User:Xenllium/7ed11: Difference between revisions
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Created page with "'''7ED11''' is the equal division of the 11th harmonic into seven parts of 593.0454 cents each. It is related to the temperament which tempers out 256/255, 2..." Tags: Mobile edit Mobile web edit |
Cmloegcmluin (talk | contribs) map → mapping |
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POTE generator: ~45/32 = 593.168 | POTE generator: ~45/32 = 593.168 | ||
Mapping: [<1 9 -13 -14 0|, <0 -15 31 34 7|] | |||
EDOs: 2, 87, 89, 176, 263 | EDOs: 2, 87, 89, 176, 263 | ||
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POTE generator: ~45/32 = 593.156 | POTE generator: ~45/32 = 593.156 | ||
Mapping: [<1 9 -13 -14 0 21|, <0 -15 31 34 7 -35|] | |||
EDOs: 2, 87, 89, 176, 263 | EDOs: 2, 87, 89, 176, 263 | ||
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POTE generator: ~24/17 = 593.165 | POTE generator: ~24/17 = 593.165 | ||
Mapping: [<1 9 -13 -14 0 21 12|, <0 -15 31 34 7 -35 -16|] | |||
EDOs: 2, 87, 89, 176g | EDOs: 2, 87, 89, 176g | ||
Revision as of 19:47, 5 November 2021
7ED11 is the equal division of the 11th harmonic into seven parts of 593.0454 cents each. It is related to the temperament which tempers out 256/255, 273/272, 364/363, 441/440, and 1690/1683 in the 17-limit, which is supported by 2edo, 87edo, and 89edo.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 593.0454 | 45/32, 24/17 | |
| 2 | 1186.0908 | 240/121, 143/72 | |
| 3 | 1779.1363 | 14/5 | |
| 4 | 2372.1817 | 55/14 | |
| 5 | 2965.2271 | 72/13 | |
| 6 | 3558.2725 | 187/24, 352/45 | |
| 7 | 4151.3179 | exact 11/1 | undecimal fourth plus three octaves |
Related temperament
11-limit 87&89
Commas: 441/440, 3388/3375, 16384/16335
POTE generator: ~45/32 = 593.168
Mapping: [<1 9 -13 -14 0|, <0 -15 31 34 7|]
EDOs: 2, 87, 89, 176, 263
13-limit 87&89
Commas: 364/363, 441/440, 2197/2187, 3388/3375
POTE generator: ~45/32 = 593.156
Mapping: [<1 9 -13 -14 0 21|, <0 -15 31 34 7 -35|]
EDOs: 2, 87, 89, 176, 263
17-limit 87&89
Commas: 256/255, 273/272, 364/363, 441/440, 2025/2023
POTE generator: ~24/17 = 593.165
Mapping: [<1 9 -13 -14 0 21 12|, <0 -15 31 34 7 -35 -16|]
EDOs: 2, 87, 89, 176g