  We classify three-tone and four-tone chords based on subgroups of the
symmetric group acting on chords contained within a twelve-tone scale. The
actions are inversion, major-minor duality, and augmented-diminished duality.
These actions correspond to elements of symmetric groups, and also correspond
directly to intuitive concepts in the harmony theory of music. We produce a
graph of how these actions relate different seventh chords that suggests a
concept of distance in the theory of harmony.
