Tetracot: Difference between revisions
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'''Tetracot''', in this article, is the rank-2 [[regular temperament]] | '''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]]. | ||
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 }}. | |||
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 == | ||
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 | 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" | {| class="wikitable right-1 right-2" | ||
|- | |- | ||
! # | ! # | ||
! Cents | ! Cents* | ||
! Approximate Ratios | ! Approximate Ratios | ||
|- | |- | ||
| Line 86: | Line 84: | ||
| 15/13 | | 15/13 | ||
|} | |} | ||
<nowiki />* In 2.3.5.11.13 subgroup CTE tuning | |||
== Scales == | == 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 == | == Tunings == | ||
| Line 97: | Line 95: | ||
{| 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 | ||
| Line 110: | Line 108: | ||
| | | | ||
| 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 | ||
|- | |- | ||
| | | | ||
| Line 212: | Line 210: | ||
| | | | ||
|} | |} | ||
<nowiki>* | <nowiki />* Besides the octave | ||
== Music == | == Music == | ||
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* "Electrostat" from ''Lesser Groove'' (2020) – [https://open.spotify.com/track/5LIPr8n6uQySeLUfM11U2W Spotify] | [https://xotla.bandcamp.com/track/electrostat-tetracot-13 Bandcamp] | [https://www.youtube.com/watch?v=5SAuoyDwpgc YouTube] – ambient electro, tetracot[13] in 34edo tuning | * "Electrostat" from ''Lesser Groove'' (2020) – [https://open.spotify.com/track/5LIPr8n6uQySeLUfM11U2W Spotify] | [https://xotla.bandcamp.com/track/electrostat-tetracot-13 Bandcamp] | [https://www.youtube.com/watch?v=5SAuoyDwpgc YouTube] – ambient electro, tetracot[13] in 34edo tuning | ||
[[Category:Tetracot| ]] <!-- Main article --> | |||
[[Category:Tetracot| ]] <!-- | [[Category:Rank-2 temperaments]] | ||
[[Category:Tetracot family]] | [[Category:Tetracot family]] | ||