352edo
Theory
352edo is consistent to the 7-odd-limit. Using the patent val, the equal temperament tempers out 2401/2400, 15625/15552, 390625/388962, and 33554432/33480783 in the 7-limit; 3025/3024, 4375/4356, 14700/14641, 19712/19683, 41503/41472, and 131072/130977 in the 11-limit. It supports newt, world calendar, septiruthenic, enki and fortune.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.32 | -1.09 | -0.64 | +0.95 | +1.52 | +0.73 | -0.92 | -1.00 | -0.03 | +0.42 |
| Relative (%) | +0.0 | +9.3 | -31.9 | -18.9 | +28.0 | +44.5 | +21.3 | -27.0 | -29.4 | -0.9 | +12.3 | |
| Steps (reduced) |
352 (0) |
558 (206) |
817 (113) |
988 (284) |
1218 (162) |
1303 (247) |
1439 (31) |
1495 (87) |
1592 (184) |
1710 (302) |
1744 (336) | |
Subsets and supersets
352 factors into 25 × 11, with subset edos 2, 4, 8, 11, 16, 22, 32, 44, 88, and 176.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3.5 | 15625/15552, [95 -57 -2⟩ | [⟨352 558 817]] | +0.0891 | 0.2801 | 8.22 |
| 2.3.5.7 | 2401/2400, 15625/15552, 33554432/33480783 | [⟨352 558 817 988]] | +0.1242 | 0.2500 | 7.33 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 35\352 | 119.32 | 15/14 | Septidiasemi |
| 1 | 65\352 | 221.59 | 8388608/7381125 | Fortune |
| 1 | 93\352 | 317.05 | 6/5 | Hanson |
| 1 | 103\352 | 351.14 | 49/40 | Newt |
| 4 | 93\352 (5\352) |
317.05 (17.05) |
6/5 (126/125) |
Quadritikleismic |
| 4 | 117\352 (29\352) |
398.86 (98.86) |
34/27 (18/17) |
World calendar |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct