# 1001edo

 ← 1000edo 1001edo 1002edo →
Prime factorization 7 × 11 × 13
Step size 1.1988¢
Fifth 586\1001 (702.498¢)
Semitones (A1:m2) 98:73 (117.5¢ : 87.51¢)
Dual sharp fifth 586\1001 (702.498¢)
Dual flat fifth 585\1001 (701.299¢) (→45\77)
Dual major 2nd 170\1001 (203.796¢)
Consistency limit 3
Distinct consistency limit 3

1001 equal divisions of the octave (abbreviated 1001edo or 1001ed2), also called 1001-tone equal temperament (1001tet) or 1001 equal temperament (1001et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1001 equal parts of about 1.2 ¢ each. Each step represents a frequency ratio of 21/1001, or the 1001st root of 2.

1001edo is inconsistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. Otherwise, it has good approximations to harmonics 7, 9, 11, 13, 19, and 23, making it suitable for a 2.9.7.11.13.19.23 subgroup interpretation, with an optional addition of either 5, or 15. 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

Approximation of odd harmonics in 1001edo
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 (%) +45.3 -25.0 -16.2 -9.5 +10.9 -14.0 +20.3 +45.0 -17.5 +29.0 -8.6
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

Since 1001 factorizes as 7 × 11 × 13, 1001edo has subset edos 7, 11, 13, 77, 91, and 143.