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| * ''[[Decimaleap]]'' (+{{monzo| 15 -18 1 4 }}) → [[Quintaleap family #Decimaleap|Quintaleap family]] | | * ''[[Decimaleap]]'' (+{{monzo| 15 -18 1 4 }}) → [[Quintaleap family #Decimaleap|Quintaleap family]] |
| * ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]] | | * ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]] |
| | * ''[[Twothirdtonic]]'' (+686/675) → [[Sengic temperaments #Twothirdtonic|Sengic temperaments]] |
| * ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison|Sensipent family]] | | * ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison|Sensipent family]] |
| * ''[[Quinkee]]'' (+1029/1000) → [[Keegic temperaments #Quinkee|Keegic temperaments]] | | * ''[[Quinkee]]'' (+1029/1000) → [[Keegic temperaments #Quinkee|Keegic temperaments]] |
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| * ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]] | | * ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]] |
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| Considered below are hendecatonic, nessafof, grendel, twothirdtonic, aufo, absurdity, polypyth, whoops, dodifo, and icositritonic, in the order of increasing [[badness]]. | | Considered below are hendecatonic, nessafof, grendel, aufo, absurdity, polypyth, whoops, dodifo, and icositritonic, in the order of increasing [[badness]]. |
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| == Hendecatonic == | | == Hendecatonic == |
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| Badness (Sintel): 1.12 | | Badness (Sintel): 1.12 |
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| == Twothirdtonic ==
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| Twothirdtonic tempers out 686/675, the [[senga]], in addition to the porwell comma, and may be described as the {{nowrap| 37 & 46 }} temperament, generated by one third of a [[5/4|classical major third]] that represents [[15/14]], [[14/13]], and [[13/12]] in the [[13-limit]] interpretation. Note that in the data below, the generator is taken to be its [[octave complement]], thirteen of which [[octave reduction|octave reduced]] make the [[3/2|perfect fifth]]; it follows that the [[ploidacot]] for this temperament is 11-sheared 13-cot. [[46edo]] may be recommended as a tuning.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 686/675, 6144/6125
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| {{Mapping|legend=1| 1 -10 5 -7 | 0 13 -3 11 }}
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| : mapping generators: ~2, ~28/15
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1199.3074{{c}}, ~28/15 = 1068.9820{{c}}
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| : [[error map]]: {{val| -0.693 +1.736 +3.278 -5.176 }}
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| * [[CWE]]: ~2 = 1200.0000{{c}}, ~28/15 = 1069.5746{{c}}
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| : error map: {{val| 0.000 +2.515 +4.962 -3.505 }}
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| {{Optimal ET sequence|legend=1| 9, 28b, 37, 46 }}
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| [[Badness]] (Sintel): 2.52
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 121/120, 176/175, 686/675
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| Mapping: {{mapping| 1 -10 5 -7 -1 | 0 13 -3 11 5 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.7068{{c}}, ~28/15 = 1069.3084{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~28/15 = 1069.5600{{c}}
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| {{Optimal ET sequence|legend=0| 9, 28b, 37, 46 }}
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| Badness (Sintel): 1.35
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 91/90, 121/120, 169/168, 176/175
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| Mapping: {{mapping| 1 -10 5 -7 -1 -7 | 0 13 -3 11 5 12 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9531{{c}}, ~13/7 = 1069.5492{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~13/7 = 1069.5893{{c}}
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| {{Optimal ET sequence|legend=0| 9, 28b, 37, 46 }}
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| Badness (Sintel): 1.07
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| == Semaja == | | == Semaja == |