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Miscellaneous 5-limit temperaments: Difference between revisions

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Line 36: Line 36:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: 268435456/263671875
[[Comma]]: 268435456/263671875


[[Mapping]]: [{{Val| 1 6 1 }}, {{Val| 0 -10 3 }}]
[[Mapping]]: [{{Val| 1 6 1 }}, {{Val| 0 -10 3 }}]
Line 81: Line 81:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: 10077696/9765625
[[Comma]]: 10077696/9765625


[[Mapping]]: [{{Val| 1 9 9 }}, {{Val| 0 -10 -9 }}]
[[Mapping]]: [{{Val| 1 9 9 }}, {{Val| 0 -10 -9 }}]
Line 135: Line 135:


[[Badness]]: 0.307073
[[Badness]]: 0.307073
== Counterhanson ==
{{See also| Ragismic microtemperaments #Counterkleismic }}
Subgroup: 2.3.5
[[Comma]]: {{Monzo| -20 -24 25 }} = 298023223876953125/296148833645101056
[[Mapping]]: [{{Val| 1 -5 -4 }}, {{Val| 0 25 24 }}]
[[POTE generator]]: ~6/5 = 316.081
{{Val list|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}
[[Badness]]: 0.317551
== Sevond ==
{{See also| Keemic temperaments #Sevond }}
Subgroup: 2.3.5
[[Comma]]: 5000000/4782969
[[Mapping]]: [{{Val| 7 0 -6 }}, {{Val| 0 1 2 }}]
[[POTE generator]]: ~3/2 = 706.288
{{Val list|legend=1| 7, 42, 49, 56, 119 }}
[[Badness]]: 0.339335


== Absurdity ==
== Absurdity ==
Line 220: Line 250:
[[POTE generator]]: ~5/4 = 391.225
[[POTE generator]]: ~5/4 = 391.225


{{Val list|legend=1| 46, 181c, 227c, 273c, 319c }}
{{Val list|legend=1| 3, 40, 43, 46, 181c, 227c, 273c, 319c }}


[[Badness]]: 0.360162
[[Badness]]: 0.360162
Line 238: Line 268:


[[Badness]]: 0.372848
[[Badness]]: 0.372848
== Countermeantone ==
Subgroup: 2.3.5
[[Comma]]: {{Monzo| 10 23 -20 }} = 96402615118848/95367431640625
[[Mapping]]: [{{Val| 1 10 12 }}, {{Val| 0 -20 -23 }}]
[[POTE generator]]: ~104976/78125 = 504.913
{{Val list|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }}
[[Badness]]: 0.373477


== Tritonic ==
== Tritonic ==
Line 403: Line 446:


[[Badness]]: 0.523182
[[Badness]]: 0.523182
== Septendecic ==
Subgroup: 2.3.5
[[Comma]]: {{monzo| 27 -17 }} = 134217728/129140163
[[Mapping]]: [{{Val| 17 27 0 }}, {{Val| 0 0 1 }}]
Mapping generators: ~531441/524288, ~5
[[POTE generator]]: ~5/4 = 389.193
{{Val list|legend=1| 17c, 34 }}
[[Badness]]: 0.541384


== Vines ==
== Vines ==
Line 424: Line 482:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: {{monzo| -50 -8 27 }}
[[Comma]]: {{monzo| -50 -8 27 }}


[[Mapping]]: [{{Val| 1 14 6 }}, {{Val| 0 -27 -8 }}]
[[Mapping]]: [{{Val| 1 14 6 }}, {{Val| 0 -27 -8 }}]
Line 478: Line 536:


[[Badness]]: 0.636715
[[Badness]]: 0.636715
== Mowgli ==
{{see also| Hemimean clan #Mowglic }}
Subgroup: 2.3.5
[[Comma]]: {{Monzo| 0 22 -15 }} = 31381059609/30517578125
[[Mapping]]: [{{Val| 1 0 0 }}, {{Val| 0 15 22 }}]
[[POTE generator]]: ~27/25 = 126.724
{{Val list|legend=1| 19, 85c, 104c, 123, 142, 161 }}
[[Badness]]: 0.653871


== Septimin ==
== Septimin ==
Line 514: Line 587:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: 8968066875/8589934592
[[Comma]]: 8968066875/8589934592


[[Mapping]]: [{{Val| 1 3 -3 }}, {{Val| 0 -4 15 }}]
[[Mapping]]: [{{Val| 1 3 -3 }}, {{Val| 0 -4 15 }}]
Line 544: Line 617:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: 1289945088/1220703125
[[Comma]]: 1289945088/1220703125


[[Mapping]]: [{{Val| 1 4 4 }}, {{Val| 0 -13 -9 }}]
[[Mapping]]: [{{Val| 1 4 4 }}, {{Val| 0 -13 -9 }}]
Line 559: Line 632:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: 6103515625/5804752896
[[Comma]]: 6103515625/5804752896


[[Mapping]]: [{{Val| 1 5 5 }}, {{Val| 0 -14 -11 }}]
[[Mapping]]: [{{Val| 1 5 5 }}, {{Val| 0 -14 -11 }}]
Line 574: Line 647:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: 258280326/244140625
[[Comma]]: 258280326/244140625


[[Mapping]]: [{{Val| 1 7 10 }}, {{Val| 0 -12 -17 }}]
[[Mapping]]: [{{Val| 1 7 10 }}, {{Val| 0 -12 -17 }}]
Line 632: Line 705:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: 793437161472/762939453125
[[Comma]]: 793437161472/762939453125


[[Mapping]]: [{{Val| 1 6 7 }}, {{Val| 0 -17 -18 }}]
[[Mapping]]: [{{Val| 1 6 7 }}, {{Val| 0 -17 -18 }}]
Line 647: Line 720:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: {{monzo| 46 -29 }}
[[Comma]]: {{monzo| 46 -29 }}


[[Mapping]]: [{{val| 29 46 0 }}, {{val| 0 0 1 }}]
[[Mapping]]: [{{val| 29 46 0 }}, {{val| 0 0 1 }}]
Line 658: Line 731:


[[Badness]]: 1.020556
[[Badness]]: 1.020556
== Cotoneum ==
{{See also| Hemimage temperaments #Cotoneum }}
[[Comma]]: {{Monzo| 80 -49 -1 }}
[[Mapping]]: [{{Val| 1 2 -18 }}, {{Val| 0 -1 49 }}]
[[POTE generator]]: ~3/2 = 702.315
{{Val list|legend=1| 41, 135c, 176, 217, 475, 1167, 1642, 2117b }}
[[Badness]]: 1.240078


== Oncle ==
== Oncle ==
Line 679: Line 765:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: 10460353203/9765625000
[[Comma]]: 10460353203/9765625000


[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -13 -21 }}]
[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -13 -21 }}]
Line 746: Line 832:


[[Badness]]: 1.434855
[[Badness]]: 1.434855
== Newt ==
{{See also| Breedsmic temperaments #Newt }}
[[Comma]]: {{Monzo| 95 -57 -2 }}
[[Mapping]]: [{{Val| 1 1 19 }}, {{Val| 0 2 -57 }}]
[[POTE generator]]: ~{{Monzo|47 -28 -1}} = 351.114
{{Val list|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 3592bc, 5523bbc }}
[[Badness]]: 1.528465


== Quasimoha ==
== Quasimoha ==
Line 797: Line 896:
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: {{monzo| 104 -70 3 }}
[[Comma]]: {{Monzo| 104 -70 3 }}


[[Mapping]]: [{{val| 1 2 12 }}, {{val| 0 -3 -70 }}]
[[Mapping]]: [{{val| 1 2 12 }}, {{val| 0 -3 -70 }}]
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