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{{Infobox ET}}
{{Infobox ET}}
'''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.
{{ED intro}}


==Related regular temperaments==
== Theory ==
===2.3.7 subgroup 877&5067===
57edf corresponds to 97.4421[[edo]]. It is related to the [[regular temperament]] which [[tempering out|tempers out]] {{monzo| -32 33 0 -6 -1 }} and {{monzo| 76 -8 0 -9 -11 }} in the [[11-limit]], which is supported by {{EDOs| 877-, 3313-, 4190-, 5067-, 5944-, 6821-, 7698-, and 11011edo }}.
Commas: |-428 371 0 -57>
 
=== Harmonics ===
{{Harmonics in equal|57|3|2}}
{{Harmonics in equal|57|3|2|start=12|collapsed=true|title=Approximation of harmonics in 57edf (continued)}}
 
== Related regular temperaments ==
=== 2.3.7 subgroup 877&5067 ===
Commas: {{monzo| -428 371 0 -57 }}


POTE generator: ~1605632/1594323 = 12.3149
POTE generator: ~1605632/1594323 = 12.3149


Mapping: [<1 1 -1|, <0 57 371|]
Mapping: [{{val| 1 1 -1 }}, {{val| 0 57 371 }}]


EDOs: {{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 ===
Commas: |-32 33 0 -6 -1>, |76 -8 0 -9 -11>
Commas: {{monzo| -32 33 0 -6 -1 }}, {{monzo| 76 -8 0 -9 -11 }}


POTE generator: ~1605632/1594323 = 12.3150
POTE generator: ~1605632/1594323 = 12.3150


Mapping: [<1 1 -1 7|, <0 57 371 -345|]
Mapping: [{{val| 1 1 -1 7 }}, {{val| 0 57 371 -345 }}]


EDOs: {{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 ===
Commas: 257330216/257298363, 53722307808/53710650917, 1786706395136/1786568061663
Commas: 257330216/257298363, 53722307808/53710650917, 1786706395136/1786568061663


POTE generator: ~1605632/1594323 = 12.3150
POTE generator: ~1605632/1594323 = 12.3150


Mapping: [<1 1 -1 7 -10|, <0 57 371 -345 1335|]
Mapping: [{{val| 1 1 -1 7 -10 }}, {{val| 0 57 371 -345 1335 }}]


EDOs: {{EDOs|877, 3313, 4190, 5067, 5944, 9257}}
EDOs: {{EDOs|877, 3313, 4190, 5067, 5944, 9257}}
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{{Interval table}}
{{Interval table}}


== Harmonics ==
{{Todo|cleanup}}
{{Harmonics in equal
| steps = 57
| num = 3
| denom = 2
}}
{{Harmonics in equal
| steps = 57
| num = 3
| denom = 2
| start = 12
| collapsed = 1
}}
 
[[Category:Edf]]
[[Category:Edonoi]]
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