I seem to have somehow failed to put my two cents in here! Fathead most assuredly is a jazz musician (and R&B and just his own bad self), as are/were Don Wilkerson and King Curtis too. I like JD Allen, FWIW, and the one I dig the most is Graphitti - it has that swagger that Saxophone Colossus and Our Man in Paris have, IMHO, YMMV.