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.

@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.

@dfkettle This article describes the computation of the -4.5dB pan law: https://www.cs.cmu.edu/~music/icm-online/readings/panlaws/

edit: Oh I think it might describe -6dB too, which is just linear. Someone correct me if I'm wrong.

@jameslo I guess it's more complicated than I thought. It seems it would also depend on whether you're listening to speakers or with headphones? The article only talks about listening on speakers in large or small rooms. The -4.5dB law uses both square root and sin/cos functions, though, not just the square root, as described in the book I mentioned.

I should have explained what I'm trying to do. I want to develop a patch in which the sounds move back-and-forth across the stereo field, their position isn't static. I want the movement to sound as natural as possible, though. I'll just have to experiment, I guess.

@dfkettle To complicate things further my friend has used VBAP (vector based amplitude panning) which I've never been able to understand fully. For mono signals panned into headphone mixes I've used Ambisonics in order to avoid having the sound in only one ear when panned to the extreme left or right, which sounds bad to me. IEM has a great VST Ambisonics library. But if you're worried about the relative computational cost of cos vs sqrt, you should run away from Ambisonics as fast as you can.