Grachan Moncur III (born June 3, 1937) is an American jazz trombonist. He is one of the few real free jazz trombonists, as well as a prolific composer. He is the son of jazz bassist Grachan Moncur II. Born and raised in Newark, New Jersey, USA, Grachan began playing the cello at age nine, and switched to the trombone at eleven. In high school he attended the Laurinburg Institute in North Carolina, the private school where Dizzy Gillespie studied.

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