43edf: Difference between revisions

(5 intermediate revisions by 5 users not shown)

Line 1:

'''43EDF''' is the [[EDF|equal division of the just perfect fifth]] into 43 parts of 16.3245 [[cent|cents]] each, corresponding to 73.5090 [[edo]] (similar to every second step of [[147edo]]). It is related to the [[microtempering|microtemperament]] which tempers out |-135 135 -86 43> (0.45970 cents) in the 7-limit, which is supported by 441, 4190, 4631, 5072, 7204, 11394, 11835, 12276, and 16466 EDOs.

==Related temperament==

== Theory ==

===7-limit 441&4631&12276===

43edf corresponds to 73.5090 [[edo]], similar to every second step of [[147edo]]. It is related to the [[microtemperament]] which [[tempering out|tempers out]] {{monzo| -135 135 -86 43 }} (0.45970 cents) in the [[7-limit]], which is supported by {{EDOs| 441-, 4190-, 4631-, 5072-, 7204-, 11394-, 11835-, 12276-, and 16466edo }}.

=== Harmonics ===

{{Harmonics in equal|43|3|2|start=12|collapsed=true|title=Approximation of harmonics in 43edf (continued)}}

== Related temperament ==

===7-limit 441 & 4631 & 12276===

Comma: |-135 135 -86 43>

POTE generators: ~5/4 = 386.3143, ~|-22 22 -14 7> = 16.3245

~~Map~~: [<1 1 0 0|, <0 43 0 -135|, <0 0 1 2|]

Mapping: [<1 1 0 0|, <0 43 0 -135|, <0 0 1 2|]

EDOs: 441, 3749, 4190, 4631, 5072, 5513, 6763, 7204, 11394, 11835, 12276, 12717, 16466, 23229, 24111

EDOs: {{EDOs|441, 3749, 4190, 4631, 5072, 5513, 6763, 7204, 11394, 11835, 12276, 12717, 16466, 23229, 24111}}

===11-limit 441&4631&12276===

Line 16:

Line 24:

POTE generators: ~5/4 = 386.3178, ~|-22 22 -14 7> = 16.3245

~~Map~~: [<1 1 0 0 -2|, <0 43 0 -135 572|, <0 0 1 2 -1|]

Mapping: [<1 1 0 0 -2|, <0 43 0 -135 572|, <0 0 1 2 -1|]

EDOs: 441, 3455, 3749, 3896, 4190, 4631, 7645, 8086, 8821, 11835, 12276, 16466, 16907, 24111, 28742

EDOs: {{EDOs|441, 3455, 3749, 3896, 4190, 4631, 7645, 8086, 8821, 11835, 12276, 16466, 16907, 24111, 28742}}

===13-limit 441&4631&12276===

===13-limit 441 & 4631 & 12276===

Commas: 33792000/33787663, 703096443/703040000, 33319272448/33317578125

POTE generators: ~5/4 = 386.3240, ~|-22 22 -14 7> = 16.3246

~~Map~~: [<1 1 0 0 -2 2|, <0 43 0 -135 572 125|, <0 0 1 2 -1 0|]

Mapping: [<1 1 0 0 -2 2|, <0 43 0 -135 572 125|, <0 0 1 2 -1 0|]

EDOs: 441, 3455, 3749, 3896, 4190, 4631, 7645, 8086, 8821, 12276

EDOs: {{EDOs|441, 3455, 3749, 3896, 4190, 4631, 7645, 8086, 8821, 12276}}

~~[[Category:Edf]]~~

~~[[Category:Edonoi]]~~

@@ Line 1: / Line 1: @@
-'''43EDF''' is the [[EDF|equal division of the just perfect fifth]] into 43 parts of 16.3245 [[cent|cents]] each, corresponding to 73.5090 [[edo]] (similar to every second step of [[147edo]]). It is related to the [[microtempering|microtemperament]] which tempers out |-135 135 -86 43&gt; (0.45970 cents) in the 7-limit, which is supported by 441, 4190, 4631, 5072, 7204, 11394, 11835, 12276, and 16466 EDOs.
+{{Infobox ET}}
+{{ED intro}}
-==Related temperament==
+== Theory ==
-===7-limit 441&amp;4631&amp;12276===
+edf corresponds to 73.5090 [[edo]], similar to every second step of [[147edo]]. It is related to the [[microtemperament]] which [[tempering out|tempers out]] {{monzo| -135 135 -86 43 }} (0.45970 cents) in the [[7-limit]], which is supported by {{EDOs| 441-, 4190-, 4631-, 5072-, 7204-, 11394-, 11835-, 12276-, and 16466edo }}.
+=== Harmonics ===
+{{Harmonics in equal|43|3|2}}
+{{Harmonics in equal|43|3|2|start=12|collapsed=true|title=Approximation of harmonics in 43edf (continued)}}
+== Related temperament ==
+===7-limit 441 &amp; 4631 &amp; 12276===
 Comma: |-135 135 -86 43&gt;
 POTE generators: ~5/4 = 386.3143, ~|-22 22 -14 7&gt; = 16.3245
-Map: [&lt;1 1 0 0|, &lt;0 43 0 -135|, &lt;0 0 1 2|]
+Mapping: [&lt;1 1 0 0|, &lt;0 43 0 -135|, &lt;0 0 1 2|]
-EDOs: 441, 3749, 4190, 4631, 5072, 5513, 6763, 7204, 11394, 11835, 12276, 12717, 16466, 23229, 24111
+EDOs: {{EDOs|441, 3749, 4190, 4631, 5072, 5513, 6763, 7204, 11394, 11835, 12276, 12717, 16466, 23229, 24111}}
 ===11-limit 441&amp;4631&amp;12276===
@@ Line 16: / Line 24: @@
 POTE generators: ~5/4 = 386.3178, ~|-22 22 -14 7&gt; = 16.3245
-Map: [&lt;1 1 0 0 -2|, &lt;0 43 0 -135 572|, &lt;0 0 1 2 -1|]
+Mapping: [&lt;1 1 0 0 -2|, &lt;0 43 0 -135 572|, &lt;0 0 1 2 -1|]
-EDOs: 441, 3455, 3749, 3896, 4190, 4631, 7645, 8086, 8821, 11835, 12276, 16466, 16907, 24111, 28742
+EDOs: {{EDOs|441, 3455, 3749, 3896, 4190, 4631, 7645, 8086, 8821, 11835, 12276, 16466, 16907, 24111, 28742}}
-===13-limit 441&amp;4631&amp;12276===
+===13-limit 441 &amp; 4631 &amp; 12276===
 Commas: 33792000/33787663, 703096443/703040000, 33319272448/33317578125
 POTE generators: ~5/4 = 386.3240, ~|-22 22 -14 7&gt; = 16.3246
-Map: [&lt;1 1 0 0 -2 2|, &lt;0 43 0 -135 572 125|, &lt;0 0 1 2 -1 0|]
+Mapping: [&lt;1 1 0 0 -2 2|, &lt;0 43 0 -135 572 125|, &lt;0 0 1 2 -1 0|]
-EDOs: 441, 3455, 3749, 3896, 4190, 4631, 7645, 8086, 8821, 12276
+EDOs: {{EDOs|441, 3455, 3749, 3896, 4190, 4631, 7645, 8086, 8821, 12276}}
-[[Category:Edf]]
+{{Todo|cleanup|expand}}
-[[Category:Edonoi]]