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| Line 473: |
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| Badness: 0.017921 | | Badness: 0.017921 |
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| == Decoid ==
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| {{See also| Quintosec family #Decoid }}
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| Decoid tempers out 2401/2400 and 67108864/66976875, as well as the [[linus comma]], {{monzo| 11 -10 -10 10 }}. Either 8/7 or 16/15 can be used as its generator. It may be described as the 130 & 270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice. It is also described as an extension of the [[quintosec]] temperament.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 2401/2400, 67108864/66976875
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| {{Mapping|legend=1| 10 0 47 36 | 0 2 -3 -1 }}
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| : Mapping generators: ~15/14, ~8192/4725
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| {{Multival|legend=1| 20 -30 -10 -94 -72 61 }}
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| [[Optimal tuning]]s:
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| * [[CTE]]: ~15/14 = 1＼10, ~8192/4725 = 951.1086 (~16/15 = 111.1086, or ~225/224 = 8.8914)
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| * [[POTE]]: ~15/14 = 1＼10, ~8192/4725 = 951.0987 (~16/15 = 111.0987, or ~225/224 = 8.9013)
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| {{Optimal ET sequence|legend=1| 10, …, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}
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| [[Badness]]: 0.033902
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 2401/2400, 5632/5625, 9801/9800
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| Mapping: {{mapping| 10 0 47 36 98 | 0 2 -3 -1 -8 }}
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| Optimal tunings:
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| * CTE: ~15/14 = 1＼10, ~400/231 = 951.0943 (~16/15 = 111.0943, or ~225/224 = 8.9057)
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| * POTE: ~15/14 = 1＼10, ~400/231 = 951.0700 (~16/15 = 111.0700, or ~225/224 = 8.9300)
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| Optimal ET sequence: {{Optimal ET sequence| 10e, …, 130, 270, 670, 940, 1210, 2150c }}
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| Badness: 0.018735
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095
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| Mapping: {{mapping| 10 0 47 36 98 37 | 0 2 -3 -1 -8 0 }}
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| Optimal tunings:
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| * CTE: ~15/14 = 1＼10, ~26/15 = 951.0943 (~16/15 = 111.0943, or ~196/195 = 8.9057)
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| * POTE: ~15/14 = 1＼10, ~26/15 = 951.0832 (~16/15 = 111.0832, or ~196/195 = 8.9168)
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| Optimal ET sequence: {{Optimal ET sequence| 10e, …, 130, 270, 940, 1210f, 1480cf }}
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| Badness: 0.013475
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| === Triacontoid ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 2401/2400, 42592/42525, 1771561/1769472
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| Mapping: {{mapping| 30 0 141 108 80 | 0 2 -3 -1 1 }}
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| : Mapping generators: ~45/44, ~8192/4725
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| Optimal tunings:
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| * CTE: ~45/44 = 1＼30, ~8192/4725 = 951.1137 (~225/224 = 8.8863)
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| * POTE: ~45/44 = 1＼30, ~8192/4725 = 951.1121 (~225/224 = 8.8879)
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| Optimal ET sequence: {{Optimal ET sequence| 120, 150, 270 }}
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| Badness: 0.075991
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 676/675, 2401/2400, 4096/4095, 6656/6655
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| Mapping: {{mapping| 30 0 141 108 80 111 | 0 2 -3 -1 1 0 }}
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| Optimal tunings:
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| * CTE: ~45/44 = 1＼30, ~26/15 = 951.1137 (~196/195 = 8.8863)
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| * POTE: ~45/44 = 1＼30, ~26/15 = 951.1130 (~196/195 = 8.8870)
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| Optimal ET sequence: {{Optimal ET sequence| 120, 150, 270 }}
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| Badness: 0.040873
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| == Neominor == | | == Neominor == |