1440edo
| ← 1439edo | 1440edo | 1441edo → |
1440 equal divisions of the octave (1440edo), or 1440-tone equal temperament (1440tet), 1440 equal temperament (1440et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1440 equal parts of about 0.833 ¢ each.
From a regular temperament perspective, 1440edo only has a consistency limit of 3 and does poorly with approximating lower harmonics. However, 1440edo is worth considering as a higher-limit system, where it has excellent representation of the 2.15.17.19.21.23 subgroup. It may also be considered as every third step of 4320edo in this regard.
Odd harmonics
| 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 (%) | -35 | +42 | +41 | +31 | +42 | +37 | +8 | +5 | -2 | +6 | +7 | |
| 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
1440edo is notable for having a lot of divisors, namely 1, 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, 720. It is also a highly factorable equal division.
As an interval size measure, one step of 1440edo is called decifarab.