493edt: Difference between revisions
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493edt is essentially equivalent to [[311edo]] (with patent vals matching through the [[43-limit]]), maintaining its extremely strong [[consistency]] record through to the 41-[[odd-limit]]. | 493edt is essentially equivalent to [[311edo]] (with patent vals matching through the [[43-limit]]), maintaining its extremely strong [[consistency]] record through to the 41-[[odd-limit]]. | ||
== Harmonics == | === Harmonics === | ||
{{Harmonics in equal|493|3|1|columns= | {{Harmonics in equal|493|3|1|columns=11}} | ||
{{Harmonics in equal|493|3|1|columns= | {{Harmonics in equal|493|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 493edt (continued)}} | ||
Revision as of 08:36, 9 March 2025
| ← 492edt | 493edt | 494edt → |
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 (with patent vals matching through the 43-limit), maintaining its extremely strong consistency record through to the 41-odd-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.19 | +0.00 | -0.37 | -0.89 | -0.19 | -0.86 | -0.56 | +0.00 | -1.08 | -0.20 | -0.37 |
| Relative (%) | -4.8 | +0.0 | -9.7 | -23.2 | -4.8 | -22.3 | -14.5 | +0.0 | -28.0 | -5.1 | -9.7 | |
| Steps (reduced) |
311 (311) |
493 (0) |
622 (129) |
722 (229) |
804 (311) |
873 (380) |
933 (440) |
986 (0) |
1033 (47) |
1076 (90) |
1115 (129) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.06 | -1.05 | -0.89 | -0.75 | -1.54 | -0.19 | -1.20 | -1.27 | -0.86 | -0.38 | -0.18 | -0.56 |
| Relative (%) | -1.6 | -27.2 | -23.2 | -19.3 | -39.9 | -4.8 | -31.1 | -32.9 | -22.3 | -9.9 | -4.7 | -14.5 | |
| Steps (reduced) |
1151 (165) |
1184 (198) |
1215 (229) |
1244 (258) |
1271 (285) |
1297 (311) |
1321 (335) |
1344 (358) |
1366 (380) |
1387 (401) |
1407 (421) |
1426 (440) | |