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]]. | |||
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 == | == Temperaments == | ||
[[Tempering out]] this comma in the 7-limit leads to the rank-3 [[sengic]] temperament. | [[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. | ||
Rank-2 temperaments tempering out this comma include [[sensi]], [[negri]] and [[liese]]. | |||
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 == | == Etymology == | ||
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== References == | == References == | ||
<references /> | <references/> | ||
[[Category:Sengic]] | [[Category:Sengic]] | ||
[[Category:Commas named by combining multiple temperament names]] | [[Category:Commas named by combining multiple temperament names]] | ||
Latest revision as of 10:22, 8 August 2026
| Interval information |
senga
686/675, the senga or sengic comma, is a small 7-limit comma measuring about 28.0 cents. 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.
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)2 in turn, making it a lopsided comma with S-expression S13⋅S142.
Temperaments
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.
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[1].