Equivalently, how can I split notes across a staff in the most "correct" way?

Something simple would be to just split the parts across a particular note (i.e., middle C), but this would be much less than ideal. Any solutions welcome: professional software, academic algorithms, or half-baked ideas.

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    Do you hope to find something that works in real time, or something that works on a recorded sequence of notes? – user1044 Nov 8 '12 at 17:10

With my MIDI sequencer, you figure that out on your own. You drag rectangles around the hand's notes that are the easiest to pick out, and that'll move them to that other hand's track.

So, manually, you:

  • Figure out if the piece is even playable by a human - sometimes it's for a computer to play (a bunch of hugely complex, blisteringly fast arpeggios a human has no hope of playing).

  • Play through the song and see where your thumbs end up.

  • Edit the MIDI and pick out the notes that need to move.

  • Move them.

You really can't do this in an automated fashion. There are too many variables (like hand span, fingering, hands hopping over each other, a finger on one hand poking in 2 notes, there's all kinds of craziness that can happen).

So, you get a piano player, and have him/her do it.

Your question kind of boils down to "how do you place your hands when playing a piano piece."

Answer: Learn to play the piano.

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    This is true enough. Plenty of metrics are possible but none will be perfectly accurate. It's not uncommon for me to take issue with the way the composer or editor has set the fingering, either; there's no objective standard, which is sort of required for something algorithmic. – user28 Nov 7 '12 at 0:30
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    yeah, if humans can't even figure it out, well, ya just can't expect a computer to be able to. – Stephen Hazel Nov 7 '12 at 1:14
  • Canonical examples which would confound an algorithm: Mozart sonata hand-crossings, Goldberg Variations hands overlapping-interwoven, Liszt and Debussy's extra staves, Ligeti Etudes hold a chord with one hand while the other races through the held notes. Get a computer to do those, and it'll probably also drive a car in rush hour. – Camille Goudeseune Jun 13 '19 at 20:38

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