Interesting topic.
This is later than Plato of course, but according to Ptolemy, the Greek modes are (relative pitch and descending):
1. Dorian = e, d, c, b, a, g, F, E
2. Phrygian = e, d, c#, b, a, g, F#, E
3. Lydian = e, d#, c#, b , a, g#, F#, E
4. Mixolydian = e, d, c, bb, a, g, F, E
5. Hypodorian = e, d, c, b, a, g, F#, E
6. Hypophrygian = e, d, c#, b, a, g#, F#, E
7. Hypolydian = e, d#, c#, b, a#, g#, F#, E
Grout, Donald Jay, A History of Western Music, (New York, Norton, 1960), p. 32.
I agree that Byzantine chant is a very important living connection also.
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