351/350: Difference between revisions

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{{Infobox Interval

~~| Ratio = 351/350~~

~~| Monzo = -1 3 -2 -1 0 1~~

~~| Cents = 4.93933~~

| Name = ratwolfsma

| Color name =

| Color name = 3orgg1, thorugugu 1sn, <br>Thorugugu comma

~~| FJS name = d1<sup>13</sup><sub>25~~, 7<~~/sub~~>

| Comma = yes

| ~~Sound~~ =

}}

The '''ratwolfsma''', '''351/350''', is a [[13-limit]] no-11 [[comma]] measuring about 4.9 cents. It is the difference between [[28/27]] and [[26/25]], between [[81/70]] and [[15/13]], and between [[35/27]] and [[13/10]].

The '''ratwolfsma''', '''351/350''', is a [[13-limit]] no-eleven [[comma]] measuring about 4.9 cents. It is the difference between [[28/27]] and [[26/25]], between [[81/70]] and [[15/13]], and between [[35/27]] and [[13/10]].

In terms of commas, it is [[~~9801~~/~~9800~~]] ~~large of~~ [[~~364~~/~~363~~]], ~~and~~ [[~~4375~~/~~4374~~]] ~~small of~~ [[325/324]]~~, and it~~ factors into ([[676/675]])([[729/728]]).

In terms of commas, it often arises as the following differences: ([[78/77]])/([[100/99]]), ([[81/80]])([[105/104]]), ([[126/125]])([[196/195]]), ([[225/224]])/([[625/624]]), and ([[325/324]])([[4375/4374]]). It factors into ([[676/675]])([[729/728]]), ([[540/539]])([[1001/1000]]), ([[441/440]])([[1716/1715]]), or ([[364/363]])([[9801/9800]]).

351/350 and [[352/351]], the minthma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is [[chalmersia|123201/123200]], the ~~chalmersma~~, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma.

351/350 and [[352/351]], the major minthma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is [[chalmersia|123201/123200]], the chalmersia, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma.

Tempering it out leads to the rank-five '''ratwolf temperament''', ~~enabling~~ the [[~~ratwolf triad~~]].

Tempering it out leads to the rank-five '''ratwolfsmic temperament''', or in the 2.3.5.7.13 subgroup '''ratwolf temperament''', and enables the [[ratwolfsmic chords]].

== See also ==

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* [[List of superparticular intervals]]

~~[[Category:13-limit]]~~

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

[[Category:Ratwolf]]

[[Category:~~Superparticular~~]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 351/350
-| Monzo = -1 3 -2 -1 0 1
-| Cents = 4.93933
 | Name = ratwolfsma
-| Color name =
+| Color name = 3orgg1, thorugugu 1sn, <br>Thorugugu comma
-| FJS name = d1<sup>13</sup><sub>25, 7</sub>
+| Comma = yes
-| Sound =
 }}
-The '''ratwolfsma''', '''351/350''', is a [[13-limit]] no-11 [[comma]] measuring about 4.9 cents. It is the difference between [[28/27]] and [[26/25]], between [[81/70]] and [[15/13]], and between [[35/27]] and [[13/10]].
+The '''ratwolfsma''', '''351/350''', is a [[13-limit]] no-eleven [[comma]] measuring about 4.9 cents. It is the difference between [[28/27]] and [[26/25]], between [[81/70]] and [[15/13]], and between [[35/27]] and [[13/10]].
-In terms of commas, it is [[9801/9800]] large of [[364/363]], and [[4375/4374]] small of [[325/324]], and it factors into ([[676/675]])([[729/728]]).
+In terms of commas, it often arises as the following differences: ([[78/77]])/([[100/99]]), ([[81/80]])([[105/104]]), ([[126/125]])([[196/195]]), ([[225/224]])/([[625/624]]), and ([[325/324]])([[4375/4374]]). It factors into ([[676/675]])([[729/728]]), ([[540/539]])([[1001/1000]]), ([[441/440]])([[1716/1715]]), or ([[364/363]])([[9801/9800]]).
-/350 and [[352/351]], the minthma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is [[chalmersia|123201/123200]], the chalmersma, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma.
+/350 and [[352/351]], the major minthma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is [[chalmersia|123201/123200]], the chalmersia, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma.
-Tempering it out leads to the rank-five '''ratwolf temperament''', enabling the [[ratwolf triad]].
+Tempering it out leads to the rank-five '''ratwolfsmic temperament''', or in the 2.3.5.7.13 subgroup '''ratwolf temperament''', and enables the [[ratwolfsmic chords]].
 == See also ==
@@ Line 22: / Line 18: @@
 * [[List of superparticular intervals]]
-[[Category:13-limit]]
-[[Category:Small comma]]
 [[Category:Ratwolf]]
-[[Category:Superparticular]]
+[[Category:Commas with unknown etymology]]