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| === Tertiaseptia === | | === Tertiaseptia === |
| | This extension was considered by [[Gene Ward Smith]] as a 41-limit temperament<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_9274.html Yahoo! Tuning Group | ''A 41-limit temperament'']</ref>. It can be extended as such by tempering out 703/702 and 697/696, and mapping 37 and 41 to -81 and +10 steps, respectively. |
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| Subgroup: 2.3.5.7.11 | | Subgroup: 2.3.5.7.11 |
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| Badness (Sintel): 1.18 | | Badness (Sintel): 1.18 |
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| ==== 37-limit ====
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| Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
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| Comma list: 595/594, 625/624, 703/702, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014
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| Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 81 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9824{{c}}, ~44/23 = 1122.8139{{c}} (~23/22 = 77.1685{{c}})
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| * CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8304{{c}} (~23/22 = 77.1696{{c}})
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| {{Optimal ET sequence|legend=0| 140, 171, 311 }}
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| Badness (Sintel): 1.19
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| ==== 41-limit ====
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| Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
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| Comma list: 595/594, 625/624, 697/696, 703/702, 714/713, 784/783, 820/819, 833/832, 875/874, 900/899, 931/930
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| Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 81 -4 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 10 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9957{{c}}, ~44/23 = 1122.8266{{c}} (~23/22 = 77.1691{{c}})
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| * CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8306{{c}} (~23/22 = 77.1694{{c}})
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| {{Optimal ET sequence|legend=0| 140, 171, 311 }}
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| Badness (Sintel): 1.20
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| === Hemitert === | | === Hemitert === |