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 | 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 }}. | ||
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. | See [[Tetracot family]] or [[No-sevens subgroup temperaments#Tetracot]] for more technical data. | ||
== Interval chain == | == Interval chain == | ||
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{| class="wikitable right-1 right-2" | {| class="wikitable right-1 right-2" | ||
|- | |- | ||
! # | ! # | ||
! Cents | ! Cents* | ||
! Approximate Ratios | ! Approximate Ratios | ||
|- | |- | ||
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| 15/13 | | 15/13 | ||
|} | |} | ||
<nowiki />* In 2.3.5.11.13 subgroup CTE tuning | |||
== Scales == | == Scales == | ||
* [[Tetracot7]] | * [[Tetracot7]] – [[6L 1s]] scale | ||
* [[Tetracot13]] | * [[Tetracot13]] – improper [[7L 6s]] | ||
* [[Tetracot20]] | * [[Tetracot20]] – improper [[7L 13s]] | ||
== Tunings == | == Tunings == | ||
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{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
! Edo<br>Generator | ! Edo<br />Generator | ||
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]] | ! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval)]]* | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
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| | | | ||
| 171.429 | | 171.429 | ||
| Lower bound of 2.3.5.11 subgroup 11-odd-limit, <br>2.3.5.11.13 subgroup 13- and 15-odd-limit diamond monotone | | Lower bound of 2.3.5.11 subgroup 11-odd-limit, <br />2.3.5.11.13 subgroup 13- and 15-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
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| | | | ||
|} | |} | ||
<nowiki>* | <nowiki />* Besides the octave | ||
== Music == | == Music == | ||
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[[Category:Temperaments]] | [[Category:Temperaments]] | ||
[[Category:Tetracot| ]] <!-- | [[Category:Tetracot| ]] <!-- Main article --> | ||
[[Category:Tetracot family]] | [[Category:Tetracot family]] | ||