# [LAU] Where do the 60 degrees for stereo come from?

Philipp Überbacher hollunder at lavabit.com
Thu Jun 16 20:56:16 UTC 2011

```Excerpts from Fons Adriaensen's message of 2011-06-16 22:35:10 +0200:
> On Thu, Jun 16, 2011 at 10:11:25PM +0200, Philipp wrote:
> > Hi there,
> > in a discussion today someone asked me where those 60 degrees necessary
> > for the production of phantom images come from and I couldn't deliver a
> > satisfactory answer. Someone tried to explain to me that it has
> > something to do with wavelengths or whatever but couldn't explain it in
> > a way that anyone would understand.
> >
> > My best guess is that with a larger angle the head gets in the way and
> > the ears have an easier time telling the signals apart. Also, I guess 60
> > degrees is a rough estimate and chosen because this leads to a nice
> > Equilateral triangle.
> >
> > So, what's the real reason behind those 60 degrees?
>
> Just what you suggest: it leads to an equilateral triangle and
> that *suggests* there is something fundamental about it. But as
> far as I know there isn't. Another reason may be that +/- 30
> degrees corresponds to the perspective of an average listener
> in a concert hall - probably more than say +/- 45 degrees.
>
> OTOH, a recording technique like e.g. Blumlein (two fig-8 mics
> at 90 degrees) would suggest a speaker angle of 90 degrees
>
> A wider angle will make near-center sources less stable. The
> number that matters here is the magnitude of the velocity
> vector which is cos(1/2 the angle): 0.866 for 60 degrees,
> 0.707 for 90 degrees, while for a 'real' source it would be 1.
>
> Ciao,

Thanks Fons,
this might be the stuff this guy was talking about. Sadly I don't
know how to understand the magnitude of the velocity vector. What does
it represent? Why does the magnitude decrease with the angle?

Best regards,
Philipp

```