686/675: Difference between revisions

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'''686/675''', the '''senga''' or '''sengic comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 28.0 [[cent]]s. It pops up as the difference between [[7/6]] and a stack of two [[15/14]]'s, or the difference between [[5/4]] and a stack of three 15/14's. Besides, it is the difference between the septimal minor second, [[28/27]], and the jubilisma, [[50/49]].

~~The interval of '''686~~/~~675'''~~, the ~~'''senga''' or '''sengic comma''' is a~~ [[~~small comma|small~~]] [[7~~-limit~~]] [[~~comma~~]]~~. It pops up as the difference between a stack of three~~ [[7/6]]~~'s and~~ a ~~stack of two~~ [[~~5/4~~]]'s.

It factors into simpler commas as ([[126/125]])⋅([[245/243]]), the stack of the two simplest commas to define the 7-limit [[sensi]] temperament. In the [[2.3.5.7.13 subgroup]], it factors into ([[91/90]])⋅([[196/195]]), which equals ([[169/168]])⋅(196/195)<sup>2</sup> in turn, making it a [[lopsided comma]] with [[S-expression]] S13⋅S14<sup>2</sup>.

== Temperaments ==

Tempering out this comma in the 7-limit leads to the rank-3 [[sengic]] temperament. ~~See~~ [[~~sengic family~~]] ~~for~~ the ~~rank-~~3 temperament ~~family where it is tempered out~~.

[[Tempering out]] this comma in the 7-limit leads to the rank-3 [[sengic]] temperament. Rank-2 temperaments tempering out this comma include [[sensi]], [[negri]] and [[liese]]. Tempering out this comma in the 3/2.5/4.7/4 fractional subgroup gives the [[ambulatory]] temperament.

~~Tempering out this comma in~~ the 3/2.~~5/4.7/4 fractional subgroup gives~~ [[~~ambulatory~~]] ~~temperament~~.

See [[Sengic family]] for the family of rank-3 temperaments where it is tempered out. See [[Sengic temperaments]] for the collection of rank-2 temperaments where it is tempered out.

== Etymology ==

The name ''senga'' was given by [[Gene Ward Smith]] in 2005. It is a contraction of ''[[sensi]]'' and ''gawel'', although ''gawel'' was later renamed to ''[[liese]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>.

== ~~Notes~~ ==

== References ==

[[Category:Sengic]]

[[Category:Commas named by combining multiple temperament names]]

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+'''686/675''', the '''senga''' or '''sengic comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 28.0 [[cent]]s. It pops up as the difference between [[7/6]] and a stack of two [[15/14]]'s, or the difference between [[5/4]] and a stack of three 15/14's. Besides, it is the difference between the septimal minor second, [[28/27]], and the jubilisma, [[50/49]].
-The interval of '''686/675''', the '''senga''' or '''sengic comma''' is a [[small comma|small]] [[7-limit]] [[comma]]. It pops up as the difference between a stack of three [[7/6]]'s and a stack of two [[5/4]]'s.
+It factors into simpler commas as ([[126/125]])⋅([[245/243]]), the stack of the two simplest commas to define the 7-limit [[sensi]] temperament. In the [[2.3.5.7.13 subgroup]], it factors into ([[91/90]])⋅([[196/195]]), which equals ([[169/168]])⋅(196/195)<sup>2</sup> in turn, making it a [[lopsided comma]] with [[S-expression]] S13⋅S14<sup>2</sup>.
 == Temperaments ==
-Tempering out this comma in the 7-limit leads to the rank-3 [[sengic]] temperament. See [[sengic family]] for the rank-3 temperament family where it is tempered out.
+[[Tempering out]] this comma in the 7-limit leads to the rank-3 [[sengic]] temperament. Rank-2 temperaments tempering out this comma include [[sensi]], [[negri]] and [[liese]]. Tempering out this comma in the 3/2.5/4.7/4 fractional subgroup gives the [[ambulatory]] temperament.
-Tempering out this comma in the 3/2.5/4.7/4 fractional subgroup gives [[ambulatory]] temperament.
+See [[Sengic family]] for the family of rank-3 temperaments where it is tempered out. See [[Sengic temperaments]] for the collection of rank-2 temperaments where it is tempered out.
 == Etymology ==
 The name ''senga'' was given by [[Gene Ward Smith]] in 2005. It is a contraction of ''[[sensi]]'' and ''gawel'', although ''gawel'' was later renamed to ''[[liese]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>.
-== Notes ==
+== References ==
+<references/>
 [[Category:Sengic]]
 [[Category:Commas named by combining multiple temperament names]]