Pan control and Pan rules

When we try to place a signal in the stereo volume or pan, we usually do this by adjusting the relative amplitudes for the left and right channel.

If we want to move the apparent signal source to the left, we increase the volume or adjust pan of the left channels signal and at the same time attenuate the signal for the right channel. This might seem self evident and not even worth to mention, however, there are other means of achieving a similar localization effect – namely, by delaying one channel with respect to the other

Let’s represent our pan-position with the variable p,

A leftmost pan-setting by the setting p = −1,

A center setting by p = 0

And a rightmost setting by p = +1.

The most simple rule for calculating a gain factor for both channels would simply be a linear pan-rule: as p goes from −1 to +1, fade in the right channel linearly from 0 to 1 and fade out the left channel linearly from 1 to 0.

To wrap that into a neat formula, we introduce the variable p’ = (p + 1)/2 which goes through 0…1 as p goes through −1…1.

Then, our gain factors for left and right channel (which we will denote as gL, gR) are
calculated as:

gL = 1 − p’ and gR = p’ with p’ = (p + 1) / 2

You can check the PAN control on image of a VST by Tek’it Audio.

They have introduced MScontrol, a freeware mid-side controller utility available in VST, VST3, and AU plugin formats for 32-bit and 64-bit host applications on PC and Mac.