# 1240edo

 ← 1239edo 1240edo 1241edo →
Prime factorization 23 × 5 × 31
Step size 0.967742¢
Fifth 725\1240 (701.613¢) (→145\248)
Semitones (A1:m2) 115:95 (111.3¢ : 91.94¢)
Dual sharp fifth 726\1240 (702.581¢) (→363\620)
Dual flat fifth 725\1240 (701.613¢) (→145\248)
Dual major 2nd 211\1240 (204.194¢)
Consistency limit 7
Distinct consistency limit 7

1240 equal divisions of the octave (abbreviated 1240edo or 1240ed2), also called 1240-tone equal temperament (1240tet) or 1240 equal temperament (1240et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1240 equal parts of about 0.968 ¢ each. Each step represents a frequency ratio of 21/1240, or the 1240th root of 2.

1240edo is consistent in the 7-odd-limit, though the error on harmonic 3 is quite large. It is a strong tuning for 5-limit soviet ferris wheel, ([-171 20 60), and a good tuning for dodifo, ([-67 -9 35).

Beyond the 7-odd-limit, there is a number of mappings to be considered. In the 2.27.7.23.29 subgroup, it is a flat system, and in 2.9.11.13.15, it is a sharp system. In the 2.5.11.13.29, it tunes the genojacobin temperament.

### Odd harmonics

Approximation of odd harmonics in 1240edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Error Absolute (¢) -0.342 -0.185 -0.116 +0.284 +0.295 +0.440 +0.441 -0.439 -0.416 -0.458 -0.210 -0.369 -0.059 +0.100
Relative (%) -35.4 -19.1 -12.0 +29.3 +30.5 +45.5 +45.6 -45.4 -43.0 -47.4 -21.7 -38.2 -6.1 +10.4
Steps
(reduced)
1965
(725)
2879
(399)
3481
(1001)
3931
(211)
4290
(570)
4589
(869)
4845
(1125)
5068
(108)
5267
(307)
5446
(486)
5609
(649)
5758
(798)
5896
(936)
6024
(1064)

### Subsets and supersets

Since 1240 factors as 23 × 5 × 31, 1240edo has subset edos 2, 4, 5, 8, 10, 20, 31, 40, 62, 124, 155, 248, 310, 620.