57edf: Difference between revisions
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'''57EDF''' is the [[EDF|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent|cents]] each, corresponding to 97.4421 [[edo]]. It is related to the regular temperament which tempers out |-32 33 0 -6 -1> and |76 -8 0 -9 -11> in the 11-limit, which is supported by 877, 3313, 4190, 5067, 5944, 6821, 7698, and 11011 EDOs. | '''57EDF''' is the [[EDF|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent|cents]] each, corresponding to 97.4421 [[edo]]. It is related to the regular temperament which tempers out |-32 33 0 -6 -1> and |76 -8 0 -9 -11> in the 11-limit, which is supported by [[877edo|877]], [[3313edo|3313]], [[4190edo|4190]], [[5067edo|5067]], [[5944edo|5944]], [[6821edo|6821]], [[7698edo|7698]], and [[11011edo|11011]] EDOs. | ||
==Related regular temperaments== | ==Related regular temperaments== | ||
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Mapping: [<1 1 -1|, <0 57 371|] | Mapping: [<1 1 -1|, <0 57 371|] | ||
EDOs: 877, 4190, 5067, 5944, 6821, 7698, 8575 | EDOs: {{EDOs|877, 4190, 5067, 5944, 6821, 7698, 8575}} | ||
===2.3.7.11 subgroup 877&5067=== | ===2.3.7.11 subgroup 877&5067=== | ||
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Mapping: [<1 1 -1 7|, <0 57 371 -345|] | Mapping: [<1 1 -1 7|, <0 57 371 -345|] | ||
EDOs: 877, 3313, 4190, 5067, 5944, 6821, 7698, 11011 | EDOs: {{EDOs|877, 3313, 4190, 5067, 5944, 6821, 7698, 11011}} | ||
===2.3.7.11.13 subgroup 877&5067=== | ===2.3.7.11.13 subgroup 877&5067=== | ||
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Mapping: [<1 1 -1 7 -10|, <0 57 371 -345 1335|] | Mapping: [<1 1 -1 7 -10|, <0 57 371 -345 1335|] | ||
EDOs: 877, 3313, 4190, 5067, 5944, 9257 | EDOs: {{EDOs|877, 3313, 4190, 5067, 5944, 9257}} | ||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 07:41, 7 May 2023
| ← 56edf | 57edf | 58edf → |
57EDF is the equal division of the just perfect fifth into 57 parts of 12.3150 cents each, corresponding to 97.4421 edo. It is related to the regular temperament which tempers out |-32 33 0 -6 -1> and |76 -8 0 -9 -11> in the 11-limit, which is supported by 877, 3313, 4190, 5067, 5944, 6821, 7698, and 11011 EDOs.
Related regular temperaments
2.3.7 subgroup 877&5067
Commas: |-428 371 0 -57>
POTE generator: ~1605632/1594323 = 12.3149
Mapping: [<1 1 -1|, <0 57 371|]
EDOs: 877, 4190, 5067, 5944, 6821, 7698, 8575
2.3.7.11 subgroup 877&5067
Commas: |-32 33 0 -6 -1>, |76 -8 0 -9 -11>
POTE generator: ~1605632/1594323 = 12.3150
Mapping: [<1 1 -1 7|, <0 57 371 -345|]
EDOs: 877, 3313, 4190, 5067, 5944, 6821, 7698, 11011
2.3.7.11.13 subgroup 877&5067
Commas: 257330216/257298363, 53722307808/53710650917, 1786706395136/1786568061663
POTE generator: ~1605632/1594323 = 12.3150
Mapping: [<1 1 -1 7 -10|, <0 57 371 -345 1335|]