treatment you do increase the DR ratio but you do so by reducing the reverb time. With directivity you increase the DR ratio, but do not shorten the reverb time. They will sound very different.
 
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Update about the dip in the response, as I said before, after moving down stairs to the carpet, the null did go away. I believe the vertical surfaces are responsible for the null. One of things I do to try source nulls and peaks is to search through the harmonics of dimensions. 13550/26/2=260hz. The damping is mainly on the floor. This old pic, shows the slot, I have now turned the whole, upside down, placing the woofer at the floor. The open space that exist below the woofer in this picture... I believe that if I add a baffle across the slot, it should push the null well above 200hz. 13550/20/2= 338.75. I would like to curve a a baffle to cup the outer diameter of the woofer. If my skills will allow this, is the question.... but the idea of not having to use damping material in the slot is strong motivator
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I am still figuring out a design for the horn stand, and am slowly coming to the conclusion that something practical that the Horn can rest on that has height and pitch adjustment is the ticket. The square tube I have is heavy, and by filling it with sand, should be heavy enough.
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I see what you did there... so what you think>? Maybe it'll sound a little more diffuse or something? It wouldn't be exactly like your pic because of the bridge between the two chambers but I could delete that part as well... Corner loading likely doesn't do anything bad to the situation I would imagine.
 
If i were to take my above woofer and turn it so the slot is facing the ground, now I have openings on both sides. Both sides would be acoustically in phase.
With the slot facing the ground, the 18" are not centered between the left and right exits in your cabinet.
The slot (phase) cancellation frequencies will be different for each exit.

The woofer's bifurcated acoustical path will make phase alignment with the high frequency horn even more position dependent that it would be as depicted in post 13023.

The woofer's bifurcated acoustical path will not allow any direct sound to reach a listening position centered on axis between the exits.

From experience, I'd expect the diffuse sound of this arrangement to be even worse than it was.
 
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The only way I know to think of diffraction involves edge interaction... abrupt changes in the baffle if you will.

Every frequency that is larger than the width or height of my slor is going to diffract. But its not very different than if the driver had of been the same size of the slot, is it?