Syntonic comma

In music theory, the syntonic comma, also known as the chromatic diesis, the comma of Didymus, the Ptolemaic comma, or the diatonic comma is a small comma type interval between two musical notes, equal to the frequency ratio 81:80 (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 referred to as a "comma of Didymus" because it is the amount by which Didymus corrected the Pythagorean major third (81:64, around 407.82 cents) to a just major third (5:4, around 386.31 cents).

Relationships

The prime factors of the just interval 81/80 known as the syntonic comma can be separated out and reconstituted into various sequences of two or more intervals that arrive at the comma, such as 81/1 * 1/80 or (fully expanded and sorted by prime) 1/2 * 1/2 * 1/2 * 1/2 * 3/1 * 3/1 * 3/1 *3/1 * 1/5. All sequences are mathematically valid, but some of the more musical sequences people use to remember and explain the comma's composition, occurrence, and usage are listed below: