683edo
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Prime factorization
683 (prime)
Step size
1.75695¢
Fifth
400\683 (702.782¢)
Semitones (A1:m2)
68:49 (119.5¢ : 86.09¢)
Dual sharp fifth
400\683 (702.782¢)
Dual flat fifth
399\683 (701.025¢)
Dual major 2nd
116\683 (203.807¢)
Consistency limit
5
Distinct consistency limit
5
| ← 682edo | 683edo | 684edo → |
683 equal divisions of the octave (abbreviated 683edo or 683ed2), also called 683-tone equal temperament (683tet) or 683 equal temperament (683et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 683 equal parts of about 1.76 ¢ each. Each step represents a frequency ratio of 21/683, or the 683rd root of 2.
Theory
683edo is consistent to the 5-odd-limit and its harmonic 3 is about halfway its steps. It can be used in the 2.9.5.11.17.23.29.31.37 subgroup, tempering out 2025/2024, 3520/3519, 557056/556875, 5800/5797, 1332/1331, 484704/484375, 1492992/1491325 and 14384/14375.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.827 | +0.216 | -0.744 | -0.103 | +0.366 | -0.703 | -0.714 | +0.462 | -0.588 | +0.083 | +0.715 |
| Relative (%) | +47.1 | +12.3 | -42.3 | -5.9 | +20.8 | -40.0 | -40.6 | +26.3 | -33.4 | +4.7 | +40.7 | |
| Steps (reduced) |
1083 (400) |
1586 (220) |
1917 (551) |
2165 (116) |
2363 (314) |
2527 (478) |
2668 (619) |
2792 (60) |
2901 (169) |
3000 (268) |
3090 (358) | |
Subsets and supersets
683edo is the 124th prime EDO. 1366edo, which doubles it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-2165 683⟩ | [⟨683 2165]] | +0.0163 | 0.0163 | 0.93 |
| 2.9.5 | [23 3 -14⟩, [-130 52 -15⟩ | [⟨683 2165 1586]] | -0.0202 | 0.0533 | 3.03 |