In this chapter I discuss the paradigmatic function which music, as a theoretical science (‘harmonics’), can have in relation to practical philosophy, in particular ethics, for the Platonists of Late Antiquity, going from Iamblichus (end of the 3rd century) and Proclus to Damascius (mid 6th century). Inspired by some passages in Plato’s Republic, in Nicomachus of Gerasa and in Ptolemy’s Harmonics, these Platonists also introduced a hierarchy of types of music and a hierarchy of types of virtue. I will attempt to show the relation between these two hierarchies, starting with the ‘ethical’ and ‘political’ levels of virtue, showing how harmonics provides conceptual paradigms for the description of these virtues, and then moving up to the higher levels of virtue, the ‘purificatory’ and ‘theoretical’ virtues, asking how music, as harmonics, might relate to the higher virtues.