On 2012-03-03, Jörn Nettingsmeier wrote:
Is there a similar relationship for order and loudspeaker array
radius?
not really. only in the sense that you need higher orders for larger
listening areas, in the general case.
One of the things that is easy to miss about ambisonic is that it really
talks about physical soundfields even at first order, even if it applies
some heady psychoacoustical optimization when reproducing them. So,
while we can have all sorts of trouble reproducing a given B-format
signal, that signal in itself does constitute a well-defined
approximation to a specific physical acoustical event, which is
completely separate from how well we might be able to reproduce it, and
by what means.
That's something that is very difficult to grasp when you first bump
into the system. I for one didn't fully get it until I bumped into the
NFC-HOA papers, which was years after joining the list. So, to make it
absolutely clear: each ambisonic signal carries with it an implicit size
around the sweet spot within which it will converge when properly
reproduced at some frequency. The radius of that area depends *only* on
the order. All of that decoder magic is basically there to make it sure
that a) even if you move your speakers around, the end result within
that area of convergence stays as much the same as it possibly can, and
b) when working with low orders, where we can't approach physical
acoustical, holophonic reproduction even over a volume approximating a
single listener's head, then what *is* reproduced *perceptually*
best approximates the real thing described by the signal.
That's completely different from what happens with speaker feed systems
like 5.1, where moving speakers around, perhaps closer or farther,
changes what is heard. In ambisonic, the decoding magic at best
completely counteracts whatever you do, within the sweet area. In this
framework, that sweet area is an immovable, almost a physical object:
put your head in it and you will hear what the mic heard. Go outside of
it, and suddenly speaker placement and counts start to become relevant
to how badly the approximation falls apart. But not before then, and the
size of that sweet area isn't measured in relative but absolute units:
each order, at each frequency, sets the size of the sweet area in
centimetres, not in relative size to the rig diameter or anything like
that.
So, in a sense you do need a certain area for a certain order system if
you push it into the holophonic limit. But even to fill an ordinary
living room with the sweet area, you'd have to push the order into the
thousands, and the B-format channel count into the millions. (At 20kHz
and 330m/s, the wavelength becomes 1.7cm, so you'll have to have a
constant 8.3mm speaker separation to pull that off.) It's safe to say
you will never hit that limit -- and if you did, then you'd just throw
off the higher orders and go from there.
In practice, one of the fundamental ambisonic papers is "Practical
Periphony" because we don't even *want* to push it close to such
extremes. Instead we want it to sound right with practical resources.
Even second order gives a little bit of practical parallax, then.
</rant>
but if you have to play back lower order material as well (such as a
native soundfield recording), i found it is advisable to have a
separate low-order decoder which uses fewer speakers, for better
clarity and less phasing.
In that vein, try searching for a discussion about Giant Geese from some
years back. I think it was Dave Malham who instigated that discussion.
There is some merit to the idea that phasing messes up the reproduction,
unless your head is *squarely* enclosed by the sweet are. And the
problem grows worse at the high frequencies proportional to the number
of speakers. (Formally, they give rise to FIR comb filtering, where
multiple echoes raise the minimum frequency where timbral and interaural
phase effects start to be perceptible. The time domain effects our
hearing seems to smooth over pretty well.)
aaron heller disputes this, he claims to have observed no detrimental
effects in vastly over-specified systems, and if you look at
simulations where N->oo, he should be right, but in practice i have
found systems with many more speakers than strictly necessary to be
significantly worse in terms of phasiness... maybe others can comment
and clarify.
Agreed. Ville pulkki was once kind enough to demonstrate this to me in
an anechoic chamber. A hexagonal decode sounded much worse than a square
one, and at 12 equally spaced speakers, it was just muddled, but
otherwise not as bad as at 6. I'm guessing there is sort of a critical
band between the minimum number necessary for first order and numbers
which start to overcome spatial aliasing from the rig (20-40?) where
things first go worse, and then slowly start to return towards better.
so as a very rough guide, for a very live room and large speaker
distance, more directive speakers might be beneficial. vice versa, in
a small and quite dead room, widely dispersing speakers might be more
pleasant to listen to, since they will excite more diffuse sound,
which helps gloss over phasing problems. a matter of taste, and your
mileage may vary.
Might help to mind the directivity and what ever deadening elements you
have in your room, as well. Shooting a relatively directive speaker
towards a rug or a book shelf rarely makes it worse.
--
Sampo Syreeni, aka decoy - [email protected], http://decoy.iki.fi/front
+358-50-5756111, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2
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