1600edo
The 1600 equal divisions of the octave (1600edo), or the 1600-tone equal temperament (1600tet), 1600 equal temperament (1600et) when viewed from a regular temperament perspective, divides the octave into 1600 equal parts of exactly 750 millicents each.
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.045 | -0.064 | +0.174 | -0.068 | +0.222 | +0.045 | +0.237 | +0.226 | +0.173 | +0.214 |
| Relative (%) | +0.0 | +6.0 | -8.5 | +23.2 | -9.1 | +29.6 | +5.9 | +31.6 | +30.1 | +23.0 | +28.6 | |
| Steps (reduced) |
1600 (0) |
2536 (936) |
3715 (515) |
4492 (1292) |
5535 (735) |
5921 (1121) |
6540 (140) |
6797 (397) |
7238 (838) |
7773 (1373) |
7927 (1527) | |
1600edo is a very strong 37-limit system, being distinctly consistent in the 37-limit with a smaller relative error than anything else with this property until 4501. It is also the first division past 311 with a lower 43-limit relative error. One step of it is the relative cent for 16.
1600's divisors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800.
In the 5-limit, it supports kwazy.
In the 7-limit, it tempers out the ragisma, 4375/4374.
In the 11-limit, it supports the rank-3 temperament thor.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal
8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3.5 | [-53, 10, 16⟩, [26, -75, 40⟩ | [⟨1600 2536 3715]] | -0.000318 | 0.022794 | |
| 2.3.5.7 | 4375/4374, [36, -5, 0, -10⟩, [-17, 5, 16, -10⟩ | [⟨1600 2536 3715 4492]] | -0.015742 | 0.033217 | |
| 2.3.5.7.11.13.17 | 2500/2499, 3025/3024, 4375/4374, 14875/14872, 154880/154791, 1724800/1724463 | [⟨1600 2536 3715 4492 5535 5921 6540]] | -0.016332 | ||