Comma: Difference between revisions

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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 [[cent]]s) and not a power such as a square or cube of any other 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]].

~~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 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]]s, and [[fudging]].

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.

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:EufaJICommasFinalV2.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 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]].

~~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.

== As an interval region ==

As an interval region, a '''comma''' can be used to refer to any interval bigger than 0{{c}}, but smaller than around 30{{c}}. Comma-sized intervals can be used in melody as an {{W|appoggiatura}}, an {{W|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 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~~. The 3.5-cent limit correlates to~~ the ~~limit~~ of ~~pitch perception (see also~~ [[just-noticeable difference]]).

* [[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~~. Intervals below the 30-cent limit are often considered melodically irrelevant~~.

* [[Small comma]]: between 3.5 and 30 cents.

* [[Medium comma]]: between 30 and 100 cents~~. Such intervals are often considered melodically relevant rather than true commas~~.

* [[Medium comma]]: between 30 and 100 cents.

* [[Large comma]]: over 100 cents in size~~. The 100-cent limit matches the 12edo semitone~~.

* [[Large comma]]: over 100 cents in size; much wider than what is typically considered to be a comma.

== See also ==

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 {{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]].
+In just intonation, a '''comma''' is a small [[interval]] that occurs between two intervals which are close in [[pitch]].
-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 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]]s, and [[fudging]].
-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.
+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:EufaJICommasFinalV2.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 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]].
-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.
+== As an interval region ==
+{{Main| Comma and diesis }}
+As an interval region, a '''comma''' can be used to refer to any interval bigger than 0{{c}}, but smaller than around 30{{c}}. Comma-sized intervals can be used in melody as an {{W|appoggiatura}}, an {{W|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 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. The 3.5-cent limit correlates to the limit of pitch perception (see also [[just-noticeable difference]]).
+* [[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. Intervals below the 30-cent limit are often considered melodically irrelevant.
+* [[Small comma]]: between 3.5 and 30 cents.
-* [[Medium comma]]: between 30 and 100 cents. Such intervals are often considered melodically relevant rather than true commas.
+* [[Medium comma]]: between 30 and 100 cents.
-* [[Large comma]]: over 100 cents in size. The 100-cent limit matches the 12edo semitone.
+* [[Large comma]]: over 100 cents in size; much wider than what is typically considered to be a comma.
 == See also ==