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| Temperaments discussed elsewhere include: | | Temperaments discussed elsewhere include: |
| * ''Octant'' → [[Schismatic family#Octant|Schismatic family]] | | * ''[[Octant]]'' → [[Schismatic family #Octant|Schismatic family]] |
| | | * ''[[Octonion]]'' → [[Diminished family #Octonion|Diminished family]] |
| == Octatonic ==
| | * ''[[Twilight]]'' → [[Undim family #Twilight|Undim family]] |
| [[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. The octatonic temperament makes a [[consistent circle]]. | | * [[Octoid]] → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]] |
| | | * ''[[Octatonic (temperament)|Octatonic]]'' → [[No-fives subgroup temperaments #Octatonic|No-fives subgroup temperaments]] |
| [[Subgroup]]: 2.3.11
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| [[Comma list]]: {{monzo|15 8 0 0 -8}}
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| {{Mapping|legend=1|8 0 15|0 1 1}}
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| : Mapping generators: ~12/11, ~3
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| [[Support]]ing [[ET]]s: {{EDOs|16, 24, 32, 48, 56, 72, 80, 120, 128, 152}}, ...
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| == Octium ==
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| Octium temperament is named after an "extended provisional" name for oxygen, the 8th element. The term [[oxygen]] itself is already the name of an exotemperament. It reaches [[24/23]] in one generator and [[19/16]] in two.
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| Subgroup: 2.3.19.23.29.31
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| Comma list: 94221/94208, 419957/419904, 219501/219488, 7997934975003/7996960669696
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| {{Mapping|legend=2| 8 2 35 25 47 2 | 0 21 -2 22 -16 74 }}
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| : Mapping generators: ~10051/9216, ~24/23
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| [[Optimal tuning]] ([[CTE]]): ~24/23 = 76.284
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| [[Support]]ing [[ET]]s: {{EDOs|472, 1400, 1872, 3272, 5144}} | |
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| == Octoid ==
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| : ''For the 7-limit temperament, see [[Ragismic microtemperaments #Octoid]].''
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| [[Subgroup]]: 2.3.5 | |
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| [[Comma list]]: 59604644775390625/59296646043258912
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| {{Mapping|legend=1| 8 1 3 | 0 3 4 }}
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| : Mapping generators: ~2125764/1953125, ~4374/3125
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2125764/1953125 = 150.001{{c}}, ~4374/3125 = 584.027{{c}}
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| * [[CWE]]: ~2125764/1953125 = 150.000{{c}}, ~4374/3125 = 584.025{{c}}
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| {{Optimal ET sequence|legend=1| 8, 56bcc, 64c, 72, 152, 224, 376, 976 }}
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| [[Badness]] (Sintel): 6.687
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| {{Navbox fractional-octave}} | | {{Navbox fractional-octave}} |