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.

==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|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

~~Map~~: [~~<~~1 1 -1|~~, <~~0 57 371|]

Mapping: [{{val| 1 1 -1 }}, {{val| 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 ===

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

~~Map~~: [~~<~~1 1 -1 7|~~, <~~0 57 371 -345|]

Mapping: [{{val| 1 1 -1 7 }}, {{val| 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 ===

Commas: 257330216/257298363, 53722307808/53710650917, 1786706395136/1786568061663

POTE generator: ~1605632/1594323 = 12.3150

~~Map~~: [~~<~~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: 877, 3313, 4190, 5067, 5944, 9257~~

== Intervals ==

~~[[Category:Edf]]~~

~~[[Category:Edonoi]]~~

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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&gt; and |76 -8 0 -9 -11&gt; in the 11-limit, which is supported by 877, 3313, 4190, 5067, 5944, 6821, 7698, and 11011 EDOs.
+{{Infobox ET}}
+{{ED intro}}
-==Related regular temperaments==
+== Theory ==
-===2.3.7 subgroup 877&amp;5067===
+edf 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&gt;
+=== 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&amp;5067 ===
+Commas: {{monzo| -428 371 0 -57 }}
 POTE generator: ~1605632/1594323 = 12.3149
-Map: [&lt;1 1 -1|, &lt;0 57 371|]
+Mapping: [{{val| 1 1 -1 }}, {{val| 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&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
-Map: [&lt;1 1 -1 7|, &lt;0 57 371 -345|]
+Mapping: [{{val| 1 1 -1 7 }}, {{val| 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&amp;5067===
+=== 2.3.7.11.13 subgroup 877&amp;5067 ===
 Commas: 257330216/257298363, 53722307808/53710650917, 1786706395136/1786568061663
 POTE generator: ~1605632/1594323 = 12.3150
-Map: [&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}}
-EDOs: 877, 3313, 4190, 5067, 5944, 9257
+== Intervals ==
+{{Interval table}}
-[[Category:Edf]]
+{{Todo|cleanup}}
-[[Category:Edonoi]]