541edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro}} == Theory == 541et is only consistent to the 5-odd-limit and the harmonic 3 is about halfway between ist steps. It has a reasonable appro..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
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== Theory == | == Theory == | ||
Revision as of 14:55, 20 December 2023
| ← 540edo | 541edo | 542edo → |
Theory
541et is only consistent to the 5-odd-limit and the harmonic 3 is about halfway between ist steps. It has a reasonable approximation to the 2.9.5.7.11.13 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.031 | -0.362 | +0.490 | +0.157 | +0.993 | +0.138 | +0.826 | -0.704 | -0.286 | -0.541 | -0.548 |
| Relative (%) | -46.5 | -16.3 | +22.1 | +7.1 | +44.7 | +6.2 | +37.2 | -31.7 | -12.9 | -24.4 | -24.7 | |
| Steps (reduced) |
857 (316) |
1256 (174) |
1519 (437) |
1715 (92) |
1872 (249) |
2002 (379) |
2114 (491) |
2211 (47) |
2298 (134) |
2376 (212) |
2447 (283) | |
Subsets and supersets
541edo is the 100th prime EDO. 1082edo, which doubles it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [1715 -541⟩ | [⟨541 1715]] | -0.0247 | 0.0247 | 1.11 |
| 2.9.5 | [-20 -12 25⟩, [63 -25 7⟩ | [⟨541 1715 1256]] | +0.0355 | 0.0874 | 3.94 |
| 2.9.5.7 | 95703125/95551488, 43046721/43025920, 1280000000/1275989841 | [⟨541 1715 1256 1519]] | -0.0171 | 0.1184 | 5.34 |
| 2.9.5.7.11 | 6250/6237, 496125/495616, 46656/46585, 275653125/275365888 | [⟨541 1715 1256 1519 1872]] | -0.0710 | 0.1512 | 6.82 |
| 2.9.5.7.11.13 | 1575/1573, 4096/4095, 6250/6237, 67392/67375, 3247695/3246152 | [⟨541 1715 1256 1519 1872 2002]] | -0.0654 | 0.1386 | 6.25 |