[Sursound] minimum number of speakers for periphonic 3rd order ambisonic reproduction

[Jan Jacob Hofmann]

I wonder what is the minimum number of speakers for periphonic 3rd
order ambisonic reproduction. I am well aware of the *theoretical*
minimum of

- 4 speakers for 1st order
- 9 speakers for 2nd order
- 16 speakers for 3rd order

obtained by the formula (order + 1) square.

But I wonder what a sufficient number of speakers might be necessary
to have a symmetric setup *and* a satisfying reproduction of the
spatial information of the 15 encoded channels of 3rd order ambisonic.

Best regards,

Jan Jacob


sound | movement | object
| space
sonic architecture | site: http://www.sonicarchitecture.de
spatial electronic composition | 2nd order ambisonic music

[Martin Leese]

Post by Jan Jacob Hofmann
I wonder what is the minimum number of speakers for periphonic 3rd
order ambisonic reproduction. I am well aware of the *theoretical*
minimum of
- 4 speakers for 1st order
- 9 speakers for 2nd order
- 16 speakers for 3rd order
obtained by the formula (order + 1) square.
But I wonder what a sufficient number of speakers might be necessary
to have a symmetric setup *and* a satisfying reproduction of the
spatial information of the 15 encoded channels of 3rd order ambisonic.

In theory, you need more speakers than
transmission channels. The numbers you
give are channels, so add one to each for the
minimum number of speakers.

In practice, five speakers is a bit impractical
for first-order full-sphere, so the minimum is
six or eight speakers depending on the
configuration.

For third-order the problem is usually siting
the speakers. For a symmetric setup, these
need to be arranged in a regular polyhedron.
There isn't a Platonic solid with 17 faces so,
in practice, the minimum is 20 speakers
arranged in an icosahedron, visit:
http://en.wikipedia.org/wiki/Platonic_solid
http://en.wikipedia.org/wiki/Icosahedron

The other approach is to use horizontal rings
of speakers. For third-order, you will need
four horizontal rings each with eight speakers.
However, this approach will use more speakers
than the minimum.

Regards,
Martin

[Fons Adriaensen]

I wonder what is the minimum number of speakers for periphonic 3rd order
ambisonic reproduction. I am well aware of the *theoretical* minimum of
- 4 speakers for 1st order
- 9 speakers for 2nd order
- 16 speakers for 3rd order
obtained by the formula (order + 1) square.
But I wonder what a sufficient number of speakers might be necessary to
have a symmetric setup *and* a satisfying reproduction of the spatial
information of the 15 encoded channels of 3rd order ambisonic.

You need more speakers than channels.
Four for 1st order is known not to work well.

Things depend to some extent where your sources
are. Most 3D work would be hemispherical rather
than including 'below ground level' sources, this
saves a bit on required speakers and excavation
work.

For 3rd order, a rough guideline is that you need
a speaker near to every 45 degrees on any great
circle. If you don't have sources near the zenith
you can afford to have a 'hole' there, allowing
e.g. three rings, horizontal with 8, mid with
6 and top with 4 speakers. Even two rings could
work well.

Ciao,

[Nils Peters]

Hi all,

where do you guys derive your recommendations from?

Did anyone carried out formal listening tests regarding these practical
questions ?


best,

Nils

Post by Fons Adriaensen

I wonder what is the minimum number of speakers for periphonic 3rd order
ambisonic reproduction. I am well aware of the *theoretical* minimum of
- 4 speakers for 1st order
- 9 speakers for 2nd order
- 16 speakers for 3rd order
obtained by the formula (order + 1) square.
But I wonder what a sufficient number of speakers might be necessary to
have a symmetric setup *and* a satisfying reproduction of the spatial
information of the 15 encoded channels of 3rd order ambisonic.

You need more speakers than channels.
Four for 1st order is known not to work well.
Things depend to some extent where your sources
are. Most 3D work would be hemispherical rather
than including 'below ground level' sources, this
saves a bit on required speakers and excavation
work.
For 3rd order, a rough guideline is that you need
a speaker near to every 45 degrees on any great
circle. If you don't have sources near the zenith
you can afford to have a 'hole' there, allowing
e.g. three rings, horizontal with 8, mid with
6 and top with 4 speakers. Even two rings could
work well.
Ciao,

[Eric Benjamin]

Post by Jan Jacob Hofmann
what is the minimum number of speakers for
periphonic 3rd order ambisonic reproduction.

Hi Jan!

The theoretical minima might more reasonably believed to be:

First order 5
Second order 10
Third order 17

But those numbers of speakers wouldn't be easy to apply in speaker arrays that can be used in practical systems. One would prefer array shapes that obey Gerzon's diagonal decoder theorem.

For practical reasons I find that it's good to use array shapes that are either in some sense cuboid, or are comprised of rings of regular polygons. As previously suggested by Peter Craven, first order periphony could ostensibly be achieved using a "bi-triangle', two triangular rings of loudspeakers, one above and one below the horizontal, one with the apex forward and one with a side forward.

Systems with two rings of loudspeakers don't fair as well for higher order reproduction because they can't reproduce the spherical harmonics such as R, although they can do very well in reproduction of higher orders for horizontal and just first order for height.

The bi-rectangle (two intersection rectangles, one horizontal and one vertical) and tri-rectangle (three intersecting rectangles, one horizontal and two vertical in two orthogonal planes) do quite well for reproducing second order material, but fail again if the requirement is to reproduce third-order height components.

This might lead one in the direction of a loudspeaker array with four rings of loudspeakers for third order, but that would tend to depopulate the horizontal direction where the 'goodness' of the high order presentation might more properly be appreciated.

I must admit that I have never tried to reproduce any third-order Ambisonic content, although I am about to do so. I'd believe my pontificating a lot more if I had ever actual done it!

Eric

Subject: Re: [Sursound] minimum number of speakers for periphonic 3rd order ambisonic reproduction
Date: Tuesday, January 27, 2009, 12:12 PM

Jan Jacob Hofmann

Post by Jan Jacob Hofmann
I wonder what is the minimum number of speakers for

periphonic 3rd order

Post by Jan Jacob Hofmann
ambisonic reproduction. I am well aware of the

*theoretical* minimum of

Post by Jan Jacob Hofmann
- 4 speakers for 1st order
- 9 speakers for 2nd order
- 16 speakers for 3rd order
obtained by the formula (order + 1) square.
But I wonder what a sufficient number of speakers

might be necessary to

Post by Jan Jacob Hofmann
have a symmetric setup *and* a satisfying reproduction

of the spatial

Post by Jan Jacob Hofmann
information of the 15 encoded channels of 3rd order

ambisonic.
You need more speakers than channels.
Four for 1st order is known not to work well.
Things depend to some extent where your sources
are. Most 3D work would be hemispherical rather
than including 'below ground level' sources, this
saves a bit on required speakers and excavation
work.
For 3rd order, a rough guideline is that you need
a speaker near to every 45 degrees on any great
circle. If you don't have sources near the zenith
you can afford to have a 'hole' there, allowing
e.g. three rings, horizontal with 8, mid with
6 and top with 4 speakers. Even two rings could
work well.
Ciao,
--
FA
Laboratorio di Acustica ed Elettroacustica
Parma, Italia
O tu, che porte, correndo si ?
E guerra e morte !
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[Martin Leese]

Post by Nils Peters
where do you guys derive your recommendations from?
Did anyone carried out formal listening tests regarding these practical
questions ?

The rule that, in Ambisonics, you need more
speakers than transmission channels is well
known (and, these days, well proven). Lets
call this Rule 1.

Pretty much everything else I wrote comes
from Jan specifying a symmetric setup. The
*only* way to achieve symmetry on a sphere is
by placing speakers on either the faces or the
vertices of a Platonic solid.

Rule 1 dictates the minimum number of
speakers. This forces your choice of Platonic
solid, from which everything else flows. This is
straightforward geometry, and there is no
need for formal listening tests.

Regards,
Martin

[Peter Lennox]

however, listening tests might well reveal more about what minima should be used in non-optimal circumstances - e.g off-centre listeners.
Dr Peter Lennox
Director of Signal Processing and Applications Research Group (SPARG)
School of Technology,
Faculty of Arts, design and Technology
University of Derby, UK
e: ***@derby.ac.uk
t: 01332 593155
w: http://sparg.derby.ac.uk/SPARG/Staff_PLX.asp
________________________________________
From: sursound-***@music.vt.edu [sursound-***@music.vt.edu] On Behalf Of Martin Leese [***@stanfordalumni.org]
Sent: 29 January 2009 17:29
To: ***@music.vt.edu
Subject: Re: [Sursound] minimum number of speakers for periphonic 3rd order ambisonic reproduction

Post by Nils Peters
where do you guys derive your recommendations from?
Did anyone carried out formal listening tests regarding these practical
questions ?

The rule that, in Ambisonics, you need more
speakers than transmission channels is well
known (and, these days, well proven). Lets
call this Rule 1.

Pretty much everything else I wrote comes
from Jan specifying a symmetric setup. The
*only* way to achieve symmetry on a sphere is
by placing speakers on either the faces or the
vertices of a Platonic solid.

Rule 1 dictates the minimum number of
speakers. This forces your choice of Platonic
solid, from which everything else flows. This is
straightforward geometry, and there is no
need for formal listening tests.

Regards,
Martin
--
Martin J Leese
E-mail: martin.leese stanfordalumni.org
Web: http://members.tripod.com/martin_leese/
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[Daniel Courville]

Post by Martin Leese

Post by Nils Peters
where do you guys derive your recommendations from?
Did anyone carried out formal listening tests regarding these practical
questions ?

The rule that, in Ambisonics, you need more
speakers than transmission channels is well
known (and, these days, well proven). Lets
call this Rule 1.

I have a feeling that the decoding algorithm have an practical impact on
that. "In-phase" decoding, for large space or for large sweet spot, and
decoding for irregular layouts (5.1 surround) might lead to a transgression
of "Rule 1".

In any case, Ambrose Field of the University of York has confirmed that
observation in an email exchange I had with him in which we were discussing
the use of 5th order planar encoding/decoding (11 channels).

- Daniel

[Fons Adriaensen]

Post by Daniel Courville

Post by Martin Leese
The rule that, in Ambisonics, you need more
speakers than transmission channels is well
known (and, these days, well proven). Lets
call this Rule 1.

I have a feeling that the decoding algorithm have an practical impact on
that. "In-phase" decoding, for large space or for large sweet spot, and
decoding for irregular layouts (5.1 surround) might lead to a transgression
of "Rule 1".

Yes. "Rule 1" applies if you do a systematic
decode (i.e. field reconstruction), and also
if you want max-rE.

For in-phase (which significantly attenuates
higher order terms anyway), and certainly for
irregular speaker layouts the only 'Ambsionics'
that remain is the signal set. Higher order
signals are used to shape the 'panning law'
or polar patterns to something that works,
and that's it. It's purely pragmatic in that
case, and "Rule 1" doesn't apply. Nor do you
have real Ambisonics of course.

Ciao,

[Jan Jacob Hofmann]

Dear list,

I really do enjoy that interesting discussion about the thread I
started! I am especially intrigued by that image of the icosahedron
on wikipedia with the orthogonal planes inscribed:

http://en.wikipedia.org/wiki/Icosahedron

I wonder if the icosahedron is *the* perfect setup for periphonic
second order ambisonic. As far as I can see it is! If the speakers
would be placed at the vertices (not on the faces) we would have a
rig with 12 speakers which would fit perfectly in any ortogonal room.
The upper speakers are parallel to the ceiling, the lower ones to the
floor and the others would be equidistant to their wall next to them
in the back: every wall having two speakers next to it. It would be
easy to measure and to set up the speakers. We coud not adress 3rd
order with that one, but for second order it would be very practical.
I am really excited!

I anyway do like the approach, to place the speakers as symmetric as
possible for ambisonic, as it yields so much efficiency, if all the
speakers are equidistant of each other. I do remember well some talks
with Richard Furse, wo always pointed out that the decoding equations
for second order went weird if the rig was not symmetric enough.

So lacking 20 speakers for 3rd order, but being close to 12, I'd go
for an Icosahedron with 12 speakers at the vertices - if there only
were some nice decoding equations for that...


All the best,

Jan Jacob

[Fons Adriaensen]

So lacking 20 speakers for 3rd order, but being close to 12, I'd go for an
Icosahedron with 12 speakers at the vertices - if there only were some nice
decoding equations for that...

That would be called a dodecahedron (the dual of
the icosahedron) setup. There's a 2,2 decoder for
it in the Ambdec distrubution. I'm not sure if it
has the nice orientation you decribed, but if not
I'd be happy to add that one as well.

Saluti from cold and rainy Parma,

[Fons Adriaensen]

Post by Fons Adriaensen

So lacking 20 speakers for 3rd order, but being close to 12, I'd go for an
Icosahedron with 12 speakers at the vertices - if there only were some nice
decoding equations for that...

That would be called a dodecahedron (the dual of
the icosahedron) setup. There's a 2,2 decoder for
it in the Ambdec distrubution. I'm not sure if it
has the nice orientation you decribed,

It has.

[Eric Benjamin]

Jan Jacob,

Strictly speaking, what you are describing is a dodecahedron, the dodecahedron being the dual of the icosahedron. But that's just jargon; you're talking about a 12-speaker array.

Richard Furse has good coverage of the 12-speaker arrays, listed as dodecahedrons, at the bottom of his web page at:
http://www.muse.demon.co.uk/ref/speakers.html

One can envision three different symmetrical ways to construct a dodecahedral speaker array. They could be described as face down, vertex down, and edge down. The one that Furse labels "Dodecahedron1" has a speaker directly below and a speaker directly above the listener. That array is impractical for me because I have no way to install a loudspeaker below the floor in my listening room. The array labeled "Dodecahedron2" has two speaker located angled beneath the listener, and again I have no way to construct the array.

I see the optimum orientation as being "vertex down"; that has three speakers angled beneath the listener, three slightly below horizontal, three slightly above horizontal, and three above the listener. That comes closest to being practical, for me. But the three bottom loudspeakers would still have to be below the floor unless the listener is seated on a very high chair!

which is why I like the Tri-rectangle as a 12 speaker array.

Eric

Subject: Re: [Sursound] minimum number of speakers for periphonic 3rd order ambisonic reproduction
Date: Monday, February 2, 2009, 3:15 PM
Dear list,
I really do enjoy that interesting discussion about the
thread I started! I am especially intrigued by that image of
the icosahedron on wikipedia with the orthogonal planes
http://en.wikipedia.org/wiki/Icosahedron
I wonder if the icosahedron is *the* perfect setup for
periphonic second order ambisonic. As far as I can see it
is! If the speakers would be placed at the vertices (not on
the faces) we would have a rig with 12 speakers which would
fit perfectly in any ortogonal room. The upper speakers are
parallel to the ceiling, the lower ones to the floor and the
others would be equidistant to their wall next to them in
the back: every wall having two speakers next to it. It
would be easy to measure and to set up the speakers. We coud
not adress 3rd order with that one, but for second order it
would be very practical. I am really excited!
I anyway do like the approach, to place the speakers as
symmetric as possible for ambisonic, as it yields so much
efficiency, if all the speakers are equidistant of each
other. I do remember well some talks with Richard Furse, wo
always pointed out that the decoding equations for second
order went weird if the rig was not symmetric enough.
So lacking 20 speakers for 3rd order, but being close to
12, I'd go for an Icosahedron with 12 speakers at the
vertices - if there only were some nice decoding equations
for that...
All the best,
Jan Jacob
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