Centisma

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Interval information

Subgroup monzo	2.3.17 [-1001 -400 400⟩
Size in cents	0.163454¢
Name	centisma
Special properties	reduced
Tenney height (log2 nd)	3269.97
Weil height (log2 max(n, d))	3269.97
Wilson height (sopfr(nd))	10002
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19847 bits
Comma size	unnoticeable
open this interval in xen-calc

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 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.