Rudolf and Radugazon, what was the angular separation between your speakers relative to the listening position during your tests ?
I find there is an optimum range of angles to get a solid phantom image, and it may not be the same angle for everyone...
Too narrow and there is too much comb filtering causing instability in the phantom channel with small head movements, too wide and the phantom image will start to stretch apart and become vague.
I find there is an optimum range of angles to get a solid phantom image, and it may not be the same angle for everyone...
Too narrow and there is too much comb filtering causing instability in the phantom channel with small head movements, too wide and the phantom image will start to stretch apart and become vague.
Perfect 60° triangle of 2 m length (almost nearfield). Dipole speakers toed in 40° instead of 30° - thus 0° axes meeting in front of the listener.
Rudolf
For the phantom localization test we all should use the same signal and repeat the test. I've created 4 different WAVs of correlated pink noise with no filter, 24dB@1500Hz, 24dB@3000Hz and 24dB@6000Hz. You can download all of them here:
http://dl.dropbox.com/u/21936387/pink_noise_localization_test.zip
Please report your findings.
http://dl.dropbox.com/u/21936387/pink_noise_localization_test.zip
Please report your findings.
Do head shapes make a difference? (comb filtering of the head/schnoz/face)
I have a big nose and narrow head. One ear lower than the other (asymmetrical).
My girl friend has a small flat nose and face, round head and her ears are further apart than mine.
Are all the real physical (human) differences compensated for with the minds software?
Or does shape and size skew the results for everyone?
When talking about hearing the phantom image, a hardly mentioned partly unexplored effect also comes into play.
For the “phantom” image to work, that requires that ideally exactly the same signal reaches each ear at the same time. This can be satisfied by a real source directly in front of you or approximated by two identical sources at an equal distance at the desired height.
The problem is just how identical two identical speakers are in this use is a large variable.
By that I mean that if you measure a given speaker outdoors or anechoicaly, you find that moving the microphone an inch or a few inches can give a very different result.
There is a LARGE variation on how much change there is with regard to a change of position. This texture in the sound field can be the result of many things like diffraction, an interference patterns between drivers at crossover and a number of other things which cause it NOT of be a simple acoustic source over a wide band.
What I observed while developing the wide band Unity and Synergy horns for work was that as I got the drivers to add coherently and acted like a single source, the harder it was to hear how far away the speaker was when your eyes are closed.
By that I mean with one speaker on, playing a good voice (what your ears were made for) recording, as the sources became one within the horn, the radiation pattern became simpler and while you could easily hear what direction the speaker was, it became much harder to “hear” how far away the speaker was. My conclusion / theory the “texture” in the radiation pattern the speaker radiates that allows our two ears to localize the position of a single loudspeaker . On the other hand, if one radiated a simple spherical radiation which has less texture, that the ability to hear the speaker as a localized source diminishes.
The ESL-63 has come up. I have a soft spot in my heart for that speaker, my old boss in the 90’s asked my to bypass the protection circuit (spark gaps) in his. They did something like I talked about above. When playing a voice and heard in the near field, they were the first speaker I ever heard that sounded like the sound originated behind the actual speaker. This means the speaker is not radiating much in the way of physical source artifacts hence you don’t hear the speakers physical location strongly.
I didn’t understand that but I did see that unlike the large panel ess speakers I made, this was made in concentric circles and driven to produce a portion of a spherical wave front. While using a different principal and 20+ years later, the Synergy horns at work also radiate a simple spherical segment and exhibit the same effect..
Anyway, this ability to disappear or standout as the source is partly why some speakers image very well and others don’t, even with no room effects. The difference between speakers is so large, it is close to futile drawing a conclusion from one ended listening with one type or another
For any who are genuinely interested in what I have been getting at, do the stereo experiment I suggested earlier.
Get a pair of small full range drivers (like a 4” fostex etc), mount them on large flat baffles (ideally with a sealed rear box) and then eq them to be flat. Set them up as a stereo, away from the walls. Sit between them and you will hear amazing stereo imaging. Obviously these are dynamically limited and response limited BUT they are a single simple radiation over a large part of the band and vividly illustrates what happened when you greatly reduce the radiation signature of the source.
With this system, you can hear the space and image in the recordings I had linked to earlier as well.
Best,
Tom Danley
Danley Sound Labs
For the “phantom” image to work, that requires that ideally exactly the same signal reaches each ear at the same time. This can be satisfied by a real source directly in front of you or approximated by two identical sources at an equal distance at the desired height.
The problem is just how identical two identical speakers are in this use is a large variable.
By that I mean that if you measure a given speaker outdoors or anechoicaly, you find that moving the microphone an inch or a few inches can give a very different result.
There is a LARGE variation on how much change there is with regard to a change of position. This texture in the sound field can be the result of many things like diffraction, an interference patterns between drivers at crossover and a number of other things which cause it NOT of be a simple acoustic source over a wide band.
What I observed while developing the wide band Unity and Synergy horns for work was that as I got the drivers to add coherently and acted like a single source, the harder it was to hear how far away the speaker was when your eyes are closed.
By that I mean with one speaker on, playing a good voice (what your ears were made for) recording, as the sources became one within the horn, the radiation pattern became simpler and while you could easily hear what direction the speaker was, it became much harder to “hear” how far away the speaker was. My conclusion / theory the “texture” in the radiation pattern the speaker radiates that allows our two ears to localize the position of a single loudspeaker . On the other hand, if one radiated a simple spherical radiation which has less texture, that the ability to hear the speaker as a localized source diminishes.
The ESL-63 has come up. I have a soft spot in my heart for that speaker, my old boss in the 90’s asked my to bypass the protection circuit (spark gaps) in his. They did something like I talked about above. When playing a voice and heard in the near field, they were the first speaker I ever heard that sounded like the sound originated behind the actual speaker. This means the speaker is not radiating much in the way of physical source artifacts hence you don’t hear the speakers physical location strongly.
I didn’t understand that but I did see that unlike the large panel ess speakers I made, this was made in concentric circles and driven to produce a portion of a spherical wave front. While using a different principal and 20+ years later, the Synergy horns at work also radiate a simple spherical segment and exhibit the same effect..
Anyway, this ability to disappear or standout as the source is partly why some speakers image very well and others don’t, even with no room effects. The difference between speakers is so large, it is close to futile drawing a conclusion from one ended listening with one type or another
For any who are genuinely interested in what I have been getting at, do the stereo experiment I suggested earlier.
Get a pair of small full range drivers (like a 4” fostex etc), mount them on large flat baffles (ideally with a sealed rear box) and then eq them to be flat. Set them up as a stereo, away from the walls. Sit between them and you will hear amazing stereo imaging. Obviously these are dynamically limited and response limited BUT they are a single simple radiation over a large part of the band and vividly illustrates what happened when you greatly reduce the radiation signature of the source.
With this system, you can hear the space and image in the recordings I had linked to earlier as well.
Best,
Tom Danley
Danley Sound Labs
I tried with isosceles 5 m long x base 3m, equilateral 3 m, isosceles long 3m x base 4m.
For Elias: bilocalisation = two apparent sources (sorry for my English)
and I repeat with different words:
when using 4" full range cone drivers in OB, under a low pass 1200/1500 Hz, there is a strong phantom central image, over this limit, the source is progressively split into two with each speaker for origin. Same conclusions with a high pass going gradually lower from 10000 to full range : the center appears under the 1200/1500 limit. (that's why I use small Full rangers instead of pure tweeters that are not very efficient at these freq)
But, what I hear, is that the real strong centered image appears only when no HF at all. It's also reinforced if I add a couple of woofers for the under 200 Hz range that these 4" in OB can't reproduce.
As Rudolf's observations go roughly in the same direction, the first idea that comes is that this limit 1200/1500 Hz is also the transition ITD-ILD. (with all the implications in the median plane determination). Impossible to forget the finding of DBM (effects of a dip 800/1200 Hz on imaging)
Schupbach (stereolith) has also a personal theory about this limit for stereo imaging, explaining why he goes with a single tweeter.
Hummmm...
Ps :Rudolf, thanks for posting, I feel better.
to morrow I try markus files, and tests on the wife too.
For Elias: bilocalisation = two apparent sources (sorry for my English)
and I repeat with different words:
when using 4" full range cone drivers in OB, under a low pass 1200/1500 Hz, there is a strong phantom central image, over this limit, the source is progressively split into two with each speaker for origin. Same conclusions with a high pass going gradually lower from 10000 to full range : the center appears under the 1200/1500 limit. (that's why I use small Full rangers instead of pure tweeters that are not very efficient at these freq)
But, what I hear, is that the real strong centered image appears only when no HF at all. It's also reinforced if I add a couple of woofers for the under 200 Hz range that these 4" in OB can't reproduce.
As Rudolf's observations go roughly in the same direction, the first idea that comes is that this limit 1200/1500 Hz is also the transition ITD-ILD. (with all the implications in the median plane determination). Impossible to forget the finding of DBM (effects of a dip 800/1200 Hz on imaging)
Schupbach (stereolith) has also a personal theory about this limit for stereo imaging, explaining why he goes with a single tweeter.
Hummmm...
Ps :Rudolf, thanks for posting, I feel better.
to morrow I try markus files, and tests on the wife too.
Big differences and no standard. Just try to listen music while changing the orientation of your outer ears with your fingers : this will sound very different, you will describe this as "colored". But after one minute only, you will take this as natural, and feel that the sound with relaxed ears lacks of something...
Dn't worry for your lower ear, nobody is perfectly symmetric, and some creatures like the owls have fully dissymetric outer ears for a better localisation.
How large were the variations you're talking about? A lot of people make the mistake to measure in the driver's nearfield. 2m or more would be better.
Were the mono tests a single speaker only playing, (located where ?) or playback of a mono recording on a normally set up stereo pair ?
If the test was in fact a single speaker, ignore the last paragraph
They were single speaker comparisons. Toole makes the point that stereo diminishes the differences between speakers. In stereo test we enjoy the stereo and forget about response differences (my paraphrase).
I understand this and have, in the past, dubbed this a "micro" vs. a "macro" view of dispersion. Still, we get this oppinion from multiple sources including the study showing that (most) professionals prefer to work with more directional speakers, even if they enjoy listening at home with wide dispersion systems. I think the general argument has been broadly made that more directional systems, of any pattern, give a dryer but more revealing image. You may or may not prefer it.
Um...a piano? A drum?
But they did know why: it was an unnatural lack of spaciousness. Not complaints of phasiness, or "sound in my head". I had electrostats in the past. I don't remember phasiness unless, of course, if I stood to the sides with the null plane between my ears.
Lack of box = no boxy sound? Thats a bit oversimplified. Have you heard of cabinet stuffing? Again, when you look at the measurements of the typical electrostatic the tons of resonances seem to be a poor tradeoff against the supposed benefit of the lack of a box.
Look through the Toole tests. Many of the top ranked systems have random crossover holes in their power response. I've pointed this out numerous times. To me it is an indicator that power response flatness doesn't matter. It falls in line with Lipshitz and Vanderkooy tesiting showing that holes in the power response are benign. Also, be aware that CD based systemw are just as likely to have power response holes at crossover. They will only be better in d.i.flatness within the drivers passband. (As a Linkwitz/Riley xover believer I think that a power response hole is a sign of good design.)
I'll concede I'm stretching the point a bit, but to me Toole's tests show so clearly that power respone shape (d.i. curve) is irrelevant that adding systems to the mix with CD characteristics wouldn't make any difference. That is, the tests had systems both with with flatter and less flat power response. (I attached the image to a post the other day.) There was no preference for flatter power response, so adding a CD system with supposedly really good power response wouldn't change results. Unfortunately, since most CD systems have higher directivity (they don't have to but they do), this higher directivity carries a penalty with it: less spacious sound.
I'm sure a CD system of wide dispersion and very smooth and flat axial and near axial response would do well it Toole's tests. I just don't think its CD nature alone gives it an advantage. (Other than hopefully improving response over a broader listening window.)
David S.
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Pink_Noise_Full_Spectrum:
"Nailed" center phantom, even when turning head. Tweeters hardly locatable, only by their comb filter when moving the head.
Pink_Noise_HP_24dB_1500Hz:
Center image absolutely dominant, but tweeters become much "better" audible, notably when turning the head 90° away from them.
Pink_Noise_HP_24dB_3000Hz:
Center image still dominant, but tweeters increasingly audible. Already a sort of "3 sources" impression.
Pink_Noise_HP_24dB_6000Hz:
Phantom and tweeter images very wide, almost connected to one wide source. All three at the same SPL.
"Nailed" center phantom, even when turning head. Tweeters hardly locatable, only by their comb filter when moving the head.
Pink_Noise_HP_24dB_1500Hz:
Center image absolutely dominant, but tweeters become much "better" audible, notably when turning the head 90° away from them.
Pink_Noise_HP_24dB_3000Hz:
Center image still dominant, but tweeters increasingly audible. Already a sort of "3 sources" impression.
Pink_Noise_HP_24dB_6000Hz:
Phantom and tweeter images very wide, almost connected to one wide source. All three at the same SPL.
So you think Elias with his "two tweeter localization feature" already took the next evolutionary step? Looks like stereo soon comes to an end
Markus, how do you hear the 4 noise samples you posted today?
- Elias
Markus wrote;
“How large were the variations you're talking about? A lot of people make the mistake to measure in the driver's nearfield. 2m or more would be better”.
You are right, in fact if one wants to use something like polar measurements to predict wherever the sound is when far away, one needs to follow the criteria here;
http://community.klipsch.com/forums/storage/3/550738/FarFieldCriteriaLdspkrBalloonData.pdf
To get the data for the data files used in the CLF format, this allows one to view many aspects of the speakers performance including a 3d view of the radiation balloon. here;
ETCINC.US - The Data
Where the sound goes is a MUCH larger concern in commercial sound as the large room's reflected sound is what makes it hard to hear the words like when your train is leaving. That reflected sound even if nice sounding only harms your ability to hear the direct sound hence undesirable where information is to be conveyed.
So far as what I am talking about, this behavior would be missed in that format as the data points are only 5 degrees around the sphere.
The thing I am talking about is at a typical listening distance, much finer than 5 degree resolution.. This is a texture which is fine enough to present the R and L ears with differences radiated from one speaker.
I am not sure how much formal work has been done on this and remember what I have said is only what I have observed so far with the point source horns for work listening at home and fiddling with that microphone array.
It is clear to me though that the speakers ability to shout out or conceal itself in depth is strongly connected to it’s ability to disappear when producing a mono phantom or stereo image. Other things enter into it like the room and recording quality but this is part of it I have not heard people talk about so remember where you heard it haha.
I do know that for the microphone array, I needed a test source that radiated a simple spherical segment like a distant source (the inverse of a measurement microphone in operation) and this proved to be difficult.
A small accuton inverted dome on a 6 foot flat baffle worked the best but was very limited in its power and obviously low frequency limited.
In other words, it was hard to make a real point source covering even half of the spectrum that didn’t have some spatial warts.
I do not know where the point of audibility is though, my concern was a blameless test source and the only way to get it was an acoustically small source on a large flat baffle.
I can say that with that source, playing band limited pink noise, that as you moved around in front of it, there was no change, no comb filtering, no swishing, audibly, a largely single spherical radiation.
With pink noise, outdoors, when you hear things moving around the sound field, you are hearing the spatial fingerprint, part of what says to your brain “here I am 6 feet in front of you.” and this you don’t want when you’re producing an image that is supposed to be between the two sources.
Also, in the last year or two KEF has also discovered that you can localize a complex acoustic source and have positioned it’s drivers to radiate like a point source (the Blade speaker) or single apparent source. I don’t know how close it comes to a spherical patch and it would not be time coherent or a single source in time like a Synergy horn without dsp but they claim improved stereo imaging.
Best,
Tom Danley
Danley Sound Labs
Danley Sound Labs, Inc. | Facebook
“How large were the variations you're talking about? A lot of people make the mistake to measure in the driver's nearfield. 2m or more would be better”.
You are right, in fact if one wants to use something like polar measurements to predict wherever the sound is when far away, one needs to follow the criteria here;
http://community.klipsch.com/forums/storage/3/550738/FarFieldCriteriaLdspkrBalloonData.pdf
To get the data for the data files used in the CLF format, this allows one to view many aspects of the speakers performance including a 3d view of the radiation balloon. here;
ETCINC.US - The Data
Where the sound goes is a MUCH larger concern in commercial sound as the large room's reflected sound is what makes it hard to hear the words like when your train is leaving. That reflected sound even if nice sounding only harms your ability to hear the direct sound hence undesirable where information is to be conveyed.
So far as what I am talking about, this behavior would be missed in that format as the data points are only 5 degrees around the sphere.
The thing I am talking about is at a typical listening distance, much finer than 5 degree resolution.. This is a texture which is fine enough to present the R and L ears with differences radiated from one speaker.
I am not sure how much formal work has been done on this and remember what I have said is only what I have observed so far with the point source horns for work listening at home and fiddling with that microphone array.
It is clear to me though that the speakers ability to shout out or conceal itself in depth is strongly connected to it’s ability to disappear when producing a mono phantom or stereo image. Other things enter into it like the room and recording quality but this is part of it I have not heard people talk about so remember where you heard it haha.
I do know that for the microphone array, I needed a test source that radiated a simple spherical segment like a distant source (the inverse of a measurement microphone in operation) and this proved to be difficult.
A small accuton inverted dome on a 6 foot flat baffle worked the best but was very limited in its power and obviously low frequency limited.
In other words, it was hard to make a real point source covering even half of the spectrum that didn’t have some spatial warts.
I do not know where the point of audibility is though, my concern was a blameless test source and the only way to get it was an acoustically small source on a large flat baffle.
I can say that with that source, playing band limited pink noise, that as you moved around in front of it, there was no change, no comb filtering, no swishing, audibly, a largely single spherical radiation.
With pink noise, outdoors, when you hear things moving around the sound field, you are hearing the spatial fingerprint, part of what says to your brain “here I am 6 feet in front of you.” and this you don’t want when you’re producing an image that is supposed to be between the two sources.
Also, in the last year or two KEF has also discovered that you can localize a complex acoustic source and have positioned it’s drivers to radiate like a point source (the Blade speaker) or single apparent source. I don’t know how close it comes to a spherical patch and it would not be time coherent or a single source in time like a Synergy horn without dsp but they claim improved stereo imaging.
Best,
Tom Danley
Danley Sound Labs
Danley Sound Labs, Inc. | Facebook
Very nice guitar work. One song reminded me of Robert Johnson. The song Everything That I Am is gorgeous.
The thing about recording is that the mic has all the same problems at the recording end that a speaker has at the playback end; room acoustics perhaps being the major challenge. Or if an instrument is close mic'd, what do you do with that signal to create a sense of soundstage. In a sense, George Martin was one of the Beatles, because he played a major role in editing and creating the final soundscape, often from discrete fragments.
I'm pretty sure we all get well used to the sounds of our own headshapes.
An interesting thing is to get in a noisy environment (continuous noice, such as an airconditioner fan or fFM interstation hiss) and carefully pin the back of your ears back. The noise spectrum changes pretty obviously as we change the reflections off of the outer ear. Still, I'm sure you would get used to the new sound in short order.
What was the test they did with volunteers wearing prism glasses that inverted their view of the world? After a few hours (days?) they got totally used to the inverted world and didn't perceive it as upside down. You could take the glasses off and they would stumble around.
The only problem comes when we record sound binaurally with a dummy head different than our own. They can only be made to generic dimensions.
David S.
With my speakers, 10" cardioid midrange and waveguide > 1 kHz (El Cuerno), all of the samples are perfectly centered. It appears though that the image of the sample with a highpass at 6 kHz is slightly broader, but definitely coming from the center and not from 2 speakers. During a lateral movement however the two distinct sources are reveiled, so it is important not to move during the test
When stopped, the location of the image is restored. A rotation of the head > 20 degrees also collapses the image.Then I let my girlfriend do the test. I asked her if she could tell where the sound is coming from. I did not tell her anything else and I played the samples at random. For all of the samples she said that the sound came from the center, the ones with a higher cutoff frequency slightly (5 tot 10 cm) to the right. I also asked her about the size of the image, but she could not really tell other than that the low-cutoff samples were louder than the high-cutoff sample.
Pink noise localization test:
With a toe-out and the Nathan's my experience is nearly identical to that of Rudolf. When using a 45° toe-in things change, the phantom center is very well defined but also near. Turning the head has less effect on localization. At worst there's some widening and ambiguity but never more than one image.
With a toe-out and the Nathan's my experience is nearly identical to that of Rudolf. When using a 45° toe-in things change, the phantom center is very well defined but also near. Turning the head has less effect on localization. At worst there's some widening and ambiguity but never more than one image.
Nathan and El Cuerno are very similar speakers, good to hear that the results are identical. BTW I can only do the 45° toe-in, the asymmetrical setup will not allow for a toe-out.
I'm absolutely sure it was brilliant.
(Gee, I hope I haven't driven you to drink.)
David S.
Well maybe from when we first met (you gave me a lot of grief back then), but I've been drinking Bourbon regularly for about 30 years now. I've sent enough change to that small county in Kentucky to buy someone a nice sailboat!
My major point was that for a given room of "typical" design, narrowing the directivity will cause a loss of spaciousness and a general degradation in what most people would deem to be a good sound. BUT, I have long proposed the use of high directivity in very reverberant rooms quite unlike what are commonly designed. Place a typical speaker in one of my rooms and it will sound awful because of the high reveberation and poor power response of most speakers.
When you consider the loudspeaker/room as an inseperable design problem, as I do and you alluded to Kantor doing the same, then you get a different approach and we can no longer use data obtained from "common" rooms as its not applicable to this new situation.
The idea is simple: minimize the <10 ms. reflections with high directivity to obtain good imaging and maximize the reflections > 10 ms. with highly reverberant rooms. Of course, the space behind the speakers must always be dead - even Floyd agrees with this.
If you use high directivity in a typically dead small room, then I would agree with your comments that there is nothing to be gained and a lot to be lost. BUT if you use high directivity in a very reverberant small room then there is a lot to be gained because the highly directional CD speaker can achieve something that the others cannot - good imaging and good LEV at the same time.
I did see from Marcus that Floyd lumps both ASW and LEV into spaciousness, which I would contend is not correct, but agree that it is open to interpretation. Since these terms and concepts come directly from Auditorium Acoustics, I would have to assume that they are relavent only to the temporal region where all reflections are > 20 ms. In this case ASW and LEV would be linked. But in the small room situation where one has significant reflections < 10 ms. this linkage would be broken and these two aspects of perception would no longer result from the same design aspects. They become different and independent things. At best, the entire concept must be taken with a grain of salt when discussing small rooms since its development never even contemplated small rooms. At worst the whole concept is inapplicable to small rooms.
I once discussed this whole subject with Henrik Kutruff and he was of the opinion that nothing of what he studied and wrote about would apply in a small room. (In his book, he didn't even show data below 10 ms.) I don't think the situation is that bad, but I do admit that we must think very carefully about using terms such as "spaciousness, ASW and LEV" in a small room.
Ken Kantor's MGC-1 speakers were hugely inspiring to me when they came out. I was going to build virtual copies of them at one point. I never did get a chance to actually hear them...
On the issue of high band pink noise comb filter audibility... If there is more than one tweeter in the room, putting out the same thing at the same time but physically displaced relative to the listeners ear, then comb filter effects are likely to exist and be audible. This is because the wavelengths of those frequencies varies from about 6 inches to about 1/2 inch, and if one tweeter is one inch closer to your ear than the other, the frequency who's half wavelength is one inch will have a cancellation at your ear (approx. 5kHZ with this example), and at all the integral multiples of that frequency (10k, 15k, 20k and so on, in this example). Is that like too many cooks in the kitchen? Yes, but...
It would seem to me that using a tweeter array (top of the line 1960's Bozak style) might minimize this particular comb filtering audibility. Where in frequency, one combination of physically displaced tweeters causes cancellations, other combinations would tend to fill those cancellations in, because of their differing time delays mandated by their different physical distances from your ears. If you had 8 little 3/4 inch dome tweeters arrayed like that, you'd totally destroy any timing cue info, which the brain doesn't use at those frequencies, but you'd have a more even amplitude delivered to each ear, even as you moved your head sideways (not necessarily twisted). Without as much distraction from these approx. >2kHZ interference patterns giving each position of the listeners head (and each ear) a noticeably different sound, the upper mid imaging might be much more consistent and less colored sounding.
This may be part of why Roger Russel of McIntosh speaker development likes vertical line arrays so much. Each cancellation that tries to exist gets filled in by so many other drivers due too their differing time delays because of their differing physical distance to the listeners ear, that the end result is a relatively smooth and consistent over physical movement sound.
On the issue of high band pink noise comb filter audibility... If there is more than one tweeter in the room, putting out the same thing at the same time but physically displaced relative to the listeners ear, then comb filter effects are likely to exist and be audible. This is because the wavelengths of those frequencies varies from about 6 inches to about 1/2 inch, and if one tweeter is one inch closer to your ear than the other, the frequency who's half wavelength is one inch will have a cancellation at your ear (approx. 5kHZ with this example), and at all the integral multiples of that frequency (10k, 15k, 20k and so on, in this example). Is that like too many cooks in the kitchen? Yes, but...
It would seem to me that using a tweeter array (top of the line 1960's Bozak style) might minimize this particular comb filtering audibility. Where in frequency, one combination of physically displaced tweeters causes cancellations, other combinations would tend to fill those cancellations in, because of their differing time delays mandated by their different physical distances from your ears. If you had 8 little 3/4 inch dome tweeters arrayed like that, you'd totally destroy any timing cue info, which the brain doesn't use at those frequencies, but you'd have a more even amplitude delivered to each ear, even as you moved your head sideways (not necessarily twisted). Without as much distraction from these approx. >2kHZ interference patterns giving each position of the listeners head (and each ear) a noticeably different sound, the upper mid imaging might be much more consistent and less colored sounding.
This may be part of why Roger Russel of McIntosh speaker development likes vertical line arrays so much. Each cancellation that tries to exist gets filled in by so many other drivers due too their differing time delays because of their differing physical distance to the listeners ear, that the end result is a relatively smooth and consistent over physical movement sound.
So you think 5° is too coarse even for small room speakers or were you talking about PA? Four Audio | ELF can do 1°.
At any rate I'd say that manufacturers don't show us enough useful data, even the ones that show polars.
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