13/12

Interval information

Ratio	13/12
Factorization	2-2 × 3-1 × 13
Monzo	[-2 -1 0 0 0 1⟩
Size in cents	138.5727¢
Name	(lesser) tridecimal neutral second
Color name	3o2, tho 2nd
FJS name	[math]\displaystyle{ \text{m2}^{13} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	7.2854
Weil norm (log2 max(n, d))	7.40088
Wilson norm (sopfr(nd))	20
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In 13-limit just intonation, 13/12 is the (lesser) tridecimal neutral second of about 138.6¢. It is a superparticular interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between 13/8 and 3/2 in the octave). It is flat of the 11-limit lesser neutral second of 12/11 by 144/143 (about 12.1¢), and sharp of the 13-limit large semitone of 14/13 by 169/168 (about 10.3¢).

Temperaments

Todo: expand

Approximation

It is approximated to within about 0.11 cents by the 3-step interval of 26edo.

Edo approximations for 13/12 (138.57 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
8	1\8	150.00	+11.43	+7.62
9	1\9	133.33	-5.24	-3.93
17	2\17	141.18	+2.60	+3.69
18	2\18	133.33	-5.24	-7.86
26	3\26	138.46	-0.11	-0.24
34	4\34	141.18	+2.60	+7.38
35	4\35	137.14	-1.43	-4.17
43	5\43	139.53	+0.96	+3.45
44	5\44	136.36	-2.21	-8.10
52	6\52	138.46	-0.11	-0.48
60	7\60	140.00	+1.43	+7.14
61	7\61	137.70	-0.87	-4.41
69	8\69	139.13	+0.56	+3.21
70	8\70	137.14	-1.43	-8.34
78	9\78	138.46	-0.11	-0.72

See also

• 24/13 – its octave complement
• 18/13 – its fifth complement
• Gallery of just intervals
• List of superparticular intervals