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{n\cdot d}[/math]) |
~2.60413 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].