343/338: Difference between revisions

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'''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''', the '''sooty fox comma''' is a~~ [[~~13-limit]] 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]] and [[41edo]].

== Etymology ==

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== See also ==

* [[Comma]]

* [[Sooty fox scale]] – equal divisions of 343/338

[[Category:Sooty fox]]

[[Category:Commas named for other reasons]]

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+'''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''', the '''sooty fox comma''' is a [[13-limit]] 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]] and [[41edo]].
 == Etymology ==
@@ Line 15: / Line 19: @@
 == See also ==
-* [[Comma]]
 * [[Sooty fox scale]] – equal divisions of 343/338
+[[Category:Sooty fox]]
 [[Category:Commas named for other reasons]]