User:Eliora/Proposed concept names: Difference between revisions
| Line 7: | Line 7: | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
Comma list: | Comma list: {{monzo|-1377 400 320}} | ||
Mapping: 80 1 343, 0 4 -5 | Mapping: [{{val|80 1 343}}, {{val|0 4 -5}}] | ||
Mapping generators: -568 165 132, 142 -41 -33 | Mapping generators: {{monzo|-568 165 132}}, {{monzo|142 -41 -33}} | ||
Optimal tuning (CTE): ~142 -41 -33 = 471.738 | Optimal tuning (CTE): ~{{monzo|142 -41 -33}} = 471.738 | ||
=== 7-limit === | === 7-limit === | ||
| Line 20: | Line 20: | ||
Comma list: 31528360107421875/31525197391593472, 3671492030322070514237964288/3666984506893654025644140625 | Comma list: 31528360107421875/31525197391593472, 3671492030322070514237964288/3666984506893654025644140625 | ||
Mapping: 80 1 343 -27, 0 4 -5 8 | Mapping:[{{val| 80 1 343 -27}}, {{val|0 4 -5 8}}] | ||
Mapping generators: ~31637227888/31381059609, ~7381125/5619712 | Mapping generators: ~31637227888/31381059609, ~7381125/5619712 | ||
| Line 31: | Line 31: | ||
Comma list: 9801/9800, 928760463360/928426965851, 68116944363978752/68116827392578125 | Comma list: 9801/9800, 928760463360/928426965851, 68116944363978752/68116827392578125 | ||
Mapping: 80 1 343 -27 434, 0 4 -5 8 5 | Mapping:[{{val|80 1 343 -27 434}}, {{val|0 4 -5 8 5}}] | ||
Mapping generators: ~262144/259875, ~2278125/1734656 | Mapping generators: ~262144/259875, ~2278125/1734656 | ||
| Line 42: | Line 42: | ||
Comma list: 9801/9800, 4100625/4100096, 14236560/14235529, 143327232/143286143 | Comma list: 9801/9800, 4100625/4100096, 14236560/14235529, 143327232/143286143 | ||
Mapping: 80 1 343 -27 434 13, 0 4 -5 8 5 9 | Mapping: [{{val|80 1 343 -27 434 13}}, {{0 4 -5 8 5 9}}] | ||
Mapping generators: ~77760/77077, ~130/99 | Mapping generators: ~77760/77077, ~130/99 | ||
Optimal tuning (CTE): ~130/99 = 471.734 | Optimal tuning (CTE): ~130/99 = 471.734 | ||
Revision as of 23:19, 19 September 2022
Prequartismic
Named because 3125edo was the only one confirmed for tempering out the quartisma before it's discovery as significance of the difference between 5 33/32s and 7/6. Defined as the 1259 & 3125 temperament.
Mercury
Defined as 720 & 1600, and named after the 80th element.
Subgroup: 2.3.5
Comma list: [-1377 400 320⟩
Mapping: [⟨80 1 343], ⟨0 4 -5]]
Mapping generators: [-568 165 132⟩, [142 -41 -33⟩
Optimal tuning (CTE): ~[142 -41 -33⟩ = 471.738
7-limit
Subgroup: 2.3.5.7
Comma list: 31528360107421875/31525197391593472, 3671492030322070514237964288/3666984506893654025644140625
Mapping:[⟨80 1 343 -27], ⟨0 4 -5 8]]
Mapping generators: ~31637227888/31381059609, ~7381125/5619712
Optimal tuning (CTE): ~7381125/5619712 = 471.734
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 928760463360/928426965851, 68116944363978752/68116827392578125
Mapping:[⟨80 1 343 -27 434], ⟨0 4 -5 8 5]]
Mapping generators: ~262144/259875, ~2278125/1734656
Optimal tuning (CTE): ~2278125/1734656 = 471.734
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 9801/9800, 4100625/4100096, 14236560/14235529, 143327232/143286143
Mapping: [⟨80 1 343 -27 434 13], Template:0 4 -5 8 5 9]
Mapping generators: ~77760/77077, ~130/99
Optimal tuning (CTE): ~130/99 = 471.734