Syntonic–diatonic equivalence continuum: Difference between revisions
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* 5 & 137 (''n'' = 5.5) | * 5 & 137 (''n'' = 5.5) | ||
== Hemiseven | == Hemiseven == | ||
{{See also|Gamelismic clan #Hemiseven}} | {{See also| Gamelismic clan #Hemiseven }} | ||
Subgroup: 2.3.5 | |||
Comma list: {{monzo| 32 -29 6 }} | |||
POTE generator: ~320/243 = 483.2474 | Mapping: [{{val| 1 4 14 }}, {{val| 0 -6 -29 }}] | ||
POTE generator: ~320/243 = 483.2474 | |||
Vals: {{Val list| 5, 62c, 67c, 72, 149, 221, 370, 591b, 961bb }} | Vals: {{Val list| 5, 62c, 67c, 72, 149, 221, 370, 591b, 961bb }} | ||
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Badness: 0.720465 | Badness: 0.720465 | ||
== Ultrapyth == | |||
{{See also| Archytas clan #Ultrapyth }} | |||
Subgroup: 2.3.5 | |||
Comma list: 5242880/4782969 | |||
POTE generator: ~4/3 = 486.1713 | Mapping: [{{val| 1 2 8 }}, {{val| 0 -1 -14 }}] | ||
POTE generator: ~4/3 = 486.1713 | |||
Vals: {{Val list| 5, 27c, 32, 37, 79bc, 116bbc }} | Vals: {{Val list| 5, 27c, 32, 37, 79bc, 116bbc }} | ||
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Badness: 0.795243 | Badness: 0.795243 | ||
== Trisatriyo (5 & 56) == | |||
Subgroup: 2.3.5 | |||
Comma list: {{monzo| 28 -22 3 }} = 33554432000/31381059609 | |||
Comma: {{ | |||
Mapping: [{{val|1 1 -2}}, {{val|0 3 22}}] | Mapping: [{{val| 1 1 -2 }}, {{val| 0 3 22 }}] | ||
POTE generator: ~2560/2187 = 235.8673 | POTE generator: ~2560/2187 = 235.8673 | ||
Vals: {{Val list| 5, 56, 61 }} | Vals: {{Val list| 5, 56, 61 }} | ||
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== Counterpental == | == Counterpental == | ||
{{See also| Orwellismic temperaments #Pentorwell }} | |||
Comma list: {{monzo| 36 -30 5 }} | |||
POTE generator: 15.4278 | Mapping: [{{val| 5 8 12 }}, {{val| 0 -1 -6 }}] | ||
POTE generator: 15.4278 | |||
Vals: {{Val list| 5, 75, 80 }} | Vals: {{Val list| 5, 75, 80 }} | ||
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[http://x31eq.com/cgi-bin/rt.cgi?ets=5_75&limit=5 The temperament finder - 5-limit 5 & 75] | [http://x31eq.com/cgi-bin/rt.cgi?ets=5_75&limit=5 The temperament finder - 5-limit 5 & 75] | ||
== Septiquarter | == Septiquarter == | ||
{{See also|Hemifamity temperaments #Septiquarter}} | {{See also| Hemifamity temperaments #Septiquarter }} | ||
Subgroup: 2.3.5 | |||
Comma: {{Monzo|44 -38 7}} | Comma: {{Monzo|44 -38 7}} | ||
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Mapping: [{{val|1 3 10}}, {{val|0 -7 -38}}] | Mapping: [{{val|1 3 10}}, {{val|0 -7 -38}}] | ||
POTE generator: ~204800/177147 = 242.4567 | POTE generator: ~204800/177147 = 242.4567 | ||
Vals: {{Val list| 5, 89c, 94, 99, 193, 292, 391 }} | Vals: {{Val list| 5, 89c, 94, 99, 193, 292, 391 }} | ||
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== 559 & 2513 == | == 559 & 2513 == | ||
Comma: {{ | Subgroup: 2.3.5 | ||
Comma list: {{monzo| -124 109 -21 }} | |||
Mapping: [{{val|1 10 46}}, {{val|0 -21 -109}}] | Mapping: [{{val| 1 10 46 }}, {{val| 0 -21 -109 }}] | ||
POTE generator: ~3355443200000/2541865828329 = 480.8595 | POTE generator: ~3355443200000/2541865828329 = 480.8595 | ||
Vals: {{Val list| 5, 267c, 272c, 277, 559, 1395, 1954, 2513, 40767, 43280, 45793, 48306, 50819, 53332, 55845, 58358, 60871, 63384, 65897, 68410, 70923, 73436, 75949, 78462 }} | Vals: {{Val list| 5, 267c, 272c, 277, 559, 1395, 1954, 2513, 40767, 43280, 45793, 48306, 50819, 53332, 55845, 58358, 60871, 63384, 65897, 68410, 70923, 73436, 75949, 78462 }} | ||
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== Quinla-tritrigu (5 & 118) == | == Quinla-tritrigu (5 & 118) == | ||
Comma: {{ | Subgroup: 2.3.5 | ||
Comma list: {{monzo| -52 46 -9 }} | |||
Mapping: [{{val|1 -2 -16}}, {{val|0 9 46}}] | Mapping: [{{val| 1 -2 -16 }}, {{val| 0 9 46 }}] | ||
POTE generator: ~320/243 = 477.9609 | POTE generator: ~320/243 = 477.9609 | ||
Vals: {{Val list| 5, 108c, 113, 118, 1057, 1175, 1293, 1411, 1529, 1647, 1765, 1883, 2001b, 3884b }} | Vals: {{Val list| 5, 108c, 113, 118, 1057, 1175, 1293, 1411, 1529, 1647, 1765, 1883, 2001b, 3884b }} | ||
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== Tribilalegu (5 & 137) == | == Tribilalegu (5 & 137) == | ||
Comma: {{Monzo|-60 54 -11}} | Subgroup: 2.3.5 | ||
Comma: {{Monzo| -60 54 -11 }} | |||
Mapping: [{{val|1 6 24}}, {{val|0 -11 -54}}] | Mapping: [{{val| 1 6 24 }}, {{val| 0 -11 -54 }}] | ||
POTE generator: ~320/243 = 481.7421 cents | POTE generator: ~320/243 = 481.7421 cents | ||