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Three ballets choreographed to violin concertos could have been a nice idea on paper but a bad one in practice. Amazingly, however, New York City Ballet's triple violin bill on Saturday night at the David H. Koch Theater offered not just a magnificent range of 20th-century scores by Barber, Prokofiev and Stravinsky, but also a dance program that seemed perfectly composed too. First came Peter Martins's ''Barber Violin Concerto'' from 1988, set to Samuel Barber's Concerto for Violin and Orchestra (Op. 14). ''Barber'' demonstrates Mr. Martins's best attributes as a choreographer: a gift for ingenious partnering; an unpredictable responsiveness to the music; a craftsmanship in moving dancers around the stage. On Saturday he was served marvelously by his performers: Sara Mearns and Charles Askegard as the classical pair; Megan Fairchild and Jared Angle as the moderns. [ABSTRACT FROM AUTHOR]