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¢)
Sharp fifth 586\1001 (702.498¢)
Flat fifth 585\1001 (701.299¢) (→45\77)
Major 2nd 170\1001 (203.796¢)
Consistency limit 3
Distinct consistency limit 3

1001edo divides the octave into parts of 1.(19880) cents each.

Theory

Approximation of prime intervals in 1001 EDO
Prime number 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error absolute (¢) +0.000 +0.543 -0.300 -0.195 +0.131 -0.168 +0.539 -0.210 -0.103 +0.193 -0.180 +0.404 +0.108 +0.370 -0.172
relative (%) +0 +45 -25 -16 +11 -14 +45 -18 -9 +16 -15 +34 +9 +31 -14
Steps (reduced) 1001 (0) 1587 (586) 2324 (322) 2810 (808) 3463 (460) 3704 (701) 4092 (88) 4252 (248) 4528 (524) 4863 (859) 4959 (955) 5215 (210) 5363 (358) 5432 (427) 5560 (555)

1001 factorizes as 7 x 11 x 13, and therefore by extension it contains all these smaller EDOs. It's composite divisors are 77, 91, and 143.

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.