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| Line 936: |
Line 936: |
| = Fractional subgroup temperaments = | | = Fractional subgroup temperaments = |
| == 2.3.… subgroups == | | == 2.3.… subgroups == |
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| === Trisect ===
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| Trisect divides every Pythagorean interval into three, and is the much more accurate subgroup restriction of [[Augmented family #Trisected|trisected]].
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| Extending this temperament to the full [[11-limit|11-]], [[13-limit|13-]], or [[17-limit]] through [[portent]] or [[landscape]] results in the [[weak extension]] known as [[tritikleismic]].
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| [[Subgroup]]: 2.3.7.11/5
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| [[Comma list]]: 1029/1024, 4000/3993
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| {{Mapping|legend=3| 3 0 10 5 | 0 3 -1 -1 }}
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| [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.742
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| {{Optimal ET sequence|legend=1| 15, 21, 36, 123, 159, 195, 231 }}
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| [[Tp tuning #T2 tuning|RMS error]]: ???
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| ==== 2.3.7.11/5.13 subgroup ====
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| [[Subgroup]]: 2.3.7.11/5.13
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| [[Comma list]]: 1029/1024, 1575/1573, 2080/2079
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| {{Mapping|legend=3| 3 0 10 5 0 | 0 3 -1 -1 7 }}
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| [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.918
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| {{Optimal ET sequence|legend=1| 15, 21f, 36, 87, 123, 159 }}
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| [[Tp tuning #T2 tuning|RMS error]]: ???
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| ==== 2.3.7.11/5.13.17 subgroup ====
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| [[Subgroup]]: 2.3.7.11/5.13.17
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| [[Comma list]]: 273/272, 833/832, 1575/1573, 2080/2079
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| {{Mapping|legend=3| 3 0 10 5 0 -2 | 0 3 -1 -1 7 9 }}
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| [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.820
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| {{Optimal ET sequence|legend=1| 15, 21fg, 36, 123, 159 }}
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| [[Tp tuning #T2 tuning|RMS error]]: ???
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| ===== Trisector =====
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| [[Subgroup]]: 2.3.7.11/5.13.17.19
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| [[Comma list]]: 210/209, 273/272, 286/285, 595/594, 2080/2079
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| {{Mapping|legend=3| 3 0 10 5 0 -2 8 | 0 3 -1 -1 7 9 3 }}
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| [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.894
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| {{Optimal ET sequence|legend=1| 15, 21fg, 36, 123h, 159h }}
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| [[Tp tuning #T2 tuning|RMS error]]: ???
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| ===== 2.3.7.11/5.13.17.19.23 subgroup =====
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| [[Subgroup]]: 2.3.7.11/5.13.17.19.23
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| [[Comma list]]: 210/209, 231/230, 273/272, 286/285, 595/594, 2080/2079
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| {{Mapping|legend=3| 3 0 10 5 0 -2 8 12 | 0 3 -1 -1 7 9 3 1 }}
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| [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 634.038
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| {{Optimal ET sequence|legend=1| 15g, 21fg, 36, 87, 123hi }}
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| [[Tp tuning #T2 tuning|RMS error]]: ???
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| ===== 2.3.7.11/5.13.17.19.23.29 subgroup =====
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| [[Subgroup]]: 2.3.7.11/5.13.17.19.23.29
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| [[Comma list]]: 210/209, 231/230, 273/272, 286/285, 320/319, 595/594, 2080/2079
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| {{Mapping|legend=3| 3 0 10 5 0 -2 8 12 13 | 0 3 -1 -1 7 9 3 1 1 }}
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| [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~29/23 = 1\3, ~13/9 = 634.102
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| {{Optimal ET sequence|legend=1| 15g, 21fg, 36, 87, 123hi }}
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| [[Tp tuning #T2 tuning|RMS error]]: ???
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| === Hypnosis === | | === Hypnosis === |
| Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Alphatricot family #Alphatricot|alphatricot]] | | Related temperaments: [[Swetismic temperaments #Hypnos|hypnos]], [[Alphatricot family #Alphatricot|alphatricot]] |