Comma: Difference between revisions
Cleanup (no one says "comma (interval region)" in speech) |
Rewrite of many parts and added a graph showcasing many common commas to scale |
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In just intonation, a '''comma''' is a small [[interval]] that occurs between two intervals which are close in [[pitch]]. Commas are always greater than [[1/1]] (0 [[cent]]s) and not a power such as a square or cube of any other just interval, and generally in a low [[prime limit]]. | In just intonation, a '''comma''' is a small [[interval]] that occurs between two intervals which are close in [[pitch]]. Commas are always greater than [[1/1]] (0 [[cent]]s) and not a power such as a square or cube of any other just interval, and generally in a low [[prime limit]]. | ||
Commas are often considered [[dissonant]] due to their small but noticeable [[interval size measure|size]] which induces an audible [[beat]]. In addition, certain chord progressions are [[comma pump]]s, 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]], [[temperament|temperaments]], and [[fudging]]. | |||
In [[regular temperament theory]], a comma | 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. | ||
[[File:EufaJIcommasFinal1.svg|thumb|A visualization of intervals commonly used as commas, built from stacked intervals, to scale.]] | |||
Commas are usually written as [[frequency ratio]]s, but they can also be written as | Commas are usually written as [[frequency ratio]]s, but they can also be written as products of primes, sometimes called [[monzo]]s 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 [[edo]]s, commonly called n-commas, such as the [[29-comma]], or the [[41-comma]]. | ||
== As an interval region == | == As an interval region == | ||
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== Lists of commas by size == | == Lists of commas by size == | ||
Commas can theoretically have any size, but in practice most are smaller than a [[12edo]] semitone (100{{cent}}). The following categories, while arbitrary, are used on the Xenharmonic Wiki to classify commas by size. | Commas can theoretically have any size, but in practice most are much smaller than a [[12edo]] semitone (100{{cent}}). The following categories, while arbitrary, are used on the Xenharmonic Wiki to classify commas by size. | ||
* [[Unnoticeable comma]]: under 3.5 cents in size | * [[Unnoticeable comma]]: under 3.5 cents in size; below the melodic [[just-noticeable difference]] and thus imperceptible. Tempering these commas out produces [[very high accuracy temperaments]] or [[Microtemperament|microtemperaments]]. | ||
* [[Small comma]]: between 3.5 and 30 cents. | * [[Small comma]]: between 3.5 and 30 cents. Tempering these commas out produces moderate accuracy temperaments. | ||
* [[Medium comma]]: between 30 and 100 cents. | * [[Medium comma]]: between 30 and 100 cents. Tempering these commas out produces low accuracy temperaments. | ||
* [[Large comma]]: over 100 cents in size. | * [[Large comma]]: over 100 cents in size; much wider than what is typically considered to be a comma. Tempering these commas out produces [[very low accuracy temperaments]] or [[Exotemperament|exotemperaments]]. | ||
== See also == | == See also == | ||
Revision as of 16:34, 5 December 2025
In just intonation, a comma is a small interval that occurs 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 just interval, and generally in a low prime limit.
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
Comma can be used to refer to any interval bigger than 0 cents, but smaller than around 30 cents.
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 melodic just-noticeable difference and thus imperceptible. Tempering these commas out produces very high accuracy temperaments or microtemperaments.
- Small comma: between 3.5 and 30 cents. Tempering these commas out produces moderate accuracy temperaments.
- Medium comma: between 30 and 100 cents. Tempering these commas out produces low accuracy temperaments.
- Large comma: over 100 cents in size; much wider than what is typically considered to be a comma. Tempering these commas out produces very low accuracy temperaments or exotemperaments.