Example: If I play an octave on the piano starting on middle C.
To my limited understanding the simple ratio of 2:1(due to sound-waves matching) and the multiple overtones that match up in this octave create a pleasing sound (consonance).
1. I was wondering what of these two phenomenon has more importance or impact? Does the overtones just add more richness to the sound/consonance?
2. Does simple ratios and musical intervals come from the overtones or vice versa?
3. Is it just a coincidence that there existed "secret" harmonics when Pythagoras first started researching intervals and ratios in music?