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Line 3: |
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| Although 21edo itself is not remarkably accurate for low-complexity harmonics, some temperaments which are multiples of 21, such as {{EDOs|441, 1407, and 1848}} are. 441 and 1848 are also members of [[zeta]] edo list. | | Although 21edo itself is not remarkably accurate for low-complexity harmonics, some temperaments which are multiples of 21, such as {{EDOs|441, 1407, and 1848}} are. 441 and 1848 are also members of [[zeta]] edo list. |
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| | Temperaments discussed elsewhere include |
| | * ''[[Akjayland]]'' → [[Landscape microtemperaments #Akjayland|Landscape microtemperaments]] |
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| == 21-23-commatic == | | == 21-23-commatic == |
| Subgroup: 2.23 | | Subgroup: 2.23 |
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Line 17: |
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| [[Support]]ing [[ET]]s: 21N, N = 1 to 96, largest: [[2016edo]] | | [[Support]]ing [[ET]]s: 21N, N = 1 to 96, largest: [[2016edo]] |
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| == Akjayland ==
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| {{See also| Landscape microtemperaments #Akjayland }}
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 250047/250000, {{monzo| 43 -1 -13 -4 }}
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| [[Mapping]]: [{{val| 21 1 38 102 }}, {{val| 0 3 1 -4 }}]
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| Mapping generators: ~1323/1280, ~131072/91875
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| [[Optimal tuning]] ([[CTE]]): ~131072/91875 = 614.9354
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| {{Optimal ET sequence|legend=1| 84, 273, 357, 441, 966, 1407, 1848, 7833, 9681, 11529, 13377c }}
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| [[Badness]]: 0.0309
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| === Vasca ===
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| Vasca can be described as the 357 & 525 temperament, extended as high as the 23-limit. It tempers out the {{monzo| 95 0 0 0 0 0 0 0 -21 }}, and sets a stack of 21 [[23/16]]'s equal with 11 octaves. The name derives from elements vanadium (23) and scandium (21), since this uses the 23rd harmonic, which itself is extremely well represented in 21edo.
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| Subgroup: 2.3.5.7.11
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| Comma list: 3025/3024, 102487/102400, {{monzo| 39 -4 -11 -5 2 }}
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| Mapping: [{{val| 21 4 39 98 58 }}, {{val| 0 6 2 -8 3 3 }}]
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| Mapping generators: ~1323/1280, ~6615/5632
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| Optimal tuning (CTE): ~6615/5632 = 278.8998
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| {{Optimal ET sequence|legend=1| 168, 357, 525, 882, 1407, 2289e }}
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| Badness: 0.0949
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 3025/3024, 4096/4095, 14641/14625, 85750/85683
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| Mapping: [{{val| 21 4 39 98 58 107 }}, {{val| 0 6 2 -8 3 -6 }}]
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| Optimal tuning (CTE): ~168/143 = 278.9058
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| {{Optimal ET sequence|legend=1| 168, 357, 525, 882 }}
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| Badness: 0.0551
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 2601/2600, 3025/3024, 4096/4095, 8624/8619, 14641/14625
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| Mapping: [{{val| 21 4 39 98 58 107 120 }}, {{val| 0 6 2 -8 3 -6 -7 }}]
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| Optimal tuning (CTE): ~168/143 = 278.9036
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| {{Optimal ET sequence|legend=1| 168, 357, 525, 882 }}
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| Badness: 0.0319
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| ==== 19-limit ====
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| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: 2376/2375, 2601/2600, 2926/2925, 3025/3024, 3213/3211, 4096/4095
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| Mapping: [{{val| 21 4 39 98 58 107 120 16 }}, {{val| 0 6 2 -8 3 -6 -7 15 }}]
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| Optimal tuning (CTE): ~168/143 = 278.9036
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| {{Optimal ET sequence|legend=1| 168h, 357, 525, 882, 1407 }}
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| Badness: 0.0270
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| ==== 23-limit ====
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| Subgroup: 2.3.5.7.11.13.17.19.23
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| Comma list: 1496/1495, 2376/2375, 2601/2600, 2646/2645, 2926/2925, 3025/3024, 3213/3211
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| Mapping: [{{val| 21 34 49 58 73 77 85 91 95 }}, {{val| 0 -6 -2 8 -3 6 7 -15 0 }}]
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| Optimal tuning (CTE): ~168/143 = 278.8971
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| {{Optimal ET sequence|legend=1| 168h, 357, 525, 882, 1407 }}
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| Badness: 0.0199
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| == Scandium == | | == Scandium == |