Miscellaneous 5-limit temperaments: Difference between revisions
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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): 10.6 | [[Badness]] (Sintel): 10.6 | ||
== Hendecatonic == | |||
: ''For extensions, see [[Porwell temperaments #Hendecatonic]] and [[Marvel temperaments #Hendeca]].'' | |||
The 5-limit version of hendecatonic simply equates a stack of eleven [[16/15]]'s with the [[octave]]. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 8796093022208/8649755859375 | |||
{{Mapping|legend=1| 11 0 43 | 0 1 -1 }} | |||
: Mapping generators: ~16/15, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~16/15 = 109.0904{{c}}, ~3/2 = 702.6861{{c}} | |||
: [[error map]]: {{val| -0.445 +0.286 +0.613 }} | |||
* [[CWE]]: ~16/15 = 109.0909{{c}}, ~3/2 = 702.9082{{c}} | |||
: error map: {{val| 0.000 +0.953 +1.687 }} | |||
{{Optimal ET sequence|legend=1| 22, 55, 77, 99, 869bcc, 968bcc, 1067bccc, 1166bccc }} | |||
[[Badness]] (Sintel): 10.7 | |||
== Nusecond == | == Nusecond == | ||
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[[Badness]] (Sintel): 17.0 | [[Badness]] (Sintel): 17.0 | ||
== Undeka == | |||
: ''For extensions, see [[Keemic temperaments #Undeka]].'' | |||
Undeka has a period of 1/11 octave, like [[#Hendecatonic|hendecatonic]], but this temperament equates a stack of eleven 6/5's and three [[octave]]s, so that three periods represent [[6/5]]. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 48828125/45349632 | |||
{{Mapping|legend=1| 11 0 8 | 0 1 1 }} | |||
: Mapping generators: ~648/625, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~648/625 = 109.1809{{c}}, ~3/2 = 704.4091{{c}} | |||
: [[error map]]: {{val| +0.990 +3.444 -7.468 }} | |||
* [[CWE]]: ~648/625 = 109.0909{{c}}, ~3/2 = 704.6983{{c}} | |||
: error map: {{val| 0.000 +2.743 -8.888 }} | |||
{{Optimal ET sequence|legend=1| 22, 77c, 99c }} | |||
[[Badness]] (Sintel): 17.1 | |||
== Kumonga == | == Kumonga == | ||
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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 == | ||
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[[Badness]] (Sintel): 203 | [[Badness]] (Sintel): 203 | ||
== Elven == | |||
: ''For extensions, see [[Sensibeta temperaments #Elven]].'' | |||
Elven has a period of 1/11 octave, like [[#Hendecatonic|hendecatonic]], but this temperament equates a stack of eleven [[3125/2916]]'s with the octave. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| -23 -66 55 }} | |||
{{Mapping|legend=1| 11 2 7 | 0 5 6 }} | |||
: mapping generators: ~3125/2916, ~{{monzo| 10 29 -24 }} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~3125/2916 = 109.0998{{c}}, ~{{monzo| 10 29 -24 }} = 336.8921{{c}} | |||
: [[error map]]: {{val| +0.097 +0.705 -1.263 }} | |||
* [[CWE]]: ~3125/2916 = 109.0909{{c}}, ~{{monzo| 10 29 -24 }} = 336.8814{{c}} | |||
: error map: {{val| 0.000 +0.634 -1.389 }} | |||
{{Optimal ET sequence|legend=1| 121, 253, 374, 627c }} | |||
[[Badness]] (Sintel): 429 | |||
== References == | == References == | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||