Miscellaneous 5-limit temperaments: Difference between revisions
m →Neon: + see also |
Move hendecatonic, undeka, and elven here |
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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 [[2/1|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 [[2/1|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): 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]] | ||