Well thank you so much Martin, Jorn and Fons.
That confirmed my hypothesis and very kindly you gave me a lot more information 
very interesting.

I'm a bit concerned now, as I would not know for sure if eight speakers and 3rd 
Order could provide quite accurately a soundfield for an area of 5x5 meters. 

Accordingly to what you wrote, it doesn't really matter in Ambisonics if I 
place the loudspeakers at 6, 8 or 10 meters diameter... (as long as the 
loudspeakers are powerful enough). Is that correct?

Do you have any suggestions? How differently would you do?

Many thanks again, I love this list

tom



> 
>   1. Re: Sweet spot precise measurement (Martin Leese)
>   2. Re: Sweet spot precise measurement (J?rn Nettingsmeier)
>   3. Re: Sweet spot precise measurement (Fons Adriaensen)
> 
> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Wed, 7 Nov 2012 10:51:50 -0700
> From: Martin Leese <martin.le...@stanfordalumni.org>
> Subject: Re: [Sursound] Sweet spot precise measurement
> To: sursound@music.vt.edu
> Message-ID:
>       <caazqgd8exaxblt7m09efpdbffesspbpx1ka9zuhjmq2dfds...@mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
> 
> Tommaso Perego wrote:
>> Dear all,
>> I was wondering how, knowing the diameter of a speaker octagon,
>> using 1st or 3rd Order ambisonics,  to calculate precisely the dimensions of
>> the sweet spot area.
>> Any ideas?
> 
> If you want to make calculations of area then
> your first problem will be defining precisely
> what you mean by the sweet spot.
> 
> Your second smaller problem will be that the
> area will have fuzzy edges.
> 
> Regards,
> Martin
> -- 
> Martin J Leese
> E-mail: martin.leese  stanfordalumni.org
> Web: http://members.tripod.com/martin_leese/
> 
> 
> ------------------------------
> 
> Message: 2
> Date: Wed, 07 Nov 2012 19:08:59 +0100
> From: J?rn Nettingsmeier  <netti...@stackingdwarves.net>
> Subject: Re: [Sursound] Sweet spot precise measurement
> To: Surround Sound discussion group <sursound@music.vt.edu>
> Message-ID: <509aa3bb.5060...@stackingdwarves.net>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
> 
> On 11/07/2012 10:04 AM, Tommaso Perego wrote:
>> Dear all,
>> I was wondering how, knowing the diameter of a speaker octagon,
>> using 1st or 3rd Order ambisonics,  to calculate precisely the dimensions of 
>> the sweet spot area.
>> Any ideas?
>> Many thanks
> 
> 
> the strict sweet spot is only a function of order and frequency, not of 
> the array diameter.
> r < N/2 * c/f is an approximation i saw mentioned in one of franz 
> zotter's papers, where N is the order, c is the speed of sound and f is 
> the frequency. in words, the order N is the number of zero-crossings of 
> a given frequency which are correctly reproduced.
> 
> that sounds pretty dire until you realize that at frequencies above a 
> few hundred hertz, phase relationships are not that important anymore...
> 
> 
> in practise, a larger diameter does help, because of two factors:
> a) the sound pressure level varies much more slowly in the far field of 
> a loudspeaker. e.g. the level halves when you move from 2 to 4 meters 
> (i.e. over 2 meters), and again when you move from 4 to 8 meters (same 
> drop, but over 4 meters). that means that while the phase relationships 
> are quite wrong outside the sweet spot, the intensity ratios of the 
> speakers are more or less correct, which helps with rE localisation.
> even more so if you can use highly directional speakers such as line arrays.
> b) more distant loudspeakers excite more reverb and have a lower 
> direct-to-reverb ratio, which helps to mask some of the oddities of 
> ambisonic playback.
> 
> but these perceptional advantages do not change the basic fact that the 
> soundfield reconstruction is incorrect outside the sweet spot.
> 
> 
> best,
> 
> 
> j?rn
> 
> -- 
> J?rn Nettingsmeier
> Lortzingstr. 11, 45128 Essen, Tel. +49 177 7937487
> 
> Meister f?r Veranstaltungstechnik (B?hne/Studio)
> Tonmeister VDT
> 
> http://stackingdwarves.net
> 
> 
> 
> ------------------------------
> 
> Message: 3
> Date: Wed, 7 Nov 2012 20:43:57 +0000
> From: Fons Adriaensen <f...@linuxaudio.org>
> Subject: Re: [Sursound] Sweet spot precise measurement
> To: sursound@music.vt.edu
> Message-ID: <20121107204357.ga17...@linuxaudio.org>
> Content-Type: text/plain; charset=iso-8859-1
> 
> On Wed, Nov 07, 2012 at 07:08:59PM +0100, J?rn Nettingsmeier wrote:
> 
>> On 11/07/2012 10:04 AM, Tommaso Perego wrote:
> 
>>> I was wondering how, knowing the diameter of a speaker octagon,
>>> using 1st or 3rd Order ambisonics,  to calculate precisely the dimensions 
>>> of the sweet spot area.
> 
>> the strict sweet spot is only a function of order and frequency, not
>> of the array diameter.
>> r < N/2 * c/f is an approximation i saw mentioned in one of franz
>> zotter's papers, where N is the order, c is the speed of sound and f
>> is the frequency. in words, the order N is the number of
>> zero-crossings of a given frequency which are correctly reproduced.
> 
> True, this defines the 'radius of reconstruction'. To get an idea of
> what's happening, have a look at the spherical Bessel functions, e.g.
> <http://mathworld.wolfram.com/SphericalBesselFunctionoftheFirstKind.html>.
> These define how the field is reconstructed. At a distance r from the
> sweet spot, the contribution of the order N spherical harmonic is
> proportional to the order N spherical Bessel function evaluated at
> x = 2 * pi * r / wavelength. For example, if x = 2, or r is roughly
> 1/3 of the wavelength, the contributions of the zero and first orders
> is more or less equal, and the higher ones contribute significantly
> less. So this distance is within the 'sweet radius' for first order.
> The distance at which 3rd order starts to fail is determined by the
> value at which the 4th and higher order Bessel functions start to
> contribute a significant part of the field.
> 
> This also explains why e.g. decoding first order to an octagon is
> not a good idea. With 8 speakers you can reconstruct up to third
> order (horizontally), and a decoder for an octagon will actually
> do that, even if it is just a first order decoder. It wil just
> force the 2nd and 3th order components (and some higher ones, by
> aliasing) to be zero. So the field reconstruction will fail for
> those r where these missing orders contribute most.
> 
>> in practise, a larger diameter does help, because of two factors:
>> a) the sound pressure level varies much more slowly in the far field
>> of a loudspeaker. e.g. the level halves when you move from 2 to 4
>> meters (i.e. over 2 meters), and again when you move from 4 to 8
>> meters (same drop, but over 4 meters). that means that while the
>> phase relationships are quite wrong outside the sweet spot, the
>> intensity ratios of the speakers are more or less correct, which
>> helps with rE localisation.
> 
> True. Large diameters to help up to the point where delay effects
> take over. 
> 
> In summary, Martin Leese's remark is very much to the point: the
> 'sweet spot' is a fuzzy concept, and much depends on the application.
> 
> Ciao,
> 
> -- 
> FA
> 
> A world of exhaustive, reliable metadata would be an utopia.
> It's also a pipe-dream, founded on self-delusion, nerd hubris
> and hysterically inflated market opportunities. (Cory Doctorow)
> 

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