The Man wrote:
Tatum's influence also extended beyond the piano and included Coleman Hawkins and Charlie Parker. But Evans was probably more influential anyway, at least in part because much of what Tatum did that was new was beyond the capabilities of most musicians. So Evans staying ahead of Tatum can be justified, though I think Tatum is generally considered the greatest jazz pianist, so it's close. Maybe Morton shopuld be ahead of both of them.
Concerning Hancock's placement, Bud Powell and Fletcher Henderson could move ahead of him, but no one else stands out to me as belonging ahead of him.
I've never heard of Tatum influencing Parker... do you have a reference to this?
I agree with Tatum was beyond the capabilities of most musicians... most of his stuff still IS beyond the capabilities of both musicians.
Tatum, Evans, Monk, and Peterson are the four who I've always considers as possibilities for number one. Tatum is definitely first in skill but in terms of influence on the piano it's very close.
As for Hancock, don't you think Django, the most influential jazz guitarist and gypsy swing artist, should be above him? Or Brubeck? Or Horace Silver?
Two sources for Tatum's influence on Parker are Gary Giddins, Visions of Jazz
, p. 441, and Grover Sales, Jazz: America's Classical Music
, pp. 122-123.
Gypsy swing is a pretty small part of jazz history, and I would consider Charlie Christian to be a more influential guitarist, though I think it's right for Reinhardt to be ahead of Christian, because Django has a lot more significant recordings. But there might be a case for him and Silver ahead of Hancock. I doubt it for Brubeck.