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You just transition with the lowest rate of change of slope as possible. But then you have to take into consideration that the transition is part of the horn. Actually, everything from the diaphragm forward is part of the horn, so you want the correct expansion rate through the phase plug, any coupler, and through to the mouth.
Yes, designing from scratch, but I can see a lot of options and pitfalls with real existing drivers and horns that don't have smooth equal flares and I can speculate on a variety of options on the best way to couple them, but I am just guessing.
I'd like to see some trends via sims.
As for the other question, pattern control was certainly at the forefront from the earliest PA and theater horns, the earliest "scientific" horns, as it were. In 1927-28, there were folded horns in Victor Credenza phonographs, an impedance transformer to get a mechanical phono diaphragm to move some air (licensed by WE), and long exponential trumpets for PA...also pattern controllers, what was later called a "long throw horn." Amps were 1.2W battery powered.
The earliest theater horns, the WE snail horns c.1927 were 13 ft long for the Z transform and load on the driver, but the dispersion was also controlled as a design feature---wide vertical, quite narrow horizontal, just like theater rooms with balconies. Add more horns for more horizontal coverage...or use two sideways for wide horizontal if you didn't need the vertical
By the third generation of theater horns, c. 1934, there were a variety of controlled coverage multicellular horns depending on the solid angle of coverage desired.
The story continues with the late 40s WE auditorium speakers like the L-9 and the voice of the theater Altecs, where a short midbass horn was used to narrow dispersion to approximate that of the midrange horn at the crossover point. VOT cabs were initially built into large flat baffles, so the waveshaping began at 60hz, became cardoid at 300-500hz, and the horn picked up with 50 or 90 degree horizontal from there.
Hints of this approach began to show up in the early 1930s WE LF baffles with integral short C horns. Largely forgotten now. And modern constant directionality horns just throw out this whole notion of controlled narrowing as function of frequency to reduce crossover discontinuities.
Both aspects occur at the same time but once PA and theater sound came along, the controlled coverage aspect is foregrounded in the practical literature. Maybe for the Bell Labs guys who designed the horns using impedance models, they were impedance transformers foremost, but not for anybody down the chain.
By the way, I heard all of the horns above, including a pr of Victor credenza horns with an adapter for a WE 555 driver, and most are better than 511s. No lie.
Martin build some weird one offs for himself. So did Jeffrey Jackson. He has a huge CNC now, but he didn't then I'd ask these guys and see what they recommend.