Hi Duke, by better horn designs, do you mean horn speaker designs, or just the horn - if the latter, are you referring to Constant directivity? If yes, CD is compatible with TAD (as well as others).
Yes, I was referring to midrange/high frequency horn(s), not to the complete loudspeaker system. I should have been more specific. I have NOTHING against horn-loaded midbass and bass, and agree that it can sound magnificent, but I'm in the biz and huge enclosures are tough to sell. My forthcoming "statement speaker" will have two 15" midwoofers, but they will not be horn loaded because that would roughly quadruple the size just to get down to 80 Hz. Maybe one day I'll go there, but not right now.
So regarding horns for the upper end of the spectrum, imo the MOST IMPORTANT consideration is minimizing coloration. In my opinion all of the other advantages of horns are of academic interest only if the horns themselves are superimposing their signature atop every piece of music.
Next, something which imo would be very nice to have is indeed Constant Directivity (CD). With constant directivity, the reflections sound like the direct sound, which is a characteristic of live music that few loudspeakers can replicate.
In my experience most Constant Directivity horns which rely on diffraction slots or abrupt angle changes to widen the high frequency dispersion have colorations which disqualify them. There is however a different approach to Constant Directivity which is inherently extremely low in coloration, and that is the Oblate Spheroid profile and its derivative the Super Elliptical Oblate Spheroid. The "Min-Phase" horn made by Autotech used in the hORNS Universum [edit: I now think that's incorrect] seems to be a cross between the L'Cleach horn and the Oblate Spheroid and from what I understand is essentially Constant Directivity over most of its passband, with some pattern-narrowing at the top end.
Personally, I have yet to hear a good CD, but all the CD users seem to be using DSP or very high EQ in the crossover to flatten out the sound.
Yes, true Constant Directivity horns require aggressive EQ. You see, the power response of any compression driver peaks maybe an octave or so above its resonant frequency, and then slopes downward above that. MOST horns have a radiation pattern which narrows as they go up in frequency, which largely if not entirely compensates for the compression driver's innate downward-sloping power response BUT results in a spectral mis-match between the direct and reflected sound. A Constant Directivity horn's on-axis response slopes downward with increasing frequency just as much as its off-axis response does, but when you have fixed the on-axis response via EQ, you have SIMULTANEOUSLY fixed the off-axis response! The downside is, the on-axis SPL will not be as high at high frequencies, which limits system efficiency (unless you are using DSP to correct it).
So as in most things audio, there is a tradeoff for using Constant Directivity horns, and that is system efficiency. They put out just as much high-frequency energy as a Tractrix or Exponential horn, but the energy is spread out much more, such that the on-axis Sound Pressure Level is not as high. By way of analogy, when you adjust the nozzle on a garden hose to give a wide pattern, the same AMOUNT of water comes out, but the on-axis PRESSURE where the water hits is less than with a narrow pattern.
I use passive crossovers (no DSP), and usually get all of the equalization needed to correct for the inherently downward-sloping response with no additional crossover components. But the component values I use in my highpass filters are drastically different from the "textbook" values.
Regarding matching on horns and drivers, this has been done. It is easy to come up with the matches unless someone is experimenting with something new.
In my opinion an important part of matching horns with compression drivers is that the exit angle of the compression driver match the entry angle of the horn. When there is a significant mis-match, that discontinuity is a source of diffraction, which in turn can cause a harshness which becomes progressively more audible and objectionable as the SPL goes up.
Which brings us to the point of why you might not want to put new wine in old bottles... or new-style compression drivers on old-style horns: Old-school compression drivers tend to have a long, narrow-angle internal passageway between the phase plug and the exit, while new-style compression drivers tend to have a much shorter and somewhat wider-angle internal passageway. While the length of that internal passageway makes a difference particularly at high frequencies, the exit angle is what matters most as far as compatibility with a given horn's entry angle.
So when someone does a "shoot-out" comparing different compression drivers and different horns, they are actually comparing FOUR things: The horns; the compression drivers; how well the driver's exit angle matches the horn's entry angle; and the combination's crossover/EQ filtering. So, doing a truly "apples to apples" comparison of dissimilar compression drivers is a lot more complicated than simply trying them on the same horn.
Finally, I could have gone with the Radian for the Beryllium option. But as an audiophile, I knew that if I ever built a speaker with the Radian, in a few years I would be chasing the 4003.
I have NOTHING against the 4003! But for what I'm trying to do, which calls for a particular type of horn, imo it's the wrong tool for the job. You see, even if I make an Oblate Spheroid horn whose entry angle matches the exit angle of the 4003, the latter's long internal passageway between phase plug and exit effectively controls the high frequency dispersion and constrains it to a narrow angle. Imo the solution would be to use a separate tweeter, which is what most people do when building a system around an "old school" format compression driver like the 4003, which in turn is another juggling of trade-offs.