Mirkwai comma

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Interval information
Ratio 16875/16807
Factorization 33 × 54 × 7-5
Monzo [0 3 4 -5
Size in cents 6.9903257¢
Name mirkwai comma
Color name r5y4-4, quinru-aquadyo negative 4th
FJS name [math]\text{dddd}{-4}^{5,5,5,5}_{7,7,7,7,7}[/math]
Special properties reduced
Tenney height (log2 nd) 28.0794
Weil height (log2 max(n, d)) 28.0852
Wilson height (sopfr (nd)) 64
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.60413 bits
Comma size small
open this interval in xen-calc

The mirkwai comma (16875/16807) is a 7-limit small comma measuring about 6.99 cents.


Tempering this comma out alone in the 7-limit leads to the rank-3 mirkwai family of temperaments, in which the main rank-3 temperament mirkwai is like canopus but with another dimension for twos. It is tempered out in rank-2 temperaments such as miracle, octoid, semisept, grendel, kwai, pluto, and mirkat. See mirkwai clan for a collection of rank-2 temperaments where it is tempered out. Also known as BP's "small diesis a" (Bohlen, www.huygens-fokker.org/bpsite/names.html).

See also