1240edo

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← 1239edo1240edo1241edo →
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 1240-tone equal temperament (1240tet), 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 of 1240edo 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 -19 -12 +29 +30 +45 +46 -45 -43 -47 -22 -38 -6 +10
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.