Alphatricot family: Difference between revisions
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The generator for '''tricot temperament''' is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&70 temperament, tempering out the [[Tricot|tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit. There are some mappings for 7-limit extension of this temperament: septimal tricot (53&70, also known as ''trimot''), trident (53&229) and trillium (53&441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads septimal tricot (supported by 53edo and 70edo), [[6144/6125|porwell comma]] (6144/6125) leads trident (supported by 53, 176, and 229 edos), and [[4375/4374|ragisma]] (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1429 edos). | The generator for '''tricot temperament''' is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&70 temperament, tempering out the [[Tricot|tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit. There are some mappings for 7-limit extension of this temperament: septimal tricot (53&70, also known as ''trimot''), trident (53&229) and trillium (53&441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads septimal tricot (supported by 53edo and 70edo), [[6144/6125|porwell comma]] (6144/6125) leads trident (supported by 53, 176, and 229 edos), and [[4375/4374|ragisma]] (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1429 edos). | ||
= Tricot = | == Tricot == | ||
[[Comma]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883 | [[Comma]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883 | ||
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[[Badness]]: 0.046093 | [[Badness]]: 0.046093 | ||
== 7-limit (aka Trimot) == | === 7-limit (aka Trimot) === | ||
{{see also|Hemifamity temperaments #Tricot}} | {{see also|Hemifamity temperaments #Tricot}} | ||
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[[Badness]]: 0.100127 | [[Badness]]: 0.100127 | ||
== 11-limit == | === 11-limit === | ||
Comma list: 99/98, 121/120, 5120/5103 | Comma list: 99/98, 121/120, 5120/5103 | ||
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Badness: 0.056134 | Badness: 0.056134 | ||
== 13-limit == | === 13-limit === | ||
Comma list: 99/98, 121/120, 169/168, 352/351 | Comma list: 99/98, 121/120, 169/168, 352/351 | ||
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Badness: 0.032102 | Badness: 0.032102 | ||
= Trident = | == Trident == | ||
[[Comma list]]: 6144/6125, 14348907/14336000 | [[Comma list]]: 6144/6125, 14348907/14336000 | ||
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[[Badness]]: 0.101694 | [[Badness]]: 0.101694 | ||
== 11-limit == | === 11-limit === | ||
Comma list: 3388/3375, 6144/6125, 8019/8000 | Comma list: 3388/3375, 6144/6125, 8019/8000 | ||
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Badness: 0.074272 | Badness: 0.074272 | ||
== 13-limit == | === 13-limit === | ||
Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125 | Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125 | ||
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Badness: 0.046593 | Badness: 0.046593 | ||
= Trillium = | == Trillium == | ||
[[Comma list]]: 4375/4374, 1099511627776/1098337086315 | [[Comma list]]: 4375/4374, 1099511627776/1098337086315 | ||
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[[Badness]]: 0.030852 | [[Badness]]: 0.030852 | ||
== 11-limit == | === 11-limit === | ||
Comma list: 4375/4374, 131072/130977, 759375/758912 | Comma list: 4375/4374, 131072/130977, 759375/758912 | ||
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Badness: 0.046758 | Badness: 0.046758 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078 | Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078 | ||
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Badness: 0.019393 | Badness: 0.019393 | ||
== Pseudotrillium == | === Pseudotrillium === | ||
Comma list: 4375/4374, 5632/5625, 4108797/4096000 | Comma list: 4375/4374, 5632/5625, 4108797/4096000 | ||
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Badness: 0.111931 | Badness: 0.111931 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374 | Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374 | ||
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Badness: 0.054837 | Badness: 0.054837 | ||
= Tritricot = | == Tritricot == | ||
[[Comma list]]: 250047/250000, 11785390260224/11767897353375 | [[Comma list]]: 250047/250000, 11785390260224/11767897353375 | ||
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[[Badness]]: 0.086081 | [[Badness]]: 0.086081 | ||
== 11-limit == | === 11-limit === | ||
Comma list: 4000/3993, 166698/166375, 200704/200475 | Comma list: 4000/3993, 166698/166375, 200704/200475 | ||
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Badness: 0.074002 | Badness: 0.074002 | ||
== 13-limit == | === 13-limit === | ||
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875 | Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875 | ||
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Badness: 0.035641 | Badness: 0.035641 | ||
== 17-limit == | === 17-limit === | ||
Comma list: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619 | Comma list: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619 | ||