Comma (music)

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In music theory, a comma is a small or very small interval between two enharmonic notes tuned in different ways. For example, an A flat tuned as a major third below C in just intonation, and a G sharp tuned as a major third above E, will not be exactly the same note. The difference between those notes, the diesis, is almost a quarter tone, easily audible.

All of the intervals mentioned below are presumed to be tuned in just intonation.

There are many commas, notably :

Pythagorean comma or ditonic comma (difference between 7 octaves and 12 perfect fifths)
syntonic comma, the difference between four perfect fifths and one major third plus two octaves
schisma, the difference between 8 perfect fifths plus one major third and 5 octaves (equal to the interval between Pythagorean comma and syntonic comma)
diaschisma, the difference between 4 fifths plus 2 thirds and 3 octaves

[edit] Tempering of commas

Commas are frequently used^{[citation needed]}in the description of musical temperaments , where they describe distinctions between musical intervals that are eliminated by that tuning system. A comma can be viewed as the distance between two musical intervals. When a given comma is tempered out in a tuning system, the ability to distinguish between those two intervals in that tuning is eliminated. For example, the difference between the diatonic semitone and chromatic semitone is called the diesis. The widely used twelve-tone equal temperament tempers out the diesis, and thus does not distinguish between the two different types of semitones. On the other hand, nineteen-tone equal temperament does not temper out this comma, and thus it distinguishes between the two semitones.

Examples:

12-TET tempers out the diesis, as well as a variety of other commas.
19-TET tempers out the septimal diesis and syntonic comma, but does not temper out the diesis.
22-TET tempers out the septimal comma of Archytas, but does not temper out the septimal diesis or syntonic comma.
31-TET tempers out the syntonic comma, as well as the comma defined by the ratio (99:98), but does not temper out the diesis, septimal diesis, or septimal comma of Archytas.

[edit] Other intervals called commas

There are also several intervals called commas, which are not technically commas because they are not rational fractions like those above, but are irrational approximations of them. These include the Holdrian comma and Mercator's comma.