Syntonic comma

"Chromatic diesis" redirects here. For 27/26, see Comma (music).

Syntonic comma (81:80) on C

Helmholtz-Ellis notation

Ben Johnston's 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.

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, 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, 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) to a justly intoned 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".