33/26: Difference between revisions

Interval information
Ratio	33/26
Factorization	2-1 × 3 × 11 × 13-1
Monzo	[-1 1 0 0 1 -1⟩
Size in cents	412.7453¢
Names	major minthmic major third,; tridecimal major third
Color name	3u1o3, thulo 3rd
FJS name	[math]\displaystyle{ \text{M3}^{11}_{13} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	9.74483
Weil norm (log2 max(n, d))	10.0888
Wilson norm (sopfr(nd))	29
	https://en.xen.wiki/w/File:Ji-33-26-csound-foscil-220hz.mp3; [sound info]
	Open this interval in xen-calc

Latest revision as of 13:01, 3 November 2025

33/26, the major minthmic major third or tridecimal major third, is a 13-limit interval measuring about 412.7 ¢. It is the fifth complement of the tridecimal minor third, 13/11. It is sharp of the Pythagorean major third (81/64) by a major minthma (352/351).

Edo approximations for 33/26 (412.75 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
3	1\3	400.00	-12.75	-3.19
6	2\6	400.00	-12.75	-6.37
9	3\9	400.00	-12.75	-9.56
23	8\23	417.39	+4.65	+8.90
26	9\26	415.38	+2.64	+5.72
29	10\29	413.79	+1.05	+2.53
32	11\32	412.50	-0.25	-0.65
35	12\35	411.43	-1.32	-3.84
38	13\38	410.53	-2.22	-7.03
55	19\55	414.55	+1.80	+8.25
58	20\58	413.79	+1.05	+5.06
61	21\61	413.11	+0.37	+1.88
64	22\64	412.50	-0.25	-1.31
67	23\67	411.94	-0.80	-4.49
70	24\70	411.43	-1.32	-7.68

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = major minthmic major third, tridecimal major third
-| Ratio = 33/26
+| Color name = 3u1o3, thulo 3rd
-| Monzo = -1 1 0 0 1 -1
-| Cents = 412.74528
-| Name = tridecimal major third
-| Color name =
-| FJS name = M3<sup>11</sup><sub>13</sub>
 | Sound = Ji-33-26-csound-foscil-220hz.mp3
 }}
-'''33/26''', the '''tridecimal major third''', is a [[13-limit]] interval measuring about 412.7 [[Cent|cents]]. It is the [[fifth complement]] of the tridecimal minor third, [[13/11]]. It is sharp of the Pythagorean major third [[81/64]] by [[352/351]].
+'''33/26''', the '''major minthmic major third''' or '''tridecimal major third''', is a [[13-limit]] interval measuring about 412.7{{cent}}. It is the [[fifth complement]] of the tridecimal minor third, [[13/11]]. It is sharp of the [[81/64|Pythagorean major third (81/64)]] by a [[352/351|major minthma (352/351)]].
+== Approximation ==
+{{Interval edo approximation|33/26}}
 == See also ==
 * [[52/33]] – its [[octave complement]]
@@ Line 17: / Line 13: @@
 * [[Gallery of just intervals]]
-[[Category:13-limit]]
-[[Category:Interval ratio]]
 [[Category:Third]]
 [[Category:Major third]]
-[[Category:Listen]]
+[[Category:Major minthmic]]
-[[Category:Minthmic]]
-[[Category:Todo:expand]]
-[[Category:Todo:improve synopsis]]