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 [[877edo|877]], [[3313edo|3313]], [[4190edo|4190]], [[5067edo|5067]], [[5944edo|5944]], [[6821edo|6821]], [[7698edo|7698]], and [[11011edo|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 {{monzo| -32 33 0 -6 -1 }} and {{monzo| 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 ==

===2.3.7 subgroup 877&5067===

=== 2.3.7 subgroup 877&5067 ===

Commas: {{monzo| -428 371 0 -57 }}

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}}

===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

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}}

===2.3.7.11.13 subgroup 877&5067===

=== 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|]

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

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

@@ Line 1: / Line 1: @@
 {{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&gt; and |76 -8 0 -9 -11&gt; 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.
+'''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 {{monzo| -32 33 0 -6 -1 }} and {{monzo| 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 ==
-===2.3.7 subgroup 877&amp;5067===
+=== 2.3.7 subgroup 877&amp;5067 ===
 Commas: {{monzo| -428 371 0 -57 }}
 POTE generator: ~1605632/1594323 = 12.3149
-Mapping: [&lt;1 1 -1|, &lt;0 57 371|]
+Mapping: [{{val| 1 1 -1 }}, {{val| 0 57 371 }}]
 EDOs: {{EDOs|877, 4190, 5067, 5944, 6821, 7698, 8575}}
-===2.3.7.11 subgroup 877&amp;5067===
+=== 2.3.7.11 subgroup 877&amp;5067 ===
-Commas: |-32 33 0 -6 -1&gt;, |76 -8 0 -9 -11&gt;
+Commas: {{monzo| -32 33 0 -6 -1 }}, {{monzo| 76 -8 0 -9 -11 }}
 POTE generator: ~1605632/1594323 = 12.3150
-Mapping: [&lt;1 1 -1 7|, &lt;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}}
-===2.3.7.11.13 subgroup 877&amp;5067===
+=== 2.3.7.11.13 subgroup 877&amp;5067 ===
 Commas: 257330216/257298363, 53722307808/53710650917, 1786706395136/1786568061663
 POTE generator: ~1605632/1594323 = 12.3150
-Mapping: [&lt;1 1 -1 7 -10|, &lt;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}}