Hello,
In Bach's two-part invention in C major (BMV 772) bar 13, one of the notes - E natural - is shared by both hands. That is, the right-hand thumb could play it, the left-hand thumb could play it, or both could strike the key simultaneously. This situation occurs in many pieces - Chopin, Rachmaninoff, Granados, etc. So the question is: Are there any general rules or guidelines for choosing how to play a note that is shared between the hands? Should you always use the right hand? The left hand? Play the note with fingers in both hands? I believe it's probably more involved than this. Perhaps you decide based on the melodic flow or harmonic progressions in the piece. Or maybe you need to consider the succeeding notes and determine which hand or finger placement will help play them.
If anyone has insight on this I would greatly appreciate it. I would imagine other pianists come across this situation as well.