Comma

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A comma is a small interval that occurs in just intonation, between two intervals which are close in pitch. Commas are always greater than 1/1 (0 cents) and not a power such as a square or cube of any other interval, and generally in a low prime limit.

The word is often used in reference to regular tempering when the comma is tempered out, which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example, the Syntonic or Didymus comma of 81/80, which occurs between 10/9 and 9/8, as well as 81/64 and 5/4, is tempered out by meantone temperament.

Commas are usually written as ratios, but they can also be written as vectors, sometimes called "monzos" or unison vectors. The following lists mostly give both forms, as well as the size in cents. The color name refers to both the comma and the temperament created when it is tempered out, except for 3-limit commas, which create edos.

Categorization by size

Commas can theoretically have any size, beginning with the smallest ones we categorize them as follows.

Unnoticeable comma
under 3.5 cents in size. The 3.5-cent limit correlates to the limit of pitch perception (see also JND).
Small comma
between 3.5 and 30 cents. Intervals below the 30-cent limit are often considered melodically irrelevant.
Medium comma
between 30 and 100 cents. Such intervals are often considered melodically relevant rather than true commas.
Large comma
over 100 cents in size. The 100-cent limit matches the 12edo semitone.

Categorization by properties

Commas can have special properties which explain how they relate to various regular temperaments.

PIFE comma (or pife)
prime limit inclusive fully dimensionally entangled comma.
TIFE comma (or tife)
target list inclusive fully dimensionally entangled comma.