617edo
| ← 616edo | 617edo | 618edo → |
617 equal divisions of the octave (abbreviated 617edo or 617ed2), also called 617-tone equal temperament (617tet) or 617 equal temperament (617et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 617 equal parts of about 1.94 ¢ each. Each step represents a frequency ratio of 21/617, or the 617th root of 2.
Theory
617edo is consistent to the 5-odd-limit. The equal temperament can be used in the 2.3.5.7.13.17.19.23.31 subgroup, tempering out 1701/1700, 1216/1215, 1729/1728, 676/675, 1127/1125, 260253/260000, 3969/3968 and 137241/137200. It supports majvam.
Using the 617c val (⟨617 978 1432 1732]), it tempers out 15625/15552, 2460375/2458624 and 3276800000/3268642167 in the 7-limit, supporting kleismic and marthirds.
Using the 617de val (⟨617 978 1433 1733 2135]), it tempers out 540/539, 5632/5631, 43923/43904 and 40960000/40920957 in the 11-limit, supporting jupiter.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.152 | +0.720 | -0.268 | -0.913 | -0.333 | +0.069 | +0.056 | -0.073 | -0.728 | +0.507 |
| Relative (%) | +0.0 | +7.8 | +37.0 | -13.8 | -46.9 | -17.1 | +3.5 | +2.9 | -3.8 | -37.4 | +26.1 | |
| Steps (reduced) |
617 (0) |
978 (361) |
1433 (199) |
1732 (498) |
2134 (283) |
2283 (432) |
2522 (54) |
2621 (153) |
2791 (323) |
2997 (529) |
3057 (589) | |
Subsets and supersets
617edo is the 113th prime EDO.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [978 -617⟩ | [⟨617 978]] | −0.0479 | 0.0479 | 2.46 |
| 2.3.5 | [39 -29 3⟩, [40 7 -22⟩ | [⟨617 978 1433]] | −0.1354 | 0.1297 | 6.67 |
| 2.3.5.7 | 420175/419904, 1959552/1953125, 67108864/66976875 | [⟨617 978 1433 1732]] | −0.0776 | 0.1504 | 7.73 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 236\617 | 458.995 | 125/96 | Majvam |
| 1 | 291\617 | 565.964 | 81920/59049 | Tricot |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct