493edt: Difference between revisions
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investigating some EDTs with strong no-twos consistency records |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} | ||
493edt is essentially equivalent to [[311edo]], maintaining its extremely strong [[consistency]] record through to the 41-[[odd-limit]]. | |||
== Harmonics == | == Harmonics == | ||
{{Harmonics in equal|493|3|1|intervals = prime|columns = 9}} | {{Harmonics in equal|493|3|1|intervals = prime|columns = 9}} | ||
{{Harmonics in equal|493|3|1|start = 12|collapsed = 1|intervals = odd|columns = 16}} | {{Harmonics in equal|493|3|1|start = 12|collapsed = 1|intervals = odd|columns = 16}} | ||
Revision as of 20:32, 7 October 2024
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493 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 493edt or 493ed3), is a nonoctave tuning system that divides the interval of 3/1 into 493 equal parts of about 3.86 ¢ each. Each step represents a frequency ratio of 31/493, or the 493rd root of 3.
493edt is essentially equivalent to 311edo, maintaining its extremely strong consistency record through to the 41-odd-limit.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.19 | +0.00 | -0.89 | -0.86 | -0.20 | -0.06 | -1.54 | -1.20 | -0.18 |
| Relative (%) | -4.8 | +0.0 | -23.2 | -22.3 | -5.1 | -1.6 | -39.9 | -31.1 | -4.7 | |
| Steps (reduced) |
311 (311) |
493 (0) |
722 (229) |
873 (380) |
1076 (90) |
1151 (165) |
1271 (285) |
1321 (335) |
1407 (421) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | 47 | 49 | 51 | 53 | 55 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.79 | +0.00 | -0.26 | +0.02 | -0.20 | -1.76 | -1.51 | -0.06 | -1.77 | +0.65 | -0.89 | +0.98 | -1.72 | -1.54 | +1.31 | -1.09 |
| Relative (%) | -46.4 | +0.0 | -6.7 | +0.5 | -5.1 | -45.5 | -39.2 | -1.6 | -45.8 | +16.9 | -23.2 | +25.4 | -44.6 | -39.9 | +34.0 | -28.3 | |
| Steps (reduced) |
1444 (458) |
1479 (0) |
1511 (32) |
1541 (62) |
1569 (90) |
1595 (116) |
1620 (141) |
1644 (165) |
1666 (187) |
1688 (209) |
1708 (229) |
1728 (249) |
1746 (267) |
1764 (285) |
1782 (303) |
1798 (319) | |