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]].

'''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 ~~cents~~ 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}} ~~EDOs~~.

It can be seen as implying a rank-2 tuning which is [[Generator|generated]] by a sub-major second of about 176 [[cent]]s 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 extensions for 7, 11 and 13-limit include monkey (34&41), bunya (34d&41), modus (27e&34d) and wollemia (27e&34).

Tetracot has many extensions for 7, 11 and 13-limit include monkey (34 & 41), bunya (34d & 41), modus (27e & 34d) and wollemia (27e & 34).

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

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! Generators

! Cents*

! Approximate ~~ratios~~

! Approximate Ratios

|-

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! Generators

! Cents*

! Approximate ~~ratios~~

! Approximate Ratios

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! Generators

! Cents*

! Approximate ~~ratios~~

! Approximate Ratios

|-

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! Generators

! Cents*

! Approximate ~~ratios~~

! Approximate Ratios

|-

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! Generators

! Cents*

! Approximate ~~ratios~~

! Approximate Ratios

|-

| 0

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{| class="wikitable center-all"

|-

! | [[Eigenmonzo|Eigenmonzo (~~unchanged interval~~]])

! [[Eigenmonzo|Eigenmonzo (Unchanged Interval)]]

! | Generator (¢)

! Generator (¢)

! | Comments

! Comments

|-

| | 11/10

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[[Category:Temperaments]]

[[Category:Tetracot family]]

{{Todo| cleanup |comment=Move 7-limit extensions to their own pages. }}

@@ Line 1: / Line 1: @@
-'''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]].
+'''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 cents 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}} EDOs.
+It can be seen as implying a rank-2 tuning which is [[Generator|generated]] by a sub-major second of about 176 [[cent]]s 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 extensions for 7, 11 and 13-limit include monkey (34&amp;41), bunya (34d&amp;41), modus (27e&amp;34d) and wollemia (27e&amp;34).
+Tetracot has many extensions for 7, 11 and 13-limit include monkey (34 &amp; 41), bunya (34d &amp; 41), modus (27e &amp; 34d) and wollemia (27e &amp; 34).
 See [[Tetracot family]] or [[No-sevens subgroup temperaments #Tetracot]] for more technical data.
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 ! Generators
 ! Cents<sup>*</sup>
-! Approximate ratios
+! Approximate Ratios
 |-
 | 0
@@ Line 87: / Line 87: @@
 ! Generators
 ! Cents<sup>*</sup>
-! Approximate ratios
+! Approximate Ratios
 |-
 | 0
@@ Line 212: / Line 212: @@
 ! Generators
 ! Cents<sup>*</sup>
-! Approximate ratios
+! Approximate Ratios
 |-
 | 0
@@ Line 337: / Line 337: @@
 ! Generators
 ! Cents<sup>*</sup>
-! Approximate ratios
+! Approximate Ratios
 |-
 | 0
@@ Line 434: / Line 434: @@
 ! Generators
 ! Cents<sup>*</sup>
-! Approximate ratios
+! Approximate Ratios
 |-
 | 0
@@ Line 534: / Line 534: @@
 {| class="wikitable center-all"
 |-
-! | [[Eigenmonzo|Eigenmonzo<br>(unchanged interval]])
+! [[Eigenmonzo|Eigenmonzo<br>(Unchanged Interval)]]
-! | Generator<br>(¢)
+! Generator<br>(¢)
-! | Comments
+! Comments
 |-
 | | 11/10
@@ Line 950: / Line 950: @@
 [[Category:Temperaments]]
 [[Category:Tetracot family]]
+{{Todo| cleanup |comment=Move 7-limit extensions to their own pages. }}