Canopic comma

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. 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. 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. Not widely accepted, it is effectively deprecated by 2026.

The name small BP diesis was given in .