Cantonisma: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 10985/10976

~~| Monzo = -2 0 1 -3 0 3~~

~~| Cents = 1.41898~~

| Name = cantonisma

| Color name =

| Color name = 3o<sup>3</sup>r<sup>3</sup>y-2, trithoru-ayo negative 2nd

| ~~FJS name =~~

| Comma = yes

~~| Sound~~ =

}}

~~'''10985/10976''', otherwise known as the~~ '''cantonisma''', is an [[unnoticeable comma]] of the [[13-limit]] with a value of approximately 1.~~4 cents~~. It forms the difference ~~between~~ a stack of three [[14/13]] trienthirds~~, and one~~ [[5/4]] major third. It is tempered out in such notable [[~~EDO|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>.

== References ==

[[Category:Cantonismic]]

[[Category:Commas named after musical traditions]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 10985/10976
-| Monzo = -2 0 1 -3 0 3
-| Cents = 1.41898
 | Name = cantonisma
-| Color name =
+| Color name = 3o<sup>3</sup>r<sup>3</sup>y-2, trithoru-ayo negative 2nd
-| FJS name =
+| Comma = yes
-| Sound =
 }}
-'''10985/10976''', otherwise known as the '''cantonisma''', is an [[unnoticeable comma]] of the [[13-limit]] with a value of approximately 1.4 cents.  It forms the difference between a stack of three [[14/13]] trienthirds, and one [[5/4]] major third.  It is tempered out in such notable [[EDO|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>.
+== References ==
+[[Category:Cantonismic]]
+[[Category:Commas named after musical traditions]]