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{{Infobox ET}} | {{Infobox ET}} | ||
'''53EDF''' is the [[EDF|equal division of the just perfect fifth]] into 53 parts of 13.2444 [[ | '''53EDF''' is the [[EDF|equal division of the just perfect fifth]] into 53 parts of 13.2444 [[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 {{EDOs|90, 91, 181, 453, 544, 634, 725, 997, 1087, and 1178}} EDOs. | |||
==Related temperament== | ==Related temperament== | ||
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EDOs: {{EDOs|453, 725, 1178, 1631, 2084, 2809}} | EDOs: {{EDOs|453, 725, 1178, 1631, 2084, 2809}} | ||
== Harmonics == | |||
{{Harmonics in equal|53|3|2|intervals=prime}} | |||
{{Harmonics in equal|53|3|2|intervals=prime|collapsed=1|start=12}} | |||
{{todo|expand}} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 04:05, 18 December 2024
| ← 52edf | 53edf | 54edf → |
53EDF is the equal division of the just perfect fifth into 53 parts of 13.2444 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
7-limit 453&544&634
Comma: |-44 44 53 -53>
POTE generators: ~5/4 = 386.2004, ~3796875/3764768 = 13.2434
Mapping: [<1 1 0 0|, <0 53 0 44|, <0 0 1 1|]
EDOs: 90, 91, 181, 453, 544, 634, 725, 997, 1087, 1178
7-limit 453&1178
Commas: 2460375/2458624, |6 -1 38 -33>
POTE generator: ~3796875/3764768 = 13.2432
Mapping: [<1 1 -1 -1|, <0 53 301 345|]
EDOs: 453, 725, 1178, 1631, 2084, 2809
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.24 | +5.24 | -4.98 | -4.74 | -5.81 | -3.64 | -4.51 | +1.59 | +1.94 | -2.03 | +1.72 |
| Relative (%) | +39.6 | +39.6 | -37.6 | -35.8 | -43.9 | -27.5 | -34.1 | +12.0 | +14.7 | -15.3 | +13.0 | |
| Steps (reduced) |
91 (38) |
144 (38) |
210 (51) |
254 (42) |
313 (48) |
335 (17) |
370 (52) |
385 (14) |
410 (39) |
440 (16) |
449 (25) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.03 | -5.51 | +4.74 | -3.56 | +0.36 | +0.11 | -4.62 | +5.13 | -2.55 | +2.34 | -1.97 |
| Relative (%) | +0.2 | -41.6 | +35.8 | -26.9 | +2.7 | +0.8 | -34.9 | +38.7 | -19.2 | +17.7 | -14.8 | |
| Steps (reduced) |
472 (48) |
485 (8) |
492 (15) |
503 (26) |
519 (42) |
533 (3) |
537 (7) |
550 (20) |
557 (27) |
561 (31) |
571 (41) | |