Comma
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.
Some commas are considered dissonant due to their small but noticeable size which induces an audible beat. In addition, certain chord progressions are comma pumps, which may cause the tonal center of a piece to drift up or down in pitch over time. These effects can be treated either as features or as problems to be solved. Examples of approaches that try to solve these problems include adaptive just intonation and temperament.
In regular temperament theory, a comma can be tempered out, which is to say reduced to a unison, by a temperament, thereby equating the intervals separated by that comma. For example, the syntonic comma (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 frequency 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.
Lists of commas by size
Commas can theoretically have any size, but in practice most are smaller than a 12edo semitone (100 ¢). The following categories, while arbitrary, are used on the Xenharmonic Wiki to classify commas by size.
- Unnoticeable comma: under 3.5 cents in size. The 3.5-cent boundary roughly correlates to the melodic just-noticeable difference of pitch perception.
- Small comma: between 3.5 and 30 cents.
- Medium comma: between 30 and 100 cents.
- Large comma: over 100 cents in size. The 100-cent limit matches the 12edo semitone.