81/80: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 81/80

| Cents = 21.~~506290~~

| Cents = 21.50629

| Monzo = -4 4 -1

| Name = syntonic comma, Didymus comma, meantone comma

| Name = syntonic comma, Didymus comma, meantone comma

| Color name = g1, Gu comma, gu unison

| FJS name = P15

| Sound =

}}

The '''syntonic''' or '''Didymus''' or '''meantone comma''' (frequency ratio '''81/80''') is helpful for comparing [[3-limit]] and 5-limit [[just intonation]]. Adding or subtracting this comma to/from any 3-limit [[ratio]] with an [[odd limit]] of 27 or higher creates a 5-limit ratio with a much lower odd-limit. Thus dissonant 3-limit harmonies can often be sweetened via a commatic adjustment. However adding/subtracting this comma to/from any 3-limit ratio of odd limit 3 or less (the 4th, 5th or 8ve), creates a wolf interval of odd limit 27 or higher. Any attempt to tune a fixed-pitch instrument (e.g. guitar or piano) to 5-limit just intonation will create such wolves, thus tempering out 81/80 is desirable. This gives a tuning for the [[Tone|whole tone]] which is intermediate between 10/9 and 9/8, and leads to [[Meantone ~~family~~|meantone temperament]], hence the name meantone comma.

The '''syntonic''' or '''Didymus''' or '''meantone comma''' (frequency ratio '''81/80''') is helpful for comparing [[3-limit]] and [[5-limit]] [[just intonation]]. Adding or subtracting this comma to/from any 3-limit [[ratio]] with an [[odd limit]] of 27 or higher creates a 5-limit ratio with a much lower odd-limit. Thus dissonant 3-limit harmonies can often be sweetened via a commatic adjustment. However, adding/subtracting this comma to/from any 3-limit ratio of odd limit 3 or less (the 4th, 5th or 8ve), creates a wolf interval of odd limit 27 or higher. Any attempt to tune a fixed-pitch instrument (e.g. guitar or piano) to 5-limit just intonation will create such wolves, thus tempering out 81/80 is desirable. This gives a tuning for the [[Tone|whole tone]] which is intermediate between 10/9 and 9/8, and leads to [[Meantone|meantone temperament]], hence the name meantone comma.

Tempering out a comma does not just depend on an EDO's size; [[105edo]] tempers 81/80 out, while [[15edo|3edo]] does not.

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If one should be so bold as to treat the syntonic comma as a musical interval in its own right as opposed to tempering it out, one can easily use it in melodies as either an [[Wikipedia:Appoggiatura|appoggitura]], an [[Wikipedia:Acciaccatura|acciaccatura]], or a quick passing tone. Furthermore, it is also very easy to exploit in [[comma pump]] modulations, as among the [[Meantone comma pump examples|known examples]] of this kind of thing are familiar-sounding chord progressions.

~~According to~~ [~~http://untwelve.org/interviews/golden.html this interview] {{dead link}},~~ Monroe Golden's ''Incongruity'' uses just-intonation chord progressions that exploit this comma.

[[Monroe Golden]]'s ''Incongruity'' uses just-intonation chord progressions that exploit this comma<ref>[http://untwelve.org/interviews/golden UnTwelve's interview to Monroe Golden]</ref>.

~~== Relations~~ to ~~other Superparticular Ratios ==~~

== Relations to other superparticular ratios ==

Superparticular ratios, like 81/80, can be expressed as products or quotients of other superparticular ratios. Following is a list of such representations r1 * r2 or r2 / r1 of 81/80, where r1 and r2 are other superparticular ratios.

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|}

== ~~External Links~~ ==

== See also ==

* [[160/81]] – its [[octave complement]]

* [[40/27]] – its [[fifth complement]]

* [[Small comma]]

* [[List of superparticular intervals]]

* [[Wikipedia: Syntonic comma]]

== Notes ==

[[Category:5-limit]]

[[Category:Small comma]]

~~[[Category:Definition]]~~

[[Category:Interval]]

[[Category:Ratio]]

[[Category:Superparticular]]

[[Category:~~Syntonic~~]]

[[Category:Meantone]]

[[de:81/80]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 81/80
-| Cents = 21.506290
+| Cents = 21.50629
 | Monzo = -4 4 -1
-| Name = syntonic comma, <br/> Didymus comma, <br/> meantone comma
+| Name = syntonic comma, <br>Didymus comma, <br>meantone comma
 | Color name = g1, Gu comma, <br/> gu unison
 | FJS name = P1<sub>5</sub>
 | Sound =
 }}
+{{Wikipedia|Syntonic comma}}
-The '''syntonic''' or '''Didymus''' or '''meantone comma''' (frequency ratio '''81/80''') is helpful for comparing [[3-limit]] and 5-limit [[just intonation]]. Adding or subtracting this comma to/from any 3-limit [[ratio]] with an [[odd limit]] of 27 or higher creates a 5-limit ratio with a much lower odd-limit. Thus dissonant 3-limit harmonies can often be sweetened via a commatic adjustment. However adding/subtracting this comma to/from any 3-limit ratio of odd limit 3 or less (the 4th, 5th or 8ve), creates a wolf interval of odd limit 27 or higher. Any attempt to tune a fixed-pitch instrument (e.g. guitar or piano) to 5-limit just intonation will create such wolves, thus tempering out 81/80 is desirable. This gives a tuning for the [[Tone|whole tone]] which is intermediate between 10/9 and 9/8, and leads to [[Meantone family|meantone temperament]], hence the name meantone comma.
+The '''syntonic''' or '''Didymus''' or '''meantone comma''' (frequency ratio '''81/80''') is helpful for comparing [[3-limit]] and [[5-limit]] [[just intonation]]. Adding or subtracting this comma to/from any 3-limit [[ratio]] with an [[odd limit]] of 27 or higher creates a 5-limit ratio with a much lower odd-limit. Thus dissonant 3-limit harmonies can often be sweetened via a commatic adjustment. However, adding/subtracting this comma to/from any 3-limit ratio of odd limit 3 or less (the 4th, 5th or 8ve), creates a wolf interval of odd limit 27 or higher. Any attempt to tune a fixed-pitch instrument (e.g. guitar or piano) to 5-limit just intonation will create such wolves, thus tempering out 81/80 is desirable. This gives a tuning for the [[Tone|whole tone]] which is intermediate between 10/9 and 9/8, and leads to [[Meantone|meantone temperament]], hence the name meantone comma.
 Tempering out a comma does not just depend on an EDO's size; [[105edo]] tempers 81/80 out, while [[15edo|3edo]] does not.
@@ Line 20: / Line 20: @@
 If one should be so bold as to treat the syntonic comma as a musical interval in its own right as opposed to tempering it out, one can easily use it in melodies as either an [[Wikipedia:Appoggiatura|appoggitura]], an [[Wikipedia:Acciaccatura|acciaccatura]], or a quick passing tone.  Furthermore, it is also very easy to exploit in [[comma pump]] modulations, as among the [[Meantone comma pump examples|known examples]] of this kind of thing are familiar-sounding chord progressions.
-According to [http://untwelve.org/interviews/golden.html this interview] {{dead link}}, Monroe Golden's ''Incongruity'' uses just-intonation chord progressions that exploit this comma.
+[[Monroe Golden]]'s ''Incongruity'' uses just-intonation chord progressions that exploit this comma<ref>[http://untwelve.org/interviews/golden UnTwelve's interview to Monroe Golden]</ref>.
-== Relations to other Superparticular Ratios ==
+== Relations to other superparticular ratios ==
 Superparticular ratios, like 81/80, can be expressed as products or quotients of other superparticular ratios. Following is a list of such representations r1 * r2 or r2 / r1 of 81/80, where r1 and r2 are other superparticular ratios.
@@ Line 139: / Line 138: @@
 |}
-== External Links ==
+== See also ==
+* [[160/81]] – its [[octave complement]]
+* [[40/27]] – its [[fifth complement]]
+* [[Small comma]]
+* [[List of superparticular intervals]]
-* [[Wikipedia: Syntonic comma]]
+== Notes ==
 [[Category:5-limit]]
 [[Category:Small comma]]
-[[Category:Definition]]
 [[Category:Interval]]
+[[Category:Ratio]]
 [[Category:Superparticular]]
-[[Category:Syntonic]]
+[[Category:Meantone]]
 <!-- interwiki -->
 [[de:81/80]]