Syntonic comma

Syntonic comma (81:80) on C
Helmholtz-Ellis notation
Just perfect fifth on D The perfect fifth above D (A+) is a syntonic comma higher than the (A) that is a just major sixth above C, assuming C and D are 9/8 apart.[1]
3-limit 9:8 major tone
5-limit 10:9 minor tone

In music theory, the syntonic comma, also known as the chromatic diesis, the Didymean comma, the Ptolemaic comma, or the diatonic comma[2] is a small comma type interval between two musical notes, equal to the frequency ratio 81/80 (= 1.0125) (around 21.51 cents). Two notes that differ by this interval would sound different from each other even to untrained ears,[3] but would be close enough that they would be more likely interpreted as out-of-tune versions of the same note than as different notes. The comma is also referred to as a Didymean comma because it is the amount by which Didymus corrected the Pythagorean major third (81/64, around 407.82 cents)[4] to a just / harmonicly consonant major third (5/4, around 386.31 cents).

The word "comma" came via Latin from Greek κόμμα, from earlier *κοπ-μα = "a thing cut off", or "a hair", as in "off by just a hair".

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Syntonic comma

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