Canopic comma: Difference between revisions
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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. | 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. It is the amount by which a stack of four [[10/7]]'s [[octave reduction|octave reduced]] exceeds [[28/27]], or in other words, the amount by which a stack of two [[50/49]]'s exceeds 28/27. Equivalently, it is the amount by which a stack of four [[15/14]] exceeds [[21/16]]. | ||
== Temperaments == | == Temperaments == | ||
[[Tempering out]] | [[Tempering out]] this comma in the [[3.5.7 subgroup]] leads to the rank-2 [[canopus]] temperament, or in the full 7-limit, the rank-3 [[canopic]] temperament. Tempering out this comma. It is also tempered out in full 7-limit rank-2 temperaments such as [[miracle]], [[octoid]], [[semisept]], [[grendel]], [[kwai]], [[pluto]], and [[mirkat]]. | ||
See [[Canopic clan]] for a collection of rank-2 temperaments where it is tempered out. | See [[Canopic clan]] for a collection of rank-2 temperaments where it is tempered out. | ||
Revision as of 14:40, 5 November 2026
| Interval information |
canopus comma
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. It is the amount by which a stack of four 10/7's octave reduced exceeds 28/27, or in other words, the amount by which a stack of two 50/49's exceeds 28/27. Equivalently, it is the amount by which a stack of four 15/14 exceeds 21/16.
Temperaments
Tempering out this comma in the 3.5.7 subgroup leads to the rank-2 canopus temperament, or in the full 7-limit, the rank-3 canopic temperament. Tempering out this comma. It is also tempered out in full 7-limit rank-2 temperaments such as miracle, octoid, semisept, grendel, kwai, pluto, and mirkat.
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].