Centisma: Difference between revisions

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{{Infobox Interval

| Monzo = -1001 -400 0 0 0 0 400

| Name = centisma

| Comma = yes

}}

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 0.163 [[cent]]s 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. Since 400edo has a quite accurate approximation (~0.045{{c}} error for both, still over 100 times less accurate than its 17/12) of 3/2 and 17/16 themselves, it's smaller multiples, such as [[1600edo]] and [[2000edo]], only support a trivial tuning of centic where 3/2 and 17/16 are mapped to multiples of the period, and not until 13600edo do we find an edo that supports a nontrivial tuning of centic by patent val.

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

[[Category:Commas with unknown etymology]]

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+{{Novelty}}
 {{Infobox Interval
 | Monzo = -1001 -400 0 0 0 0 400
 | Name = centisma
+| Comma = yes
 }}
-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 0.163 [[cent]]s 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. Since 400edo has a quite accurate approximation (~0.045{{c}} error for both, still over 100 times less accurate than its 17/12) of 3/2 and 17/16 themselves, it's smaller multiples, such as [[1600edo]] and [[2000edo]], only support a trivial tuning of centic where 3/2 and 17/16 are mapped to multiples of the period, and not until 13600edo do we find an edo that supports a nontrivial tuning of centic by patent val.
+For technical data, see [[400th-octave temperaments#Centismic]].
+[[Category:Commas with unknown etymology]]