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Ragismic microtemperaments: Difference between revisions

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Mapping generators: ~27/25, ~5/3
Mapping generators: ~27/25, ~5/3


[[POTE generator]]s: ~5/3 = 884.3129
[[POTE generator]]s: ~5/3 = 884.3129 or ~36/35 = 49.0205


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 67: Line 67:
Mapping: [{{val| 9 1 1 12 -75 }}, {{val| 0 2 3 2 16 }}]
Mapping: [{{val| 9 1 1 12 -75 }}, {{val| 0 2 3 2 16 }}]


POTE generator: ~5/3 = 884.4679
POTE generator: ~5/3 = 884.4679 or ~36/35 = 48.8654


Optimal GPV sequence: {{Val list| 99e, 171e, 270, 909, 1179, 1449c, 1719c }}
Optimal GPV sequence: {{Val list| 99e, 171e, 270, 909, 1179, 1449c, 1719c }}
Line 80: Line 80:
Mapping: [{{val| 9 1 1 12 -75 93 }}, {{val| 0 2 3 2 16 -9 }}]
Mapping: [{{val| 9 1 1 12 -75 93 }}, {{val| 0 2 3 2 16 -9 }}]


POTE generator: ~5/3 = 884.4304
POTE generator: ~5/3 = 884.4304 or ~36/35 = 48.9030


Optimal GPV sequence: {{Val list| 99e, 171e, 270 }}
Optimal GPV sequence: {{Val list| 99e, 171e, 270 }}
Line 95: Line 95:
Mapping: [{{val| 9 1 1 12 124 }}, {{val| 0 2 3 2 -14 }}]
Mapping: [{{val| 9 1 1 12 124 }}, {{val| 0 2 3 2 -14 }}]


POTE generator: ~5/3 = 884.4089
POTE generator: ~5/3 = 884.4089 or ~36/35 = 48.9244


Optimal GPV sequence: {{Val list| 99, 171, 270, 711, 981, 1251, 2232e }}
Optimal GPV sequence: {{Val list| 99, 171, 270, 711, 981, 1251, 2232e }}
Line 108: Line 108:
Mapping: [{{val| 9 1 1 12 124 93 }}, {{val| 0 2 3 2 -14 -9 }}]
Mapping: [{{val| 9 1 1 12 124 93 }}, {{val| 0 2 3 2 -14 -9 }}]


POTE generator: ~5/3 = 884.3997
POTE generator: ~5/3 = 884.3997 or ~36/35 = 48.9336


Optimal GPV sequence: {{Val list| 99, 171, 270, 711, 981, 1692e, 2673e }}
Optimal GPV sequence: {{Val list| 99, 171, 270, 711, 981, 1692e, 2673e }}
Line 123: Line 123:
Mapping: [{{val| 9 1 1 12 -2 }}, {{val| 0 2 3 2 5 }}]
Mapping: [{{val| 9 1 1 12 -2 }}, {{val| 0 2 3 2 5 }}]


POTE generator: ~5/3 = 883.9386
POTE generator: ~5/3 = 883.9386 or ~36/35 = 49.3948


Tuning ranges:  
Tuning ranges:  
Line 141: Line 141:
Mapping: [{{val| 9 1 1 12 -2 -33 }}, {{val| 0 2 3 2 5 10 }}]
Mapping: [{{val| 9 1 1 12 -2 -33 }}, {{val| 0 2 3 2 5 10 }}]


POTE generator: ~5/3 = 883.9920
POTE generator: ~5/3 = 883.9920 or ~36/35 = 49.3414


Tuning ranges:  
Tuning ranges:  
Line 159: Line 159:
Mapping: [{{val| 9 1 1 12 -2 -33 -3 }}, {{val| 0 2 3 2 5 10 6 }}]
Mapping: [{{val| 9 1 1 12 -2 -33 -3 }}, {{val| 0 2 3 2 5 10 6 }}]


POTE generator: ~5/3 = 883.9981
POTE generator: ~5/3 = 883.9981 or ~36/35 = 49.3353


Tuning ranges:  
Tuning ranges:  
Line 177: Line 177:
Mapping: [{{val| 9 1 1 12 -2 20 }}, {{val| 0 2 3 2 5 2 }}]
Mapping: [{{val| 9 1 1 12 -2 20 }}, {{val| 0 2 3 2 5 2 }}]


POTE generator: ~5/3 = 883.6257
POTE generator: ~5/3 = 883.6257 or ~36/35 = 49.7076


Optimal GPV sequence: {{Val list| 27e, 45ef, 72 }}
Optimal GPV sequence: {{Val list| 27e, 45ef, 72 }}
Line 190: Line 190:
Mapping: [{{val| 9 1 1 12 51 }}, {{val| 0 2 3 2 -3 }}]
Mapping: [{{val| 9 1 1 12 51 }}, {{val| 0 2 3 2 -3 }}]


POTE generator: ~5/3 = 883.8298
POTE generator: ~5/3 = 883.8298 or ~36/35 = 49.5036


Optimal GPV sequence: {{Val list| 27, 45, 72, 171e, 243e, 315e }}
Optimal GPV sequence: {{Val list| 27, 45, 72, 171e, 243e, 315e }}
Line 203: Line 203:
Mapping: [{{val| 9 1 1 12 51 20 }}, {{val| 0 2 3 2 -3 2 }}]
Mapping: [{{val| 9 1 1 12 51 20 }}, {{val| 0 2 3 2 -3 2 }}]


POTE generator: ~5/3 = 883.8476
POTE generator: ~5/3 = 883.8476 or ~36/35 = 49.4857


Optimal GPV sequence: {{Val list| 27, 45f, 72, 171ef, 243ef }}
Optimal GPV sequence: {{Val list| 27, 45f, 72, 171ef, 243ef }}
Line 481: Line 481:


Mapping: [{{val|38 0 28 -74 11}}, {{val|0 1 1 3 2}}]
Mapping: [{{val|38 0 28 -74 11}}, {{val|0 1 1 3 2}}]
Mapping generators: ~55/54, ~3


POTE generator: ~3/2 = 701.881
POTE generator: ~3/2 = 701.881
Line 1,264: Line 1,266:


=== Hitchcock ===
=== Hitchcock ===
{{see also|Amity family #Hitchcock}}
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 1,303: Line 1,303:


Badness: 0.019395
Badness: 0.019395
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189
Mapping: [{{val| 1 3 6 -2 6 2 -1 0 }}, {{val| 0 -5 -13 17 -9 6 18 15 }}]
POTE generator: ~11/9 = 339.407
Optimal GPV sequence: {{Val list| 7, 39h, 46, 53, 99h }}
Badness: 0.017513
=== Catamite ===
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891, 4375/4374
Mapping: [{{val|1 3 6 -2 -7}}, {{val|0 -5 -13 17 37}}]
POTE generator: ~128/105 = 339.340
Optimal GPV sequence: {{Val list| 46, 99e, 145, 244e }}
Badness: 0.040976
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 4375/4374
Mapping: [{{val|1 3 6 -2 -7 -11}}, {{val|0 -5 -13 17 37 52}}]
POTE generator: ~128/105 = 339.313
Optimal GPV sequence: {{Val list| 46, 99ef, 145 }}
Badness: 0.034215
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155
Mapping: [{{val|1 3 6 -2 -7 -11 -1}}, {{val|0 -5 -13 17 37 52 18}}]
POTE generator: ~17/14 = 339.313
Optimal GPV sequence: {{Val list| 46, 99ef, 145 }}
Badness: 0.021193
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475
Mapping: [{{val|1 3 6 -2 -7 -11 -1 -13}}, {{val|0 -5 -13 17 37 52 18 61}}]
POTE generator: ~17/14 = 339.325
Optimal GPV sequence: {{Val list| 46, 99ef, 145 }}
Badness: 0.018864


=== Hemiamity ===
=== Hemiamity ===
Line 1,311: Line 1,376:
Mapping: [{{val| 2 1 -1 13 13 }}, {{val| 0 5 13 -17 -14 }}]
Mapping: [{{val| 2 1 -1 13 13 }}, {{val| 0 5 13 -17 -14 }}]


POTE generator: ~64/55 = 339.439
Mapping generators: ~99/70, ~64/55
 
POTE generator: ~64/55 = 260.561


Optimal GPV sequence: {{Val list| 14cde, 46, 106, 152, 350, 502d }}
Optimal GPV sequence: {{Val list| 14cde, 46, 106, 152, 350, 502d }}


Badness: 0.031307
Badness: 0.031307
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 1716/1715, 3025/3024
Mapping: [{{val| 2 1 -1 13 13 20 }}, {{val| 0 5 13 -17 -14 -29 }}]
POTE generator: ~64/55 = 260.583
Optimal GPV sequence: {{Val list| 46, 106f, 152f, 198, 350f, 548cdff }}
Badness: 0.025784


== Parakleismic ==
== Parakleismic ==
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