Tetracot: Difference between revisions
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7-limit extensions moved to tetracot extensions page |
Formatting and adopt CTE tuning |
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== 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 ~ 45/44 ~ 55/54 ~ 65/64 ~ 66/65 ~ 81/80 ~ 121/120 all tempered together. In the following table, | 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'''. | ||
{| class="wikitable right-1 right-2" | {| class="wikitable right-1 right-2" | ||
| Line 27: | Line 27: | ||
|- | |- | ||
| 1 | | 1 | ||
| 176. | | 176.3 | ||
| 11/10, 10/9 | | 11/10, 10/9 | ||
|- | |- | ||
| 2 | | 2 | ||
| 352. | | 352.7 | ||
| 11/9, '''16/13''' | | 11/9, '''16/13''' | ||
|- | |- | ||
| 3 | | 3 | ||
| | | 529.0 | ||
| 15/11 | | 15/11 | ||
|- | |- | ||
| 4 | | 4 | ||
| | | 705.3 | ||
| '''3/2''' | | '''3/2''' | ||
|- | |- | ||
| 5 | | 5 | ||
| | | 881.7 | ||
| 5/3 | | 5/3 | ||
|- | |- | ||
| 6 | | 6 | ||
| | | 1058.0 | ||
| 11/6, 24/13 | | 11/6, 24/13 | ||
|- | |- | ||
| 7 | | 7 | ||
| | | 34.4 | ||
| 55/54, 45/44, 40/39 | | 55/54, 45/44, 40/39 | ||
|- | |- | ||
| 8 | | 8 | ||
| | | 210.7 | ||
| 9/8 | | '''9/8''' | ||
|- | |- | ||
| 9 | | 9 | ||
| | | 387.0 | ||
| '''5/4''' | | '''5/4''' | ||
|- | |- | ||
| 10 | | 10 | ||
| | | 563.4 | ||
| '''11/8''', 18/13 | | '''11/8''', 18/13 | ||
|- | |- | ||
| 11 | | 11 | ||
| | | 739.7 | ||
| 20/13 | | 20/13 | ||
|- | |- | ||
| 12 | | 12 | ||
| | | 916.0 | ||
| 22/13 | | 22/13 | ||
|- | |- | ||
| 13 | | 13 | ||
| | | 1092.4 | ||
| 15/8 | | '''15/8''' | ||
|- | |- | ||
| 14 | | 14 | ||
| | | 68.7 | ||
| 33/32, 27/26, 25/24 | | 33/32, 27/26, 25/24 | ||
|- | |- | ||
| 15 | | 15 | ||
| | | 245.0 | ||
| 15/13 | | 15/13 | ||
|} | |} | ||
: <nowiki>*</nowiki> in 2.3.5.11.13 | : <nowiki>*</nowiki> in 2.3.5.11.13 subgroup CTE tuning | ||
== Scales == | == Scales == | ||
| Line 95: | Line 95: | ||
== Music == | == Music == | ||
; [[Flora Canou]] | ; [[Flora Canou]] | ||
* [https://soundcloud.com/floracanou/october-dieting-plan?in=floracanou/sets/totmc-suite-vol-1 "October Dieting Plan"] from [https://soundcloud.com/floracanou/sets/totmc-suite-vol-1 ''TOTMC Suite Vol. 1''] (2023) – modus in 34edo tuning | * [https://soundcloud.com/floracanou/october-dieting-plan?in=floracanou/sets/totmc-suite-vol-1 "October Dieting Plan"] from [https://soundcloud.com/floracanou/sets/totmc-suite-vol-1 ''TOTMC Suite Vol. 1''] (2023) – [[modus]] in 34edo tuning | ||
; [[Zhea Erose]] | ; [[Zhea Erose]] | ||
* [https://www.youtube.com/watch?v=xYZwye9PWSo ''Modal Studies in Tetracot''] (2021) – in 34edo | * [https://www.youtube.com/watch?v=xYZwye9PWSo ''Modal Studies in Tetracot''] (2021) – in 34edo tuning | ||
; [[Xotla]] | ; [[Xotla]] | ||
* "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 | * "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:Temperaments]] | [[Category:Temperaments]] | ||
[[Category:Tetracot| ]] <!-- main article --> | [[Category:Tetracot| ]] <!-- main article --> | ||
[[Category:Tetracot family]] | [[Category:Tetracot family]] | ||
Revision as of 12:09, 1 January 2024
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 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 27, 34, and 41.
Tetracot has many extensions 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.
| # | Cents* | Approximate Ratios |
|---|---|---|
| 0 | 0.00 | 1/1 |
| 1 | 176.3 | 11/10, 10/9 |
| 2 | 352.7 | 11/9, 16/13 |
| 3 | 529.0 | 15/11 |
| 4 | 705.3 | 3/2 |
| 5 | 881.7 | 5/3 |
| 6 | 1058.0 | 11/6, 24/13 |
| 7 | 34.4 | 55/54, 45/44, 40/39 |
| 8 | 210.7 | 9/8 |
| 9 | 387.0 | 5/4 |
| 10 | 563.4 | 11/8, 18/13 |
| 11 | 739.7 | 20/13 |
| 12 | 916.0 | 22/13 |
| 13 | 1092.4 | 15/8 |
| 14 | 68.7 | 33/32, 27/26, 25/24 |
| 15 | 245.0 | 15/13 |
- * in 2.3.5.11.13 subgroup CTE tuning
Scales
- Tetracot7 – 6L 1s scale
- Tetracot13 – improper 7L 6s
- Tetracot20 – improper 7L 13s
Music
- "October Dieting Plan" from TOTMC Suite Vol. 1 (2023) – modus in 34edo tuning
- Modal Studies in Tetracot (2021) – in 34edo tuning