2113edo
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Prime factorization
2113 (prime)
Step size
0.567913¢
Fifth
1236\2113 (701.94¢)
Semitones (A1:m2)
200:159 (113.6¢ : 90.3¢)
Consistency limit
21
Distinct consistency limit
21
| ← 2112edo | 2113edo | 2114edo → |
2113 equal divisions of the octave (abbreviated 2113edo or 2113ed2), also called 2113-tone equal temperament (2113tet) or 2113 equal temperament (2113et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2113 equal parts of about 0.568 ¢ each. Each step represents a frequency ratio of 21/2113, or the 2113th root of 2.
2113edo is consistent in the 21-odd-limit and also a strong 2.3.7.13.29 subgroup system. In the 11-limit and the 13-limit, it provides the optimal patent val for the moulin temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.015 | -0.133 | +0.034 | +0.126 | -0.017 | +0.108 | +0.073 | -0.163 | +0.049 | -0.123 |
| Relative (%) | +0.0 | -2.6 | -23.4 | +5.9 | +22.1 | -2.9 | +19.1 | +12.9 | -28.6 | +8.6 | -21.7 | |
| Steps (reduced) |
2113 (0) |
3349 (1236) |
4906 (680) |
5932 (1706) |
7310 (971) |
7819 (1480) |
8637 (185) |
8976 (524) |
9558 (1106) |
10265 (1813) |
10468 (2016) | |
Subsets and supersets
2113edo is the 319th prime edo.