1440edo: Difference between revisions
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{{EDO intro|1440}} | {{EDO intro|1440}} | ||
1440edo is in[[consistent]] 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 === | === Odd harmonics === | ||
{{Harmonics in equal|1440}} | {{Harmonics in equal|1440}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
1440edo is notable for having a lot of | Since 1440 factors into {{factorization|1440}}, 1440edo is notable for having a lot of subset edos, the nontrivial ones being {{EDOs| 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 composite equal division #Highly factorable numbers|highly factorable equal division]]. | ||
As an interval size measure, one step of 1440edo is called ''decifarab''. | As an interval size measure, one step of 1440edo is called ''decifarab''. | ||
Revision as of 09:13, 31 October 2023
| ← 1439edo | 1440edo | 1441edo → |
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
| 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.