# [PD] Re: multi-speaker panning.. problamtic maths

Mathieu Bouchard matju at artengine.ca
Tue Oct 24 01:18:24 CEST 2006

```On Mon, 23 Oct 2006, alexandre r. decoupigny wrote:

> explain what you mean with "the sum of squares of your output signal"

This is because sound power is the square of sound amplitude. Therefore if
you want to halve the sound level you need to do [*~ 0.7071] instead of
[*~ 0.5]. You need to do this with panning, if you want it to be
energy-preserving (no change in used watts no matter how's the mix like).

I made this mistake again last thursday - I computed sound amplitude of
some kind of omnidirectional source as being r^-2 where r is the distance.
However, I believe that it's energy that should be r^-2, therefore
amplitude should be r^-1. That's assuming ideal 3-D dispersion (no
ceilings and no walls). Is that right?

> i also wonder if there is a way to have a full representation of all the
> intermediate values: eg. resting the joystick in the middle means to
> distribute it evenly amongst all four..

If you have 0<=x<=1 and 0<=y<=1, then you could use those two formulas for
the volumes a,b,c,d of the four speakers:

a =    x  *    y
b = (1-x) *    y
c =    x  * (1-y)
d = (1-x) * (1-y)

but then to preserve energy, you should use some square root there.
another idea is to use sin and cos, which already add up to 1 when
squared:

a = cos(x) * cos(y)
b = sin(x) * cos(y)
c = cos(x) * sin(y)
d = sin(x) * sin(y)

> complicity.. simplexity..

Personally I reserve those two words for when complexity becomes genuinely
counterintuitive and I want to mean that simplicity is not a simple thing
to think about and so on.

_ _ __ ___ _____ ________ _____________ _____________________ ...
| Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
| Freelance Digital Arts Engineer, Montréal QC Canada
```