He graduated from Columbia University and later studied music at the Curtis Institute in Philadelphia and Juilliard School in New York City.
Barnett then studied piano with Alfred Cortot in Paris, where he received his teaching degree.
Returning to the U.S., Barnett taught piano and music theory, and continued touring and composing.
Barnett taught at Harvard, Columbia, Wellesley and the New England Conservatory of Music.
He also served as Headmaster of the Thomas School in Rowayton, Connecticut, and taught at the University of Bridgeport.