Comma (music)

In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. Traditionally, there are two most common commata: the syntonic comma (81:80), the amount by which four just perfect fifths exceed two octaves plus a just major third; and the Pythagorean comma (531441:524288, approximately 74:73), the amount by which twelve just perfect fifths exceed seven octaves. The word comma used without qualification refers to the syntonic comma, which can be defined, for instance, as the difference between an F♯ tuned using the D-based Pythagorean tuning system, and another F♯ tuned using the D-based quarter-comma meantonetuning system. Pitches separated by either comma are considered the same note because conventional notation does not distinguish Pythagorean intervals from 5-limit intervals. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53 TET, the harmonic seventh B♭ and A♯ are both approximated by the same interval although they are a septimal kleisma apart.