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| {{Technical data page}}
| | #redirect [[Miscellaneous 5-limit temperaments#Shibboleth]] |
| The '''shibboleth family''' tempers out the [[shibboleth comma]], 1953125/1889568.
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| Temperaments discussed elsewhere include:
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| * [[superthird]], {245/243, 78125/76832} → [[Sensamagic clan #Superthird]]
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| == Shibboleth ==
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: 1953125/1889568
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| {{Mapping|legend=1| 1 4 5 | 0 -9 -10 }}
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| [[Optimal tuning]]s:
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| * [[CTE]]: ~2 = 1\1, ~6/5 = 321.773
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| * [[POTE]]: ~2 = 1\1, ~6/5 = 321.852
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| {{Optimal ET sequence|legend=1| 15, 26, 41, 179c, 220c, 261cc, 302cc }}
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| [[Badness]]: 0.227553
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| == Superkleismic ==
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| {{Main| Superkleismic }}
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| The [[S-expression]]-based comma list of superkleismic is {[[875/864|S5/S6]], [[1029/1024|S7/S8]], [[100/99|S10]], [[144/143|S12]](, [[441/440|S21]])}. Through careful observation of the equivalences therein one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 875/864, 1029/1024
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| {{Mapping|legend=1| 1 4 5 2 | 0 -9 -10 3 }}
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| {{Multival|legend=1| 9 10 -3 -5 -30 -35 }}
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| [[Optimal tuning]]s:
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| * [[CTE]]: ~2 = 1\1, ~6/5 = 321.798
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| * [[POTE]]: ~2 = 1\1, ~6/5 = 321.930
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| {{Optimal ET sequence|legend=1| 11c, 15, 26, 41 }}
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| [[Badness]]: 0.047932
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 100/99, 245/242, 385/384
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| Mapping: {{mapping| 1 4 5 2 4 | 0 -9 -10 3 -2 }}
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| Optimal tunings:
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| * CTE: ~2 = 1\1, ~6/5 = 321.815
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| * POTE: ~2 = 1\1, ~6/5 = 321.847
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| Optimal ET sequence: {{Optimal ET sequence| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
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| Badness: 0.025659
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 100/99, 105/104, 144/143, 245/242
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| Mapping: {{mapping| 1 4 5 2 4 8 | 0 -9 -10 3 -2 -16 }}
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| Optimal tunings:
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| * CTE: ~2 = 1\1, ~6/5 = 321.986
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| * POTE: ~2 = 1\1, ~6/5 = 321.994
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| Optimal ET sequence: {{Optimal ET sequence| 11cf, 15, 26, 41 }}
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| Badness: 0.021478
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| == Gilead ==
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 126/125, 343/324
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| {{Mapping|legend=1| 1 4 5 6 | 0 -9 -10 -12 }}
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| {{Multival|legend=1| 9 10 12 -5 -6 0 }}
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| [[Optimal tuning]]s:
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| * [[CTE]]: ~2 = 1\1, ~6/5 = 321.109
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| * [[POTE]]: ~2 = 1\1, ~6/5 = 321.423
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| {{Optimal ET sequence|legend=1| 11cd, 15, 41dd, 56dd }}
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| [[Badness]]: 0.115292
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| [[Category:Temperament families]]
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| [[Category:Shibboleth family| ]] <!-- main article -->
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| [[Category:Rank 2]]
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