Mondo Knows Facts
Twelve pure fifths overshoot seven octaves
The gap is called the Pythagorean comma, about 23 cents A perfect fifth is a ratio of three to two, and stacking twelve of them does not land back on the starting note. The leftover gap has to be hidden somewhere, which is why tuning systems differ. Historically the comma was distributed across a few keys. It sits in Mondo's music collection, one of 200 facts that each trace back to the reference below.
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Facts that can change over time are reviewed and updated. If something here looks wrong, Mondo would rather know than be confidently incorrect.
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More facts like this
Musicians tune by listening for beatsTwo nearly matched frequencies produce a slow throb that stops when they agreeHalving a string raises it an octaveOther simple length ratios give fifth, fourth and thirdSimple frequency ratios sound calmOctaves are two to one and fifths three to two, and they blend rather than clashA guitar is tuned mostly in fourthsE, A, D and G are fourths apart, with a third gap before BWarm air makes instruments play sharpSound travels faster as temperature rises, lifting the pitch of wind instrumentsOrchestras tune to A at 440 hertz by international agreementThe standard was agreed in London in 1939
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Tags: intervals, tuning, history
Twelve pure fifths overshoot seven octaves: the short answers
- Where does this come from, and can I check it?
- The gap is called the Pythagorean comma, about 23 cents. The figure is taken from Britannica, which is linked in full on this page. Every fact on Mondo Knows names its source rather than repeating an unsourced claim.
- Is this really a music fact?
- Yes. It sits on the Music shelf, one of 2,600 sourced facts grouped into space, animals, the human body, history, science and more. Category pages collect every fact in the same field.
- What else can I read about it?
- The links under the fact point to a quiz, game, puzzle or calculator on the same subject, and the shelf below shows related facts. The wording here is original, and quoted phrases are marked as quotations.