My comments under the heading "Song Structure and Style" about Ringo's bass drum is concerning his playing the bass drum while at his drum kit on the rhythm track. He definately does play the timpani during the chorus as an overdub as mentioned under the heading "Recording History." As to whether the song was written by John or Paul, all we have to go on is their quotes. And I agree that it is difficult to determine from listening whether Paul is singing with John in the verses or if it's just John double-tracked, credible sources suggest that it is both of them singing in unison. I hear more of John in the released version, but both of them definately sang in unison on earlier takes of the song. This seems to suggest that John happens to be mixed higher than Paul on the released version.