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Mint temperaments: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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: ''For the 5-limit version of this temperament, see [[High badness temperaments #Lafayette]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Lafayette]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 392/375
[[Comma list]]: 36/35, 392/375


[[Mapping]]: [{{val| 1 1 2 2 }}, {{val| 0 5 3 7 }}]
{{Mapping|legend=1| 1 1 2 2 | 0 5 3 7 }}
 
: mapping generators: ~2, ~15/14


{{Multival|legend=1| 5 3 7 -7 -3 8 }}
{{Multival|legend=1| 5 3 7 -7 -3 8 }}


[[POTE generator]]: ~15/14 = 140.927
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 140.927


{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
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Comma list: 36/35, 56/55, 77/75
Comma list: 36/35, 56/55, 77/75


Mapping: [{{val| 1 1 2 2 3 }}, {{val| 0 5 3 7 4 }}]
Mapping: {{mapping| 1 1 2 2 3 | 0 5 3 7 4 }}


POTE generators: ~12/11 = 140.747
Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 140.747


{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
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Comma list: 26/25, 36/35, 56/55, 66/65
Comma list: 26/25, 36/35, 56/55, 66/65


Mapping: [{{val| 1 1 2 2 3 3 }}, {{val| 0 5 3 7 4 6 }}]
Mapping: {{mapping| 1 1 2 2 3 3 | 0 5 3 7 4 6 }}


POTE generators: ~13/12 = 140.751
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.751


{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
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Comma list: 26/25, 36/35, 51/50, 56/55, 66/65
Comma list: 26/25, 36/35, 51/50, 56/55, 66/65


Mapping: [{{val| 1 1 2 2 3 3 4 }}, {{val| 0 5 3 7 4 6 1 }}]
Mapping: {{mapping| 1 1 2 2 3 3 4 | 0 5 3 7 4 6 1 }}


POTE generators: ~13/12 = 141.404
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 141.404


{{Optimal ET sequence|legend=1| 8d, 9, 17cg }}
{{Optimal ET sequence|legend=1| 8d, 9, 17cg }}
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Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65
Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65


Mapping: [{{val| 1 1 2 2 3 3 4 4 }}, {{val| 0 5 3 7 4 6 1 2 }}]
Mapping: {{mapping| 1 1 2 2 3 3 4 4 | 0 5 3 7 4 6 1 2 }}


POTE generators: ~13/12 = 140.479
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.479


{{Optimal ET sequence|legend=1| 8d, 9, 17cg }}
{{Optimal ET sequence|legend=1| 8d, 9, 17cg }}
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{{see also| Ripple family #Ripple }}
{{see also| Ripple family #Ripple }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 2560/2401
[[Comma list]]: 36/35, 2560/2401


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -5 -8 -2 }}]
{{Mapping|legend=1| 1 2 3 3 | 0 -5 -8 -2 }}


{{Multival|legend=1| 5 8 2 1 -11 -18 }}
{{Multival|legend=1| 5 8 2 1 -11 -18 }}


[[POTE generator]]: ~21/20 = 99.483
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 99.483


{{Optimal ET sequence|legend=1| 12 }}
{{Optimal ET sequence|legend=1| 12 }}
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Comma list: 36/35, 80/77, 126/121
Comma list: 36/35, 80/77, 126/121


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -5 -8 -2 -6 }}]
Mapping: {{mapping| 1 2 3 3 4 | 0 -5 -8 -2 -6 }}


POTE generator: ~21/20 = 99.385
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 99.385


{{Optimal ET sequence|legend=1| 12 }}
{{Optimal ET sequence|legend=1| 12 }}
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Comma list: 36/35, 40/39, 66/65, 147/143
Comma list: 36/35, 40/39, 66/65, 147/143


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -5 -8 -2 -6 -3 }}]
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -5 -8 -2 -6 -3 }}


POTE generator: ~21/20 = 98.572
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 98.572


{{Optimal ET sequence|legend=1| 12f }}
{{Optimal ET sequence|legend=1| 12f }}
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== Smate ==
== Smate ==
{{see also| Smate family #Smate }}
{{See also| Smate family #Smate }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 2048/1875
[[Comma list]]: 36/35, 2048/1875


[[Mapping]]: [{{val| 1 3 2 6 }}, {{val| 0 -4 1 -9 }}]
{{Mapping|legend=1| 1 3 2 6 | 0 -4 1 -9 }}


{{Multival|legend=1| 4 -1 9 -11 3 24 }}
{{Multival|legend=1| 4 -1 9 -11 3 24 }}


[[POTE generator]]: ~5/4 = 422.275
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 422.275


{{Optimal ET sequence|legend=1| 3d, 11d, 14, 17c, 37ccdd }}
{{Optimal ET sequence|legend=1| 3d, 11d, 14, 17c, 37ccdd }}
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Comma list: 36/35, 56/55, 243/242
Comma list: 36/35, 56/55, 243/242


Mapping: [{{val| 1 3 2 6 7 }}, {{val| 0 -4 1 -9 -10 }}]
Mapping: {{mapping| 1 3 2 6 7 | 0 -4 1 -9 -10 }}


POTE generator: ~5/4 = 422.217
Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 422.217


{{Optimal ET sequence|legend=1| 3de, 14, 17c, 37ccddee }}
{{Optimal ET sequence|legend=1| 3de, 14, 17c, 37ccddee }}
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Comma list: 26/25, 36/35, 56/55, 243/242  
Comma list: 26/25, 36/35, 56/55, 243/242  


Mapping: [{{val| 1 3 2 6 7 3 }}, {{val| 0 -4 1 -9 -10 2 }}]
Mapping: {{mapping| 1 3 2 6 7 3 | 0 -4 1 -9 -10 2 }}


POTE generator: ~5/4 = 423.020
Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 423.020


{{Optimal ET sequence|legend=1| 3de, 14, 17c }}
{{Optimal ET sequence|legend=1| 3de, 14, 17c }}
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: ''For the 5-limit version of this temperament, see [[High badness temperaments #Delorean]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Delorean]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 1029/1000
[[Comma list]]: 36/35, 1029/1000


[[Mapping]]: [{{val| 1 3 4 4 }}, {{val| 0 -6 -7 -5 }}]
{{Mapping|legend=1| 1 3 4 4 | 0 -6 -7 -5 }}


{{Multival|legend=1| 6 7 5 -3 -9 -8 }}
{{Multival|legend=1| 6 7 5 -3 -9 -8 }}


[[POTE generator]]: ~6/5 = 284.219
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 284.219


{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }}
{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }}
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Comma list: 36/35, 77/75, 352/343
Comma list: 36/35, 77/75, 352/343


Mapping: [{{val| 1 3 4 4 7 }}, {{val| 0 -6 -7 -5 -15 }}]
Mapping: {{mapping| 1 3 4 4 7 | 0 -6 -7 -5 -15 }}


POTE generator: ~6/5 = 283.253
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 283.253


{{Optimal ET sequence|legend=1| 17c, 55ccd }}
{{Optimal ET sequence|legend=1| 17c, 55ccd }}
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Comma list: 26/25, 36/35, 66/65, 352/343  
Comma list: 26/25, 36/35, 66/65, 352/343  


POTE generator: ~6/5 = 282.856
Mapping: {{mapping| 1 3 4 4 7 7 | 0 -6 -7 -5 -15 -14 }}
 
Mapping: [{{val| 1 3 4 4 7 7 }}, {{val| 0 -6 -7 -5 -15 -14 }}]


POTE generator: ~6/5 = 282.856
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 282.856


{{Optimal ET sequence|legend=1| 17c }}
{{Optimal ET sequence|legend=1| 17c }}
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Comma list: 36/35, 56/55, 1029/1000
Comma list: 36/35, 56/55, 1029/1000


Mapping: [{{val| 1 3 4 4 3 }}, {{val| 0 -6 -7 -5 2 }}]
Mapping: {{mapping| 1 3 4 4 3 | 0 -6 -7 -5 2 }}


POTE generator: ~6/5 = 283.822
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 283.822


{{Optimal ET sequence|legend=1| 4, 17c, 21, 38ce, 55ccde }}
{{Optimal ET sequence|legend=1| 4, 17c, 21, 38ce, 55ccde }}
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Comma list: 36/35, 56/55, 66/65, 640/637
Comma list: 36/35, 56/55, 66/65, 640/637


Mapping: [{{val| 1 3 4 4 3 3 }}, {{val| 0 -6 -7 -5 2 3 }}]
Mapping: {{mapping| 1 3 4 4 3 3 | 0 -6 -7 -5 2 3 }}


POTE generator: ~6/5 = 283.882
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 283.882


{{Optimal ET sequence|legend=1| 4, 17c, 21, 38ce, 55ccde }}
{{Optimal ET sequence|legend=1| 4, 17c, 21, 38ce, 55ccde }}
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: ''For the 5-limit version of this temperament, see [[High badness temperaments #Slurpee]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Slurpee]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 51200/50421
[[Comma list]]: 36/35, 51200/50421


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -7 -11 -3 }}]
{{Mapping|legend=1| 1 2 3 3 | 0 -7 -11 -3 }}


{{Multival|legend=1| 7 11 3 1 -15 -24 }}
{{Multival|legend=1| 7 11 3 1 -15 -24 }}


[[POTE generator]]: ~21/20 = 72.303
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 72.303


{{Optimal ET sequence|legend=1| 16, 17c, 33, 50cd, 83bccd }}
{{Optimal ET sequence|legend=1| 16, 17c, 33, 50cd, 83bccd }}
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Comma list: 36/35, 121/120, 352/343  
Comma list: 36/35, 121/120, 352/343  


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -7 -11 -3 -9 }}]
Mapping: {{mapping| 1 2 3 3 4 | 0 -7 -11 -3 -9 }}


POTE generator: ~21/20 = 72.297
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 72.297


{{Optimal ET sequence|legend=1| 16, 17c, 33, 50cd, 83bccd }}
{{Optimal ET sequence|legend=1| 16, 17c, 33, 50cd, 83bccd }}
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Comma list: 36/35, 66/65, 143/140, 352/343
Comma list: 36/35, 66/65, 143/140, 352/343


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -7 -11 -3 -9 -5 }}]
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -7 -11 -3 -9 -5 }}


POTE generator: ~21/20 = 72.409
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 72.409


{{Optimal ET sequence|legend=1| 16, 17c, 33, 83bccd }}
{{Optimal ET sequence|legend=1| 16, 17c, 33, 83bccd }}
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== Penta ==
== Penta ==
{{see also| Gamelismic clan #Gidorah }}
{{See also| Gamelismic clan #Gidorah }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 28/25, 36/35
[[Comma list]]: 28/25, 36/35


[[Mapping]]: [{{val| 1 1 2 2 }}, {{val| 0 3 2 4 }}]
{{Mapping|legend=1| 1 1 2 2 | 0 3 2 4 }}


{{Multival|legend=1| 3 2 4 -4 -2 4 }}
{{Multival|legend=1| 3 2 4 -4 -2 4 }}


[[POTE generator]]: ~6/5 = 239.977
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 239.977


{{Optimal ET sequence|legend=1| 1bd, 5 }}
{{Optimal ET sequence|legend=1| 1bd, 5 }}
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[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Mint]]
[[Category:Mint temperaments| ]] <!-- main article -->
[[Category:Mint| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Mint_temperaments"