43edf: Difference between revisions

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


==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}}
{{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>
Comma: |-135 135 -86 43>


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Mapping: [<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===
===11-limit 441&4631&12276===
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Mapping: [<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
Commas: 33792000/33787663, 703096443/703040000, 33319272448/33317578125


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Mapping: [<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]]
{{Todo|cleanup|expand}}
[[Category:Edonoi]]