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]] in the 2.3.5.11.13 [[subgroup]] [[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 such generators make a perfect fifth which approximates [[3/2]], which cannot occur in [[12edo]], resulting in [[100/99]], [[144/143]], and [[243/242]] being [[tempering out|tempered out]]. This is in contrast to [[meantone]], where 10/9 is tuned sharper than or equal to just in order to be equated with [[9/8]].

~~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]]. 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]]~~.

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

== Interval chain ==

Tetracot is considered as a [[cluster temperament]] with seven clusters of notes in an octave. The chroma interval between adjacent notes in each cluster represents 40/39 ~ 45/44 ~ 55/54 ~ 65/64 ~ 66/65 ~ 81/80 ~ 121/120 all ~~tempered together~~. In the following table, odd harmonics and subharmonics 1–15 are in '''bold'''.

Tetracot is considered as a [[cluster temperament]] with seven clusters of notes in an octave. The chroma interval between adjacent notes in each cluster represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], [[81/80]], and [[121/120]] all at once. In the following table, odd harmonics and subharmonics 1–15 are in '''bold'''.

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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]] in the 2.3.5.11.13 [[subgroup]] [[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 such generators make a perfect fifth which approximates [[3/2]], which cannot occur in [[12edo]], resulting in [[100/99]], [[144/143]], and [[243/242]] being [[tempering out|tempered out]]. This is in contrast to [[meantone]], where 10/9 is tuned sharper than or equal to just in order to be equated with [[9/8]].
-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]]. 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]].
 See [[Tetracot family]] or [[No-sevens subgroup temperaments#Tetracot]] for more technical data.
 == Interval chain ==
-Tetracot is considered as a [[cluster temperament]] with seven clusters of notes in an octave. The chroma interval between adjacent notes in each cluster represents 40/39 ~ 45/44 ~ 55/54 ~ 65/64 ~ 66/65 ~ 81/80 ~ 121/120 all tempered together. In the following table, odd harmonics and subharmonics 1–15 are in '''bold'''.
+Tetracot is considered as a [[cluster temperament]] with seven clusters of notes in an octave. The chroma interval between adjacent notes in each cluster represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], [[81/80]], and [[121/120]] all at once. In the following table, odd harmonics and subharmonics 1–15 are in '''bold'''.
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