Centisma: Difference between revisions
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== Temperaments == | == 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 | 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]]. | For technical data, see [[400th-octave temperaments#Centismic]]. | ||
[[Category:Commas with unknown etymology]] | [[Category:Commas with unknown etymology]] | ||
Latest revision as of 04:44, 27 January 2026
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| Interval information |
The centisma is a 17-limit (2.3.17 subgroup) unnoticeable comma measuring about 0.163 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. Since 400edo has a quite accurate approximation (~0.045 ¢ 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.