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Line 66: |
| * [[Windrose]] ([[32nd-octave temperaments|1\32 period]]) | | * [[Windrose]] ([[32nd-octave temperaments|1\32 period]]) |
| * [[Compton family #Decades|Decades]] (1\36 period) | | * [[Compton family #Decades|Decades]] (1\36 period) |
| | * Rubidium, dzelic ([[37th-octave temperaments]]) |
| * [[Ragismic microtemperaments #Enneadecal|Hemienneadecal]] (1\38 period) | | * [[Ragismic microtemperaments #Enneadecal|Hemienneadecal]] (1\38 period) |
| * [[Counterpyth family|Counterpyth temperaments]], [[niobium]] (1\41 period) | | * [[Counterpyth family|Counterpyth temperaments]], [[niobium]] (1\41 period) |
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| Badness: 0.0269 | | Badness: 0.0269 |
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| == 37th-octave temperaments ==
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| [[37edo]] is accurate for harmonics 5, 7, 11, and 13, so various 37th-octave temperaments actually make sense.
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| === Rubidium ===
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| The name of rubidium temperament comes from Rubidium, the 37th element.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 3136/3125, 4194304/4117715
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| [[Mapping]]: [{{val| 37 0 86 104 }}, {{val| 0 1 0 0 }}]
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| Mapping generators: ~50/49, ~3
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| [[Optimal tuning]] ([[POTE]]): ~3/2 = 703.3903
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| {{Val list|legend=1| 37, 74, 111 }}
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| [[Badness]]: 0.312105
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| ==== 11-limit ====
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| Subgroup: 2.3.5.7.11
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| Comma list: 176/175, 1375/1372, 65536/65219
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| Mapping: [{{val| 37 0 86 104 128 }}, {{val| 0 1 0 0 0 }}]
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| Optimal tuning (POTE): ~3/2 = 703.0355
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| Optimal GPV sequence: {{Val list| 37, 74, 111 }}
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| Badness: 0.101001
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 176/175, 640/637, 847/845, 1375/1372
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| Mapping: [{{val| 37 0 86 104 128 137 }}, {{val| 0 1 0 0 0 0 }}]
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| Optimal tuning (POTE): ~3/2 = 703.0520
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| Optimal GPV sequence: {{Val list| 37, 74, 111 }}
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| Badness: 0.048732
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| === Triacontaheptoid ===
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 244140625/242121642, 283115520/282475249
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| [[Mapping]]: [{{val| 37 2 67 85 }}, {{val| 0 3 1 1 }}]
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| Mapping generator: ~50/49, ~24000/16807
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| [[Optimal tuning]] ([[CTE]]): ~24000/16807 = 612.4003
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| {{Val list|legend=1| 37, 222b, 259b, 296, 629 }}
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| [[Badness]]: 0.784746
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| ==== 11-limit ====
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| Subgroup: 2.3.5.7.11
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| Comma list: 1375/1372, 4000/3993, 226492416/226474325
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| Mapping: [{{val| 37 2 67 85 128 }}, {{val| 0 3 1 1 0 }}]
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| Optimal tuning (CTE): ~768/359 = 612.4003
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| Optimal GPV sequence: {{Val list| 37, 259b, 296, 629 }}
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| Badness: 0.167327
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 625/624, 1375/1372, 4000/3993, 15379/15360
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| Mapping: [{{val| 37 2 67 85 128 118 }}, {{val| 0 3 1 1 0 1 }}]
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| Optimal tuning (CTE): ~462/325 = 612.4206
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| Optimal GPV sequence: {{Val list| 37, 259b, 296, 629f }}
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| Badness: 0.076183
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 625/624, 715/714, 1225/1224, 4000/3993, 11271/11264
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| Mapping: [{{val| 37 2 67 85 128 118 189 }}, {{val| 0 3 1 1 0 1 -2 }}]
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| Optimal tuning (CTE): ~121/85 = 612.4187
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| Optimal GPV sequence: {{Val list| 37, 259b, 296, 629f }}
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| Badness: 0.052475
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| == 44th-octave temperaments == | | == 44th-octave temperaments == |