11th-octave temperaments: Difference between revisions
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== 5-limit temperaments == | == 5-limit temperaments == | ||
=== Hendecapent === | === Hendecapent === | ||
This temperament has a period of 1/11 octave, which represents [[16/15]] in the 5-limit. There are some 7-limit extensions include [[#Hendecatonic|hendecatonic]] (22 & | This temperament has a period of 1/11 octave, which represents [[16/15]] in the 5-limit. There are some 7-limit extensions include [[Porwell temperaments #Hendecatonic|hendecatonic]] ({{nowrap| 22 & 77 }}) and [[#Hendeca|hendeca]] ({{nowrap| 22 & 33 }}). | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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: Mapping generators: ~16/15, ~3 | : Mapping generators: ~16/15, ~3 | ||
[[Optimal tuning]] ([[POTE]]): ~16/15 = | [[Optimal tuning]] ([[POTE]]): ~16/15 = 109.091, ~3/2 = 702.947 | ||
{{Optimal ET sequence|legend=1| 22, 55, 77, 99 }} | {{Optimal ET sequence|legend=1| 22, 55, 77, 99 }} | ||
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: Mapping generators: ~648/625, ~3 | : Mapping generators: ~648/625, ~3 | ||
[[Optimal tuning]] ([[POTE]]): ~648/625 = | [[Optimal tuning]] ([[POTE]]): ~648/625 = 109.091, ~3/2 = 703.829 | ||
{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }} | {{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }} | ||
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[[Badness]]: 0.727539 | [[Badness]]: 0.727539 | ||
== | == Hendeca == | ||
{{Distinguish|Hendec}} | |||
{{ | |||
This temperament has a period of 1/11 octave, nine of them represent [[7/4]] in the 7-limit, as well as [[#undeka|undeka]]. | This temperament has a period of 1/11 octave, nine of them represent [[7/4]] in the 7-limit, as well as [[#undeka|undeka]]. | ||
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{{Multival|legend=1| 11 -11 0 -43 -31 31 }} | {{Multival|legend=1| 11 -11 0 -43 -31 31 }} | ||
[[Optimal tuning]] ([[POTE]]): ~16/15 = | [[Optimal tuning]] ([[POTE]]): ~16/15 = 109.091, ~3/2 = 703.313 | ||
{{Optimal ET sequence|legend=1| 11, 22, 55d, 77d, 99dd }} | {{Optimal ET sequence|legend=1| 11, 22, 55d, 77d, 99dd }} | ||
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Mapping: {{mapping| 11 0 43 31 38 | 0 1 -1 0 0 }} | Mapping: {{mapping| 11 0 43 31 38 | 0 1 -1 0 0 }} | ||
Optimal tuning (POTE): ~16/15 = | Optimal tuning (POTE): ~16/15 = 109.091, ~3/2 = 703.090 | ||
{{Optimal ET sequence|legend=0| 11, 22, 55d, 77d, 99dd }} | {{Optimal ET sequence|legend=0| 11, 22, 55d, 77d, 99dd }} | ||
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{{Multival|legend=1| 11 11 0 -8 -31 -31 }} | {{Multival|legend=1| 11 11 0 -8 -31 -31 }} | ||
[[Optimal tuning]] ([[POTE]]): ~21/20 = | [[Optimal tuning]] ([[POTE]]): ~21/20 = 109.091, ~3/2 = 708.792 | ||
{{Optimal ET sequence|legend=1| 11c, 22 }} | {{Optimal ET sequence|legend=1| 11c, 22 }} | ||
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Mapping: {{mapping| 11 0 8 31 38 | 0 1 1 0 0 }} | Mapping: {{mapping| 11 0 8 31 38 | 0 1 1 0 0 }} | ||
Optimal tuning (POTE): ~21/20 = | Optimal tuning (POTE): ~21/20 = 109.091, ~3/2 = 706.768 | ||
{{Optimal ET sequence|legend=0| 11c, 22 }} | {{Optimal ET sequence|legend=0| 11c, 22 }} | ||
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Mapping: {{mapping| 11 0 8 31 38 23 | 0 1 1 0 0 1 }} | Mapping: {{mapping| 11 0 8 31 38 23 | 0 1 1 0 0 1 }} | ||
Optimal tuning (POTE): ~13/12 = | Optimal tuning (POTE): ~13/12 = 109.091, ~3/2 = 707.764 | ||
{{Optimal ET sequence|legend=0| 11cf, 22 }} | {{Optimal ET sequence|legend=0| 11cf, 22 }} | ||