415edt: Difference between revisions
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{{Harmonics in equal|415|3|1|intervals=odd|columns=15}} | {{Harmonics in equal|415|3|1|intervals=odd|columns=15}} | ||
{{Harmonics in equal|415|3|1|intervals=odd|start=16|columns=18|collapsed=1|title=Approximation of odd harmonics in 415edt (continued)}} | {{Harmonics in equal|415|3|1|intervals=odd|start=16|columns=18|collapsed=1|title=Approximation of odd harmonics in 415edt (continued)}} | ||
Revision as of 04:45, 21 September 2024
| ← 414edt | 415edt | 416edt → |
415EDT is the equal division of the third harmonic into 415 parts of 4.5830cents each, corresponding to 261.8358 edo. It is notable for its impressive consistency records in very high no-evens throdd limits: specifically, it is consistent to the entirety of the no-23s no-47s no-59s add-71 65-throdd limit, and all additional intervals if primes 59, 67, and 73 are added to this are within 60.2% of a step of their patent val approximation.
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.16 | -0.30 | +0.00 | +0.90 | +0.42 | +0.16 | -1.12 | -1.19 | -0.30 | -1.97 | +0.33 | +0.00 | +0.03 | -0.85 |
| Relative (%) | +0.0 | +3.6 | -6.6 | +0.0 | +19.7 | +9.2 | +3.6 | -24.4 | -26.0 | -6.6 | -43.1 | +7.2 | +0.0 | +0.6 | -18.6 | |
| Steps (reduced) |
415 (0) |
608 (193) |
735 (320) |
830 (0) |
906 (76) |
969 (139) |
1023 (193) |
1070 (240) |
1112 (282) |
1150 (320) |
1184 (354) |
1216 (386) |
1245 (0) |
1272 (27) |
1297 (52) | |
| Harmonic | 33 | 35 | 37 | 39 | 41 | 43 | 45 | 47 | 49 | 51 | 53 | 55 | 57 | 59 | 61 | 63 | 65 | 67 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.90 | -0.14 | -0.10 | +0.42 | +0.92 | +0.96 | +0.16 | -1.79 | -0.61 | -1.12 | +1.03 | +1.07 | -1.19 | -1.31 | +0.55 | -0.30 | +0.59 | -1.46 |
| Relative (%) | +19.7 | -3.0 | -2.2 | +9.2 | +20.1 | +20.9 | +3.6 | -39.0 | -13.2 | -24.4 | +22.5 | +23.3 | -26.0 | -28.7 | +12.0 | -6.6 | +12.8 | -32.0 | |
| Steps (reduced) |
1321 (76) |
1343 (98) |
1364 (119) |
1384 (139) |
1403 (158) |
1421 (176) |
1438 (193) |
1454 (209) |
1470 (225) |
1485 (240) |
1500 (255) |
1514 (269) |
1527 (282) |
1540 (295) |
1553 (308) |
1565 (320) |
1577 (332) |
1588 (343) | |