Concrete Bass Horn Design Question

Eric said:
Here's point sources, showing destructive vs constructive interference:
The angle of incidence and overlap of the "narrow angle" wavefronts mixing looks just like the example 2 horns wavefronts mixing with the slight difference that the horn wavefront is a bit flatter (but still curved).
whgeiger said:
To combine multiple sources, ideally point source distances should approach infinity.
AllenB said:
the radius will be larger
 
Even in that picture (which appears to be a tiny conical horn feeding a lens from a couple feet back) the wavefront is curved.

I never said that sound waves from an exponential horn were flat. My point was simply that they are more flat, then they are hemispherical. Generally speaking - point-sources radiate in all directions, whereas horns have a degree of directivity.

The lobing simulations you've been running are based on two main variables - the inclination-angle of the combining waves (a spatial dependent variable), and the thickness of the combining waves (a frequency dependent variable). If you model 450 square feet of side-by-side horn mouths as point sources, you'll skew the results of your FEA.
 
There's a few things that could skew the results, the shape of the wavefront is pretty minor. Even if the wavefront was flat as a pancake you still have overlap regions of the beams and that will result in interference. The pattern might change a bit but the trends will remain the same.
 
Hi Entropy455,

Here is a link to Inlow Sounds site, go to the '135 hz mid bass horn', scrolling down the page you'll find a mid bass horn suggestion that covers 100 = 1200 Hz (or so) @ high SPL by using four B&C 8PE21 drivers. That, and lots of other horns on that site, look interesting.

inlowsound.com

Regards,
 
1)I've seen it (the "Schumann resonance") on the sonar display - no mater where you look, the Earth has a low frequency hum. Some people think its from the solar wind striking the Earth's magnetic field. Others think its from different layers of the Earth's core spinning at different velocities.
2)When submariners get bored, we'll fart into the microphone, then play it back through the sonar equipment - slowing it WAY down. But first we'll place bets as to how many distinct flaps were contained in said fart - whoever's closest, wins. Needless to say, the sonar techs always won. They sure know their farts. . . . .
3)I don't think the ELF transmitters are operational anymore.
The shape of the wave exiting the horn is frequency dependent. Low frequencies spread out, and high frequencies beam - implying a very pronounced change in wave shape is occurring across the horn's frequency band. But that is not the point I'm trying to make. No one is arguing that horns do not beam at higher frequencies.
4)Assume for a moment that instead of bass horns, I install two 15' x 15' electrostatic speakers, side-by-side. How would you model that?
5)Two point sources 15 feet apart? Or two large planar surfaces, joined directly side-by-side?
6)I know it is not a truly equal comparison, but similarities exist nonetheless - which is that the mouth of a bass horn resembles a large radiating surface, and not necessarily a small point-source. What is happening way back in the throat, is happening way back in the throat. The mouth of the horn does not discriminate. The wave that exists the mouth is what propagates into free-space.
1) Very interesting, all my prior information regarding the Schumann resonance was second hand, and I don't recall the hearing the speculation about solar wind striking the Earth's magnetic field causing it.
2) Also interesting, but is illustrative of the difference between a "pitched down" version of a sound source and an instrument designed to play low. Assume a big guys fart's fundamental frequency (pitch) was an 80 Hz "E". Assume a petite lady's fart is an octave higher, 160 Hz.
Although the harmonics of each of those farts will be similar, if you pitch the higher pitch "instrument" down two octaves to 40 Hz, it will sound "fake", while dropping the 80 Hz note just one octave to 40 Hz will be a fairly convincing representation of an elephant fart. When you take either fart down to the range where you can count the cycles ("flaps") they don't have a "pitch" any more. Good "sampling" keyboards can sound just like the real instrument because they don't just "sample" (record) one note and pitch it up and down, they sample at least one note per octave, or now, with huge computer memory storage costing next to nothing, every note.
Sorry if the above may seem off topic or boring, but it is another way of explaining why the argument that "notes" will go "missing" if there is a -10 or -20 dB "hole" that they fell into is ludicrous- every musical note (other than a pure sine wave) has a fundamental frequency, and a series of harmonics above it. Bass instrument's second harmonic (twice the fundamental note's frequency) is almost always louder than the fundamental frequency. Even if the fundamental is completely eliminated, one can easily identify the note, as well as the instrument playing it- a lead guitar does not sound like a bass guitar if it is "pitched down", and a bass guitar does not sound like a lead guitar if it is "pitched up".

The long explanation is why bass extension is not required to enjoy music that has very low notes, though once you have experienced the fundamental frequencies of those notes, you do tend to miss them when listening to the usual 50 Hz and up "sub-woofers" that are advertised as "earth shaking".

Since you operate heavy machinery, you know what earth-shaking sounds and feels like, and sub-woofers with high build quality, high excursion and high power handling are capable of duplicating an "earth-moving" experience, as I mentioned before, feeling concrete slabs moving with the kick drum is kind of "fun", like pulling a 6 second 1/4 mile run.
3) What is used for submarine communication communication since (or if) they shut down those ELF transmitters? My guess would be the military moved them to New Mexico, probably on top of where we bury our nation's nuclear waste, or perhaps to Taos, where there have been reports of a mysterious VLF "hum"…
4) OK, electrostatics- Toronto Ben's audio "weapon of choice". The first, and only time I heard electrostatic speakers it was truly a "jaw dropping" experience, I heard musical detail I had not heard before while sitting in the "sweet spot". Unfortunately, because the large electrostatic panel is basically one large "full range" transducer, the "sweet spot" is quite narrow, basically the width of the transducer. Outside of the "sweet spot" the sound the planar electrostatic produces is a mess of peaks and valleys that varies with frequency. As Ben has said, you would never be convinced that the singer on the recording was in your home theater if you were down the hall listening to his electrostatic speakers. Having been "fooled" on several different recording sessions into thinking a recorded piece was the actual person singing in my studio, the difference between the two is quite obvious, other than when in the "sweet spot". Trade offs, glorious sound in one spot, vs excellent sound everywhere, there are speaker designs for every taste.
Functionally, you could simulate an electrostatic as an infinite series of individual "full range" sources (the low excursion capabilities of electrostatic membranes limits bass output to girl playing a ukulele low frequency levels) located on a panel of whatever size you choose. Since you only can hear to 17 kHz, no reason to simulate the spacing any more than .06647 of a foot apart.
Remember to include the output from both sides of the panel, unless you prefer to encase the opposite polarity of the electrostatic panel.
The simulation, if the back wave is eliminated, will show a planar wave emanating from the panel, the wave will be planar (sort of, but with a series of peaks and notches in upper response because of the huge width) to around 75 Hz for a 15 foot panel, below 75 Hz the wave will look progressively more spherical.
5) At high frequencies, an exponential horn "beams" a narrow "cone" of sound waves determined by the throat angle, at frequencies lower than the mouth dimension can "support", the waves diffract around the mouth, unless boundaries are placed around the mouth to reduce the "wrap".
Because of the problems with HF "beaming" I generally have stopped using exponential horns for mid and high frequencies, and now use "constant directivity" conical/exponential hybrids, some of which are a virtual single point source from 80Hz and up.
Conical horns are not nearly as space efficient for a given LF SPL as are exponential, or hyp/ex (hyperbolic/exponential hybrid) expansions. Hypex expansions give the most "bang for the buck", but the cutoff below FC is more rapid than an exponential flare. Considering how little recorded musical content below 15 Hz exists, unless you are planning to HP below 14 Hz, a hypex bass horn would save you money in materials for a given SPL, and also can seamlessly blend to "barn door" boundaries, should you decide to take advantage of the forward gain they afford.
6) The waves that exist at the mouth and at any point within an exponential horn not only behave differently, they "look" and sound different at various points off axis, though if the horn is crossed over below 100 Hz, the differences are largely only of academic concern.

Thus ends today's lesson, off to work on the sail boat rig.

Cheers,

Art
 

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Sorry if the above may seem off topic or boring, but it is another way of explaining why the argument that "notes" will go "missing" if there is a -10 or -20 dB "hole" that they fell into is ludicrous- every musical note (other than a pure sine wave) has a fundamental frequency, and a series of harmonics above it.

Yes it is true that the higher harmonics of any given note will remain intact even if the fundamental is gone. So what? The whole point of having a subwoofer is so you can experience the fundamental. If you have deep notches two octaves wide in the sub frequencies what's the point of even having a subwoofer? That two octaves is most of the subwoofer's bandwidth, and with a two octave wide notch you could potentially miss the fundamental AND the first harmonic (although this is not likely going to happen much). You can listen to music through a telephone receiver (while on hold for instance) and receive the vast majority of the music because the telephone bandwidth is where most of the action is. But there's a reason people choose to chase after full audio bandwidth sound and having deep notches two octaves wide in the bass is a huge problem when trying to achieve that goal. I can't imagine why you are still arguing that it simply doesn't make any difference, doesn't matter at all. It matters a lot.

Then there's the case of newer electronic music. Some of that stuff doesn't have any harmonics for the bass notes. In that case, if you miss the fundamental the note is completely MIA.
 
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Then there's the case of newer electronic music. Some of that stuff doesn't have any harmonics for the bass notes.
Yeah, and I hate listening to that boring crap, and it does not have to be new, electronic music has been made that way since the days of the first analog synths over 50 years ago. Those synths had "patches" that allowed a mix of sine, square and saw-tooth oscillators, and LFO modulators to "wobble" the oscillator's pitch and frequency. Some folks just used mostly the sine wave oscillator output.
Some of the "newer electronic music" is using the old discrete analog technology again. Coincidentally, Matt Zwager, the guy that purchased my Madrid NM property, builds analog synths for those folks as his primary source of income.

And one thing to consider- some of the few sources of actual "stereo bass" are produced by the makers of "electronic music", which actually can sound quite interesting (for a few minutes) when you hear a 30-40 Hz LFO sweeping back and forth between stereo subs placed 40-50 feet apart.

I don't only mix jazz, country and rock and roll bands, I have mixed (and produced my own) electronic music for decades :^)

Cheers,

Art
 
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Yeah, and I hate listening to that boring crap ...

I like it, and it's not always boring like car audio bass cds, there's some really interesting stuff. Perhaps this is where the difference of opinion on the importance of this matter comes from. In my world where bass music is awesome, missing 2 octaves of sub frequencies is basically the end of the world, might as well pack it up and not even bother listening at all. In your world where bass music is stupid and you might miss the fundamental of a couple of low notes on a bass guitar in the country or rock or whatever music genre you prefer none of this matters a whole lot.

And one thing to consider- some of the few sources of actual "stereo bass" are produced by the makers of "electronic music", which actually can sound quite interesting (for a few minutes) when you hear a 30-40 Hz LFO sweeping back and forth between stereo subs placed 40-50 feet apart.

Cheers,

Art

The stereo effect of panning bass hard right and left is what I would call boring, not even worth thinking about when you consider the problems that stereo subs with large separation distance cause. If the audience area was a couple acres that would be a different story and well worth using dual separated subs, but not for a small audience area barely as wide as the sub itself.
 
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For example this is just the latest in an ongoing series of bass music threads at avs - Low bass tracks - AVS Forum | Home Theater Discussions And Reviews

The first track is pretty interesting if you have really good subs. If not it's really really stupid.

Also interesting is the "rebassing" tracks in post 16. Add a bit of bass to a stupid song and it becomes a good song. If you have good subs.

There's also the Enya track that is just dumb unless you have good subs, then it's pretty cool.

And there's also the usual car audio tracks mixed into that list with all the low bass and bass effects. This stuff is just monumentally stupid without subs but with subs it's extremely interesting. Especially if you have subs clean enough and powerful enough so you can feel the push and pull of each bass cycle instead of a mush of bloated droning bass. This is what big horns do best, especially when they are corner loaded and you stand in between the horn and the corner, which I have done, it's especially cool to lean against the wall and feel it pushing and pulling even at low spl. It's a terrible spot for higher frequency fidelity but a fantastic spot if you want to experience the bass as actual pushing and pulling cycles instead of the usual mushy drone.
 
In your world where bass music is stupid and you might miss the fundamental of a couple of low notes on a bass guitar in the country or rock or whatever music genre you prefer none of this matters a whole lot.
Dear Troll,

I guess you missed the fact that I have mixed (and produced my own) electronic music for four decades, and some of that music has content down to 20 Hz. I prefer good music of any genre, electronic music can be good, bad or boring just as any genre can.

Although I generally don't pan LF content, there are plenty of electronic music producers that do, and if you want to hear the sound as they intended, stereo subs are required.

If you just want to please yourself, do what ever turns you on, but don't fool yourself into thinking you will convince me that stereo subs are some sort of problem after hearing them sound OK indoors and outdoors with spacing from as little as 20 feet (6 meters) to 80 feet or more (25 meters) in every possible listening location from directly in front of either stack to hundreds of meters distant. In over fourty-two years of mixing, I have heard plenty of complaints, but not one single complaint from several million paying concert customers saying "I couldn't hear the bass notes" due to stereo sub placement.

Yes, stereo speaker placement does cause frequency dependent peaks and nulls off axis.
Those off axis nulls are not a problem for any genre of music.

The OP's preferred listening position will be directly on axis, where stereo mains and subs will produce no nulls, and (if correctly deployed) will result in +6dB more output than a single mono sub of the same design.

I'd ask you to give it a rest, but trolls don't rest, do they?

Art
 
Dear Troll,

LOL.

Yes, stereo speaker placement does cause frequency dependent peaks and nulls off axis.
Those off axis nulls are not a problem for any genre of music.

The OP's preferred listening position will be directly on axis, where stereo mains and subs will produce no nulls, and (if correctly deployed) will result in +6dB more output than a single mono sub of the same design.

I'd ask you to give it a rest, but trolls don't rest, do they?

Art

I'll give it a rest as soon as you stop saying deep notches 2 octaves wide aren't a problem.

The preferred listening position is a fairly large green circle on a map he drew, there's no reason you can't have good coverage over that entire area without massive notches.

A single sub is just as loud if you use more Sd or turn up the volume knob 6db.

I've given up on trying to convince you of anything but I have proven that the single sub is technically superior for this installation. If you chose the ignore the evidence that's your problem not mine. Just don't ask me to shut up while you continue spouting your nonsense.
 
1)I'll give it a rest as soon as you stop saying deep notches 2 octaves wide aren't a problem.
2)The preferred listening position is a fairly large green circle on a map he drew, there's no reason you can't have good coverage over that entire area without massive notches.
3)A single sub is just as loud if you use more Sd or turn up the volume knob 6db.
Dear Troll,

1) Your simulations are not reality, if you had any actual experience measuring and listening to real stereo horn subs outdoors you would realize how far they are from reality.
2)There is no reason that a stereo set up rather than a mono sub won't provide good coverage in the "green circle", and the stereo subs have the distinct advantage over a stereo mains/mono sub of not being "wrong" in terms of time alignment in the crossover overlap region every where but one tiny spot on the map.
3) A pair of subs using the the same Sd are 3 dB louder than a single sub. A pair of subs using the same applied voltage and Sd are six dB louder than a single. At 40 Hz, +6dB sounds roughly "twice as loud" to people with average hearing.

I use a mono sub in my home theater and studio control room. At the preferred listening position in either room the system is "locked in" phase in the acoustic crossover region, but that "locked in" effect only occurs at that specific location.

I have heard and operated mono subs (FLH, BR and TH designs) on stereo outdoor systems in center, one side, or directly under the L/R mains locations, as well as distributed mono subs spanning the distance between stereo mains, and definitely prefer stereo subs with mains directly over them to any mono sub configuration, other than mono subs under each of the mains.

The OP has already voiced his preference for stereo subs, I happen to agree with him, as stereo subs are the only way to properly hear the LF of of a stereo mix.

I doubt you ever will change your mind, as you prefer listening to music in a completely different manner than me.
You wrote you like listening to a "cartoon version" of music, with bass boosted some arbitrary amount to satisfy your taste.
I prefer to hear music reproduced as close to the recording as is possible on whatever system I listen to.

Any readers are well aware you disagree with me.
I am well aware I won't change your mind, you can't even read my posts without mucking up half of what I write when you post your rants.

If you were trolling in one of my threads, I'd have a moderator "pull your plug".
But as Entropy Eric has much tougher skin than I, he can continue to ignore or encourage your trolling, I will try to ignore you.

Cheers,

Art
 
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Dear Troll,

1) Your simulations are not reality ...

Let's forget about the PCD software and address Direct. This is the software a well known professional company had developed and uses to provide coverage in areas as complex as entire stadiums with dozens of audience positions. It's expected that their dealer network will use this software to promote sales and help customers set up their systems. Arguing that the Danley software isn't realistic is a bit over the top, even for you, even for this thread.

The only thing the Danley software is lacking is the directivity of a huge horn and since the OP's audience area is fully inside the horn's beam pattern this isn't really any concern.

Now let's back around to PCD again. PCD is showing the same thing Direct is showing, valleys of 20 db deep notches two octaves wide.

I know you have quite an aversion to simulators since you don't use many of them, you don't use them properly and you don't use them accurately. On occasion you will fire up Hornresp but only crudely sim your design as an initial starting point.

On the other hand, I've been able to sim just about everything I've ever come across accurately including your barn doors which you didn't think were possible to sim accurately (you didn't even understand how they were related to diffraction).

My sims are fine and if OP plays pink noise and walks around his yard he'll be able to draw the coverage map by hand on paper and it will pretty accurately match the sims I provided.

2)There is no reason that a stereo set up rather than a mono sub won't provide good coverage in the "green circle" ...

Deep notches two octaves wide ring any bells?

I use a mono sub in my home theater and studio control room. At the preferred listening position in either room the system is "locked in" phase in the acoustic crossover region, but that "locked in" effect only occurs at that specific location.

Give me a break, small room acoustics is so complex there's no way this is true. This has more to do with erratic frequency response of a single sub in a small room than anything else. If you want to get "locked in" sound in a much larger area maybe try multiple subs, when you fix the room's frequency response everything will be better in every location in the room.

I doubt you ever will change your mind, as you prefer listening to music in a completely different manner than me.
You wrote you like listening to a "cartoon version" of music, with bass boosted some arbitrary amount to satisfy your taste.

Yes for bassy music I prefer a bass boost. I also said for "normal" music I don't even turn the subs on. Pay attention. My system has been on non stop for the last few months. In that time I've turned the subs on a couple of times for maybe 20 minutes at a time.

If you were trolling in one of my threads, I'd have a moderator "pull your plug".

Do it. Seriously, I dare you. Every one of my posts contains technical information. You, on the other hand, took over 700 posts to make a recommendation for dual subs because you were holding out in an attempt to profit off a free diy forum You've made more personal attacks in this thread than most people will in a lifetime and all your posts are proudly sporting a namecalling theme now. You've called me ignorant, a pig and a troll as well as many other things. Go ahead and tattle, let's see what happens.
 
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The "fingering" pattern in figure 34 is a direct result of destructive interference.
That's exactly my point. That "fingering" pattern is shown at 10kHz.

For 10 point sources with 20-50cm gaps between them, the destructive interference should be MUCH lower (50cm is half a wavelength at 340Hz).

Therefore a simple point source model does not fit what has been measured.

...so to me, the OP's ideas (specifically, post 831) seem to be correct.

No, sound is round. The wavefront exiting the horn mouth is always roughly hemispherical. If you have links, evidence, proof that contradicts that post it. The mouth of a horn is a duct, a hole, not a radiating surface.

At the horn mouth the wave isn't planar either, it's a bubble shape as you would expect from a sound wave since sound is round. [...] The wavefront is round (roughly hemispherical)

That claim has been hobbled and re-stated as this:

specifically pic 14 [...] the wavefronts are definitely curved [...] Just look at the pics.

Figure 14 shows a single horn operating at cutoff frequency. Yes, there's definitely a bit of curve. I think there are 2 reasons for this curve:

ONE
The walls are curved, and as the article says, WRT this figure: "the wave-fronts are very nearly normal to the walls."
TWO
at frequencies lower than the mouth dimension can "support", the waves diffract around the mouth, unless boundaries are placed around the mouth to reduce the "wrap"

So wavefronts are (sort of) round, only for a single horn operating at cutoff frequency. That's quite a long way from ALWAYS and HEMISPHERICAL (or ROUND).

You can claim (again) that you were actually exaggerating to make a point, or that by "always" you obviously meant "only at the LF cutoff of the horn" or "only in a tractrix horn". However, I'd be more impressed if you simply admitted that the OP was right, and some of your assumptions turned out to be incorrect.

Also: above cutoff, as shown in the next two figures in that article, the waves are much closer to planar. The OP is talking about 15Hz horns, in which case, most of the signal will be well above cutoff - so what does that imply?

A multicell horn is not the same as side by side massive subwoofers.

Correct. Subwoofers are bigger.

The OP was talking about dividing a single horn into 4 parts with same length & abutting mouths. That seems to have more than a casual resemblance to a multicell.

Also: each of the 4 cells cells would have 1/4 as much curvature to their walls as the equivalent whole. As stated in the article you referenced "the wave-fronts are very nearly normal to the walls" - so what does that imply?
 

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You need some space to provide stereo separation of course, but I've been saying stick it in the mouth from the beginning, you can still get probably over 14 feet separation.

14 feet is enough for stereo separation when JAG suggests it, but 24 feet was not enough when I suggested a layout (post 797)?

As I mentioned, they aren't far enough apart to provide a stereo image at any distance. And at low frequencies you don't hear stereo anyway because of localization issues.

Remember this?

your own statements MADE ON THE SAME DAY directly contradict each other [...] IT APPEARS YOU ARE NOT EVEN PAYING ATTENTION TO THE THINGS YOU SAID JUST A FEW HOURS AGO

Or this?

http://www.diyaudio.com/forums/subw...bass-horn-design-question-27.html#post4866506

Do you often forget that you are contradicting yourself?
OR
are you doing it on purpose so you can spend more of your time disagreeing with a larger number of people?

By your own claim, it shouldn't be the former.

BECAUSE I'M PAYING ATTENTION TO EVERYTHING EVERYONE SAYS
 
That's exactly my point. That "fingering" pattern is shown at 10kHz.

For 10 point sources with 20-50cm gaps between them, the destructive interference should be MUCH lower (50cm is half a wavelength at 340Hz).

If they were all pointed directly ahead (in the same direction) this would be true. But they are not, they are splayed out, each pointing a few degrees away from the next. This goes a long way to reducing the interference of a narrowly beaming horn array.

Therefore a simple point source model does not fit what has been measured.

The walls of the horn clearly affect the wavefront shape but it's still a lot closer to point source than planar.

That claim has been hobbled and re-stated as this:

I clearly said "roughly hemispherical" a number of times, although I admit I didn't say it EVERY time. Those images in the paper clearly show a wavefront that is closer to round than flat, images that support the "horn bubble" we all are aware of that exists at the mouth.

So wavefronts are (sort of) round, only for a single horn operating at cutoff frequency. That's quite a long way from ALWAYS and HEMISPHERICAL (or ROUND).

Look at the images David McBean provided. At low frequencies and at high frequencies, the wavefront is always curved at the horn exit (at least for an EXP horn).

You can claim (again) that you were actually exaggerating to make a point, or that by "always" you obviously meant "only at the LF cutoff of the horn" or "only in a tractrix horn". However, I'd be more impressed if you simply admitted that the OP was right, and some of your assumptions turned out to be incorrect.

Also: above cutoff, as shown in the next two figures in that article, the waves are much closer to planar. The OP is talking about 15Hz horns, in which case, most of the signal will be well above cutoff - so what does that imply?

If I was wrong I would say I was wrong. The images and the concept of a "horn bubble" imply the wavefront is curved. If you think it looks more planar than curved that's a difference of opinion and one I'm not particularly interesting in discussing further.

As I mentioned several posts ago - even if the wavefront is flat as a pancake it makes little difference - as long as the beams are overlapping there will be interference and I've shown clearly what interference looks like. The pattern of interference might change slightly with different wavefront shapes but the interference itself isn't going to go away if the wavefront isn't perfectly hemispherical.

Multicell horns don't control interference by having a planar wavefront, which is what I think you are trying to imply.

Correct. Subwoofers are bigger.

The OP was talking about dividing a single horn into 4 parts with same length & abutting mouths. That seems to have more than a casual resemblance to a multicell.

If he splayed them out so they were pointing away from each other then it would be exactly a multicell horn. If they are not splayed apart it's just side by side horns and unless the directivity of those horns is EXTREMELY narrow the beams will overlap to a great degree and there will be a large area of interference which you don't get in a multicell. That's specifically the point - the multicells prevent too much interference by beaming and pointing in different directions. It's still not enough to completely eliminate interference but it's a dramatic difference from side by side horns pointed straight ahead.
 
14 feet is enough for stereo separation when JAG suggests it, but 24 feet was not enough when I suggested a layout (post 797)?

Remember this?

Or this?

Do you often forget that you are contradicting yourself?
OR
are you doing it on purpose so you can spend more of your time disagreeing with a larger number of people?

By your own claim, it shouldn't be the former.

I remember it all very well and I'm not contradicting myself.

At very low frequencies localization is very difficult and below the crossover point of 80 hz that I've suggested it's nearly impossible if the slope is steep and the sub is very low distortion.

At high frequencies localization is very easy.

That is why you need a very large separation if you want any chance at all of perceiving stereo bass but relatively little separation to perceive separation at mid/high frequencies.

You even said yourself "I don't think that, with a blindfold on, you could play an 80Hz tone through a line of 12 of these boxes, and point to each of the 24 woofers or "centers".

This implies two things.
1. Why bother with stereo bass if you can't localize it well?
2. If you can't point directly at the sub when blindfolded, it's going to be even harder to point at it when it's relatively close to another sub. The further apart they are the more chance you have of pointing in the right general direction of the sub you are trying to locate. But the further apart they are the more they interfere with each other destructively.

To be really clear, the only time you will hear any stereo effect at all is when something is panned hard to one side, and if the subs are close together you might even miss out on most or all of that effect.
 
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The big issue here is not the comb filtering at mid and high frequencies, those notches are not very wide and won't be distracting.

when you chop that single horn up into modular pieces, all the pieces will comb filter with each other (this is not shown here, maybe I'll sim that up later).

Both of these points seem valid.

That's why I think Bob's sim of a wide array of subs looked good. With just 2 point sources, you could simulate a bunch deep, wide notches. With multiple diffuse sources (the DBH218 folded horn != a point source), you'd get a more complex pattern of notches that are not very wide and won't be distracting.