Multabolic Planar Array (MBPA): Audiophile sound everywhere in large venues

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What is a multabolic planar array?  First we have to learn a little about sound or waves or fields.  The take home message is that waves interact and waves come from point sources.  Point sources are very inefficient at getting information in the direction you want it to go.  If you put a few point sources in a row, they form a linear array.  What happens is the point sources interact to form a line source.  Line sources are much much better at getting waves to be directed in the direction intended.  Basically the other point sources constrain the field from the others to not go in their direction thus "pushing" the wave or field in the other directions.  The logical conclusion of this is the planar array where every point source is pushing the other point sources to all direct their waves outward from the plane.  Theoretically no sound is pointed in any direction except directly outwards (perpendicular) to the plane.  Now this is great if you have a planar reciever.  Unfortunately most all recievers are points.  Take a human listening to music for example.  For simplification sake you can think of the persons head as the point of recieving the sound.  For a planar array to be best at directing sound to a point reciever then you must angle the array to point towards the point at all places.  Just like a parabolic mirror reflects light to a single point, a parabolic array will direct all sound to a point.  Now what happens when you have multiple point recievers (an audience)? Best to just go to a planar array? Not quite.  What if we had multiple parabolas, one for each audience member?  Sound impossible?  Well perhaps it is to make perfect parabolas for everyone, but you can approximate parabolas for everyone by making what I will call a multabola.  A multabola is multiple parabolas flattened into a single multi-angled plane.  This is very tricky to draw but a basic N=2 multabola is drawn below.  Basically it is just a parabola modeled in only 3 angles, upward, flat, and downward.  Then another one of these parabolas weaved into the first.  For six speakers this looks like the angles shown in the picture.  For 3 parabolas with the same 3 angles you get 3 up, 3 flat, and 3 down.  When you add more than 3 angles per parabola you get a more interesting picture (which I can't seem to draw)!  Anyway what this does is give anyone standing virtually anywhere in the venue at least 1 speaker from the left pointing at them and one on the right pointing at them giving them a personalized audiophilic experience.

As far as the planar (or multabolic planar) array aspect of this is concerned you have two considerations: make a 2D (multibolic) plane with speakers (larger the plane and the closer the speaker spacing the better) and also the higher frequency the sound the closer the speaker placement needs to be.  This is because high frequency sounds dont travel as far and straight so they need more "boost" from their neighbors.  You end up with something in the bottom picture below.  In my case the big circles are going to be rokit 10" speakers, the filled in dots will be rokit 8" speakers, and the small circles will be rockit 4" speakers.  Again, the higher the frequency the speakers (smaller size) the more you need so they can support each other better.  Also you can also make the array concave to point at the audience members heads in the vertical direction as well not just the horizontal. 

And that's about it.

Oh and I guess I can draw other multabolas, below (the drawing with the numbers) is an N=3 R=6 multabola (N is number of flattened parabolas and R is number of angles per parabola).  The good thing about multabolas is there isn't too much interference.  I'm guessing that ideally you will want N=R for most efficient results.

Also of course you can have these multabolic planar arrays on multiple sides of the audience not just in front of them and also you can have above and below, just up to you whatever setup is most efficient.  Also of course it need not be a surface only NJ plane but it can have depth too, speakers behind/ in front of others.

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