|
|
| (7 intermediate revisions by 3 users not shown) |
| Line 3: |
Line 3: |
| 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. |
|
| |
|
| == 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 ===
| |
| 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 & 77) and [[#Hendeca|hendeca]] (22 & 33).
| |
| | |
| [[Subgroup]]: 2.3.5
| |
| | |
| [[Comma list]]: 8796093022208/8649755859375
| |
| | |
| {{Mapping|legend=1| 11 0 43 | 0 1 -1 }}
| |
| | |
| : Mapping generators: ~16/15, ~3
| |
| | |
| [[Optimal tuning]] ([[POTE]]): ~16/15 = 1＼11, ~3/2 = 702.947
| |
| | |
| {{Optimal ET sequence|legend=1| 22, 55, 77, 99 }}
| |
| | |
| [[Badness]]: 0.454083
| |
| | |
| === Undekapent ===
| |
| This temperament has a period of 1/11 octave, three of them represent [[6/5]] in the 5-limit.
| |
| | |
| [[Subgroup]]: 2.3.5 | |
| | |
| [[Comma list]]: 48828125/45349632
| |
| | |
| {{Mapping|legend=1| 11 0 8 | 0 1 1 }}
| |
| | |
| : Mapping generators: ~648/625, ~3
| |
| | |
| [[Optimal tuning]] ([[POTE]]): ~648/625 = 1＼11, ~3/2 = 703.829
| |
| | |
| {{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}
| |
| | |
| [[Badness]]: 0.727539
| |
| | |
| == Hendecatonic ==
| |
| : <Small>''For 11-limit extensions, see [[Porwell temperaments #Hendecatonic]].''</small>
| |
| | |
| This temperament has a period of 1/11 octave, four of them represent [[9/7]] in the 7-limit.
| |
| | |
| [[Subgroup]]: 2.3.5.7
| |
| | |
| [[Comma list]]: 6144/6125, 10976/10935
| |
| | |
| {{Mapping|legend=1| 11 0 43 -4 | 0 1 -1 2 }}
| |
| | |
| : Mapping generators: ~16/15, ~3
| |
| | |
| {{Multival|legend=1| 11 -11 22 -43 4 82 }}
| |
| | |
| [[Optimal tuning]] ([[POTE]]): ~16/15 = 1＼11, ~3/2 = 703.054
| |
| | |
| {{Optimal ET sequence|legend=1| 22, 55, 77, 99 }}
| |
| | |
| [[Badness]]: 0.041081
| |
| | |
| == 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]].
| |
| | |
| [[Subgroup]]: 2.3.5.7
| |
| | |
| [[Comma list]]: 225/224, 122880/117649
| |
| | |
| {{Mapping|legend=1| 11 0 43 31 | 0 1 -1 0 }}
| |
| | |
| : Mapping generators: ~16/15, ~3
| |
| | |
| {{Multival|legend=1| 11 -11 0 -43 -31 31 }}
| |
| | |
| [[Optimal tuning]] ([[POTE]]): ~16/15 = 1＼11, ~3/2 = 703.313
| |
| | |
| {{Optimal ET sequence|legend=1| 11, 22, 55d, 77d, 99dd }}
| |
| | |
| [[Badness]]: 0.172714
| |
| | |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 121/120, 225/224, 352/343
| |
| | |
| Mapping: {{mapping| 11 0 43 31 38 | 0 1 -1 0 0 }}
| |
| | |
| Optimal tuning (POTE): ~16/15 = 1＼11, ~3/2 = 703.090
| |
| | |
| {{Optimal ET sequence|legend=0| 11, 22, 55d, 77d, 99dd }}
| |
| | |
| Badness: 0.074543
| |
| | |
| == Undeka ==
| |
| [[Subgroup]]: 2.3.5.7
| |
| | |
| [[Comma list]]: 875/864, 3200/3087
| |
| | |
| {{Mapping|legend=1| 11 0 8 31 | 0 1 1 0 }}
| |
| | |
| : Mapping generators: ~21/20, ~3
| |
| | |
| {{Multival|legend=1| 11 11 0 -8 -31 -31 }}
| |
| | |
| [[Optimal tuning]] ([[POTE]]): ~21/20 = 1＼11, ~3/2 = 708.792
| |
| | |
| {{Optimal ET sequence|legend=1| 11c, 22 }}
| |
| | |
| [[Badness]]: 0.141782
| |
| | |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 100/99, 352/343, 385/384
| |
| | |
| Mapping: {{mapping| 11 0 8 31 38 | 0 1 1 0 0 }}
| |
| | |
| Optimal tuning (POTE): ~21/20 = 1＼11, ~3/2 = 706.768
| |
| | |
| {{Optimal ET sequence|legend=0| 11c, 22 }}
| |
| | |
| Badness: 0.068672
| |
| | |
| === 13-limit ===
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 65/63, 100/99, 169/165, 352/343
| |
| | |
| Mapping: {{mapping| 11 0 8 31 38 23 | 0 1 1 0 0 1 }}
| |
| | |
| Optimal tuning (POTE): ~13/12 = 1＼11, ~3/2 = 707.764
| |
| | |
| {{Optimal ET sequence|legend=0| 11cf, 22 }}
| |
| | |
| Badness: 0.056528
| |
|
| |
|
| {{Navbox fractional-octave}} | | {{Navbox fractional-octave}} |
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
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.
Temperaments discussed elsewhere are undeka, hendeka, hendecatonic, and elven.