22/13: Difference between revisions

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

Latest revision as of 14:48, 22 July 2026

In 13-limit just intonation, 22/13 is a tridecimal major sixth, specifically the major-minthmic major sixth, 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).

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

@@ Line 1: / Line 1: @@
-'''22/13'''
+{{Infobox Interval
-|1 0 0 0 1 -1&gt;
+| Name = tridecimal major sixth, major-minthmic major sixth
+| Color name = 3u1o6, thulo 6th
+| Sound = jid_22_13_pluck_adu_dr220.mp3
+}}
-.7903 cents
+In [[13-limit]] [[just intonation]], '''22/13''' is a '''tridecimal major sixth''', specifically the '''major-minthmic major sixth''', measuring about 910.8 [[cent]]s. It is the inverse of [[13/11]], the tridecimal minor third. It is sharp of the [[27/16|Pythagorean major sixth (27/16)]] by a [[352/351|major minthma (352/351)]].
-[[File:jid_22_13_pluck_adu_dr220.mp3]] [[:File:jid_22_13_pluck_adu_dr220.mp3|sound sample]]
+== Approximation ==
+This interval is well approximated by [[17edo|13\17]] (917.647 cents), and even better, by [[29edo|22\29]] (910.345 cents).
-See also
+{{Interval edo approximation|22/13}}
-<ul><li>[[13/11|13/11]] the octave-complementary interval</li><li>[[17edo|13\17]] (917.647 cents)</li><li>[[Gallery_of_Just_Intervals|Gallery of Just Intervals]]</li></ul>      [[Category:major_sixt]]
+== See also ==
-[[Category:todo:expand]]
+* [[13/11]] – its [[octave complement]]
-[[Category:tredecimal]]
+* [[Gallery of just intervals]]
+[[Category:Sixth]]
+[[Category:Major sixth]]
+[[Category:Major minthmic]]