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.
'''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| 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 ==

Revision as of 06:02, 19 November 2025

Interval information
Ratio 10985/10976
Factorization 2-5 × 5 × 7-3 × 133
Monzo [-5 0 1 -3 0 3
Size in cents 1.41898¢
Name cantonisma
Color name 3o3r3y-2, trithoru-ayo negative 2nd
FJS name [math]\displaystyle{ \text{M}{-2}^{5,13,13,13}_{7,7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 26.8453
Weil norm (log2 max(n, d)) 26.8465
Wilson norm (sopfr(nd)) 75
Comma size unnoticeable
S-expression S13/S14
Open this interval in xen-calc

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 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 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].

See also

Notes