5544edo: Difference between revisions
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proposed lale |
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In addition, it is every fifth step of [[27720edo]], which is a [[highly composite EDO]]. | In addition, it is every fifth step of [[27720edo]], which is a [[highly composite EDO]]. | ||
{{Harmonics in equal|5544}} | === Proposal for an interval size measure === | ||
Eliora proposes that one step of 5544edo be called '''lale''' /`leil/, due to the fact that this EDO maps lalesu-agu comma, {{Monzo|14 21 -1 0 0 0 -11}}, to one step.{{Harmonics in equal|5544}} | |||
Revision as of 14:47, 13 January 2023
| ← 5543edo | 5544edo | 5545edo → |
Theory
5544edo is consistent in the 17-odd-limit. Past the 17-limit, it has good approximations to prime harmonics 31, 37, 43, 61, 71, 79, 83, 97.
Divisors
A notable divisor is 1848edo, which which it shares the mapping for the 11-limit. To the set of divisors of 1848edo, 5544edo also adds 18, 72, 36, 63, 126, 168, 198, 252, 396, 504, 693, 792, 924, 1386, 2772.
In addition, it is every fifth step of 27720edo, which is a highly composite EDO.
Proposal for an interval size measure
Eliora proposes that one step of 5544edo be called lale /`leil/, due to the fact that this EDO maps lalesu-agu comma, [14 21 -1 0 0 0 -11⟩, to one step.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0069 | +0.0499 | +0.0053 | -0.0192 | -0.0515 | +0.0229 | +0.1060 | +0.0806 | +0.0765 | -0.0139 |
| Relative (%) | +0.0 | -3.2 | +23.1 | +2.4 | -8.9 | -23.8 | +10.6 | +49.0 | +37.3 | +35.3 | -6.4 | |
| Steps (reduced) |
5544 (0) |
8787 (3243) |
12873 (1785) |
15564 (4476) |
19179 (2547) |
20515 (3883) |
22661 (485) |
23551 (1375) |
25079 (2903) |
26933 (4757) |
27466 (5290) | |