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{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.


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.


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].