Mirkwai comma
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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{nd}[/math])
~1.64418 bits
Comma size
small
open this interval in xen-calc
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
The mirkwai comma (ratio: 16875/16807, monzo: [0 3 4 -5⟩), also known as small BP diesis, is a small 7-limit comma measuring about 6.99 cents.
Temperaments
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.
Etymology
The name mirkwai was given by Gene Ward Smith in 2005 as a contraction of miracle and kwai[1].
The name small BP diesis was given in [2].