23/18

Interval information

Ratio	23/18
Subgroup monzo	2.3.23 [-1 -2 1⟩
Size in cents	424.3643¢
Name	vicesimotertial major third
Color name	23o4, twetho 4th
FJS name	[math]\displaystyle{ \text{M3}^{23} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.69349
Weil norm (log2 max(n, d))	9.04712
Wilson norm (sopfr(nd))	31
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23/18, the vicesimoterial major third, is a 23-limit interval that is the mediant between 9/7 and 14/11, giving it a character that is somewhere between the gentle undecimal thirds and the more strident septimal supermajor ones. It is sharp of the Pythagorean major third by a vicesimoterial formal comma, 736/729.

Approximation

This interval is decently represented by 6 steps of 17edo, and near perfectly by 29 steps of 82edo. If used as a generator, it creates squares temperament.

Edo approximations for 23/18 (424.36 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
3	1\3	400.00	-24.36	-6.09
14	5\14	428.57	+4.21	+4.91
17	6\17	423.53	-0.83	-1.18
20	7\20	420.00	-4.36	-7.27
28	10\28	428.57	+4.21	+9.82
31	11\31	425.81	+1.44	+3.73
34	12\34	423.53	-0.83	-2.37
37	13\37	421.62	-2.74	-8.46
45	16\45	426.67	+2.30	+8.63
48	17\48	425.00	+0.64	+2.54
51	18\51	423.53	-0.83	-3.55
54	19\54	422.22	-2.14	-9.64
62	22\62	425.81	+1.44	+7.45
65	23\65	424.62	+0.25	+1.36
68	24\68	423.53	-0.83	-4.73
79	28\79	425.32	+0.95	+6.27

See also

• 36/23 – its octave complement
• 27/23 – its fifth complement
• Gallery of just intervals