Mirkwai comma

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{nd}[/math])	~1.64418 bits
Comma size	small
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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.

The name small BP diesis was given in .