Mirkwai comma: Difference between revisions

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m Added Heinz Bohlen's name for this comma, the "small diesis a."
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== Temperaments ==
== 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.
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. Also known as BP's "small diesis a" (Bohlen, [https://www.huygens-fokker.org/bpsite/names.html www.huygens-fokker.org/bpsite/names.html]).


== See also ==
== See also ==

Revision as of 20:40, 13 May 2023

Interval information
Ratio 16875/16807
Factorization 33 × 54 × 7-5
Monzo [0 3 4 -5
Size in cents 6.990326¢
Name mirkwai comma
FJS name [math]\displaystyle{ \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
Comma size small
Open this interval in xen-calc

The mirkwai comma (16875/16807) is a 7-limit small 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. Also known as BP's "small diesis a" (Bohlen, www.huygens-fokker.org/bpsite/names.html).

See also