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Medieval sacred music was a special case in many ways. We have some records (albeit comparatively scant ones) of secular/folk music from pre-Renaissance times, and it was a lot more tonally structured (a more meaningful term than "harmonic") than that.
I'd believe that; my knowledge of music history isn't that great and seeing teleology where there isn't any is an easy mistake.
I guess what I'm saying, speaking very vaguely, is that melodies existing within their own tonal contexts are as old as bone flutes, and their theory goes back at least as far as Pythagoras. And most folk music traditions cooked up their own favorite scale system, which you can just stay in and make music as long as you want to. For that matter, notes in these scale systems can be played as chords and a lot of the combinations make... (read more)