User:Francium/1031edo
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Prime factorization
1031 (prime)
Step size
1.16392 ¢
Fifth
603\1031 (701.843 ¢)
Semitones (A1:m2)
97:78 (112.9 ¢ : 90.79 ¢)
Consistency limit
9
Distinct consistency limit
9
| ← 1030edo | 1031edo | 1032edo → |
1031 equal divisions of the octave (abbreviated 1031edo or 1031ed2), also called 1031-tone equal temperament (1031tet) or 1031 equal temperament (1031et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1031 equal parts of about 1.16 ¢ each. Each step represents a frequency ratio of 21/1031, or the 1031st root of 2.
Theory
1031edo is consistent to the 9-odd-limit. It is strong in the 2.3.5.13.17 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.112 | +0.107 | -0.446 | +0.379 | -0.178 | -0.203 | +0.450 | +0.242 | +0.491 | +0.260 |
| Relative (%) | +0.0 | -9.6 | +9.2 | -38.3 | +32.6 | -15.3 | -17.4 | +38.7 | +20.8 | +42.2 | +22.4 | |
| Steps (reduced) |
1031 (0) |
1634 (603) |
2394 (332) |
2894 (832) |
3567 (474) |
3815 (722) |
4214 (90) |
4380 (256) |
4664 (540) |
5009 (885) |
5108 (984) | |
Subsets and supersets
1031edo is the 273rd prime edo.