3991edo
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Prime factorization
13 × 307
Step size
0.300677¢
Fifth
2335\3991 (702.08¢)
Semitones (A1:m2)
381:298 (114.6¢ : 89.6¢)
Dual sharp fifth
2335\3991 (702.08¢)
Dual flat fifth
2334\3991 (701.779¢)
Dual major 2nd
678\3991 (203.859¢)
Consistency limit
5
Distinct consistency limit
5
| ← 3990edo | 3991edo | 3992edo → |
3991 equal divisions of the octave (abbreviated 3991edo or 3991ed2), also called 3991-tone equal temperament (3991tet) or 3991 equal temperament (3991et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3991 equal parts of about 0.301 ¢ each. Each step represents a frequency ratio of 21/3991, or the 3991st root of 2.
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.125 | +0.056 | -0.046 | -0.051 | +0.123 | -0.137 | -0.120 | -0.019 | -0.144 | +0.079 | +0.140 |
| Relative (%) | +41.5 | +18.5 | -15.3 | -17.1 | +40.8 | -45.5 | -40.0 | -6.4 | -47.9 | +26.1 | +46.4 | |
| Steps (reduced) |
6326 (2335) |
9267 (1285) |
11204 (3222) |
12651 (678) |
13807 (1834) |
14768 (2795) |
15592 (3619) |
16313 (349) |
16953 (989) |
17530 (1566) |
18054 (2090) | |
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