23/22

Interval information

Ratio	23/22
Factorization	2-1 × 11-1 × 23
Monzo	[-1 0 0 0 -1 0 0 0 1⟩
Size in cents	76.9564¢
Name	greater vicesimotertial semitone
Color name	23o1u2, twetholu 2nd
FJS name	[math]\displaystyle{ \text{A1}^{23}_{11} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	8.98299
Weil norm (log2 max(n, d))	9.04712
Wilson norm (sopfr(nd))	36
Comma size	medium
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23/22, the greater vicesimotertial semitone, is a 23-limit interval. It is the first superparticular interval that is mapped to 0 steps in 12edo, which means it is treated as a comma, although it is more than half the size of a 12edo semitone.

Approximation

Edo approximations for 23/22 (76.96 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
15	1\15	80.00	+3.04	+3.80
16	1\16	75.00	-1.96	-2.61
17	1\17	70.59	-6.37	-9.02
30	2\30	80.00	+3.04	+7.61
31	2\31	77.42	+0.46	+1.20
32	2\32	75.00	-1.96	-5.22
46	3\46	78.26	+1.30	+5.00
47	3\47	76.60	-0.36	-1.41
48	3\48	75.00	-1.96	-7.83
61	4\61	78.69	+1.73	+8.80
62	4\62	77.42	+0.46	+2.39
63	4\63	76.19	-0.77	-4.02
77	5\77	77.92	+0.97	+6.20
78	5\78	76.92	-0.03	-0.22
79	5\79	75.95	-1.01	-6.63

See also

• 24/23 – the lesser vicesimotertial semitone
• Gallery of just intervals