444edo

← 443edo

444edo

445edo →

Prime factorization	22 × 3 × 37
Step size	2.7027 ¢
Fifth	260\444 (702.703 ¢) (→ 65\111)
Semitones (A1:m2)	44:32 (118.9 ¢ : 86.49 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

444et is only consistent to the 5-limit. Using the patent val, it tempers out 67108864/66976875, 29360128/29296875 and 250047/250000 in the 7-limit; 100663296/100656875, 2097152/2096325, 131072/130977, 172032/171875, 5632/5625, 47265625/47258883, 3025/3024, 160083/160000, 42592/42525, 391314/390625, 102487/102400, 322102/321489 and 1771561/1769472 in the 11-limit. It provides the optimal patent val for the magnesium temperament.

Odd harmonics

Approximation of odd harmonics in 444edo

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

444 factors into 2₂ × 3 × 37, with 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

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[176 -111⟩	[⟨444 704]]	-0.2359	0.2358	8.72
2.3.5	[41 -20 -4⟩, [-29 -11 20⟩	[⟨444 704 1031]]	-0.1821	0.2071	7.66

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)*	Cents (reduced)*	Associated Ratio*	Temperaments
1	13\444	35.14	1990656/1953125	Gammic
4	184\444 (38\444)	497.30 (102.70)	4/3 (35/33)	Undim

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct