Why a piano can never be perfectly in tune: twelve fifths overshoot seven octaves
30seconds
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 semitone.
Drag the fifths wider or narrower and watch the circle fail to close, then see what each choice does to the major thirds. Pure fifths, equal temperament and meantone each hide the gap in a different place.
Deep dive · 4 min
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