1001edo
| ← 1000edo | 1001edo | 1002edo → |
1001 equal divisions of the octave (1001edo), or 1001-tone equal temperament (1001tet), 1001 equal temperament (1001et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1001 equal parts of about 1.2 ¢ each.
The best prime subgroup for 1001edo is 2.7.11.13.19.23. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832. Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775. Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520, as well as the parakleisma.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.543 | -0.300 | -0.195 | -0.114 | +0.131 | -0.168 | +0.243 | +0.539 | -0.210 | +0.348 | -0.103 |
| relative (%) | +45 | -25 | -16 | -9 | +11 | -14 | +20 | +45 | -18 | +29 | -9 | |
| Steps (reduced) |
1587 (586) |
2324 (322) |
2810 (808) |
3173 (170) |
3463 (460) |
3704 (701) |
3911 (908) |
4092 (88) |
4252 (248) |
4397 (393) |
4528 (524) | |
Subsets and supersets
1001 factorizes as 7 x 11 x 13, and has subset EDOs 7, 11, 13, 77, 91, and 143.