Duke,
please elaborate “ (I take a controversial position regarding early sidewall reflections - I believe they are generally overall undesirable, though they do have desirable aspects. I can go into detail if anyone would like.)
Early same-side-wall reflections increase the "apparent source width", to use Floyd Toole's terminology. In other words, they can made the soundstage sound like it extends laterally beyond the left and right speakers (even if such information is not on the recording), which most listeners (including yours truly) think is pretty cool.
But this can come at a price.
Quoting Earl Geddes on the subject: "The earlier and the greater in level the first room reflections are, the worse they are. This aspect of sound perception is controversial. Some believe that all reflections are good because they increase the listeners feeling of space – they increase the spaciousness of the sound. While it is certainly true that all reflections add to spaciousness, the very early ones (< 10 ms.) do so at the sake of imaging and coloration."
The same effect which spreads the image wider also smears the precise location of sound images. And regarding coloration, what happens is this: Once the direct sound and that early same-side-wall sidewall reflection have mixed in the ear canal, they are combined. The most beneficial early reflections are the ones which arrive at the opposite ear from the direct sound, because the ear/brain system can process them separately.
Here is Earl Geddes' paper on his speaker design philosophy, most of which I subscribe to. See page five in particular:
http://www.gedlee.com/Papers/Philosophy.pdf
Also, I think that strong early same-side-wall reflections can contribute to a "small room signature" which tends to dominate over the (highly desirable) spatial cues on the recording. (Imo we want to minimize "small room signature" and effectively present the recording's acoustic signature, whether it be real or engineered.)
To offset the loss of soundstage width from minimizing those early same-side-wall reflections we can move the speakers a bit further apart, but I must admit that "soundstage wider than the speakers" thing was pretty cool.
Toole finds that listeners generally prefer good wide-pattern speakers over good narrow-pattern speakers, but I'm not convinced that it is because those early same-side-wall reflections are desirable. I think it may be because having more reverberant energy is generally desirable, and that more than offsets any detrimental effects of those early same-side-wall reflections. (The approach I use results in approximately the same amount of in-room reverberant energy as a good wide-pattern speaker but without significant early same-side-wall reflections, so it's like I'm taking Toole's wide pattern and chopping it up into two narrower slices and serving them up a separately.)
and “implications of dispersion on sweet spot width... some of which is intuitive, some of which is not.”
The ear localizes sound by two mechanisms: Arrival time and intensity. (Most image localization happens north of 500 Hz.)
When you are seated in the central sweet spot, arrival time is the same from both speakers, and so is intensity. This is the ideal. But what happens when you move off to one side?
Well if the speakers have a very narrow radiation pattern (like a wide, flat-panel eletrostat) and are toed in just enough to cover the sweet spot, when you move off to one side a bit you may well be moving outside the effective coverage pattern of the far speaker. So now the near speaker "wins" arrival time slightly, but it "wins" intensity by a very large margin. So the sound images are pulled hard towards the near speaker.
Suppose we are listening to conventional wide-pattern speakers, with some toe-in. Once again when we move off to the side a bit the near speaker "wins" arrival time, and it "wins" intensity as well, largely because we are more on-axis of the near speaker and further off-axis of the far speaker. So the image is still pulled towards the near speaker, but not as much.
Next let's try omnidirectional speakers. Now we are equally "on axis" of both speakers even when we are off the centerline, so the intensity discrepancy is reduced, but the image is stilled pulled somewhat towards the near speaker.
We can significantly reduce the intensity discrepancy by using speakers which approximate a line source, as SPL falls off by only 3 dB for each doubling of distance from a line source, in contrast with 6 dB per doubling of distance from a point source. Sound Lab's big faceted-curved panels have wide enough patterns that you can move off to the side a bit and still be well within the coverage pattern of the far speaker. So the near speaker (which ineviably "wins" arrival time) still "wins" intensity, but by a very small margin, so the image is only pulled a little bit.
Now for the counter-intuitive part: Suppose we take a pair of speakers with constant-directivity horns whose pattern is about 90 degrees wide (-6 dB at 45 degrees off-axis to either side). And let's toe them in severely, like 45 degrees, such that their axes criss-cross in front of central sweet spot. Something very interesting happens as we move off to the side:
Off to the side of the centerline, we are now quite far off-axis of the near speaker, but on-axis (or nearly so) of the far speaker! So the near speaker inevitably "wins" arrival time, but the far speaker "wins" intensity! The result is that we still have a pretty good spread to the instruments even from well off to either side. This doesn't work perfectly, and some off-centerline locations are better than others, but the net result can be enjoyable even from outside the plane of the speakers!
At audio shows I usually set one chair up against a side wall, outside the plane of the speakers, and every now and then the room is so full that somebody reluctantly sits in it. After the song I will ask that person how it sounded from there, and they are invariably pleasantly surprised. I ask if they could still hear an enjoyable spread of the instruments and they have always said yes.
The SECRET to this extreme toe-in technique working well is, the output of that near speaker must fall off smoothly and rapidly as you move off-axis. So it calls for a rather unusual set of characteristics, which most speakers do not have.
Thus, in my opinion (and somewhat counter-intuitively), the widest sweet spot comes from a specific type of fairly narrow-pattern speaker, set up a certain way.
And do you recall just above when I said that "the most beneficial early reflections are the ones which arrive at the opposite ear from the direct sound, because the ear/brain system can process them separately"? Well keep picturing that aggressive 45-degree toe-in we used with our horns to get that wide sweet spot: The left-side speaker is toed in so much that its pattern "misses" the left-side wall, but instead it is aimed across the room towards the right-side wall. So the first strong lateral reflection for the left-side speaker will be off the OPPOSITE wall and will arrive at the OPPOSITE ear, and same for the right-side speaker! Wide sweet spot + spaciousness without coloration, two birds with one stone. Credit to Earl Geddes for both of them.