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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 [[ | '''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 [[microtemperament]] which [[tempers out]] |-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 16466}} EDOs. | |||
==Related temperament== | ==Related temperament== | ||
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EDOs: {{EDOs|441, 3455, 3749, 3896, 4190, 4631, 7645, 8086, 8821, 12276}} | EDOs: {{EDOs|441, 3455, 3749, 3896, 4190, 4631, 7645, 8086, 8821, 12276}} | ||
==Harmonics== | |||
{{Harmonics in equal|43|3|2}} | |||
{{Harmonics in equal|43|3|2|start=12|title=(contd.)}} | |||
{{todo|expand}} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 04:53, 18 December 2024
| ← 42edf | 43edf | 44edf → |
43EDF is the equal division of the just perfect fifth into 43 parts of 16.3245 cents each, corresponding to 73.5090 edo (similar to every second step of 147edo).
It is related to the 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
7-limit 441&4631&12276
Comma: |-135 135 -86 43>
POTE generators: ~5/4 = 386.3143, ~|-22 22 -14 7> = 16.3245
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
11-limit 441&4631&12276
Commas: |-31 29 -11 5 -1>, |20 -10 -31 18 5>
POTE generators: ~5/4 = 386.3178, ~|-22 22 -14 7> = 16.3245
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
13-limit 441&4631&12276
Commas: 33792000/33787663, 703096443/703040000, 33319272448/33317578125
POTE generators: ~5/4 = 386.3240, ~|-22 22 -14 7> = 16.3246
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
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.02 | +8.02 | -0.29 | +5.18 | -0.29 | -5.97 | +7.72 | -0.29 | -3.13 | -4.89 | +7.72 |
| Relative (%) | +49.1 | +49.1 | -1.8 | +31.7 | -1.8 | -36.6 | +47.3 | -1.8 | -19.2 | -29.9 | +47.3 | |
| Steps (reduced) |
74 (31) |
117 (31) |
147 (18) |
171 (42) |
190 (18) |
206 (34) |
221 (6) |
233 (18) |
244 (29) |
254 (39) |
264 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.25 | +2.04 | -3.13 | -0.59 | -7.59 | +7.72 | -4.26 | +4.89 | +2.04 | +3.13 | +7.80 |
| Relative (%) | -1.6 | +12.5 | -19.2 | -3.6 | -46.5 | +47.3 | -26.1 | +29.9 | +12.5 | +19.2 | +47.8 | |
| Steps (reduced) |
272 (14) |
280 (22) |
287 (29) |
294 (36) |
300 (42) |
307 (6) |
312 (11) |
318 (17) |
323 (22) |
328 (27) |
333 (32) | |