Catasma

Interval information

Ratio	140625/140608
Factorization	2-6 × 32 × 56 × 13-3
Monzo	[-6 2 6 0 0 -3⟩
Size in cents	0.2092996¢
Name	catasma
Color name	L3u3y6-3, Latrithuyoyo negative 3rd
FJS name	[math]\displaystyle{ \text{5d}{-3}^{5,5,5,5,5,5}_{13,13,13} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	34.2028
Weil norm (log2 max(n, d))	34.203
Wilson norm (sopfr(nd))	87
Comma size	unnoticeable
S-expression	S25/S26
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140625/140608, the catasma, is a no-sevens, no-elevens, 13-limit unnoticeable comma measuring about 0.209 cents. It is the difference between the whole tone, 9/8, and three intervals of 26/25, or alternatively between 3/1 and three intervals of 75/52; therefore tempering this comma out splits the perfect twelfth into three equal parts.

Etymology

The name was proposed by Tristan Bay in 2023, as it is the difference between 625/624 and 676/675, two important commas tempered out in cata temperament. It is also tempered out in catabolic temperament, which bears a similarity in that it is a 2.3.5.13 subgroup temperament with ~6/5 as a generator, but cata is kleismic; catabolic is an extension of egads, and thus, much more complex.