5544edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == 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. | 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. | ||
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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}} | |||
Latest revision as of 07:01, 20 February 2025
| ← 5543edo | 5544edo | 5545edo → |
5544 equal divisions of the octave (abbreviated 5544edo or 5544ed2), also called 5544-tone equal temperament (5544tet) or 5544 equal temperament (5544et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5544 equal parts of about 0.216 ¢ each. Each step represents a frequency ratio of 21/5544, or the 5544th root of 2.
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) | |