# [music-dsp] re: octaphonic panning equations

Steve Conner steve.conner at optosci.com
Thu Apr 8 09:19:35 EDT 2004

```>Now, I would like to make it into an octaphonic
>panner, but I can't figure out the right equations for
>the gain at each of the 8 speakers.
>The speakers are still arranged in a square, but
>instead of being only at the corners of the square
>(quadraphonic) now we have a speaker along each of the
>sides:

Here's what I'd do (cheap and nasty) I'd consider it as two sets of four
speakers, one set rotated by 45o relative to the other.

Calculate the gains for the 4 corner speakers as you did before.

Now transform the (x,y) coordinates to a new set of axes- call them (u,v)-
that are at 45o to the old ones. IIRC, this works out as:

u= x cos 45o + y sin 45o
v= y cos 45o - x sin 45o

(but don't trust me, my maths is rusty)

Now calculate the gains for the 4 added speakers, using the new coordinates,
but the same equations as before. Maybe scale them to account for the side
speakers being closer to the listener than the corner ones.

Steve Conner
http://www.scopeboy.com/

```