Cantonisma

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).

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
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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.