A graduate of the New England Conservatory and the Juilliard School of Music, Harper worked on many Broadway shows as arranger, musical director, and/or conductor. His credits include Company, Irene (1973 revisal, starring Debbie Reynolds), The Grand Tour, Peter Pan (1979 revival, starring Sandy Duncan), A Day in Hollywood/A Night in the Ukraine, Brigadoon (1980 revival), Nine, My One and Only, and Grand Hotel. In addition to those successes, he worked on the short-lived Billy, So Long, 174th Street, The Grand Tour, The Three Musketeers, My Favorite Year, and The Best Little Whorehouse Goes Public.
Though not primarily known as a composer, Harper did work in that area: For Irene, he wrote "The World Must Be Bigger Than an Avenue" (lyrics by Jack Lloyd) and the dance number "Riviera Rage." Though his official credit for the Stephen Sondheim musical Company was "dance arrangements," Harper said that he also wrote the vamp for the song "Another Hundred People." His other credits as a composer include the musical Sensations, which had an Off-Broadway run, and Say Yes!, which was produced in 2001 at the Berkshire Theatre Festival in Stockbridge, Massachusetts.
Most recently, Harper was the musical director and on-stage pianist for Barbara Cook's Broadway, a concert of musical theater songs that played in two venues at Lincoln Center (the Vivian Beaumont and the Mitzi Newhouse) as well as on tour. A cast album of the show is available from DRG, the label that had previously released live recordings of the Cook-Harper shows It's Better With a Band (for which Harper wrote the title song and "The Ingenue" with lyricist David Zippel) and Barbara Cook Sings Mostly Sondheim. Also available from DRG are the Cook-Harper studio recordings Oscar Winners and Count Your Blessings (a Christmas album).
Harper produced such cast albums as A Day in Hollywood/A Night in the Ukraine (for DRG) and My One and Only (for Atlantic). During his career, he conducted symphony orchestras in many cities around the world.