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: trimot (53&70), trident (53&229) and trillium (53&441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads trimot (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: trimot (53&70), trident (53&229) and trillium (53&441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads trimot (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 = | |||
Comma: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883 | Comma: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883 | ||
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Badness: 0.0461 | Badness: 0.0461 | ||
= Trimot (53&70) = | |||
Commas: 2430/2401, 5120/5103 | Commas: 2430/2401, 5120/5103 | ||
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Badness: 0.1001 | Badness: 0.1001 | ||
== 11-limit == | |||
Commas: 99/98, 121/120, 5120/5103 | Commas: 99/98, 121/120, 5120/5103 | ||
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Badness: 0.0561 | Badness: 0.0561 | ||
== 13-limit == | |||
Commas: 99/98, 121/120, 169/168, 352/351 | Commas: 99/98, 121/120, 169/168, 352/351 | ||
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Badness: 0.0321 | Badness: 0.0321 | ||
= Trident (53&229) = | |||
Commas: 6144/6125, 14348907/14336000 | Commas: 6144/6125, 14348907/14336000 | ||
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Badness: 0.1017 | Badness: 0.1017 | ||
== 11-limit == | |||
Commas: 3388/3375, 6144/6125, 8019/8000 | Commas: 3388/3375, 6144/6125, 8019/8000 | ||
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Badness: 0.0743 | Badness: 0.0743 | ||
== 13-limit == | |||
Commas: 351/350, 2080/2079, 2197/2187, 3146/3125 | Commas: 351/350, 2080/2079, 2197/2187, 3146/3125 | ||
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Badness: 0.0466 | Badness: 0.0466 | ||
= Trillium (53&441) = | |||
Commas: 4375/4374, 1099511627776/1098337086315 | Commas: 4375/4374, 1099511627776/1098337086315 | ||
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Badness: 0.0309 | Badness: 0.0309 | ||
== 11-limit == | |||
Commas: 4375/4374, 131072/130977, 759375/758912 | Commas: 4375/4374, 131072/130977, 759375/758912 | ||
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Badness: 0.0468 | Badness: 0.0468 | ||
== 13-limit == | |||
Commas: 2080/2079, 4096/4095, 4375/4374, 78125/78078 | Commas: 2080/2079, 4096/4095, 4375/4374, 78125/78078 | ||
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Badness: 0.0194 | Badness: 0.0194 | ||
== Pseudotrillium (53&388) == | |||
Commas: 4375/4374, 5632/5625, 4108797/4096000 | Commas: 4375/4374, 5632/5625, 4108797/4096000 | ||
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Badness: 0.1119 | Badness: 0.1119 | ||
=== 13-limit === | |||
Commas: 847/845, 1001/1000, 4096/4095, 4375/4374 | Commas: 847/845, 1001/1000, 4096/4095, 4375/4374 | ||
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Badness: 0.0548 | Badness: 0.0548 | ||
= Tritricot (159&282) = | |||
Commas: 250047/250000, 11785390260224/11767897353375 | Commas: 250047/250000, 11785390260224/11767897353375 | ||
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Badness: 0.0861 | Badness: 0.0861 | ||
== 11-limit == | |||
Commas: 4000/3993, 166698/166375, 200704/200475 | Commas: 4000/3993, 166698/166375, 200704/200475 | ||
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Badness: 0.0740 | Badness: 0.0740 | ||
== 13-limit == | |||
Commas: 1575/1573, 2080/2079, 34398/34375, 43904/43875 | Commas: 1575/1573, 2080/2079, 34398/34375, 43904/43875 | ||
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Badness: 0.0356 | Badness: 0.0356 | ||
== 17-limit == | |||
Commas: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619 | Commas: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619 | ||
Revision as of 10:02, 14 March 2021
The generator for tricot temperament is the real cube root of third harmonic, 31/3, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&70 temperament, tempering out the tricot comma, [39 -29 3⟩ in the 5-limit. There are some mappings for 7-limit extension of this temperament: trimot (53&70), trident (53&229) and trillium (53&441). Tempering out hemifamity comma (5120/5103) leads trimot (supported by 53edo and 70edo), porwell comma (6144/6125) leads trident (supported by 53, 176, and 229 edos), and ragisma (4375/4374) leads trillium (supported by 53, 441, 494, 935, and 1429 edos).
Tricot
Comma: [39 -29 3⟩ = 68719476736000/68630377364883
POTE generator: ~59049/40960 = 634.012
Map: [<1 0 -13|, <0 3 29|]
Wedgie: <<3 29 39||
EDOs: 53, 229, 282, 335, 388, 441, 1376, 1817, 2258
Badness: 0.0461
Trimot (53&70)
Commas: 2430/2401, 5120/5103
POTE generator: ~81/56 = 634.0259
Map: [<1 0 -13 -3|, <0 3 29 11|]
Wedgie: <<3 29 11 39 9 -56||
EDOs: 17c, 36c, 53, 70, 229dd, 282dd
Badness: 0.1001
11-limit
Commas: 99/98, 121/120, 5120/5103
POTE generator: ~63/44 = 634.0273
Map: [<1 0 -13 -3 -5|, <0 3 29 11 16|]
EDOs: 17c, 36ce, 53, 70, 123de
Badness: 0.0561
13-limit
Commas: 99/98, 121/120, 169/168, 352/351
POTE generator: ~13/9 = 634.0115
Map: [<1 0 -13 -3 -5 0|, <0 3 29 11 16 7|]
EDOs: 17c, 36ce, 53, 70, 123de
Badness: 0.0321
Trident (53&229)
Commas: 6144/6125, 14348907/14336000
POTE generator: ~4096/2835 = 634.0480
Map: [<1 0 -13 25|, <0 3 29 -42|]
Wedgie: <<3 29 -42 39 -75 -179||
Badness: 0.1017
11-limit
Commas: 3388/3375, 6144/6125, 8019/8000
POTE generator: ~231/160 = 634.0669
Map: [<1 0 -13 25 -33|, <0 3 29 -42 69|]
Badness: 0.0743
13-limit
Commas: 351/350, 2080/2079, 2197/2187, 3146/3125
POTE generator: ~13/9 = 634.0652
Map: [<1 0 -13 25 -33 0|, <0 3 29 -42 69 7|]
Badness: 0.0466
Trillium (53&441)
Commas: 4375/4374, 1099511627776/1098337086315
POTE generator: ~23625/16384 = 634.0118
Map: [<1 0 -13 53|, <0 3 29 -95|]
Wedgie: <<3 29 -95 39 -159 -302||
EDOs: 53, 441, 494, 935, 1376, 3193, 4569
Badness: 0.0309
11-limit
Commas: 4375/4374, 131072/130977, 759375/758912
POTE generator: ~3888/2695 = 634.0094
Map: [<1 0 -13 53 -89|, <0 3 29 -95 175|]
Badness: 0.0468
13-limit
Commas: 2080/2079, 4096/4095, 4375/4374, 78125/78078
POTE generator: ~75/52 = 634.0095
Map: [<1 0 -13 53 -89 -28|, <0 3 29 -95 175 60|]
Badness: 0.0194
Pseudotrillium (53&388)
Commas: 4375/4374, 5632/5625, 4108797/4096000
POTE generator: ~231/160 = 634.0190
Map: [<1 0 -13 53 -61|, <0 3 29 -95 122|]
Badness: 0.1119
13-limit
Commas: 847/845, 1001/1000, 4096/4095, 4375/4374
POTE generator: ~75/52 = 634.0181
Map: [<1 0 -13 53 -61 -28|, <0 3 29 -95 122 60|]
Badness: 0.0548
Tritricot (159&282)
Commas: 250047/250000, 11785390260224/11767897353375
POTE generator: ~100352/91125 = 165.9837
Map: [<3 6 19 30|, <0 -3 -29 -52|]
Wedgie: <<9 87 156 117 222 118||
EDOs: 159, 282, 441, 2487, 2928, 3369
Badness: 0.0861
11-limit
Commas: 4000/3993, 166698/166375, 200704/200475
POTE generator: ~11/10 = 165.9835
Map: [<3 6 19 30 22|, <0 -3 -29 -52 -28|]
Badness: 0.0740
13-limit
Commas: 1575/1573, 2080/2079, 34398/34375, 43904/43875
POTE generator: ~11/10 = 165.9842
Map: [<3 6 19 30 22 36|, <0 -3 -29 -52 -28 -60|]
Badness: 0.0356
17-limit
Commas: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619
POTE generator: ~11/10 = 165.9805
Map: [<3 6 19 30 22 36 16|, <0 -3 -29 -52 -28 -60 -9|]
Badness: 0.0260