Mirkwai comma
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Ratio | 16875/16807 |
Factorization | 3^{3} × 5^{4} × 7^{-5} |
Monzo | [0 3 4 -5⟩ |
Size in cents | 6.9903257¢ |
Name | mirkwai comma |
Color name | r^{5}y^{4}-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 (log_{2} nd) | 28.0794 |
Weil height (log_{2} 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 |
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]}.