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| Temperaments discussed elsewhere are: | | Temperaments discussed elsewhere are: |
| * [[Godzilla]] (+49/48 or 81/80) → [[Slendro clan #Godzilla|Slendro clan]] | | * [[Godzilla]] (+49/48 or 81/80) → [[Semaphoresmic clan #Godzilla|Semaphoresmic clan]] |
| | * ''[[Kleischismic]]'' (+32805/32768) → [[Schismatic family #Kleischismic|Schismatic family]] |
| | * ''[[Pentaorwell]]'' (+1728/1715) → [[Orwellismic temperaments #Pentaorwell|Orwellismic temperaments]] |
| | * ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]] |
| | * ''[[Hemiquindromeda]]'' (+67108864/66976875) → [[Quindromeda family #Hemiquindromeda|Quindromeda family]] |
| * ''[[Betic]]'' (+225/224) → [[Sycamore family #Betic|Sycamore family]] | | * ''[[Betic]]'' (+225/224) → [[Sycamore family #Betic|Sycamore family]] |
| * ''[[Pentaorwell]]'' (+1728/1715) → [[Orwellismic temperaments #Pentaorwell|Orwellismic temperaments]]
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| * ''[[Amicable]]'' (+2401/2400) → [[Breedsmic temperaments #Amicable|Breedsmic temperaments]]
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| * [[Parakleismic]] (+3136/3125 or 4375/4374) → [[Ragismic microtemperaments #Parakleismic|Ragismic microtemperaments]] | | * [[Parakleismic]] (+3136/3125 or 4375/4374) → [[Ragismic microtemperaments #Parakleismic|Ragismic microtemperaments]] |
| * ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]] | | * ''[[Turkey (temperament)|Turkey]]'' (+5250987/5242880) → [[Vulture family #Turkey|Vulture family]] |
| | * ''[[Kaboom]]'' (+65625/65536) → [[Vavoom family #Kaboom|Vavoom family]] |
| | * ''[[Amicable]]'' (+2401/2400) → [[Amity family #Amicable|Amity family]] |
| * ''[[Marthirds]]'' (+15625/15552) → [[Kleismic family #Marthirds|Kleismic family]] | | * ''[[Marthirds]]'' (+15625/15552) → [[Kleismic family #Marthirds|Kleismic family]] |
| * ''[[Kleischismic]]'' (+32805/32768) → [[Schismatic family #Kleischismic|Schismatic family]] | | * ''[[Semiluna]]'' (+95703125/95551488) → [[Luna family #Semiluna|Luna family]] |
| * ''[[Kaboom]]'' (+65625/65536) → [[Vavoom family #Kaboom|Vavoom family]]
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| * ''[[Quartiquart]]'' (+390625/388962) → [[Quartonic family #Quartiquart|Quartonic family]] | | * ''[[Quartiquart]]'' (+390625/388962) → [[Quartonic family #Quartiquart|Quartonic family]] |
| * ''[[Turkey (temperament)|Turkey]]'' (+5250987/5242880) → [[Vulture family #Turkey|Vulture family]]
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| * ''[[Hemiquindromeda]]'' (+67108864/66976875) → [[Quindromeda family #Hemiquindromeda|Quindromeda family]]
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| * ''[[Semiluna]]'' (+95703125/95551488) → [[Luna family #Semiluna|Luna family]]
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| Considered below are satin and superlimmal.
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| == Satin ==
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| : ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Satin]].''
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| Satin tempers out the [[rainy comma]], the canousma, and the [[garischisma]], and may be described as the {{nowrap| 94 & 217 }} temperament. It uses [[~]][[11/10]] as a generator, three of which gives a [[4/3|perfect fourth]], tempering out [[4000/3993]] in the 11-limit and onwards. Its [[ploidacot]] is omega-tricot.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 2100875/2097152, 4802000/4782969
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| {{Mapping|legend=1| 1 2 12 -3 | 0 -3 -70 42 }}
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| : mapping generators: ~2, ~8575/7776
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1200.0198{{c}}, ~8575/7776 = 165.9161{{c}}
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| : [[error map]]: {{val| +0.020 +0.336 -0.200 -0.411 }}
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| * [[CWE]]: ~2 = 1200.0000{{c}}, ~8575/7776 = 165.9133{{c}}
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| : error map: {{val| 0.000 +0.305 -0.241 -0.469 }}
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| {{Optimal ET sequence|legend=1| 94, 217, 311, 839, 1150 }}
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| [[Badness]] (Sintel): 4.99
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 4000/3993, 19712/19683, 41503/41472
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| Mapping: {{mapping| 1 2 12 -3 13 | 0 -3 -70 42 -69 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9931{{c}}, ~11/10 = 165.9145{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9155{{c}}
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| {{Optimal ET sequence|legend=0| 94, 217, 311 }}
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| Badness (Sintel): 1.92
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 1575/1573, 2080/2079, 4096/4095, 13720/13689
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| Mapping: {{mapping| 1 2 12 -3 13 -1 | 0 -3 -70 42 -69 34 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9607{{c}}, ~11/10 = 165.9085{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9141{{c}}
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| {{Optimal ET sequence|legend=0| 94, 217, 311, 839e }}
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| Badness (Sintel): 1.25
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| === 17-limit ===
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095
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| Mapping: {{mapping| 1 2 12 -3 13 -1 11 | 0 -3 -70 42 -69 34 -50 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9843{{c}}, ~11/10 = 165.9110{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9132{{c}}
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| {{Optimal ET sequence|legend=0| 94, 217, 311, 839e }}
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| Badness (Sintel): 1.02
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| === 19-limit ===
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| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573
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| Mapping: {{mapping| 1 2 12 -3 13 -1 11 16 | 0 -3 -70 42 -69 34 -50 -85 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9875{{c}}, ~11/10 = 165.9111{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9129{{c}}
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| {{Optimal ET sequence|legend=0| 94, 217, 311, 839e }}
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| Badness (Sintel): 0.881
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| === 23-limit ===
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| Subgroup: 2.3.5.7.11.13.17.19.23
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| Comma list: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155
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| Mapping: {{mapping| 1 2 12 -3 13 -1 11 16 16 | 0 -3 -70 42 -69 34 -50 -85 -83 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9745{{c}}, ~11/10 = 165.9103{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9140{{c}}
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| {{Optimal ET sequence|legend=0| 94, 217, 311 }}
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| Badness (Sintel): 0.871
| | Considered below is superlimmal. |
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| == Superlimmal == | | == Superlimmal == |