53edf: Difference between revisions
Created page with "'''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..." Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | |||
{{ED intro|53}} | |||
==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}} | |||
{{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=== | ===7-limit 453&544&634=== | ||
Comma: |-44 44 53 -53> | Comma: |-44 44 53 -53> | ||
| Line 7: | Line 15: | ||
POTE generators: ~5/4 = 386.2004, ~3796875/3764768 = 13.2434 | 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 | EDOs: {{EDOs|90, 91, 181, 453, 544, 634, 725, 997, 1087, 1178}} | ||
===7-limit 453&1178=== | ===7-limit 453&1178=== | ||
| Line 16: | Line 24: | ||
POTE generator: ~3796875/3764768 = 13.2432 | POTE generator: ~3796875/3764768 = 13.2432 | ||
Mapping: [<1 1 -1 -1|, <0 53 301 345|] | |||
EDOs: 453, 725, 1178, 1631, 2084, 2809 | EDOs: {{EDOs|453, 725, 1178, 1631, 2084, 2809}} | ||
{{Todo|cleanup|expand}} | |||
Latest revision as of 17:20, 17 January 2025
| ← 52edf | 53edf | 54edf → |
53 equal divisions of the octave (abbreviated 53edo or 53ed2), also called 53-tone equal temperament (53tet) or 53 equal temperament (53et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 53 equal parts of about 22.6 ¢ each. Each step represents a frequency ratio of 21/53, or the 53rd root of 2.
Theory
53edf corresponds to 90.6041edo, 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 1178edo.
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) | |
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|]