Xenharmonic Wiki

Comma: Difference between revisions

← Older editNewer edit →
VisualWikitext
Improve lead section, reorganize sections, misc. edits
Line 6: Line 6:
}}
}}
{{Wikipedia|Comma (music)}}
{{Wikipedia|Comma (music)}}
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 [[cent]]s) and not a power such as a square or cube of any other interval, and generally in a low [[prime limit]].
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 [[cent]]s) 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 Temperaments|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.
Some commas are 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 or as problems to be solved. Examples of approaches that try to solve these problems include [[adaptive just intonation]] and [[temperament]].


Commas are usually written as [[ratio]]s, but they can also be written as vectors, sometimes called "[[monzo]]s" or unison vectors. The following lists mostly give both forms, as well as the size in [[cent]]s. The [[Color notation|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.
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.


== Categorization by size ==
Commas are usually written as [[frequency ratio]]s, but they can also be written as vectors, sometimes called [[monzo]]s 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 [[edo]]s.


Commas can theoretically have any size, beginning with the smallest ones we categorize them as follows.
== 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.
* [[Unnoticeable comma]]: under 3.5 cents in size. The 3.5-cent limit correlates to the limit of pitch perception (see also [[just-noticeable difference]]).
* [[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.


; [[Unnoticeable comma]]: under 3.5 cents in size. The 3.5-cent limit correlates to the limit of pitch perception (see also [[JND]]).
== See also ==
; [[Small comma]]: between 3.5 and 30 cents. Intervals below the 30-cent limit are often considered melodically irrelevant.
* [[PIFE comma]]
; [[Medium comma]]:between 30 and 100 cents. Such intervals are often considered melodically relevant rather than true commas.
* [[TIFE comma]]
; [[Large comma]]:over 100 cents in size. The 100-cent limit matches the [[12edo]] semitone.
* [[Superparticular ratio]]
* [[Wolf interval]]


== Categorization by properties ==
== External links ==
Commas can have special properties which explain how they relate to various [[Regular temperament|regular temperaments]].
* [http://www.tonalsoft.com/enc/c/comma.aspx Comma] on [[Tonalsoft Encyclopedia]]
 
; [[PIFE comma]] (or pife): prime limit inclusive fully dimensionally entangled comma.
; [[TIFE comma]] (or tife): target list inclusive fully dimensionally entangled comma.


[[Category:Commas| ]]
[[Category:Commas| ]]
<!-- main article -->
<!-- main article -->
Retrieved from "https://en.xen.wiki/w/Comma"