1650edo
| ← 1649edo | 1650edo | 1651edo → |
1650 equal divisions of the octave (abbreviated 1650edo or 1650ed2), also called 1650-tone equal temperament (1650tet) or 1650 equal temperament (1650et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1650 equal parts of about 0.727 ¢ each. Each step represents a frequency ratio of 21/1650, or the 1650th root of 2.
1650edo is consistent in the 11-odd-limit, being a flat system in the no-13s 19-limit. Being a landscape system, it tunes 11-limit temperaments semiseptichrome and zinc. A comma basis in the 2.3.5.7.11.17.19 subgroup is {5832/5831, 5985/5984, 9801/9800, 57375/57344, 151263/151250, 2646875/2646016}.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.137 | -0.132 | -0.099 | -0.045 | +0.200 | -0.228 | -0.058 | +0.089 | +0.241 | -0.308 |
| Relative (%) | +0.0 | -18.8 | -18.1 | -13.6 | -6.2 | +27.4 | -31.4 | -8.0 | +12.3 | +33.1 | -42.4 | |
| Steps (reduced) |
1650 (0) |
2615 (965) |
3831 (531) |
4632 (1332) |
5708 (758) |
6106 (1156) |
6744 (144) |
7009 (409) |
7464 (864) |
8016 (1416) |
8174 (1574) | |
Subsets and supersets
Since 1650 factors as 2 × 3 × 52 × 11, 1650edo has subset edos 2, 3, 5, 6, 10, 11, 15, 22, 25, 30, 33, 50, 55, 66, 75, 110, 150, 165, 275, 330, 550, and 825.