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]].

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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]].