1440edo

 ← 1439edo 1440edo 1441edo →
Prime factorization 25 × 32 × 5
Step size 0.833333¢
Fifth 842\1440 (701.667¢) (→421\720)
Semitones (A1:m2) 134:110 (111.7¢ : 91.67¢)
Dual sharp fifth 843\1440 (702.5¢) (→281\480)
Dual flat fifth 842\1440 (701.667¢) (→421\720)
Dual major 2nd 245\1440 (204.167¢) (→49\288)
Consistency limit 3
Distinct consistency limit 3

1440 equal divisions of the octave (abbreviated 1440edo or 1440ed2), also called 1440-tone equal temperament (1440tet) or 1440 equal temperament (1440et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1440 equal parts of about 0.833 ¢ each. Each step represents a frequency ratio of 21/1440, or the 1440th root of 2.

1440edo is inconsistent to the 5-odd-limit and does poorly with approximating lower harmonics. However, 1440edo is worth considering as a higher-limit system, where it has excellent representation of the 2.27.15.21.33.17.19.23.31 subgroup. It may also be considered as every third step of 4320edo in this regard.

Odd harmonics

Approximation of odd harmonics in 1440edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.288 +0.353 +0.341 +0.257 +0.349 +0.306 +0.065 +0.045 -0.013 +0.052 +0.059
Relative (%) -34.6 +42.4 +40.9 +30.8 +41.8 +36.7 +7.8 +5.4 -1.6 +6.3 +7.1
Steps
(reduced)
2282
(842)
3344
(464)
4043
(1163)
4565
(245)
4982
(662)
5329
(1009)
5626
(1306)
5886
(126)
6117
(357)
6325
(565)
6514
(754)

Subsets and supersets

Since 1440 factors into 25 × 32 × 5, 1440edo is notable for having a lot of subset edos, the nontrivial ones being 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, and 720. It is also a highly factorable equal division.

As an interval size measure, one step of 1440edo is called decifarab.