The expatriate American experimentalist composer Conlon Nancarrow is increasingly recognized as having had one of the most innovative musical minds of the twentieth century. His music, almost all written for player piano, is the most rhythmically complex ever written, couched in intricate contrapuntal systems using up to twelve different tempi at the same time. Yet despite its complexity, Nancarrow’s music drew its early influences from the jazz pianism of Art Tatum and Earl Hines and from the rhythms of Indian music; Nancarrow’s whirlwinds of notes are joyously physical in their energy. Composed in almost complete isolation from 1940, this music has achieved international fame only in the last few years. The author has discussed Nancarrow’s music with him, and analyses sixty-five works, virtually the composer’s complete output.