What is the ideal directivity pattern for stereo speakers?

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I agree with you that a corner is the natural extension of a low frequency horn. You get maximum efficiency & maximum modal excitation. The corner actually sets the radiation angle to 90° from the Schroeder frequency upwards, to the point where the sound source becomes acoustically distant from the apex of the corner. It acts like a large constant directivity waveguide for the lower frequencies, again, down to the Schroeder frequency.

Of course, below the Schroeder frequency, the walls aren't setting the directivity as "waveguides" anymore, they're just boundaries for standing waves, forming pockets of sound, standing wave nodes. So in that region, panel absorbers and/or multisubs help.

I also suggest that the corner is useful up through the midrange, provided the midrange horn is snuggled in closely enough that its mouth is tightly coupled. It just has to be acoustically close. When this is done, there is no more midrange reflection, and no more self-interference ripple in the 100Hz to 200Hz range.

As for absorbers that might be useful in this range, of course, it is possible to make one, but the oft-mentioned "absorbent foam" on the wall is ineffective. Panel absorbers work best in this range, made with the right depth to tune them for the frequency where self-interference is worst. So you have to make a semi-permanent installation of speakers and panel dampers, one where the distance from speakers to walls is fixed (setting the reflection distance) and making panel absorbers of the right depth to treat the self-interference frequency created by this reflection distance.

For systems that cannot be setup this way, I recommend flanking subs because they fill in the holes. It's essentially an array, and it tends to smooth response. It's also like the multisub concept, just that the distances are shorter, more in line with the wavelengths involved.
 
Maybe 20 years ago, I've been lucky enough to assist to a demo organized by La Maison de l' Audiophile in Paris. This was taking place in a small concert hall nearby, not a very reverberant acoustic, 100 spectators at least, seats in terrace style.
...
The results were at the hallucinatory level, let's forget these poor man's notions of spaciousness, pin pointed imaging, phantom image, envelopment, dynamic range, as "they are here" or "I am there". Just the cracks of the vinyl were absolutely indecent at this level of realism.

This was not even a 60° triangle, more 20° to 30° for the majority of the listeners. I dunno what was the most important factor : the system or the plausible space (plausible for a concert). Since this blessed day, I do my best to have a huge room.

Glad you enjoyed it! Those demos at Espace Kiron were my idea, you know. :D
The system was all Mr. Hiraga, of course. Quite literally jaw dropping.

Ok Pano, now I understand. That's a really prestigious reference.

As you remember much better than I do, what conclusions can be drawn wrt the actual topic ? This demo was stereo, but for the listeners of the last seats, the speakers were viewed in a narrow angle, I don't remember of anyone complaining of listening in a corridor or of not being in the axis.

It's hard to say wrt to topic.

perhaps the audience in the reverberant field -> decorrelation -> low IACC -> spaciousness?

certainly it was not conventional stereo with "not even a 60° triangle, more 20° to 30° for the majority of the listeners"
 
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Yeah, room corners always seem to have a hall, a door, window or alcove in them. Hard to use.
I did try the corner horns in my room but wasn't crazy about it as I lost some center image. Will try it again, tho, as it's such and interesting idea.
 
Here's something I hadn't thought about. How a difference in imaging cues in the lower mid (time or phase based) and upper mid (amplitude based) can damage each other, when they don't tell you the same image location for a given whole sound...

This is from a paper that someone recommended reading several pages ago.

Speaker imaging info from Deutsche Welle Radio Training Centre, Dieter Beheng

"Level differences and delay time differences interact if they occur at the same time. If they are causing the same effect, they sum up. If they are causing contrary effects they cancel each other partly or entirely."
 
I never had a place that had suitable corners. I was in one yesterday though! Couldn't get it out of my mind. The owner actually listens to her iPhone placed in one of the corners. Nothing else, just her iPhone. It gets surprisingly loud there for such a little device. Definitely usable for listening to internet radio and such. Organic(joking ppl) amplification rocks.

Dan
 
Yeah, room corners always seem to have a hall, a door, window or alcove in them. Hard to use.
I did try the corner horns in my room but wasn't crazy about it as I lost some center image. Will try it again, tho, as it's such and interesting idea.

I could do it in my room, but I wouldn't. The way I see it, placing a sub in the corner, and I do that, is the same thing as a "corner horn". In what way is it any different? Lower bandwidth? Thats depends on how you do the whole system. I am free to place mains anywhere I want for a better optimization of the mains design and placement. I've never bought into the "corner horn" thing, not even when Klipsch did it. Put your subs in a corner sure, I've always done that.
 
If the sidewall can be considered to be a part of the horn itself, then the ipsilateral reflection is avoided altogether. That could be an advantage. If the diffraction in the upper midrange/treble can indeed be worked around (as Wayne explained), then I think the corner horn could be an interesting contender. I'd love to see some measurements that show the influence of the near wall!
 
I could do it in my room, but I wouldn't. The way I see it, placing a sub in the corner, and I do that, is the same thing as a "corner horn". In what way is it any different? Lower bandwidth? Thats depends on how you do the whole system. I am free to place mains anywhere I want for a better optimization of the mains design and placement. I've never bought into the "corner horn" thing, not even when Klipsch did it. Put your subs in a corner sure, I've always done that.

As I see it, when it's done right, it prevents a lot of problems in the midrange. It's like an extension of the waveguide, one that makes it work all the way down to the Schroeder frequency. You can fit your waveguide into the corner as you see fit, blending its flare contour with the walls if you wish. The only disadvantage, as I see it, is it limits placement options. Not all rooms are suitable.
 
perhaps, there is some difficulty in that neither clarity nor spaciousness can be objectively measured

graaf, you have a point here. I suggest that "clarity" is the opposite to "diffusity", and "spaciousness" is the opposite to "dryness".

2 channel reproduction forces a compromise between clarity and spaciousness (we agree).

but what is clarity? in fact there is a scentific convention on factors of clarity -

for Leo Beranek ("Concert hall acoustics", Journal of the Acoustical society of America 92, 1992) clarity is about the "adequate ratio between the energy of the first 80ms and that in the next 2s":

"Clarity means the ability of distinguishing successive musical notes and different instrumental groups or the clear detection of words. It seems to be a degree for intimacy. As an objective criteria for music it means the ratio between the energy of the first 80ms and the energy after 80ms."
see picture below
"For speech applications the same criteria is used but with the limit of 50ms."

looks like neither clarity nor clarity/spaciousness is a question of early reflections AT ALL
 

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That may or may not be true. I don't think early reflections are good, but it's not just the clarity thing. There are big problems just in terms of amplitude response from early reflections in some frequency bands. If the delay of the reflection is close to the half period of the waveform, it makes roller coaster response. It's very noticeable when compared with another speaker that doesn't do this, night and day.

When you have a dip at 120Hz caused by self-interference from the wall behind the speakers or floor bounce or a room mode, it messes up vocals and instruments like piano, guitar and trombone. Some sound too thin, others sound throaty. It depends on where the null is in relation to the peaks surrounding it.

This notch isn't always a sharp thin notch, either. I suspect if that were the case, it would be maybe a little less audible. Sometimes it's wide, like half an octave. Even if thinner, when it makes a 15dB notch that spans two notes, then you can really hear it as singers, piano keys or whatever progress through the range.

The thing is, so many people have never compared two similar speakers, one set up as a constant directivity cornerhorn, another in a more traditional cabinet. So it is easy to get used to the sound of the midrange ripple and not notice it. But your microphone will clearly show it. And if you take two speakers - one a constant directivity cornerhorn and another a traditional box pulled away from the walls a few feet - you'll definitely hear the difference, as plain as day.
 
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Wayne I've tried several times to simulate this in the CARA room software and just can't see a big difference. But I'll keep trying!

If you can give me some typical box dimensions and frequency ranges to look at, I might have more luck finding it. Also: Would it have to be a horn loaded cabinet, or would the effect be similar on a direct radiator placed on a corner baffle?
 
So what does everyone experience when they lean to the side? Wintermute gets an image shift to the opposite side, I get a shift that stays on front of me.

Same side: 1
Opposite side: 1

Dan
Without data on the speaker directivity, angular separation, toe in, and general room set-up, is such information of any use ? If the data can't be correlated to anything, then nothing will be learnt from it.
 
I think everyone knows their speaker's pattern here and how to use a tape measure. I hope so anyway. Can't really discuss optimal patterns w/o some idea of that info. I'm surprised that in this group, the thought hasn't sparked any conversation especially since we are discussing ideals.

Dan
 
Your scenario sounds good and I accept your math but you are being a little misleading regarding where this started from and what I said. When I suggested that nulls where the cause of the contrary shift in stereo image you said that it was more likely an overcompensation of the time intensity tradeoff.
Dave, I take your point, and I'm not attempting to be misleading. In fact when I did the numbers and it didn't come out as favourably as I expected them to, I still presented the results anyway instead of being disingenuous by letting the matter quietly drop.
My mental math said that sound at about 1 foot per msec would take a 1 foot net distance shift for 2 msec. This is because the difference is double the lateral shift since you are getting closer to one unit and farther from the other. I realized there would be a vector slope factor so I upped the 1 ft to 1.5. Your math is more accurate. Sound travels a foot in .87 msec and the geometry of your 60 degree triangle cuts the shift by a factor of 2 (not the 1.5 I guessed). In the end the 1.5 feet (I did not say 1 foot) I mentioned would require a 13dB balancing shift, plus your 1 dB for drop due to distance. So we are at 14dB by proper calculation rather than 16 dB by my estimate!

Note that 14dB and the 1.5 ft lateral shift would be perfectly complimentary amounts. One would balance the other out and the image would not shift at all (in theory). Your contention was that we had overcompensated for the time intensity difference to the point where the image shift went in the wrong direction. How much level shift would that take? Would it take as much as twice the 16dB per 2 msec that maintains a stationary image? It would have to be significantly greater than 16 for 2 to cause the contralateral shift.

If your speakers fall off 7dB in 6 degrees then they will just balance out (not overcompensate). Thats a pretty steep slope. A speaker's polar might make it at some frequency. I wonder if it will be flat in response at that point in the polar curve?
I think expecting it to work over +/- 1.5 feet in horizontal location is expecting too much. Part of the reason I used 1 foot for the calculation was that +/- 1 foot lateral movement is about the widest I've experienced in practice where the phantom image stays roughly in the middle 25% without collapsing.

More might be possible with better directivity control, but my speakers are only horizontal CD (~90-100 degrees) above 4Khz, and have a significant pattern narrowing (and power response dip) at 3Khz, as the crossover frequency is too high to match the directivity of the full range driver with the ribbon tweeter as you normally would in a proper CD design. (I cross it over higher for other - to me - more important considerations than strict directivity matching)

Still, the sweet spot widening effect seems to work with crossing in front of the listener instead of crossing behind, it's just now that I've done these calculations its left me unsure as to exactly what's behind it, and I'm now thinking that straight intensity/time trading can't be the sole explanation, even if it does help somewhat.

Perhaps other factors are also at work, such as reduced ipsilateral wall reflections, and the extra pattern narrowing at 3Khz may be playing a role as well - a significant reduction in output in the presence region of the nearer going-further-off-axis speaker may have more effect on image location than full spectrum intensity/time trade-off would suggest. (I've found small errors in left-right balance in the presence region can have quite an effect on pulling the image to the louder side, more so than at many other frequency ranges)

In short, I'm not sure exactly what's happening.
 
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