607edo
| ← 606edo | 607edo | 608edo → |
607 equal divisions of the octave (abbreviated 607edo or 607ed2), also called 607-tone equal temperament (607tet) or 607 equal temperament (607et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 607 equal parts of about 1.98 ¢ each. Each step represents a frequency ratio of 21/607, or the 607th root of 2.
Theory
607edo is consistent to the 9-odd-limit. Using the patent val, the equal temperament tempers out 32805/32768, 420175/419904 and 244140625/243045684 in the 7-limit; 3025/3024, 6250/6237, 32805/32768 and 420175/419904 in the 11-limit. It supports countertertiaschis. Essentially tempered chords available in 607et include baladismic chords and xenismic chords.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.143 | -0.811 | -0.127 | +0.247 | -0.330 | -0.178 | -0.973 | +0.391 | +0.406 | -0.390 |
| Relative (%) | +0.0 | -7.2 | -41.0 | -6.4 | +12.5 | -16.7 | -9.0 | -49.2 | +19.8 | +20.6 | -19.7 | |
| Steps (reduced) |
607 (0) |
962 (355) |
1409 (195) |
1704 (490) |
2100 (279) |
2246 (425) |
2481 (53) |
2578 (150) |
2746 (318) |
2949 (521) |
3007 (579) | |
Subsets and supersets
607edo is the 111th prime EDO.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-962 607⟩ | [⟨607 962]] | 0.0451 | 0.0451 | 2.28 |
| 2.3.5 | 32805/32768, [-58 -63 68⟩ | [⟨607 962 1409]] | 0.1465 | 0.1481 | 7.49 |
| 2.3.5.7 | 32805/32768, 420175/419904, 244140625/243045684 | [⟨607 962 1409 1704]] | 0.1212 | 0.1355 | 6.85 |
| 2.3.5.7.11 | 3025/3024, 6250/6237, 32805/32768, 420175/419904 | [⟨607 962 1409 1704 2100]] | 0.0827 | 0.1437 | 7.27 |
| 2.3.5.7.11.13 | 2080/2079, 625/624, 3025/3024, 78975/78848, 218700/218491 | [⟨607 962 1409 1704 2100 2246]] | 0.0838 | 0.1312 | 6.64 |
| 2.3.5.7.11.13.17 | 2080/2079, 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831 | [⟨607 962 1409 1704 2100 2246 2481]] | 0.0780 | 0.1222 | 6.18 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 252\607 | 498.188 | 4/3 | Helmholtz |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct