1001edo

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← 1000edo1001edo1002edo →
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 1001-tone equal temperament (1001tet), 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 of 1001edo 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 -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

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