Cantonisma: Difference between revisions
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| Ratio = 10985/10976 | | Ratio = 10985/10976 | ||
| Name = cantonisma | | Name = cantonisma | ||
| Color name = 3o<sup>3</sup>r<sup>3</sup>y-2, trithoru-ayo negative 2nd | |||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
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 == | == Etymology == | ||
This comma was named by [[Margo Schulter]] in 2013 after [[Gene Ward Smith]]'s [[ | 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:Cantonismic]] | ||
[[Category:Commas named after musical traditions]] | |||
Latest revision as of 10:11, 22 April 2026
| Interval information |
The cantonisma is an unnoticeable comma of the 13-limit with a ratio of 10985/10976 and a value of approximately 1.42 cents. 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 edos as 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[1].