614edo
614 equal divisions of the octave (abbreviated 614edo or 614ed2), also called 614-tone equal temperament (614tet) or 614 equal temperament (614et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 614 equal parts of about 1.95 ¢ each. Each step represents a frequency ratio of 21/614, or the 614th root of 2.
| ← 613edo | 614edo | 615edo → |
614edo is inconsistent to the 5-odd-limit as harmonics 3 and 5 are off in opposite directions. While harmonics 5 and 7 have close to 1/3 relative error, 11 and 13 are more accurate, meaning 614edo can be used as a tuning for the 2.3.15.21.11.13 subgroup in the 13-limit. 3684edo, which slices each step in 6, corrects the 3rd and 5th harmonics, however the 11 and 13 are now too inaccurate.
614edo is notable for being the edo with the edostep closest to the schisma by direct approximation; however it does not consistently represent the schisma, as it actually tempers out the schisma by patent val. 3684edo consistently represents the schisma as 1\614.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.326 | +0.657 | +0.555 | -0.178 | -0.137 | +0.582 | -0.445 | -0.913 | +0.390 | +0.241 |
| Relative (%) | +0.0 | -16.7 | +33.6 | +28.4 | -9.1 | -7.0 | +29.8 | -22.7 | -46.7 | +20.0 | +12.3 | |
| Steps (reduced) |
614 (0) |
973 (359) |
1426 (198) |
1724 (496) |
2124 (282) |
2272 (430) |
2510 (54) |
2608 (152) |
2777 (321) |
2983 (527) |
3042 (586) | |