527edt: Difference between revisions
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investigating some EDTs with strong no-twos consistency records |
investigating some EDTs with strong no-twos consistency records |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} | ||
527edt is essentially identical to every other step of [[665edo]]. | |||
== Harmonics == | == Harmonics == | ||
{{Harmonics in equal|527|3|1|intervals = prime|columns = 9}} | {{Harmonics in equal|527|3|1|intervals = prime|columns = 9}} | ||
{{Harmonics in equal|527|3|1|start = 12|collapsed = 1|intervals = odd|columns = 16}} | {{Harmonics in equal|527|3|1|start = 12|collapsed = 1|intervals = odd|columns = 16}} | ||
Revision as of 20:34, 7 October 2024
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| ← 526edt | 527edt | 528edt → |
527 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 527edt or 527ed3), is a nonoctave tuning system that divides the interval of 3/1 into 527 equal parts of about 3.61 ¢ each. Each step represents a frequency ratio of 31/527, or the 527th root of 3.
527edt is essentially identical to every other step of 665edo.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.80 | +0.00 | -0.15 | -1.61 | -0.94 | -1.43 | -0.29 | -1.57 | -0.30 |
| Relative (%) | -50.0 | +0.0 | -4.1 | -44.5 | -26.1 | -39.6 | -8.1 | -43.6 | -8.4 | |
| Steps (reduced) |
332 (332) |
527 (0) |
772 (245) |
933 (406) |
1150 (96) |
1230 (176) |
1359 (305) |
1412 (358) |
1504 (450) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | 47 | 49 | 51 | 53 | 55 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.30 | +0.00 | -1.01 | -0.98 | -0.94 | -1.76 | -0.52 | -1.43 | -1.39 | -0.84 | -0.15 | +0.36 | +0.39 | -0.29 | +1.68 | -1.09 |
| Relative (%) | -8.2 | +0.0 | -27.9 | -27.0 | -26.1 | -48.7 | -14.3 | -39.6 | -38.6 | -23.3 | -4.1 | +9.9 | +10.9 | -8.1 | +46.7 | -30.2 | |
| Steps (reduced) |
1544 (490) |
1581 (0) |
1615 (34) |
1647 (66) |
1677 (96) |
1705 (124) |
1732 (151) |
1757 (176) |
1781 (200) |
1804 (223) |
1826 (245) |
1847 (266) |
1867 (286) |
1886 (305) |
1905 (324) |
1922 (341) | |