Aaron Heller wrote
> Marc Lavall, Eric Benjamin, and I put together a Trifield (three speaker 
> stereo) plugin and demo'ed it a Burning Amp last fall. It is hosted at
https://bitbucket.org/ajheller/trifield/overview....
> There are also some plots that use Gerzon velocity and energy localization 
> vectors (rV and rE) to analyze, +/-45 deg stereo vs Trifield  vs +/- 30 deg 
> stereo that shed some light on why "the +/- 30 deg stereo triangle" works 
> well.
Thanks for this Aaron, Eric & Marc.
There's a small error in the last pic "Magnitude of Localisation Vectors +/- 
30".
The x-axis should be from -30 to +30.  You can extend the info to -45 to +45 
virtual sources by panning beyond the speaker positions and show +/- 30 is 
still 'better' than +/- 45 speakers.
You can also show the DIRECTIONS of the rV & rE vectors are more in synch for 
the +/- 30 case
I did a lot of this stuff in my mispent youth trying to apply Gerzons theories 
to stereo.
Another big effect of wide speaker spacing is the frequency response of the 
virtual source varies a LOT more with position.  It's bad enough with +/- 30 
speakers.  You can test this for yourself by comparing a mono source panned to 
the centre (or near centre) with it panned to L or R.
The exact centre is also prone to HUGE comb filter effects.
All these effects (image stability via rE & rV, frequency response, comb 
filtering) are reduced if the speaker spacing is reduced (with proper 
compensation via more L-R bla bla ... to maintain image width).  The various 
Transaural / Stereo Dipole / Ambiophonic systems may be considered 
sophisticated variants of this.
Stefan Schreiber wrote :
How can rV > 1 be true??! (second last image...)
Gerzon's infamous vector magnitudes rV & rE are a measure of image stability 
with head movement.  Small magnitudes mean the image moves LESS than you'd 
expect in 'real life'.  In theoretical 'real life' (?!?) rV = rE = 1 .. but 
actually the magnitudes are usually slightly less than 1.0  An rV > 1 means the 
image moves MORE than in 'real life'.  Very large rV s are unnatural & 
disturbing as they are VERY uncommon in 'real life'.  You can get a taste of 
this by listening to normal +/- 30 stereo with L-R turned up.  Also some of the 
more naive early surround sound systems.
All explained in the Appendix of Gerzon's "General Metatheory of Auditory 
Localisation," Preprints from the 92nd Convention, Vienna, no. 3306, 1992.  He 
shows how his rV & rE theories model (give the same answers as) all models of 
auditory localisation except for the impulsive HF and pinnae colouration 
models.  This Appendix is required reading for anyone interested in auditory 
localisation. please reply to rica...@justnet.com.au NOT to the yahoo address 
which is riddled with spam. I never look at it.
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