444edo
Theory
444edo is only consistent to the 5-odd-limit since harmonic 7 is about halfway between its steps. 444 = 4 × 111, and its harmonic 3 derives from 111edo. Using the patent val, the equal temperament tempers out 250047/250000, 29360128/29296875, 67108864/66976875 and in the 7-limit; 3025/3024, 5632/5625, 42592/42525, 102487/102400, 131072/130977, 160083/160000, 172032/171875, 322102/321489, 391314/390625 and 1771561/1769472 in the 11-limit. It supports the magnesium temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.75 | +0.17 | -1.26 | -1.21 | +0.03 | +0.01 | +0.92 | +0.45 | -0.22 | -0.51 | -1.25 |
| Relative (%) | +27.7 | +6.4 | -46.6 | -44.7 | +1.2 | +0.5 | +34.1 | +16.6 | -8.0 | -18.9 | -46.2 | |
| Steps (reduced) |
704 (260) |
1031 (143) |
1246 (358) |
1407 (75) |
1536 (204) |
1643 (311) |
1735 (403) |
1815 (39) |
1886 (110) |
1950 (174) |
2008 (232) | |
Subsets and supersets
Since 444 factors into 22 × 3 × 37, 444edo has subset edos 2, 3, 4, 6, 12, 37, 74, 111, 148, and 222. 1332edo, which triples it, gives a good correction to the harmonic 7.
Regular temperament properties
Template:Comma basis begin |- | 2.3.5 | [41 -20 -4⟩, [-29 -11 20⟩ | [⟨444 704 1031]] | -0.1821 | 0.2071 | 7.66 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 13\444
| 35.14
| 1990656/1953125
| Gammic (5-limit)
|-
| 4
| 184\444
(38\444)
| 497.30
(102.70)
| 4/3
(35/33)
| Undim (444d)
Template:Rank-2 end
Template:Orf