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I was wondering if it is possible to play a four hands piano piece with just two hands. Were any classical musicians capable of doing that?

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It clearly depends on the piece. One could very easily write a piece containing a chord where all the notes are more than a hand span apart. In fact, I just did! It's called "7 Octaves of C" and it's one bar long. –  slim Apr 30 '12 at 15:08
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There is a famous story about the blind jazz piano player Art Tatum. When he was a child, circa 1920, he heard a piano piece from a player piano roll. It was recorded by two pianists playing four hands on the piano. However, Tatum did not know that it was a four-hand piece, and had no sheet music (which he could not see anyway) so he learned it by ear and played it by himself, with two hands. This is recounted in the Jazz documentary television series by director Ken Burns.

However, in a quote from a published book mentioned in the Wikipedia article on Art Tatum, it's said that Tatum himself denied that this story was true.

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This doesn't directly answer the question. Tatum denied he did it himself, as you said. This doesn't prove anything beyond the fact that Tatum couldn't do it. The two questions are "Were any classical musicians capable of playing a four hands piano piece with just two hands?" and "is it possible to play a four hands piano piece with just two hands?". As far as I can see, this doesn't answer either question. –  American Luke May 1 '12 at 18:20
    
No, it doesn't answer the question directly, but it's a fascinating anecdote, don't you think? –  Wheat Williams May 1 '12 at 22:33
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Short answer: yes, but...

Longer answer: A piece for piano four hands generally has movement of notes in opposing directions that can "tie up" a single player's fingers, and/or spans of notes that two hands generally cannot cover. Depending on the piece, it is possible for a single player to improvise something similar, but they probably won't hit every note on the page and so the harmonies and movements won't be as "deep" as with two players.

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