22/19

22/19, the undevicesimal semifourth, is a 19-limit interseptimal interval measuring about 254 cents. It is classified as a major second in FJS and HEJI, sharp of the Pythagorean major second by 176/171, which is the difference between 33/32 and 513/512. Margo Schulter has called it the minimal minor third instead, in which case it is flat of the Pythagorean minor third by 304/297. A stack of two 22/19's exceeds 4/3 by 363/361.

Interval information

Ratio	22/19
Factorization	2 × 11 × 19-1
Monzo	[1 0 0 0 1 0 0 -1⟩
Size in cents	253.8049¢
Names	undevicesimal semifourth, minimal minor third, godzilla semifourth
Color name	19u1o2, nulo 2nd
FJS name	[math]\displaystyle{ \text{M2}^{11}_{19} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.70736
Weil norm (log2 max(n, d))	8.91886
Wilson norm (sopfr(nd))	32
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Since it is a good tuning for the godzilla generator in the 11-limit and 13-limit, it can also be called the godzilla semifourth: in godzilla, it serves for both 8/7 and 7/6.

Approximation

Edo approximations for 22/19 (253.80 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
5	1\5	240.00	-13.80	-5.75
9	2\9	266.67	+12.86	+9.65
14	3\14	257.14	+3.34	+3.89
19	4\19	252.63	-1.17	-1.86
24	5\24	250.00	-3.80	-7.61
28	6\28	257.14	+3.34	+7.79
33	7\33	254.55	+0.74	+2.04
38	8\38	252.63	-1.17	-3.72
43	9\43	251.16	-2.64	-9.47
47	10\47	255.32	+1.51	+5.93
52	11\52	253.85	+0.04	+0.18
57	12\57	252.63	-1.17	-5.57
61	13\61	255.74	+1.93	+9.82
66	14\66	254.55	+0.74	+4.07
71	15\71	253.52	-0.28	-1.68
76	16\76	252.63	-1.17	-7.43
80	17\80	255.00	+1.20	+7.97

See also

• 19/11 – its octave complement
• Gallery of just intervals