Tetracot: Difference between revisions

Line 5:

| ja =

}}

'''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 generator make a perfect fifth which approximates [[3/2]], which cannot occur in [[12edo]]. This results in [[100/99]], [[144/143]], and [[243/242]] being [[tempering out|tempered out]].

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 }}.

It can be seen as implying a rank-2 tuning 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]].

Line 14:

== 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'''.

{| class="wikitable right-1 right-2"

@@ Line 5: / Line 5: @@
 | ja =
 }}
-'''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 generator make a perfect fifth which approximates [[3/2]], which cannot occur in [[12edo]]. This results in [[100/99]], [[144/143]], and [[243/242]] being [[tempering out|tempered out]].
-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 }}.
+It can be seen as implying a rank-2 tuning  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]].
@@ Line 14: / Line 14: @@
 == 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'''.
 {| class="wikitable right-1 right-2"