On 2013-04-25, Fons Adriaensen wrote:
For first order the 'extrapolation' works well up to a distance of around 1/4 to 1/3 of a wavelength.
So, in English, what your subwoofer plays back is usually cut off at 80 or 120Hz. There the wavelength would be a bit over 4 metres to under 3. The ideal reconstruction area would be 1/4 of that, so a circle 3/4 to 1 metre in radius. Good enough for a living room sofa, definitely not good enough for a gallery or an open party.
At middle C, 440Hz, you're downto under 20 centimetres. At 1kHz which is about at the center of our most acute hearing, it's only 8-9 centimetres. And we don't reach for that with plain old first degree ambisonic: the psychoacoustical optimization seems to work best when it cuts in much earlier in frequnecy than that, even for single listeners. Say, at about 400Hz.
So for MF and HF Ambisonic decoders use an ad-hoc approximation which is based on psycho-acoustics and which works well in practice.
Or, let's say, the theory underlying the approximation is a bit old and simplistic, and the frequency above which it is applied has been found via trial and error. As such the theory is well founded, psychoacoustically, and relies on the same theory which lets more common sound systems such as stereo panning or Dolby Digital to work even so-so. But as Fons said, it's more derived from long term experience than written-in-stone physical facts.
Higher order Ambisonics provides two things. First, the area in which the sound field is reconstructed 'exactly' becomes larger, more or less proportional to order.
If we ever got to an order in the multiple hundreds, the system would be guaranteed to converge into full holophony. Under that kind of system, it'd no longer need any psychoacoustical gimmickry, it'd work perfectly over a wider area, and so you could hear even what is called "auditory parallax". That is, when you changed your position within the soundfield, you could hear the sound source staying put, and the sources' relative position changing in arrival angle.
The highest order systems we have now do not reach that far. Not even close. 3rd or perhaps imperfect 4th order is as high as we can go. The reason for that is that within the ambisonic framework, we try to do things perfectly before doing more of them. The system builds up from a central, coincident pickup which doesn't suffer from what is called "directional aliasing" or "spatial aliasing". I.e. it evens out/averages over directional detail it can't handle, instead of glossing over it and letting it potentially cause surprises.
That approach has a heavy cost attached to it: going to truly high orders is very difficult, and so the best we can do for now should be thought of as making the directional selectivity of the system better. Not as being able to reconstruct the sonic field over wider areas, with parallax and whatnot. On the plus side, though, you get what you expected, without any surprises, instabilities or caveats. Wavefield synthesis (WFS) takes the other route, with much higher channels counts and reconstruction areas, but more caveats to worry about.
This allows HOA to work in a much larger listening area than first order, i.e. to serve a large audience, and also to be usable in situations were for practical reasons (related to speaker placement) first order would not work well.
This is basically because it's not just the microphone you should analyse in ambisonic's spherical harmonic framework. You should do the same for the playback rig as well. In both cases regularity and symmetry help you work over many nasty details, because mathematically speaking symmetry leads to cancellation of the stuff we can't handle at low, less than perfect orders. When you then go to typical modern day rigs which aren't regular at all, that cancellation breaks down and you have to start worrying about higher order "stuff" even if what you're playing back was originally first order, plain old ambisonic (POA) stuff; suddenly your microphone and your recording are well behaved, but your playback rig isn't.
Ambisonic is unique in that it has the theory to deal even with this situation. It's just that the math becomes rather sticky if you *really* want to do it right and "be all you can be" with the signals and the rig you're given.
To really fully understand the why and how you'll need the maths.
And we're more than happy to help with it. But at the same time, yes, you'll have to do what all of us did when we first bumped into ambisonic: reading and homework. This shit has some serious levels going on, right downto the very basics of physical acoustics, if you ever want to go there. :)
What I wrote above is an attempt to explain things in intuitive terms, which means to simplify things, but hopefully not to the point where the essence is lost.
Fons, obviously, is one of the friendly gurus I already mentioned. -- Sampo Syreeni, aka decoy - [email protected], http://decoy.iki.fi/front +358-50-5756111, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 _______________________________________________ Sursound mailing list [email protected] https://mail.music.vt.edu/mailman/listinfo/sursound
