Tetracot: Difference between revisions

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'''Tetracot''', in this article, is the rank-2 [[regular temperament]] for the 2.3.5.11.13 [[subgroup]] defined by [[tempering out]] [[100/99]], [[144/143]], and [[243/242]].

It can be seen as implying a rank-2 tuning which is [[generator|generated]] by a sub-major second of about ~~176~~{{c}} which represents both [[10/9]] and [[11/10]]. It is so named because the generator is a quarter of fifth: four generators make a fifth which approximates [[3/2]], which cannot occur in [[12edo]]. Equal temperaments that support tetracot include {{EDOs| 27, 34, and 41 }}.

It can be seen as implying a rank-2 tuning which is [[generator|generated]] by a "sub-major" second of about 174–178{{cent}} which represents both [[10/9]] and [[11/10]]. It is so named because the generator is a quarter of fifth: four generators make a fifth which approximates [[3/2]], which cannot occur in [[12edo]]. Equal temperaments that support tetracot include {{EDOs| 27, 34, and 41 }}.

Tetracot has many [[extension]]s for the 7-, 11- and 13-limit. See [[Tetracot extensions]].

Tetracot has many [[extension]]s for the 7-, 11-, and 13-limit. See [[Tetracot extensions]].

See [[Tetracot family]] or [[No-sevens subgroup temperaments#Tetracot]] for more technical data.

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== Scales ==

* [[Tetracot7]] ~~–~~ [[6L 1s]] scale

* [[Tetracot7]] – [[6L 1s]] scale

* [[Tetracot13]] ~~–~~ improper [[7L 6s]]

* [[Tetracot13]] – improper [[7L 6s]]

* [[Tetracot20]] ~~–~~ improper [[7L 13s]]

* [[Tetracot20]] – improper [[7L 13s]]

== Tunings ==

@@ Line 7: / Line 7: @@
 '''Tetracot''', in this article, is the rank-2 [[regular temperament]] for the 2.3.5.11.13 [[subgroup]] defined by [[tempering out]] [[100/99]], [[144/143]], and [[243/242]].
-It can be seen as implying a rank-2 tuning which is [[generator|generated]] by a sub-major second of about 176{{c}} which represents both [[10/9]] and [[11/10]]. It is so named because the generator is a quarter of fifth: four generators make a fifth which approximates [[3/2]], which cannot occur in [[12edo]]. Equal temperaments that support tetracot include {{EDOs| 27, 34, and 41 }}.
+It can be seen as implying a rank-2 tuning which is [[generator|generated]] by a "sub-major" second of about 174–178{{cent}} which represents both [[10/9]] and [[11/10]]. It is so named because the generator is a quarter of fifth: four generators make a fifth which approximates [[3/2]], which cannot occur in [[12edo]]. Equal temperaments that support tetracot include {{EDOs| 27, 34, and 41 }}.
-Tetracot has many [[extension]]s for the 7-, 11- and 13-limit. See [[Tetracot extensions]].
+Tetracot has many [[extension]]s for the 7-, 11-, and 13-limit. See [[Tetracot extensions]].
 See [[Tetracot family]] or [[No-sevens subgroup temperaments#Tetracot]] for more technical data.
@@ Line 89: / Line 89: @@
 == Scales ==
-* [[Tetracot7]] &ndash; [[6L 1s]] scale
+* [[Tetracot7]] – [[6L&nbsp;1s]] scale
-* [[Tetracot13]] &ndash; improper [[7L 6s]]
+* [[Tetracot13]] – improper [[7L&nbsp;6s]]
-* [[Tetracot20]] &ndash; improper [[7L 13s]]
+* [[Tetracot20]] – improper [[7L&nbsp;13s]]
 == Tunings ==