As a composer, Vincent's music is known for its rhythmic vitality and lyricism. Although his music is essentially classical in form it is distinctly individual. The free tonality of his work makes use of what he calls ‘paratonality’: the predominance of a diatonic element in a polytonal or atonal passage. Vincent wrote numerous orchestral works, chamber music pieces, art songs, and choral works. He also wrote one ballet, 3 Jacks (1942), a film score, Red Cross (1948), and an opera, Primeval Void (1969).
In 1951 his book The Diatonic Modes in Modern Music was published. He also conducted orchestras throughout the USA and South America, and he was a director of the Huntington Hartford Foundation from 1952–1965.