5544edo
|
This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
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) | |