• ### Equal power panning -- square roots or cosines?

Which is the "correct" way to implement equal power panning, using square roots or cosines? After doing some googling, I found posts recommending both methods. And which would be more efficient, if they're both "correct"? I've tried both and they both sound the same to me, and seem to give the same results, as far as I can tell. I compared the output from [env~] of the input signal with the summed output signals (left and right), and didn't see any difference. When panned near the middle, the RMS of the output signal is a little higher than the input signal, using either method (see screen prints below). But that may be due to the way [env~] calculates RMS, I don't know.

Here are my two implementations, [pan~] using the square root method and [pan2~] using the cosine method.

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• @dfkettle I always use cosines, but I think there might not be one right way given that many DAWs give you your choice of "pan law". This is the explanation that the Reaper manual links to: https://samplecraze.com/tutorials/the-pan-law/

• @jameslo Interesting article, but it doesn't say how it's calculated, it just refers to the amount (-3. -4.5 or -6dB). I don't have to be concerned about converting to mono, either. If I wanted a mono version, I'd just create it as mono in the first place. But thanks.

• P.S. The square root method is described in "Programming Sound with Pure Data" by Tony Hillerson on pp. 89 - 90 of the 2014 edition, if anyone wants more details. I couldn't find anything about equal power panning in Miller Puckette's book, "The Theory and Technique of Electronic Music". But if anyone knows of any books or articles that deal with the subject, please let me know.