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Why a piano can never be perfectly in tune: twelve fifths overshoot seven octaves
Climb twelve perfect fifths and you should land back on your starting note, seven octaves up. You don't: you overshoot by 23.46 cents, nearly a quarter of a…
Why a piano has 12 notes: the circle of fifths that never quite closes
Stack pure 3:2 fifths, the most consonant interval after the octave, and you'd expect to eventually land back on your starting note. You never do. After twelve…