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Alphatricot family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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== Tricot ==
== Tricot ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883
[[Comma list]]: {{monzo| 39 -29 3 }} = 68719476736000/68630377364883


[[Mapping]]: [{{val| 1 0 -13 }}, {{val| 0 3 29 }}]
{{Mapping|legend=1| 1 0 -13 | 0 3 29 }}


Mapping generators: ~2, ~59049/40960
: mapping generators: ~2, ~59049/40960


{{Multival|legend=1| 3 29 39 }}
{{Multival|legend=1| 3 29 39 }}


[[POTE generator]]: ~59049/40960 = 634.012
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~59049/40960 = 634.012


{{Optimal ET sequence|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}
{{Optimal ET sequence|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}
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[[Comma list]]: 2430/2401, 5120/5103
[[Comma list]]: 2430/2401, 5120/5103


[[Mapping]]: [{{val| 1 0 -13 -3 }}, {{val| 0 3 29 11 }}]
{{Mapping|legend=1| 1 0 -13 -3 | 0 3 29 11 }}


{{Multival|legend=1| 3 29 11 39 9 -56 }}
{{Multival|legend=1| 3 29 11 39 9 -56 }}
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Comma list: 99/98, 121/120, 5120/5103
Comma list: 99/98, 121/120, 5120/5103


Mapping: [{{val| 1 0 -13 -3 -5 }}, {{val| 0 3 29 11 16 }}]
Mapping: {{mapping| 1 0 -13 -3 -5 | 0 3 29 11 16 }}


Optimal tuning (POTE): ~2 = 1\1, ~63/44 = 634.0273
Optimal tuning (POTE): ~2 = 1\1, ~63/44 = 634.0273
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Comma list: 99/98, 121/120, 169/168, 352/351
Comma list: 99/98, 121/120, 169/168, 352/351


Mapping: [{{val| 1 0 -13 -3 -5 0 }}, {{val| 0 3 29 11 16 7 }}]
Mapping: {{mapping| 1 0 -13 -3 -5 0 | 0 3 29 11 16 7 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/9 = 634.0115
Optimal tuning (POTE): ~2 = 1\1, ~13/9 = 634.0115
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== Trident ==
== Trident ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 6144/6125, 14348907/14336000
[[Comma list]]: 6144/6125, 14348907/14336000


[[Mapping]]: [{{val| 1 0 -13 25 }}, {{val| 0 3 29 -42 }}]
{{Mapping|legend=1| 1 0 -13 25 | 0 3 29 -42 }}


{{Multival|legend=1| 3 29 -42 39 -75 -179 }}
{{Multival|legend=1| 3 29 -42 39 -75 -179 }}


[[POTE generator]]: ~4096/2835 = 634.0480
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~4096/2835 = 634.0480


{{Optimal ET sequence|legend=1| 53, 176, 229, 282, 511 }}
{{Optimal ET sequence|legend=1| 53, 176, 229, 282, 511 }}
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Comma list: 3388/3375, 6144/6125, 8019/8000
Comma list: 3388/3375, 6144/6125, 8019/8000


Mapping: [{{val| 1 0 -13 25 -33 }}, {{val| 0 3 29 -42 69 }}]
Mapping: {{mapping| 1 0 -13 25 -33 | 0 3 29 -42 69 }}


POTE generator: ~231/160 = 634.0669
Optimal tuning (POTE): ~2 = 1\1, ~231/160 = 634.0669


{{Optimal ET sequence|legend=1| 53, 176, 229 }}
{{Optimal ET sequence|legend=1| 53, 176, 229 }}
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Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125
Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125


Mapping: [{{val| 1 0 -13 25 -33 0 }}, {{val| 0 3 29 -42 69 7 }}]
Mapping: {{mapping| 1 0 -13 25 -33 0 | 0 3 29 -42 69 7 }}


POTE generator: ~13/9 = 634.0652
Optimal tuning (POTE): ~2 = 1\1, ~13/9 = 634.0652


{{Optimal ET sequence|legend=1| 53, 176, 229 }}
{{Optimal ET sequence|legend=1| 53, 176, 229 }}
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== Trillium ==
== Trillium ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 4375/4374, 1099511627776/1098337086315
[[Comma list]]: 4375/4374, 1099511627776/1098337086315


[[Mapping]]: [{{val| 1 0 -13 53 }}, {{val| 0 3 29 -95 }}]
{{Mapping|legend=1| 1 0 -13 53 | 0 3 29 -95 }}


{{Multival|legend=1| 3 29 -95 39 -159 -302 }}
{{Multival|legend=1| 3 29 -95 39 -159 -302 }}


[[POTE generator]]: ~23625/16384 = 634.0118
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~23625/16384 = 634.0118


{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1376, 3193, 4569 }}
{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1376, 3193, 4569 }}
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Comma list: 4375/4374, 131072/130977, 759375/758912
Comma list: 4375/4374, 131072/130977, 759375/758912


Mapping: [{{val| 1 0 -13 53 -89 }}, {{val| 0 3 29 -95 175 }}]
Mapping: {{mapping| 1 0 -13 53 -89 | 0 3 29 -95 175 }}


POTE generator: ~3888/2695 = 634.0094
Optimal tuning (POTE): ~2 = 1\1, ~3888/2695 = 634.0094


{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1429 }}
{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1429 }}
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Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078
Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078


Mapping: [{{val| 1 0 -13 53 -89 -28 }}, {{val| 0 3 29 -95 175 60 }}]
Mapping: {{mapping| 1 0 -13 53 -89 -28 | 0 3 29 -95 175 60 }}


POTE generator: ~75/52 = 634.0095
Optimal tuning (POTE): ~2 = 1\1, ~75/52 = 634.0095


{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1429 }}
{{Optimal ET sequence|legend=1| 53, 441, 494, 935, 1429 }}
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Comma list: 4375/4374, 5632/5625, 4108797/4096000
Comma list: 4375/4374, 5632/5625, 4108797/4096000


Mapping: [{{val| 1 0 -13 53 -61 }}, {{val| 0 3 29 -95 122 }}]
Mapping: {{mapping| 1 0 -13 53 -61 | 0 3 29 -95 122 }}


POTE generator: ~231/160 = 634.0190
Optimal tuning (POTE): ~2 = 1\1, ~231/160 = 634.0190


{{Optimal ET sequence|legend=1| 53, 335, 388 }}
{{Optimal ET sequence|legend=1| 53, 335, 388 }}
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Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374
Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374


Mapping: [{{val| 1 0 -13 53 -61 -28 }}, {{val| 0 3 29 -95 122 60 }}]
Mapping: {{mapping| 1 0 -13 53 -61 -28 | 0 3 29 -95 122 60 }}


POTE generator: ~75/52 = 634.0181
Optimal tuning (POTE): ~2 = 1\1, ~75/52 = 634.0181


{{Optimal ET sequence|legend=1| 53, 335, 388 }}
{{Optimal ET sequence|legend=1| 53, 335, 388 }}
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== Tritricot ==
== Tritricot ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 250047/250000, 11785390260224/11767897353375
[[Comma list]]: 250047/250000, 11785390260224/11767897353375


[[Mapping]]: [{{val| 3 6 19 30 }}, {{val| 0 -3 -29 -52 }}]
{{Mapping|legend=1| 3 6 19 30 | 0 -3 -29 -52 }}


{{Multival|legend=1| 9 87 156 117 222 118 }}
{{Multival|legend=1| 9 87 156 117 222 118 }}


[[POTE generator]]: ~100352/91125 = 165.9837
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~100352/91125 = 165.9837


{{Optimal ET sequence|legend=1| 159, 282, 441, 2487, 2928, 3369 }}
{{Optimal ET sequence|legend=1| 159, 282, 441, 2487, 2928, 3369 }}
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Comma list: 4000/3993, 166698/166375, 200704/200475
Comma list: 4000/3993, 166698/166375, 200704/200475


Mapping: [{{val| 3 6 19 30 22 }}, {{val| 0 -3 -29 -52 -28 }}]
Mapping: {{mapping| 3 6 19 30 22 | 0 -3 -29 -52 -28 }}


POTE generator: ~11/10 = 165.9835
Optimal tuning (POTE): ~63/50 = 1\3, ~11/10 = 165.9835


{{Optimal ET sequence|legend=1| 159, 282, 441 }}
{{Optimal ET sequence|legend=1| 159, 282, 441 }}
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Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875


Mapping: [{{val| 3 6 19 30 22 36 }}, {{val| 0 -3 -29 -52 -28 -60 }}]
Mapping: {{mapping| 3 6 19 30 22 36 | 0 -3 -29 -52 -28 -60 }}


POTE generator: ~11/10 = 165.9842
Optimal tuning (POTE): ~63/50 = 1\3, ~11/10 = 165.9842


{{Optimal ET sequence|legend=1| 159, 282, 441 }}
{{Optimal ET sequence|legend=1| 159, 282, 441 }}
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Mapping: [{{val| 3 6 19 30 22 36 16 }}, {{val| 0 -3 -29 -52 -28 -60 -9 }}]
Mapping: [{{val| 3 6 19 30 22 36 16 }}, {{val| 0 -3 -29 -52 -28 -60 -9 }}]


POTE generator: ~11/10 = 165.9805
Optimal tuning (POTE): ~34/27 = 1\3, ~11/10 = 165.9805


{{Optimal ET sequence|legend=1| 159, 282, 441 }}
{{Optimal ET sequence|legend=1| 159, 282, 441 }}
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[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Tricot family| ]] <!-- main article -->
[[Category:Tricot family| ]] <!-- main article -->
[[Category:Tricot| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Tricot]]
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