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) > _______________________________________________ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
