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| A 13th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 13. Although [[13edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 13 are. | | A 13th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 13. Although [[13edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 13 are. |
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| == Aluminium ==
| | Temperaments discussed elsewhere are [[ragismic microtemperaments #Aluminium|aluminium]], [[octagar temperaments #Tridecatonic|tridecatonic]], [[ragismic microtemperaments #Trideci|trideci]], and [[orwellismic temperaments #Triskaidekic|triskaidekic]]. |
| : ''For extensions, see [[Ragismic microtemperaments #Aluminium]].''
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| Aluminium tempers out {{monzo| 92 -39 -13 }} in the 5-limit, and sets [[135/128]] to 1/13 of an [[octave]].
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: {{monzo| 92 -39 -13 }}
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| {{Mapping|legend=1| 13 0 92 | 0 1 -3 }}
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| : mapping generators: ~135/128, ~3
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| [[Optimal tuning]]s:
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| * [[WE]]: ~135/128 = 92.3068{{c}}, ~3/2 = 701.9791{{c}}
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| : [[error map]]: {{val| -0.012 +0.012 +0.009 }}
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| * [[CWE]]: ~135/128 = 92.3077{{c}}, ~3/2 = 701.9897{{c}}
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| : error map: {{val| 0.000 +0.032 +0.033 }}
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| {{Optimal ET sequence|legend=1| 65, 299, 364, 429, 494, 559, 1053, 1612, 5889, 7501, 9113, 10725, 23062bc, 33787bcc, 44512bbcc }}
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| [[Badness]] (Sintel): 2.89
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| == Tridecatonic ==
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| : ''For extensions, see [[Octagar temperaments #Tridecatonic]], [[Ragismic microtemperaments #Trideci]], and [[Varunismic temperaments #Bosonic]].''
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| Tridecatonic tempers out the [[devil's tridecalimma]], the comma which associates the [[10/9]] minor tone with [[13edo|2\13]].
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: {{monzo| -11 26 -13 }}
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| {{Mapping|legend=1| 13 0 -11 | 0 1 2 }}
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| : mapping generators: ~531441/500000, ~3
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| [[Optimal tuning]]s:
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| * [[WE]]: ~531441/500000 = 92.3166{{c}}, ~3/2 = 701.2353{{c}}
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| : [[error map]]: {{val| +0.116 -0.688 +0.737 }}
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| * [[CWE]]: ~531441/500000 = 92.3077{{c}}, ~3/2 = 701.2353{{c}}
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| : error map: {{val| 0.000 -0.797 +0.617 }}
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| {{Optimal ET sequence|legend=1| 26, 39, 65, 286, 351, 416, 481, 546 }}
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| [[Badness]] (Sintel): 10.3
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| == Triskaidekic ==
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| : ''For extensions, see [[Orwellismic temperaments #Triskaidekic]].''
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: 1220703125/1073741824
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| {{Mapping|legend=1| 13 0 30 | 0 1 0 }}
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| : Mapping generators: ~128/125, ~3
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| [[Optimal tuning]]s:
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| * [[WE]]: ~128/125 = 92.589{{c}}, ~3/2 = 698.263{{c}}
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| : [[error map]]: {{val| +3.656 -0.036 -8.647 }}
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| * [[CWE]]: ~128/125 = 92.308{{c}}, ~3/2 = 698.068{{c}}
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| : error map: {{val| 0.000 -3.887 -17.083 }}
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| {{Optimal ET sequence|legend=1| 13, 26, 91cc }}
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| [[Badness]] (Sintel): 52.6
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| {{Navbox fractional-octave}} | | {{Navbox fractional-octave}} |