Thanks to you both. If_then- I'll check those out when I can. Jez- yes I'd figure the math out first and graph the transfer function.
My use for such a thing is potentially twofold. I'm sitting on a lot of four-channel baffled L/R/C/B recordings that I've made over the years using microphones facing in all four directions. I have a few different methods for mixing those down to L/R stereo that I really like, and alternately for playing them back over multichannel playback systems.
One application is as a potential stereo mixdown tool for some of them where the angular orientation of the recording array was not optimally aligned with the orientation of the stage, room, and audience. For example, in some the Left mic channel faces the "perceptual center" rather than the Center mic channel. Such a situation would be standing off to the left with the closest PA to my Left and the majority of the audience and room off to my Right. Fixing that is easy by just reassigning the channel routing as follows: L to C; C to R; R to B; and B to L. I don't need the circular panner to do that. And I do have some effective mix methods for correcting the ones which are askew by less than a full 90 degrees, but I've always been curious about alternate, faster, and potentially better ways of doing so. Having the four cardinal directed channels available provides a much larger degree of freedom in doing this in comparison to having just two L/R channels. I realize that simple sum-based panning may not work as well as I'd like in doing this, but I'd still love to try it. Would be great to just "turn the knob" to reorient the 4-directional recording as desired. A set and forget type of static adjustment.
The other application is essentially a dynamic implementation of the same for a somewhat more esoteric end, in enabling active mix-down of those four channel recordings to headphones while providing a rudimentary form of head-tracking. Turning the knob in synchronously with my head would "turn the virtual mic array" in the same direction. The B channel already gets filtering applied to it to perceptually spatialize it so as to sounds more diffuse and "coming from all around behind". Turning the knob would dynamically assign what information gets routed where. Similarly I can EQ the Left, Right, Center, and Back inputs and outputs differently before and after going through the circular balance control. Before fixes the recording the same as I would in a typical stereo mix down. Afterward would affects a form of HTRF filtering to better emulate the actual directional perception of sound arrival from different directions to the head, and even more advanced filtering could be applied if needed. If it works, the obvious next step would be tying the circular pan-knob to a physical head tracker device. If would enable the ability to virtually turn my head in the recorded performance space and listen in any direction during playback.
Been thinking about this since starting to make recordings in this way back in 2006 or so. And especially so after demoting the Smyth Realizer that does this to a far, far more advanced degree via manipulation of binaural convolution, so astoundingly convincing that at first I thought the headphones were turned off and I was hearing the actual sound sources distributed around the room as I turned around to look at them.