613edo
| ← 612edo | 613edo | 614edo → |
Theory
613edo is only consistent to the 3-odd-limit and the harmonic 3 is about halfway its steps. It can be used in the 2.9.5.7.13.19.23.29.31.37 subgroup, tempering out 1521/1520, 875/874, 1863/1862, 38475/38416, 2205/2204, 1520/1519, 186875/186624, 1665/1664 and 194560/194481.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.818 | -0.669 | +0.179 | -0.321 | +0.721 | -0.723 | +0.149 | +0.754 | +0.040 | -0.960 | +0.111 |
| Relative (%) | +41.8 | -34.2 | +9.1 | -16.4 | +36.8 | -37.0 | +7.6 | +38.5 | +2.0 | -49.1 | +5.7 | |
| Steps (reduced) |
972 (359) |
1423 (197) |
1721 (495) |
1943 (104) |
2121 (282) |
2268 (429) |
2395 (556) |
2506 (54) |
2604 (152) |
2692 (240) |
2773 (321) | |
Subsets and supersets
613edo is the 112th prime EDO. 1226edo, 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 | [-1943 613⟩ | [⟨613 1943]] | 0.0506 | 0.0506 | 2.58 |
| 2.9.5 | 32805/32768, [-97 -69 136⟩ | [⟨613 1943 1423]] | 0.1299 | 0.1194 | 6.10 |
| 2.9.5.7 | 32805/32768, 40500000/40353607, [-23 -7 11 7⟩ | [⟨613 1943 1423 1721]] | 0.0814 | 0.1331 | 6.80 |