Duke Ellington and Billy Strayhorn , who had worked together for a long time , both played on half the set 's 38 tracks , and wrote two new pieces of music for the album : `` The E and D Blues '' , and a musical piece about Fitzgerald ( the only `` Songbook '' track that Fitzgerald does not sing on ) . Duke Ellington and his longtime collaborator Billy Strayhorn both appeared on exactly half the set 's 38 tracks and wrote two new pieces of music for the album : `` The E and D Blues '' and a four-movement musical portrait of Fitzgerald ( the only Songbook track on which Fitzgerald does not sing ) .