686/675: Difference between revisions

(10 intermediate revisions by 5 users not shown)

Line 1:

{{Infobox Interval

~~| Ratio = 686/675~~

| Name = sengic comma, senga

~~| Monzo = 1 -3 -2 3~~

~~| Cents = 27.98529~~

| Name = sengic comma, ~~ ~~senga ~~comma~~

| Color name = z3gg3, Trizo-agugu comma

| ~~FJS name = dd37, 7, 725~~

| Comma = yes

~~| Sound~~ =

}}

'''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~~ comma~~''' or '''sengic comma''' is a~~ [[7-limit]] [[~~small comma~~]]~~. It pops up as the difference between a stack of three~~ [[~~7/6~~]]s and ~~a stack of two~~ [[5/4]]s. It is tempered out in ~~temperaments~~ of ~~the~~ [[~~sengic family~~]].

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]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>.

== References ==

~~[[Category:7-limit]]~~

~~[[Category:Small comma]]~~

[[Category:Sengic]]

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 686/675
+| Name = sengic comma, senga
-| Monzo = 1 -3 -2 3
-| Cents = 27.98529
-| Name = sengic comma, <br>senga comma
 | Color name = z<sup>3</sup>gg3, Trizo-agugu comma
-| FJS name = dd3<sup>7, 7, 7</sup><sub>25</sub>
+| Comma = yes
-| Sound =
 }}
+'''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 comma''' or '''sengic comma''' is a [[7-limit]] [[small comma]]. It pops up as the difference between a stack of three [[7/6]]s and a stack of two [[5/4]]s. It is tempered out in temperaments of the [[sengic family]].
+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. 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]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>.
+== References ==
+<references/>
-[[Category:7-limit]]
-[[Category:Small comma]]
 [[Category:Sengic]]
+[[Category:Commas named by combining multiple temperament names]]