Catasma: Difference between revisions

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140625/140608, the '''catasma''', is a [[No-sevens subgroup temperaments|no-sevens]], [[No-elevens subgroup temperaments|no-elevens]], [[13-limit]] [[unnoticeable comma]] measuring about 0.209 [[Cent|cents]]. The name was proposed by [[User:Tristanbay|Tristan Bay]] in 2023, as it is the difference between [[625/624]] and [[676/675]], two important commas tempered out in [[Cata|cata temperament]].
140625/140608, the '''catasma''', is a [[No-sevens subgroup temperaments|no-sevens]], [[No-elevens subgroup temperaments|no-elevens]], [[13-limit]] [[unnoticeable comma]] measuring about 0.209 [[Cent|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 [[User:Tristanbay|Tristan Bay]] in 2023, as it is the difference between [[625/624]] and [[676/675]], two important commas tempered out in [[Cata|cata temperament]].


[[Category:Catasmic]]
[[Category:Catasmic]]

Revision as of 23:03, 20 October 2024

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
Open this interval in xen-calc

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.