If there were one thing that most musicians could cite as the original spark that ignited their curiosity about ancient Greek music, it would surely be the encounter with book 3 of Plato's Republic, in which Socrates names certain musical “modes” as edifying and others as corrupting. In English translation, Plato has the great philosopher describe the Dorian “mode” as promoting steadfastness and bravery in war and the Phrygian “mode” as a useful accompaniment to the constructive occupations of peacetime. Socrates declares these “modes” desirable for the education of the guardians of his ideal city-state because of the good and useful moral character that they promote. Other “modes,” such as the mixed, or half, Lydian (Mixolydian), the tense Lydian, the ordinary Lydian, and the Ionian, drag down the moral character of the state by encouraging lamentation and the drunken singing associated with the symposium.

The typical novice's reaction to these readings is one of astonishment. Were Greek listeners so hypersensitive that they could be moved to bravery, civic virtue, or loose morals merely by listening to music in the minor mode with natural 6 and flat 7 (Dorian), or flat 2 (Phrygian), or the major mode with sharp 4 (Lydian)? Of course, their mistake is understandable. The majority of English translations of the Republic translate Plato's word harmonia (ἁρμονία) as “mode.” Only in the most recent musicological treatments is the word presented without translation simply as harmonia. The reasons for doing so are compelling, and the failure of translators to observe this crucial musical distinction is much to be deplored. Readers acquainted with the history of Western music are bound to associate the term mode with the eight ecclesiastical modes (four authentic, four plagal, with finals on D, E, F, and G), or the twelve modes of Renaissance polyphony (with additional finals on A and C), or the seven octachords of modal jazz. None of these modes, as far as we know, have anything to do with Plato's harmoniai.

If not to these things, then to what do Plato's harmoniai refer? Indeed, to what do the harmoniai from Terpander (seventh century B.C.E.) to Aristoxenus (fourth century B.C.C.) refer?