343/338

Interval information

Ratio	343/338
Factorization	2-1 × 73 × 13-2
Monzo	[-1 0 0 3 0 -2⟩
Size in cents	25.4224¢
Name	sooty fox comma
Color name	3uuz32, thuthutrizo 2nd
FJS name	[math]\displaystyle{ \text{M2}^{7,7,7}_{13,13} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	16.8229
Weil norm (log2 max(n, d))	16.8441
Wilson norm (sopfr(nd))	49
Comma size	small
S-expression	S142⋅S15
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343/338, the sooty fox comma, is a small 13-limit comma of 25.422 cents. It is the amount by which a stack of two 14/13's exceeds 8/7, or the amount by which a stack of two 26/21's falls short of 14/9.

It factors into simpler commas as (105/104)⋅(196/195), which in turn equals (196/195)²⋅(225/224).

Temperaments

Tempering out this comma in the 13-limit leads to the rank-5 sooty fox temperament, and enables sooty fox chords. An obvious further temperament is to temper out 196/195 and/or 225/224, equating 14/13 with 15/14 as well as 16/15. This in the 2.3.5.7.13 subgroup is an extension of marvel and a restriction of tripod.

It is tempered out in edos such as 19edo, 31edo and 41edo.

Etymology

The comma is named after the Aleutian sooty fox sparrow, taxa #343388 on iNaturalist.

It was named by Budjarn Lambeth in 2024, but he retracted the name one day later out of fear that it would be poorly received due to its arbitrary nature. However, another editor added the name back two months later, which Lambeth and others did not oppose, so the name stuck.

See also

• Sooty fox scale – equal divisions of 343/338