Harmonia

[…]concerning the ancient Greek harmoniai, or modes, in the diatonic genus.[…]degree signify the harmonia in which it appears and what degree it represents; for instance, “D-2” means that this ratio—11/10—is the second degree (ascending) in the Dorian harmonia.

In the case of Mixolydian harmonia, the framework chord is ¹⁄₁, ¹⁴⁄₁₁, ¹⁴⁄₁₀, and ²⁄₁.[…]while the various diatonic harmoniai are modes of each other, this is not true of the other two genera, which are uniquely derived from their corresponding diatonic forms.

In 1935, Hamilton trained a chamber orchestra in Stuttgart to perform in the harmoniai.

While Pollux attributed to Diodorus of Thebes the expansion of the aulos beyond four trupemata, Athenaeus and Pausanias refer to Pronomus of Thebes as the one who developed an aulos that was capable of playing aulema in Dorian, Phrygian, or Lydian harmoniai. In his description of a statue of Pronomus in Boeotia, Pausanias observes: For a time, auletes had three types of auloi. They played Dorian aulema on one, different auloi were made for pieces in the Phrygian harmonia, and the so-called Lydian aulema was played on other auloi.

That rhythm was somehow implicated in the identity of the harmoniai is suggested in Aristotle’s anecdote about the composer Philoxenus, who attempted to compose a dithyramb, The Mysians, in the Dorian harmonia, but was unable to do so.

Socrates argued against the idea of the soul being a harmonia.