Finding optimal piano fingerings

While preparing to perform a piece of music, a pianist must work out a fingering for the piece. Sometimes, the optimal fingering is obvious and emerges naturally during sight-reading. Other times, when the easiest fingering is unclear, the sheet music will show a suggested fingering that was offered by an experienced player. But often, neither of these is the case, and the pianist must try out a variety of different fingerings. The intent of this paper is to present an efficient ‘dynamic programming’ method for finding optimal fingerings.