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'''''Pythagorean Tuning''''' was a common tuning system in Western civilization from the time of the ancient Greeks to not long after the Renaissance began. It is based upon using the 3:2 ratio for a perfect fifth and traversing the circle of fiths in both directions from a tonic pitch to derive all other notes. As pitches move upwards in 5ths, they quickly leave the octave of the starting pitch - these pitches are divided by 2 (lowered by an octave) until they fit back into the tonic's octave.
→Pythagorean Tuning
== Other Tuning Systems ==
=== Pythagorean Tuning ===
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