22/13

Interval information
Ratio	22/13
Factorization	2 × 11 × 13-1
Monzo	[1 0 0 0 1 -1⟩
Size in cents	910.7903¢
Names	tridecimal major sixth,; major minthmic major sixth
Color name	3u1o6, thulo 6th
FJS name	[math]\displaystyle{ \text{M6}^{11}_{13} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.15987
Weil norm (log2 max(n, d))	8.91886
Wilson norm (sopfr(nd))	26
	https://en.xen.wiki/w/File:Jid_22_13_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

22/13, the tridecimal major sixth or major minthmic major sixth, is a 13-limit just intonation interval measuring about 910.8 cents. It is the inverse of 13/11, the tridecimal minor third. It is sharp of the Pythagorean major sixth (27/16) by a major minthma (352/351).

Approximation

This interval is well approximated by 13\17 (917.647 cents), and even better, by 22\29 (910.345 cents).

Edo approximations for 22/13 (910.79 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
4	3\4	900.00	-10.79	-3.60
8	6\8	900.00	-10.79	-7.19
17	13\17	917.65	+6.86	+9.71
21	16\21	914.29	+3.50	+6.12
25	19\25	912.00	+1.21	+2.52
29	22\29	910.34	-0.45	-1.08
33	25\33	909.09	-1.70	-4.67
37	28\37	908.11	-2.68	-8.27
46	35\46	913.04	+2.25	+8.64
50	38\50	912.00	+1.21	+5.04
54	41\54	911.11	+0.32	+1.44
58	44\58	910.34	-0.45	-2.15
62	47\62	909.68	-1.11	-5.75
66	50\66	909.09	-1.70	-9.35
75	57\75	912.00	+1.21	+7.56
79	60\79	911.39	+0.60	+3.96