Abstract: The second law of thermodynamics declares that the universe proceeds from a state of lower entropy to a state of higher entropy. This explains why certain processes seem to happen only forwards in time. For example, a wineglass falls off a table and shatters, but shards of glass never rise from the floor and spontaneously assemble themselves into a wineglass. Like a physical process, a melody is irreversible. That is, a series of notes (usually) only sounds correct to a listener when played in forward order. Can we define a 'musical arrow of time' by encoding this irreversibility as an entropy?