On TV I saw not long ago someone performing one of Art Tatum’s piano solos. Some of them have been transcribed, & can be played as if they were concert pieces. I found it unsatisfying. Not because Tatum isn’t an inventive composer, deserving of at least the same treatment accorded to even quite obscure contemporaries of Bach, but because it was no longer improvised.
Different performances of the same song by Tatum do have a great deal in common. He was almost playing from score. A score not on paper but in his mind, but a score even so. Liszt’s improvisations were similar: contemporaries report that from one performance to the next they hardly changed. Nevertheless, the almost matters. Jazz thrives on a certain degree of unpredictability. Improvisation derives a special character from its real or fictive becoming in-the-moment—taking chances, being “out there”.
You know in general what Tatum or Monk is going to do with a standard chart. Each has a distinct style. But sometimes there’s a surprise. As a composer, Tatum might best be compared to classical virtuosi who, like Anton Rubenstein, wrote “characteristic” pieces for their own concert repertoire or for sale to amateurs. His works are variations on a theme—the underlying tune by Gershwin or Cole Porter or (in one case that I know of) Dvořak. Variations in a broad sense, like Brahms’s on Paganini. Of course that is the norm for jazz based on standards, and for much other music too: Renaissance masses based on popular tunes like “L’homme armé”, for example. Jazz has become quasi-classical. It is given “museum” performances like those of classical music and opera, which ceased to be a living form after World War I. (Lulu, Nixon in China and the like are not counterexamples: they are opera-as-high-art, not the living opera of Bizet and Verdi.) No doubt the same will happen—has happened—with rock ‘n’ roll (it began when the “roll” disappeared…).