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| Like miracle, it is naturally an 11-limit temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]]. | | Like miracle, it is naturally an 11-limit temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]]. |
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| | The 31 & 145 extension in the 13- and 17-limit used to be called "countermiraculous" before becoming canonical. |
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| [[Subgroup]]: 2.3.5.7 | | [[Subgroup]]: 2.3.5.7 |
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| Badness (Sintel): 1.29 | | Badness (Sintel): 1.29 |
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| ==== Countermiraculous ==== | | === 13-limit === |
| Subgroup: 2.3.5.7.11.13 | | Subgroup: 2.3.5.7.11.13 |
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| Badness (Sintel): 1.62 | | Badness (Sintel): 1.62 |
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| ===== 17-limit =====
| | === 17-limit === |
| Subgroup: 2.3.5.7.11.13.17 | | Subgroup: 2.3.5.7.11.13.17 |
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| Badness (Sintel): 1.50 | | Badness (Sintel): 1.50 |
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| ==== Counterbenediction ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 351/350, 441/440, 3146/3125, 3584/3575
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| Mapping: {{mapping| 1 -21 -4 1 -39 29 57 | 0 25 7 2 47 -59 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9460{{c}}, ~144/77 = 1084.0178{{c}} (~77/72 = 115.9283{{c}})
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| * CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.0663{{c}} (~77/72 = 115.9337{{c}})
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| {{Optimal ET sequence|legend=0| 31, 145f, 176, 207 }}
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| Badness (Sintel): 1.88
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| ===== 17-limit =====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 351/350, 441/440, 561/560, 1632/1625, 3146/3125
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| Mapping: {{mapping| 1 -21 -4 1 -39 29 57 61 | 0 25 7 2 47 -59 -63 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9950{{c}}, ~144/77 = 1084.0564{{c}} (~77/72 = 115.9386{{c}})
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| * CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.0609{{c}} (~77/72 = 115.9391{{c}})
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| {{Optimal ET sequence|legend=0| 31, 176, 207 }}
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| Badness (Sintel): 1.85
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| === Counterrevelation ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 121/120, 176/175, 50421/50000
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| Mapping: {{mapping| 1 -21 -4 1 -11 | 0 25 7 2 16 }}
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| Optimal tunings:
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| * WE: ~2 = 1200.1897{{c}}, ~275/147 = 1084.2521{{c}} (~343/320 = 115.9375{{c}})
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| * CWE: ~2 = 1200.0000{{c}}, ~275/147 = 1084.0850{{c}} (~343/320 = 115.9150{{c}})
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| {{Optimal ET sequence|legend=0| 31, 114, 145e }}
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| Badness (Sintel): 2.12
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 121/120, 176/175, 196/195, 13750/13689
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| Mapping: {{mapping| 1 -21 -4 1 -11 29 | 0 25 7 2 16 -28 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.7651{{c}}, ~220/117 = 1083.9253{{c}} (~117/110 = 115.8398{{c}})
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| * CWE: ~2 = 1200.0000{{c}}, ~220/117 = 1084.1357{{c}} (~117/110 = 115.8643{{c}})
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| {{Optimal ET sequence|legend=0| 31, 83, 114 }}
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| Badness (Sintel): 2.38
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 121/120, 154/153, 176/175, 196/195, 10647/10625
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| Mapping: {{mapping| 1 -21 -4 1 -11 29 33 | 0 25 7 2 16 -28 -32 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.6935{{c}}, ~170/91 = 1083.8704{{c}} (~91/85 = 115.8231{{c}})
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| * CWE: ~2 = 1200.0000{{c}}, ~170/91 = 1084.1464{{c}} (~91/85 = 115.8536{{c}})
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| {{Optimal ET sequence|legend=0| 31, 83, 114 }}
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| Badness (Sintel): 2.24
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| == Subgroup extensions == | | == Subgroup extensions == |