The ancient Greeks invented and used the diatonic scales that are part of the foundation of western music theory. Whole books have been written on the subject, and I'm not going to beat a dead horse. However, here's an interesting (and potentially important) wrinkle: Because of a misunderstanding in the middle ages about the ancient Greek references, the names the Greeks associated with each scale are actually different than the scales we use today.
|Greek name||Modern name||How it's played|
|Lydian||Ionian||all white keys C to C|
|Phrygian||Dorian||all white keys D to D|
|Dorian||Phrygian||all white keys E to E|
|Hypolydian||Lydian||all white keys F to F|
|Hypophrygian||Mixolydian||all white keys G to G|
|Hypodorian||Aeolian||all white keys A to A|
|Mixolydian||Locrian||all white keys B to B|
So the only region actually in Greece that the ancient Greeks associated with a scale mode was Doria. While ancient musicians might have used any modes known to them, it seems likely that a particular mode might have been more common in the region it was named after. Presumably, if you wanted to write a song set in Athens and have it sound like an archetypical Dorian song, you should use what we now call Phrygian mode. If you wanted to write a song set in Gordium and have it sound like an archetypical Phrygian song, you should use what we now call Dorian mode. And if you wanted to write a song set on Mount Olympus, your guess is as good as mine, because the ancient Greeks didn't even have a scale mode called Aeolian, and what we now call Aeolian mode was considered by the Greeks to be a subcategory of Dorian. Make sense to you yet?
Me neither. I just ended up using whatever felt right for songs about Alexander set in Greece and Macedon.