343/338: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = Thuthutrizo comma
| Name = sooty fox comma
| Color name = 3uuz<sup>3</sup>2, thuthutrizo 2nd
| Color name = 3uuz<sup>3</sup>2, thuthutrizo 2nd
| Comma = yes
| Comma = yes
}}
}}
'''343/338''', the '''sooty fox comma''', is a [[small comma|small]] [[13-limit]] [[comma]] of 25.422 [[cent]]s. 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]].


'''343/338''', an interval of 25.422 [[cent]]s, is the amount by which three [[8/7]]s and two [[13/8]]s fall short of two octaves. Alternatively, it is the amount by which three [[7/4]]s exceed two [[13/8]]s plus an octave.
It factors into simpler commas as ([[105/104]])⋅([[196/195]]), which in turn equals ([[196/195]])<sup>2</sup>⋅([[225/224]]).  


It is tempered by [[19edo]].
== 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 [[edo]]s such as [[19edo]], [[31edo]], [[41edo]], and [[50edo]].
 
== Etymology ==
The comma is named after the Aleutian sooty fox sparrow, [https://www.inaturalist.org/taxa/343338-Passerella-iliaca-unalaschcensis taxa #343338] 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 ==
== See also ==
* [[Comma]]
* [[Sooty fox scale]] – equal divisions of 343/338


[[Category:Commas named after their color name]]
[[Category:Sooty fox]]
[[Category:Commas named for other reasons]]

Latest revision as of 22:37, 13 May 2026

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
Open this interval in xen-calc

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, 41edo, and 50edo.

Etymology

The comma is named after the Aleutian sooty fox sparrow, taxa #343338 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