Syntonic comma

The syntonic comma, also didymisches comma ( according to Didymus the Musician) called, is a small musical interval of about one fifth semitone.

The syntonic comma is the difference between the Pythagorean third ( Ditonus ) and the pure third (see just intonation ). Assuming namely two ( Pythagorean ) whole tones ( frequency ratio 9/8) high and a major third ( frequency ratio 5/4) deep, you get a sound that differs from Ursprungston to the syntonic comma:

Thus:

Its frequency ratio is calculated as:

The syntonic comma also occurs as the difference between large ( frequency ratio 9/8) and a small whole tone ( frequency ratio of 10/9 ):

The syntonic comma meantone temperament plays in an important role, as per third precisely this interval must be balanced: between large and small whole tone is averaged.

Example

Frequency ratio.

Because this change in keyboard instruments can not be realized, these mean-, well-tempered or - nowadays almost universally - voted equally-.

The syntonic comma as a problem when tuning of keyboard instruments

See the remarks at the Pythagorean comma