Cantonisma: Difference between revisions

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~~'''10985/10976''', otherwise known as the~~ '''cantonisma''', is an [[unnoticeable comma]] of the [[13-limit]] with a value of approximately 1.4 [[cent]]s. It forms the difference by which a stack of three [[14/13]]'s (trienthirds) falls short of [[5/4]] (classical major third). It factors into ([[1716/1715]])([[4225/4224]]). It is tempered out in such notable [[edo]]s as {{EDOs| 46, 84~~, 94~~, 103~~, 111~~, 121, 130~~, 159~~, 224, 270, 494 and 764 }}, leading to a variety of temperaments in which three trienthirds make up a 5/4 major third.

The '''cantonisma''' is an [[unnoticeable comma]] of the [[13-limit]] with a ratio of 10985/10976 and a value of approximately 1.42 [[cent]]s. It forms the difference by which a stack of three [[14/13]]'s (trienthirds) falls short of [[5/4]] (classical major third). It factors into ([[1716/1715]])⋅([[4225/4224]]).

== Temperaments ==

[[Tempering out]] this comma in the 13-limit leads to the rank-5 '''cantonismic''' temperament, or in the 2.5.7.13 subgroup, the rank-3 '''cantonic''' temperament. It is tempered out in such notable [[edo]]s as {{EDOs| 10, 19, 27, 38, 46, 84, 103, 121, 130, 224, 270, 494 and 764 }}, leading to a variety of temperaments in which three trienthirds make up a 5/4 major third.

== Etymology ==

This comma was named by [[Margo Schulter]] in 2013 after [[Gene Ward Smith]]'s [[~~canton~~]] scale<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106251.html Yahoo! Tuning Group | ''Gene's 10985/10976 or (14/13)^3 vs. 5/4 as cantonisma'']</ref>.

This comma was named by [[Margo Schulter]] in 2013 after [[Gene Ward Smith]]'s [[Canton]] scale<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106251.html Yahoo! Tuning Group | ''Gene's 10985/10976 or (14/13)^3 vs. 5/4 as cantonisma'']</ref>.

~~== See also ==~~

* [[Unnoticeable comma]]

== ~~Notes~~ ==

== References ==

[[Category:Cantonismic]]

[[Category:Commas named after musical traditions]]

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-'''10985/10976''', otherwise known as the '''cantonisma''', is an [[unnoticeable comma]] of the [[13-limit]] with a value of approximately 1.4 [[cent]]s. It forms the difference by which a stack of three [[14/13]]'s (trienthirds) falls short of [[5/4]] (classical major third). It factors into ([[1716/1715]])([[4225/4224]]). It is tempered out in such notable [[edo]]s as {{EDOs| 46, 84, 94, 103, 111, 121, 130, 159, 224, 270, 494 and 764 }}, leading to a variety of temperaments in which three trienthirds make up a 5/4 major third.
+The '''cantonisma''' is an [[unnoticeable comma]] of the [[13-limit]] with a ratio of 10985/10976 and a value of approximately 1.42 [[cent]]s. It forms the difference by which a stack of three [[14/13]]'s (trienthirds) falls short of [[5/4]] (classical major third). It factors into ([[1716/1715]])⋅([[4225/4224]]).
+== Temperaments ==
+[[Tempering out]] this comma in the 13-limit leads to the rank-5 '''cantonismic''' temperament, or in the 2.5.7.13 subgroup, the rank-3 '''cantonic''' temperament. It is tempered out in such notable [[edo]]s as {{EDOs| 10, 19, 27, 38, 46, 84, 103, 121, 130, 224, 270, 494 and 764 }}, leading to a variety of temperaments in which three trienthirds make up a 5/4 major third.
 == Etymology ==
-This comma was named by [[Margo Schulter]] in 2013 after [[Gene Ward Smith]]'s [[canton]] scale<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106251.html Yahoo! Tuning Group | ''Gene's 10985/10976 or (14/13)^3 vs. 5/4 as cantonisma'']</ref>.
+This comma was named by [[Margo Schulter]] in 2013 after [[Gene Ward Smith]]'s [[Canton]] scale<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106251.html Yahoo! Tuning Group | ''Gene's 10985/10976 or (14/13)^3 vs. 5/4 as cantonisma'']</ref>.
-== See also ==
-* [[Unnoticeable comma]]
-== Notes ==
+== References ==
 [[Category:Cantonismic]]
+[[Category:Commas named after musical traditions]]