11859211/11859210: Difference between revisions

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'''11859211/11859210''', the '''tredekisma''', is the smallest [[superparticular ratio]] in the [[19-limit]] and [[23-limit]].

It can be seen as the difference between a stack of a [[25/16]] ~~plus~~ a [[~~minisma]] plus a [[131072~~/~~130321|undevicesimal diminished comma~~]], and a [[~~1024~~/~~729|diminished fifth~~]] ~~plus two [[128~~/~~121|Axirabian limmas]]:~~

It can be seen as the difference between a stack of four [[38/33]]'s and a stack consisting of [[10/7]] and [[16/13]]: (38/33)<sup>4</sup>/((10/7)⋅(16/13)).

~~((25/16)⋅(4096/4095)⋅(131072/130321))/((1024/729)(128/121)<sup>2</sup>)~~

A possible S-expression of it is (S76⋅S441)/(S77⋅S324).

~~Its~~ S-expression is (~~(S76)(S441)~~)/(~~(S77)(S324)~~)

== Temperaments ==

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[[Optimal tuning]]s: TBA

[[Badness]] (Sintel): TBA

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== Etymology ==

The name ''tredekisma'' comes from ''tredek'', which is one step of [[270edo]], ~~which~~ is an excellent 2.3.5.7.11.13.19 subgroup system that tempers it out.

This comma was named by [[Eufalesio]] in 2026. The name ''tredekisma'' comes from ''tredek'', which is the name of one step of [[270edo]] by [[Joseph Monzo]], and 270edo is an excellent 2.3.5.7.11.13.19-subgroup system that tempers it out.

[[Category:Commas named for their regular temperament properties]]

@@ Line 7: / Line 7: @@
 '''11859211/11859210''', the '''tredekisma''', is the smallest [[superparticular ratio]] in the [[19-limit]] and [[23-limit]].
-It can be seen as the difference between a stack of a [[25/16]] plus a [[minisma]] plus a [[131072/130321|undevicesimal diminished comma]], and a [[1024/729|diminished fifth]] plus two [[128/121|Axirabian limmas]]:
+It can be seen as the difference between a stack of four [[38/33]]'s and a stack consisting of [[10/7]] and [[16/13]]: (38/33)<sup>4</sup>/((10/7)⋅(16/13)).
-((25/16)⋅(4096/4095)⋅(131072/130321))/((1024/729)(128/121)<sup>2</sup>)
+A possible S-expression of it is (S76⋅S441)/(S77⋅S324).
-Its S-expression is ((S76)(S441))/((S77)(S324))
 == Temperaments ==
@@ Line 35: / Line 33: @@
 [[Optimal tuning]]s: TBA
-{{Optimal ET sequence||legend=1 TBA }}
+{{Optimal ET sequence||legend=1|TBA }}
 [[Badness]] (Sintel): TBA
@@ Line 65: / Line 63: @@
 == Etymology ==
-The name ''tredekisma'' comes from ''tredek'', which is one step of [[270edo]], which is an excellent 2.3.5.7.11.13.19 subgroup system that tempers it out.
+This comma was named by [[Eufalesio]] in 2026. The name ''tredekisma'' comes from ''tredek'', which is the name of one step of [[270edo]] by [[Joseph Monzo]], and 270edo is an excellent 2.3.5.7.11.13.19-subgroup system that tempers it out.
 [[Category:Commas named for their regular temperament properties]]