Miscellaneous 5-limit temperaments: Difference between revisions
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Move aluminium, tridecatonic, and triskaidekic here |
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[[Badness]] (Sintel): 2.88 | [[Badness]] (Sintel): 2.88 | ||
== Aluminium == | |||
: ''For extensions, see [[Ragismic microtemperaments #Aluminium]].'' | |||
Aluminium tempers out {{monzo| 92 -39 -13 }} in the 5-limit, and sets [[135/128]] to 1/13 of an [[octave]]. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| 92 -39 -13 }} | |||
{{Mapping|legend=1| 13 0 92 | 0 1 -3 }} | |||
: mapping generators: ~135/128, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~135/128 = 92.3068{{c}}, ~3/2 = 701.9791{{c}} | |||
: [[error map]]: {{val| -0.012 +0.012 +0.009 }} | |||
* [[CWE]]: ~135/128 = 92.3077{{c}}, ~3/2 = 701.9897{{c}} | |||
: error map: {{val| 0.000 +0.032 +0.033 }} | |||
{{Optimal ET sequence|legend=1| 65, 299, 364, 429, 494, 559, 1053, 1612, 5889, 7501, 9113, 10725, 23062bc, 33787bcc, 44512bbcc }} | |||
[[Badness]] (Sintel): 2.89 | |||
== Avila == | == Avila == | ||
| Line 553: | Line 575: | ||
Scales (Scala files): [[wizard22]] | Scales (Scala files): [[wizard22]] | ||
== Tridecatonic == | |||
: ''For extensions, see [[Octagar temperaments #Tridecatonic]], [[Ragismic microtemperaments #Trideci]], and [[Varunismic temperaments #Bosonic]].'' | |||
Tridecatonic tempers out the [[devil's tridecalimma]], the comma which associates the [[10/9]] minor tone with [[13edo|2\13]]. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| -11 26 -13 }} | |||
{{Mapping|legend=1| 13 0 -11 | 0 1 2 }} | |||
: mapping generators: ~531441/500000, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~531441/500000 = 92.3166{{c}}, ~3/2 = 701.2353{{c}} | |||
: [[error map]]: {{val| +0.116 -0.688 +0.737 }} | |||
* [[CWE]]: ~531441/500000 = 92.3077{{c}}, ~3/2 = 701.2353{{c}} | |||
: error map: {{val| 0.000 -0.797 +0.617 }} | |||
{{Optimal ET sequence|legend=1| 26, 39, 65, 286, 351, 416, 481, 546 }} | |||
[[Badness]] (Sintel): 10.3 | |||
== Merman == | == Merman == | ||
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[[Badness]] (Sintel): 52.3 | [[Badness]] (Sintel): 52.3 | ||
== Triskaidekic == | |||
: ''For extensions, see [[Orwellismic temperaments #Triskaidekic]].'' | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 1220703125/1073741824 | |||
{{Mapping|legend=1| 13 0 30 | 0 1 0 }} | |||
: Mapping generators: ~128/125, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~128/125 = 92.589{{c}}, ~3/2 = 698.263{{c}} | |||
: [[error map]]: {{val| +3.656 -0.036 -8.647 }} | |||
* [[CWE]]: ~128/125 = 92.308{{c}}, ~3/2 = 698.068{{c}} | |||
: error map: {{val| 0.000 -3.887 -17.083 }} | |||
{{Optimal ET sequence|legend=1| 13, 26, 91cc }} | |||
[[Badness]] (Sintel): 52.6 | |||
== Satin == | == Satin == | ||