Uniform Directivity - How important is it?

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I don't think that a corner horn (or any transducer positioned that way) should be called an omnidirectional speaker, it is such one of a kind. Things get mixed easily if we do that. I would rather say that corner speaker (arrangement) is non-directional.

I would like to reserve "omnidirectional" only to free-standing speakers that radiate evenly to 360¤ horizontal (2-dimensionally).

True 3D omnis exist too, but we seldom see them at homes.

Omnipolar radiation pattern is not same as omnipolar speaker. Like someone said earlier - any loudspear put in a trihedral corner becomes omnipolar. But that is because the space is then only 1/8 of sphere.

True 3D omnipolar speakers are used mainly for acoustic studies and tests. This is not certainly the best of them but we get the idea
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Okay, I'm still struggling with the notion of CD horns blended into a corner. It seems superfluous.

In a trihedral corner you are already constrained to 1/8th space which is a d.i. of 9dB, I think. Unless you want even more directional than that, what are the CD horns doing?

For a speaker in the middle of a room the directivity will create a difference between the axial level (aimed presumably at the listener's ears) and the overall reverberent level. This is why we would want to go for a CD system in the first place. As soon as you put the speaker into the corner it is radiating into 1/8th space, but it is behaving much like an omni in the same situation. There may be no primary reflections from the 3 adjacent surfaces, but there is no difference being created between the axial level and the power response (directivity is effectively lost). Unless you design for a d.i. greater than 9 then the horns aren't adding anything.

Am I missing something?
I'm sure you aren't really missing anything I would get, so my use of question marks here is not rhetorical: Ignoring the surfaces not attached to the corner, any old speaker jammed in the corner behaves like itself with 7 more of itself reflected around the corner axes, right?

A cluster of 8 regular speakers doesn't make for a very good omni, so you want to get something more like a point or 1/8 sphere source, right? If you actually had one, with constantly-zero directivity (or 1, if we're talking DI, I guess), that would be fine, but you don't, so you want to kind of cluster some drivers around the corner and avoid narrowing directivity, which brings up some problems, so you look at how Danely did it, right?

What else could you do? Seems like you pretty much have to have a compression driver at the end, which means you have to blend the exit somehow. If you put a 5/8" dome in the corner, seems like nothing could be jammed up close enough to cross to it without making trouble, right?
 
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There may be no primary reflections from the 3 adjacent surfaces, but there is no difference being created between the axial level and the power response (directivity is effectively lost). Unless you design for a d.i. greater than 9 then the horns aren't adding anything.

That's exaxctly right, Dave. At least, that has been my thinking when doing speakers like these.

A long time ago, when I first started playing with CD horns, I decided to try a Klipsch-like cornerhorn design with them. To remove the path-length delay, I got rid of the folded basshorn, just basically mounting a woofer in the corner. That removed the benefit of the acoustic loading from an exponential horn, but it still gave the 9dB DI from eighth-space. And without the path-length delay, it's pretty easy to get summing right with a midrange, which is then also easy to match phase with a tweeter. This gives the possibility for constant directivity without weird lobes from delay/phasing problems.

Of course the problem is what so many have pointed out, that if the midrange and tweeter aren't acoustically close to the boundaries, then they suffer from early reflections. One could always soffit mount them, do some kind of permanent installation that blended them into the apex of the corner. That would probably be ideal. But I was searching for a freestanding solution, and to do that, it seemed to me like constant directivity horns with 90° beamwidth (or maybe a smidge less) would be best.

I also found that if the midhorn was run low enough in frequency, it could be placed acoustically close the the walls at the low end of its passband. That helped it blend down low, leaving only the higher frequencies being acoustically distant from the boundaries, where horn directivity attenuates off-axis radiation and reduces reflections that way. This approach also gives a smooth transition from eighth-space to quarter-space, and allows the designer to place the midrange and tweeter locations up closer to ear-level, where the apparent source location is most realistic sounding for mains.

Higher frequencies are a little easier to absorb, so curtains or whatever help attenuate the grazing reflections, but in practice, I've found this approach sounds really great even in untreated rooms with plain old sheetrock walls. As I keep saying, I've honestly never heard any approach that I like as much as this.
 
Soffit mount is what my drawings were intended for. If the horn is made from the same thickness material as the Gyprock (10mm) it could be plastered right into the corner and all the listener (or his wife) would see is half a dozen little holes in the corner of the ceiling.

if you wanted to get fancy one could always use a pyramid of wall coloured foam in the corner ala Geddes to hide the holes. Presto, invisible speakers with CD down to whatever frequency you want.
 
Architectural speakers is a growing market and looks like there will be room for hifi solutions

Ultimate Guide to Architectural Speakers 2013 - CE Pro Magazine Article from CE Pro

Pro audio is a different scene, but Genelec has also some solutions for home environment Genelec / Architectural

I didn't find any corner solutions, only soffit/flush versions. Studio soffit speakers are usually near ceiling but not close enough to corner to work well

Main monitors for Control Rooms | Monitoring Systems from Genelec
JBL Pro Installed Sound

This kind of speaker would fit a corner quite well too and we sometimes see these installed that way at clubs and congress rooms etc.
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I experimented with two-way constant directivity cornerhorns for a while, but ultimately went back to three-ways.

If the midwoofer is large enough, the beamwidth collapses (just like in a DI-matched two-way) and this helps attenuate energy illuminating the sidewalls at high frequency. That's important, reducing the off-axis energy at high frequencies where the driver becomes acoustically far from the boundary.

But adding a midhorn extends the directivity control down in frequency, which I think is worthwhile. It's not hard to get the source acoustically close up through several hundred Hertz but it gets increasingly harder to maintain as frequency rises above that. And no direct radiator is becoming directional enough in the mid-hundreds, so a midhorn is helpful.
 
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