What is this rotation effect/processor called? (Stereo rotation)

Question

I haven't been able to find this a plugin effect (or hardware processor for that matter), partly because I don't know what generic name it's known by so I could search. Its purpose is to "rotate" the stereo field by an adjustable angle.

There is only one control, the angle (or α).

The outputs L_OUT and R_OUT are defined in terms of inputs L_IN and R_IN by the rotation formula:

L_OUT = L_IN × cos α - R_IN × sin α

and

R_OUT = L_IN × sin α + R_IN × cos α

When used with an angle of 45° it's essentially equivalent to a mid-side encoder.

When used on a true stereo source (e.g. from a Blumlein pair) with a varying angle it would theoretically give the impression that the sound source is rotating around the listener.

Web searching so far has turned up the names of some plugins that may have done it, but the websites/product pages are defunct or no longer maintained (e.g. roundpan).

Answer 1

Something like the Waves S1 and Brauer Motion might be the type of effect you are looking for. If not then I don’t think the product exists.

Answer 2

Have a look at the plugins of Dear Reality. They have "dearVR MUSIC" and "dearVR PRO". I have used MUSIC to let an instrument circle around the listener's head with acceptable results. You can automate a rotation in your DAW.

(Note: Plugin Alliance has several sales over the course of a year.)