493edt: Difference between revisions
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| Consistency = 42 | |||
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493edt is | == Theory == | ||
493edt is related to [[311edo]], but with the [[3/1|twelfth]] rather than the [[2/1|octave]] being just. The octave is about 0.187 cents compressed. The patent val matches with 311edo's through the [[43-limit]], maintaining the extremely strong [[consistency]] record through to the [[integer limit|42-integer-limit]]. However, it has a flat-tending tuning profile, with harmonics 1–42 all tuned flat except for [[31/1|31]]. | |||
== 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)}} | ||
=== Subsets and supersets === | |||
Since 493 factors into primes as {{nowrap| 17 × 29 }}, 493edt contiains [[17edt]] and [[29edt]] as its subset edts. | |||
=== See also === | |||
* [[311edo]] – relative edo | |||
Latest revision as of 16:11, 8 February 2026
| ← 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.
Theory
493edt is related to 311edo, but with the twelfth rather than the octave being just. The octave is about 0.187 cents compressed. The patent val matches with 311edo's through the 43-limit, maintaining the extremely strong consistency record through to the 42-integer-limit. However, it has a flat-tending tuning profile, with harmonics 1–42 all tuned flat except for 31.
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) | |
Subsets and supersets
Since 493 factors into primes as 17 × 29, 493edt contiains 17edt and 29edt as its subset edts.
See also
- 311edo – relative edo