Canopic comma: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 16875/16807
| Ratio = 16875/16807
| Name = mirkwai comma
| Name = canopic comma, canopus comma
| Color name = r<sup>5</sup>y<sup>4</sup>-4, quinru-aquadyo negative 4th
| Color name = r<sup>5</sup>y<sup>4</sup>-4, quinru-aquadyo negative 4th
| Comma = yes
| Comma = yes
}}
}}
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. This comma is tempered in 49edo, among others.
The '''canopic comma''' or '''canopus comma''' ([[ratio]]: 16875/16807, {{monzo|legend=1| 0 3 4 -5 }}), formerly ''mirkwai comma'', is a [[small comma|small]] [[7-limit]] (specifically [[3.5.7 subgroup|3.5.7-subgroup]]) [[comma]] measuring about 6.99 [[cent]]s. It is also known as ''small BP diesis'' in [[Bohlen–Pierce]] practice.  


== 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 out]] this comma alone in the 7-limit leads to the rank-3 [[canopic]] temperament. It is tempered out in rank-2 temperaments such as [[miracle]], [[octoid]], [[semisept]], [[grendel]], [[kwai]], [[pluto]], and [[mirkat]], which comprise the rank-2 canopic clan.  
 
See [[Canopic clan]] for a collection of rank-2 temperaments where it is tempered out.  


== Etymology ==
== Etymology ==
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>.  
''Canopic'' and ''canopus'' are named after the 3.5.7-subgroup temperament [[canopus]], following a convention of naming tritave-based regular temperaments after stars.
 
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>. Not widely accepted, it is effectively deprecated by 2026.  


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>.
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 ==
== References ==


[[Category:Mirkwai]]
[[Category:Canopic]]
[[Category:Commas named by combining multiple temperament names]]
[[Category:Commas named for other reasons]]

Latest revision as of 12:10, 6 June 2026

Interval information
Ratio 16875/16807
Factorization 33 × 54 × 7-5
Monzo [0 3 4 -5
Size in cents 6.990326¢
Names canopic comma,
canopus 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 norm (log2 nd) 28.0794
Weil norm (log2 max(n, d)) 28.0852
Wilson norm (sopfr(nd)) 64
Comma size small
Open this interval in xen-calc

The canopic comma or canopus comma (ratio: 16875/16807, monzo[0 3 4 -5), formerly mirkwai comma, is a small 7-limit (specifically 3.5.7-subgroup) comma measuring about 6.99 cents. It is also known as small BP diesis in Bohlen–Pierce practice.

Temperaments

Tempering out this comma alone in the 7-limit leads to the rank-3 canopic temperament. It is tempered out in rank-2 temperaments such as miracle, octoid, semisept, grendel, kwai, pluto, and mirkat, which comprise the rank-2 canopic clan.

See Canopic clan for a collection of rank-2 temperaments where it is tempered out.

Etymology

Canopic and canopus are named after the 3.5.7-subgroup temperament canopus, following a convention of naming tritave-based regular temperaments after stars.

The name mirkwai was given by Gene Ward Smith in 2005 as a contraction of miracle and kwai[1]. Not widely accepted, it is effectively deprecated by 2026.

The name small BP diesis was given in [2].

References