Thank you for the interesting content.
1.) I'm not suggesting that the metric I outlined would be a general performance indicator or that it should on its own be used to create a ranking. I qualified it further by restricting its usefulness to people willing to use equalization. To those people however, such a metric would be highly useful.
2.) I'm not suggesting to rate the differences between the listening window and early reflections curves. Clearly there can be no universal standard of an ideal drop-off: Some may prefer a steeper drop-off and narrower directivity, others a more gentle drop-off and wider/more diffuse directivity.
3.) What I've been trying to suggest is to measure the evenness of the drop-off (whatever it may be) between the listening window and early reflections curves across the frequency spectrum. Followin Amirs explanations, everybody should want the early-reflections curve to track/run parallel to the listening-window-curve, irrespective of one's preference for wider or narrower directivity.
4.) It seems at least worth exploring whether such a metric combined with others would allow us to contruct a simple graphical representation of a speakers overall performance, that would a.) be indicative of actual performance in most contexts and b.) be easily readable by interested novices not familiar with audio science. For that purpose I suggested radar diagramms.
PS 1: Now to fully expose how unfamiliar I actually am with speaker design, from simply visually inspecting the curves you posted, the Rega's early reflections curve seems to most closely track the on-axis curve, which... would seem to fit the preference distribution... What am I getting wrong here?
PS 2: To illustrate: Imagine I printed and cut out a a number of on-axis curves without anything else and without db-scale. Just the curves themselves without context. Imagine I then printed and cut out the early-reflections curves of the same speakers, again without anything else and without db-scale. Now I would lay all those cut out curves out on a table. If the speakers had been well designed in this regard, I should easily be able to identify matching pairs of curves, without having any need for a db-scale. The absolute drop-off wouldnt matter - and it wouldnt matter in the metric I propose. Only the closeness of tracking would be evaluated.
All Fair points! I didn't meant to shut down your idea either, so I hope I didn't come off that way. I just wanted to make clear that when comparing two different speakers, things get more complicated.
But yeah, as long as its made clear to readers that they shouldn't take the even-ness of the early response curve as an absolute when comparing to other speakers, I'm fine with it.
I bet if the listening room was narrow, the speaker with wider dispersion would not be as preferred. It's situation dependent, which is why I don't think directivity past the listening window should be factored into a sonic quality score.
My impressions from reading Dr Toole's book and a few of the studies is that preference tend to be more a matter of use case and even individual preference than the space being tested in. This is something that definitely needs more research though.
Anecdotally, I have a very narrow listening room(13ft) - my speakers are only about 2-3 feet from the sidewalls - and I almost universally prefer wide-directivity designs for regular listening, despite always thinking I'd have preferred narrower designs. Narrow designs tend to have more pinpoint soundstage and more flexibility for adjusting the sound with placement, but I end up preferring the more expansive sound of wide designs. All sighted individual opinions of course, so not of much scientific value, but just some context for where I'm coming from.
I'd like to agree with you having owned and loved Quad ESL63 speakers, and liking panels. But I'm not reading those graphs to indicate the Quad looks better. It would appear Quads look worse except above 10 khz. I would have looked at those graphs and predicted Quads to finish last. Quad ESL 63s were designed as something of a quasi-point source, and seem to get close to it over the midrange at least. Less so above about 11 khz.
The Quads' off-axis response is ragged as hell there. Objectively not good in that regard.
But... it's like 10 or 20dB down compared to the other speakers' off-axis sound. The off-axis response is worse but you are barely hearing it. It is hardly interacting with the room compared to the other two.
Subjectively this matches up with what I heard when I got to spent a little while listening to them.
The quad is 'messy' but it's pretty well established that evenly spaced high-Q errors, especially in the treble, are less audible than wide, low q problems, which both of the other speakers exhibit. Similar to the errors we see on axis with coaxial speakers, a big reason we take averaged measurements in the first place. Granted, the ESL's peaks and dips are quite tall, but I'd be willing to bet they'd average out significantly.
So my guess would be the quad has better off-axis performance. But that's also what Dr Toole says right in the chapter so obviously that's what I believed:
"In Figure 7.12 the higher broadband directivity of the ESL 63 results in lower level first-order lateral reflections than either of the cone and dome designs. Both cone and dome systems exhibit fairly unattractive off-axis performance compared to the electrostatic system." And:
"Earlier it was speculated, based on current understanding of loudspeaker measurements, that the Quad might have had an advantage in terms of sound quality, or at the very least, not a disadvantage. That speculation was not borne out. For the same reason, the notion that early lateral reflections in the listening room would be audible problems was not reinforced."
Anyway, it's section 7.4.2 of the book, if anyone wants to check in for themselves. Ultimately it's just one study. I would much like to see a similar test repeated with modern speakers that have cleaner off-axis performance and more polar data.
That's why I keep bringing up the M2 vs Salon2 example, which I know I've touched upon with
@Blumlein 88 on another thread. To recap for everyone else, here's the spinoramas for the JBL M2:
And here's the Revel Ultima Salon2:
The M2 has 'prettier' curves, but the Salon2 won by 80:20 and 65:35 ratios in two double-blind listening sessions with 15 listeners. Wider directivity and maybe a cleaner ERDI curve seem to be the reasons. I wonder how the listening session would have fared with mixing engineers or in different spaces.
Anyway, just a friendly reminder to everyone in this thread that the prettier curve isn't necessarily the better one =]