Wizmic microtemperaments: Difference between revisions
m Removing from Category:Regular temperament theory using Cat-a-lot |
Add 19-limit tertiathirds (121&149) |
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{{Multival|legend=1| 41 14 60 -73 -20 100 }} | {{Multival|legend=1| 41 14 60 -73 -20 100 }} | ||
[[POTE generator]]: ~ | [[POTE generator]]: ~125/96 = 456.144 | ||
{{Val list|legend=1| 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd }} | {{Val list|legend=1| 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd }} | ||
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{{Multival|legend=1| 13 67 -6 76 -46 -202 }} | {{Multival|legend=1| 13 67 -6 76 -46 -202 }} | ||
[[POTE generator]]: ~ | [[POTE generator]]: ~147/128 = 238.599 | ||
{{Val list|legend=1| 5, 161c, 166, 171, 1544d, 1715d, 1886d, 2057d, 2228d, 2399d, 2570d, 2741d, 2912dd, 3083cdd }} | {{Val list|legend=1| 5, 161c, 166, 171, 1544d, 1715d, 1886d, 2057d, 2228d, 2399d, 2570d, 2741d, 2912dd, 3083cdd }} | ||
| Line 67: | Line 67: | ||
{{Multival|legend=1| 52 3 82 -116 -16 182 }} | {{Multival|legend=1| 52 3 82 -116 -16 182 }} | ||
[[POTE generator]]: ~ | [[POTE generator]]: ~3375/3136 = 128.888 | ||
{{Val list|legend=1| 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc }} | {{Val list|legend=1| 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc }} | ||
| Line 80: | Line 80: | ||
Mapping: [{{val| 1 48 5 76 107 }}, {{val| 0 -52 -3 -82 -116 }}] | Mapping: [{{val| 1 48 5 76 107 }}, {{val| 0 -52 -3 -82 -116 }}] | ||
POTE generator: ~245 | POTE generator: ~264/245 = 128.890 | ||
Optimal GPV sequence: {{Val list| 121, 149, 270, 2551bc, 2821bc, 3091bc, 3361bc, 3631bbcc, 3901bbccd, 4171bbccd, 4441bbccd, 4711bbccd }} | Optimal GPV sequence: {{Val list| 121, 149, 270, 2551bc, 2821bc, 3091bc, 3361bc, 3631bbcc, 3901bbccd, 4171bbccd, 4441bbccd, 4711bbccd }} | ||
| Line 93: | Line 93: | ||
Mapping: [{{val| 1 48 5 76 107 76 }}, {{val| 0 -52 -3 -82 -116 -81 }}] | Mapping: [{{val| 1 48 5 76 107 76 }}, {{val| 0 -52 -3 -82 -116 -81 }}] | ||
POTE generator: ~13 | POTE generator: ~14/13 = 128.890 | ||
Optimal GPV sequence: {{Val list| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }} | Optimal GPV sequence: {{Val list| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }} | ||
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Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
Comma list: 676/675, 715/714, | Comma list: 676/675, 715/714, 936/935, 1225/1224, 4225/4224 | ||
Mapping: [{{val| 1 48 5 76 107 76 63 }}, {{val| 0 -52 -3 -82 -116 -81 -66 }}] | Mapping: [{{val| 1 48 5 76 107 76 63 }}, {{val| 0 -52 -3 -82 -116 -81 -66 }}] | ||
POTE generator: ~13 | POTE generator: ~14/13 = 128.891 | ||
Optimal GPV sequence: {{Val list| 121, 149, 270 }} | Optimal GPV sequence: {{Val list| 121, 149, 270 }} | ||
Badness: 0.019107 | Badness: 0.019107 | ||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 676/675, 715/714, 936/935, 1225/1224, 1540/1539, 2128/2125 | |||
Mapping: [{{val|1 48 5 76 107 76 63 -2}}, {{val|0 -52 -3 -82 -116 -81 -66 7}}] | |||
POTE generator: ~14/13 = 128.890 | |||
Optimal GPV sequence: {{Val list| 121, 149, 270 }} | |||
Badness: 0.015621 | |||
== Witch == | == Witch == | ||
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{{Multival|legend=1| 25 65 14 45 -48 -150 }} | {{Multival|legend=1| 25 65 14 45 -48 -150 }} | ||
[[POTE generator]]: ~63 | [[POTE generator]]: ~80/63 = 412.098 | ||
{{Val list|legend=1| 99, 265, 364, 463, 562, 1025 }} | {{Val list|legend=1| 99, 265, 364, 463, 562, 1025 }} | ||
| Line 140: | Line 153: | ||
Mapping: [{{val| 1 18 45 12 77 }}, {{val| 0 -25 -65 -14 -112 }}] | Mapping: [{{val| 1 18 45 12 77 }}, {{val| 0 -25 -65 -14 -112 }}] | ||
POTE generator: ~63 | POTE generator: ~80/63 = 412.079 | ||
Optimal GPV sequence: {{Val list| 99e, 166, 265 }} | Optimal GPV sequence: {{Val list| 99e, 166, 265 }} | ||
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Mapping: [{{val| 1 18 45 12 77 93 }}, {{val| 0 -25 -65 -14 -112 -136 }}] | Mapping: [{{val| 1 18 45 12 77 93 }}, {{val| 0 -25 -65 -14 -112 -136 }}] | ||
POTE generator: ~ | POTE generator: ~33/26 = 412.070 | ||
Optimal GPV sequence: {{Val list| 99ef, 166, 265, 431c, 696cc }} | Optimal GPV sequence: {{Val list| 99ef, 166, 265, 431c, 696cc }} | ||