53edf: Difference between revisions

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~~'''53EDF''' is the [[EDF~~|~~equal division of the just perfect fifth]] into~~ 53 parts of 13.2444 [[cent|cents]] each, corresponding to 90.6041 [[edo]] (similar to every fifth step of [[453edo]]). It is related to the regular temperament which tempers out |-44 44 53 -53> in the 7-limit, which is supported by 90, 91, 181, 453, 544, 634, 725, 997, 1087, and 1178 EDOs.

==Related temperament==

== Theory ==

53edf corresponds to 90.6041[[edo]], similar to every fifth step of [[453edo]]. It is related to the [[regular temperament]] which [[tempering out|tempers out]] {{monzo| -44 44 53 -53 }} in the [[7-limit]], which is supported by {{EDOs| 90-, 91-, 181-, 453-, 544-, 634-, 725-, 997-, 1087-, and 1178edo }}.

=== Harmonics ===

{{Harmonics in equal|53|3|2|intervals=prime|collapsed=1|start=12|Approximation of prime harmonics in 53edf (continued)}}

== Related temperament ==

===7-limit 453&544&634===

Comma: |-44 44 53 -53>

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POTE generators: ~5/4 = 386.2004, ~3796875/3764768 = 13.2434

~~Map~~: [<1 1 0 0|, <0 53 0 44|, <0 0 1 1|]

Mapping: [<1 1 0 0|, <0 53 0 44|, <0 0 1 1|]

EDOs: 90, 91, 181, 453, 544, 634, 725, 997, 1087, 1178

EDOs: {{EDOs|90, 91, 181, 453, 544, 634, 725, 997, 1087, 1178}}

===7-limit 453&1178===

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POTE generator: ~3796875/3764768 = 13.2432

~~Map~~: [<1 1 -1 -1|, <0 53 301 345|]

Mapping: [<1 1 -1 -1|, <0 53 301 345|]

EDOs: 453, 725, 1178, 1631, 2084, 2809

EDOs: {{EDOs|453, 725, 1178, 1631, 2084, 2809}}

~~[[Category:Edf]]~~

~~[[Category:Edonoi]]~~

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-'''53EDF''' is the [[EDF|equal division of the just perfect fifth]] into 53 parts of 13.2444 [[cent|cents]] each, corresponding to 90.6041 [[edo]] (similar to every fifth step of [[453edo]]). It is related to the regular temperament which tempers out |-44 44 53 -53&gt; in the 7-limit, which is supported by 90, 91, 181, 453, 544, 634, 725, 997, 1087, and 1178 EDOs.
+{{Infobox ET}}
+{{ED intro|53}}
-==Related temperament==
+== Theory ==
+edf corresponds to 90.6041[[edo]], similar to every fifth step of [[453edo]]. It is related to the [[regular temperament]] which [[tempering out|tempers out]] {{monzo| -44 44 53 -53 }} in the [[7-limit]], which is supported by {{EDOs| 90-, 91-, 181-, 453-, 544-, 634-, 725-, 997-, 1087-, and 1178edo }}.
+=== Harmonics ===
+{{Harmonics in equal|53|3|2|intervals=prime}}
+{{Harmonics in equal|53|3|2|intervals=prime|collapsed=1|start=12|Approximation of prime harmonics in 53edf (continued)}}
+== Related temperament ==
 ===7-limit 453&amp;544&amp;634===
 Comma: |-44 44 53 -53&gt;
@@ Line 7: / Line 15: @@
 POTE generators: ~5/4 = 386.2004, ~3796875/3764768 = 13.2434
-Map: [&lt;1 1 0 0|, &lt;0 53 0 44|, &lt;0 0 1 1|]
+Mapping: [&lt;1 1 0 0|, &lt;0 53 0 44|, &lt;0 0 1 1|]
-EDOs: 90, 91, 181, 453, 544, 634, 725, 997, 1087, 1178
+EDOs: {{EDOs|90, 91, 181, 453, 544, 634, 725, 997, 1087, 1178}}
 ===7-limit 453&amp;1178===
@@ Line 16: / Line 24: @@
 POTE generator: ~3796875/3764768 = 13.2432
-Map: [&lt;1 1 -1 -1|, &lt;0 53 301 345|]
+Mapping: [&lt;1 1 -1 -1|, &lt;0 53 301 345|]
-EDOs: 453, 725, 1178, 1631, 2084, 2809
+EDOs: {{EDOs|453, 725, 1178, 1631, 2084, 2809}}
-[[Category:Edf]]
+{{Todo|cleanup|expand}}
-[[Category:Edonoi]]