1440edo: Difference between revisions
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{{EDO intro|1440}} | {{EDO intro|1440}} | ||
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. | 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 2.15.17.19.21.23.25.27.31.33 subgroup. It may also be considered as every third step of [[4320edo]] in this regard. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|1440}} | {{Harmonics in equal|1440}} | ||
Revision as of 18:37, 14 September 2023
| ← 1439edo | 1440edo | 1441edo → |
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 2.15.17.19.21.23.25.27.31.33 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 (%) | -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
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.