A study of Elliott Carter’s harmony and harmonic practice, including his use of pitch-class sets and set classes, interval classes and interval repertories, all-interval tetrachords and the all-trichord hexachord, his Harmony Book, core harmonies, derived core harmonies, aggregates, twelve-note eleven-interval chords (all-interval rows), and “linking and morphing.” The emphasis is on Carter’s dynamic conception of harmony in motion, and his use of harmony to define the character-continuities in his compositions.