Comma
In just intonation, a comma is a small interval that occurs between two intervals which are close in pitch.
Commas are often 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 to be desired or as problems to be solved. Examples of approaches that try to solve these problems include adaptive just intonation, temperaments, and fudging.
In regular temperament theory, a comma is something to be tempered out, equating two mathematically distinct intervals. For example, the syntonic comma (81/80), which occurs between 10/9 and 9/8 as well as between 81/64 and 5/4, is tempered out by meantone temperament and thus conflates these two pairs of intervals.
Commas are usually written as frequency ratios, but they can also be written as products of primes, sometimes called monzos or unison vectors. 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, commonly called n-commas, such as the 29-comma, or the 41-comma.
As an interval region
As an interval region, a comma can be used to refer to any interval bigger than 0 ¢, but smaller than around 30 ¢. Comma-sized intervals can be used in melody as an appoggiatura, an acciaccatura, or a quick passing tone. Two notes that differ by a comma can be played together for a "shimmer" effect that results from beating between the tones.
Most commonly, commas serve as the separation between two close intervals, such as 9/8 and 8/7. Playing notes a comma apart in succession usually sounds like a "dirty" variation of the same note rather than a distinct melodic step, with the smallest intervals that sounds like a distinct step being around a quartertone in size.
Lists of commas by size
Commas can theoretically have any size, but in practice most are much 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; below the rough boundary of melodic just-noticeable difference and thus imperceptible.
- Small comma: between 3.5 and 30 cents.
- Medium comma: between 30 and 100 cents.
- Large comma: over 100 cents in size; much wider than what is typically considered to be a comma.