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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 ==
| | == Hendecapent == |
| === 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 }}). | | 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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| [[Badness]] (Sintel): 10.7 | | [[Badness]] (Sintel): 10.7 |
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| === Undekapent ===
| | == Undekapent == |
| This temperament has a period of 1/11 octave, three of them represent [[6/5]] in the 5-limit. | | This temperament has a period of 1/11 octave, three of them represent [[6/5]] in the 5-limit. |
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| [[Badness]] (Sintel): 17.1 | | [[Badness]] (Sintel): 17.1 |
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| === Elven ===
| | == Elven == |
| {{See also| Sensibeta temperaments #Elven }} | | {{See also| Sensibeta temperaments #Elven }} |
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| [[Badness]] (Sintel): 429 | | [[Badness]] (Sintel): 429 |
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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]]s:
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| * [[WE]]: ~16/15 = 108.9526{{c}}, ~3/2 = 702.4215{{c}}
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| : [[error map]]: {{val| -1.521 -1.055 -2.252 +8.705 }}
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| * [[CWE]]: ~16/15 = 109.0909{{c}}, ~3/2 = 703.2071{{c}}
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| : error map: {{val| 0.000 +1.252 +1.388 +12.992 }}
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| {{Optimal ET sequence|legend=1| 11, 22, 55d, 77d, 99dd }}
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| [[Badness]] (Sintel): 4.37
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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 tunings:
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| * WE: ~16/15 = 109.0109{{c}}, ~3/2 = 702.5746{{c}}
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| * CWE: ~16/15 = 109.0909{{c}}, ~3/2 = 703.0395{{c}}
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| {{Optimal ET sequence|legend=0| 11, 22, 55d }}
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| Badness (Sintel): 2.46
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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]]s:
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| * [[WE]]: ~21/20 = 108.9318{{c}}, ~3/2 = 707.7579{{c}}
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| : [[error map]]: {{val| -1.750 +4.053 -8.852 +8.059 }}
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| * [[CWE]]: ~21/20 = 109.0909{{c}}, ~3/2 = 707.7526{{c}}
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| : error map: {{val| 0.000 +5.798 -5.834 +12.992 }}
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| {{Optimal ET sequence|legend=1| 11b, 22 }}
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| [[Badness]] (Sintel): 3.59
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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 tunings:
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| * WE: ~21/20 = 109.0321{{c}}, ~3/2 = 706.3870{{c}}
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| * CWE: ~21/20 = 109.0909{{c}}, ~3/2 = 706.4785{{c}}
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| {{Optimal ET sequence|legend=0| 11c, 22 }}
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| Badness (Sintel): 2.27
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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 tunings:
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| * WE: ~13/12 = 109.1184{{c}}, ~3/2 = 707.9422{{c}}
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| * CWE: ~13/12 = 109.0909{{c}}, ~3/2 = 707.9065{{c}}
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| {{Optimal ET sequence|legend=0| 11cf, 22 }}
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| Badness (Sintel): 2.34
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| {{Navbox fractional-octave}} | | {{Navbox fractional-octave}} |