Mirkwai comma: Difference between revisions

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m Added Heinz Bohlen's name for this comma, the "small diesis a."
Undo revision 169812 by MisterShafXen (talk). There's a whole temp section right below it
Tag: Undo
 
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| Ratio = 16875/16807
| Ratio = 16875/16807
| Name = mirkwai comma
| Name = mirkwai comma
| Color name = r<sup>5</sup>y<sup>4</sup>-4, quinru-aquadyo negative 4th
| Comma = yes
| Comma = yes
}}
}}
The '''mirkwai comma''' ('''16875/16807''') is a [[7-limit]] [[small comma]] measuring about 6.99 [[cent]]s.  
The '''mirkwai comma''' ([[ratio]]: 16875/16807, {{monzo|legend=1| 0 3 4 -5 }}), also known as ''small BP diesis'', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 6.99 [[cent]]s.  


== 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. Also known as BP's "small diesis a" (Bohlen, [https://www.huygens-fokker.org/bpsite/names.html www.huygens-fokker.org/bpsite/names.html]).
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.  


== See also ==
== Etymology ==
* [[Small comma]]
The name ''mirkwai'' was given by [[Gene Ward Smith]] in 2005 as a contraction of ''[[miracle]]'' and ''[[kwai]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>.
 
The name ''small BP diesis'' was given in <ref>[https://www.huygens-fokker.org/bpsite/names.html The Bohlen-Pierce Site | ''BP Names and Definitions'']</ref>.
 
== Notes ==


[[Category:Mirkwai]]
[[Category:Mirkwai]]
[[Category:Commas named by combining multiple temperament names]]

Latest revision as of 08:28, 12 December 2024

Interval information
Ratio 16875/16807
Factorization 33 × 54 × 7-5
Monzo [0 3 4 -5
Size in cents 6.990326¢
Name mirkwai comma
Color name r5y4-4, quinru-aquadyo negative 4th
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 (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].

Notes