Centisma: Difference between revisions

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The '''centisma''' is a [[17-limit]] (2.3.17 subgroup) unnoticeable comma measuring about 0.189 cents in size. It is the difference between a stack of 400 [[17/12]]'s and the octave. The tempering out of this results in a period of 1 step of [[400edo]] (3 cents) and makes [[17/12]], an astronomically close interval to 603 cents (603.00041), exactly 603 cents. Similarly, it makes the [[289/288|semitonisma]] exactly 6 cents. As such this temperament is very abursdly accurate and it isn't supported by any [[patent val]] other than [[400edo]] until reaching 13400edo.
The '''centisma''' is a [[17-limit]] (2.3.17 subgroup) unnoticeable comma measuring about 0.189 cents in size. It is the difference between a stack of 400 [[17/12]]'s and the octave.
 
== Temperaments ==
Tempering it out in the full 17-limit results in the rank-6 '''centismic''' temperament, and rank-2 2.3.17 '''centic''' temperament. The tempering out of this results in a period of 1 step of [[400edo]] (3 cents) and makes [[17/12]], an astronomically close interval to 603 cents (603.00041), exactly 603 cents. Similarly, it makes the [[289/288|semitonisma]] exactly 6 cents. As such this temperament is very abursdly accurate and it isn't supported by any [[patent val]] other than [[400edo]] until reaching 13400edo. It is not tempered out in [[1600edo]] and [[2000edo]], despite them being high-consistency multiples of 400edo.
 
For technical data, see [[400th-octave temperaments#Centismic]].

Revision as of 18:21, 17 September 2023

Interval information
Subgroup monzo 2.3.17 [-1001 -400 400
Size in cents 0.163454¢
Name centisma
Special properties reduced
Tenney norm (log2 nd) 3269.97
Weil norm (log2 max(n, d)) 3269.97
Wilson norm (sopfr(nd)) 10002
Open this interval in xen-calc

The centisma is a 17-limit (2.3.17 subgroup) unnoticeable comma measuring about 0.189 cents in size. It is the difference between a stack of 400 17/12's and the octave.

Temperaments

Tempering it out in the full 17-limit results in the rank-6 centismic temperament, and rank-2 2.3.17 centic temperament. The tempering out of this results in a period of 1 step of 400edo (3 cents) and makes 17/12, an astronomically close interval to 603 cents (603.00041), exactly 603 cents. Similarly, it makes the semitonisma exactly 6 cents. As such this temperament is very abursdly accurate and it isn't supported by any patent val other than 400edo until reaching 13400edo. It is not tempered out in 1600edo and 2000edo, despite them being high-consistency multiples of 400edo.

For technical data, see 400th-octave temperaments#Centismic.