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| An 11th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 11. Although [[11edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 11 are. | | An 11th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 11. Although [[11edo]] itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 11 are. |
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| == 5-limit temperaments ==
| | Temperaments discussed elsewhere are [[keemic temperaments #Undeka|undeka]], [[marvel temperaments #Hendeka|hendeka]], [[porwell temperaments #Hendecatonic|hendecatonic]], and [[Sensibeta temperaments #Elven|elven]]. |
| === Hendecapent ===
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| 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 }}).
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: 8796093022208/8649755859375
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| {{Mapping|legend=1| 11 0 43 | 0 1 -1 }}
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| : Mapping generators: ~16/15, ~3
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| [[Optimal tuning]]s: | |
| * [[CTE]]: ~16/15 = 109.091¢, ~3/2 = 702.794¢
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| * [[CWE]]: ~16/15 = 109.091¢, ~3/2 = 702.908¢
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| {{Optimal ET sequence|legend=1| 22, 55, 77, 99 }}
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| [[Badness]] (Sintel): 10.652
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| === Undekapent ===
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| This temperament has a period of 1/11 octave, three of them represent [[6/5]] in the 5-limit.
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: 48828125/45349632 | |
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| {{Mapping|legend=1| 11 0 8 | 0 1 1 }}
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| : Mapping generators: ~648/625, ~3
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| [[Optimal tuning]]s:
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| * [[CTE]]: ~648/625 = 109.091¢, ~3/2 = 705.652¢
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| * [[CWE]]: ~648/625 = 109.091¢, ~3/2 = 704.698¢
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| {{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}
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| [[Badness]] (Sintel): 17.067
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| === Elven ===
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| {{see also| Sensibeta temperaments #Elven }}
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| This temperament has a period of 1/11 octave, which represents [[3125/2916]] in the 5-limit.
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| [[Subgroup]]: 2.3.5
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| [[Comma list]]: {{monzo|-23 -66 55}}
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| {{Mapping|legend=1| 11 2 7 | 0 5 6 }}
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| : Mapping generators: ~3125/2916, ~{{monzo| 10 29 -24 }}
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| [[Optimal tuning]]s:
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| * [[CTE]]: ~3125/2916 = 109.091¢, ~5/3 = 882.353¢
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| * [[CWE]]: ~3125/2916 = 109.091¢, ~5/3 = 882.336¢
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| {{Optimal ET sequence|legend=1| 121, 253, 374 }}
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| [[Badness]] (Sintel): 429.4
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| == Hendeca ==
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| {{Distinguish|Hendec}}
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| 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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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 225/224, 122880/117649
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| {{Mapping|legend=1| 11 0 43 31 | 0 1 -1 0 }}
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| : Mapping generators: ~16/15, ~3
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| [[Optimal tuning]] ([[POTE]]): ~16/15 = 109.091, ~3/2 = 703.313
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| {{Optimal ET sequence|legend=1| 11, 22, 55d, 77d, 99dd }}
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| [[Badness]] (Sintel): 4.371
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 121/120, 225/224, 352/343
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| Mapping: {{mapping| 11 0 43 31 38 | 0 1 -1 0 0 }}
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| Optimal tuning (POTE): ~16/15 = 109.091, ~3/2 = 703.090
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| {{Optimal ET sequence|legend=0| 11, 22, 55d, 77d, 99dd }}
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| Badness (Sintel): 2.464
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| == Undeka ==
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 875/864, 3200/3087
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| {{Mapping|legend=1| 11 0 8 31 | 0 1 1 0 }}
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| : Mapping generators: ~21/20, ~3
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| [[Optimal tuning]] ([[POTE]]): ~21/20 = 109.091, ~3/2 = 708.792
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| {{Optimal ET sequence|legend=1| 11c, 22 }}
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| [[Badness]] (Sintel): 3.588
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 100/99, 352/343, 385/384
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| Mapping: {{mapping| 11 0 8 31 38 | 0 1 1 0 0 }}
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| Optimal tuning (POTE): ~21/20 = 109.091, ~3/2 = 706.768
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| {{Optimal ET sequence|legend=0| 11c, 22 }}
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| Badness (Sintel): 2.270
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 65/63, 100/99, 169/165, 352/343
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| Mapping: {{mapping| 11 0 8 31 38 23 | 0 1 1 0 0 1 }}
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| Optimal tuning (POTE): ~13/12 = 109.091, ~3/2 = 707.764
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| {{Optimal ET sequence|legend=0| 11cf, 22 }}
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| Badness (Sintel): 2.336
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| {{Navbox fractional-octave}} | | {{Navbox fractional-octave}} |