45/38

45/38 is a 19-limit interval, 292.7 cents in size. In the Functional Just System and Helmholtz-Ellis notation, it is an augmented second, obtained by subtracting 81/80 and 513/512 to the Pythagorean augmented second, but it may be called the Eratosthenes' minor third as it is flatter than the Pythagorean minor third by the password aka Eratosthenes' comma (1216/1215), an unnoticeable comma of about 1.4243 cents.

Interval information

Ratio	45/38
Subgroup monzo	2.3.5.19 [-1 2 1 -1⟩
Size in cents	292.7107¢
Name	Eratosthenes' minor third
Color name	19uy2, nuyo 2nd
FJS name	[math]\displaystyle{ \text{A2}^{5}_{19} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	10.7398
Weil norm (log2 max(n, d))	10.9837
Wilson norm (sopfr(nd))	32
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Approximation

Edo approximations for 45/38 (292.71 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
4	1\4	300.00	+7.29	+2.43
8	2\8	300.00	+7.29	+4.86
12	3\12	300.00	+7.29	+7.29
16	4\16	300.00	+7.29	+9.72
25	6\25	288.00	-4.71	-9.81
29	7\29	289.66	-3.06	-7.38
33	8\33	290.91	-1.80	-4.95
37	9\37	291.89	-0.82	-2.52
41	10\41	292.68	-0.03	-0.09
45	11\45	293.33	+0.62	+2.33
49	12\49	293.88	+1.17	+4.76
53	13\53	294.34	+1.63	+7.19
57	14\57	294.74	+2.03	+9.62
66	16\66	290.91	-1.80	-9.91
70	17\70	291.43	-1.28	-7.48
74	18\74	291.89	-0.82	-5.05
78	19\78	292.31	-0.40	-2.62

See also

• 76/45 – its octave complement
• 19/15 – its fifth complement
• Gallery of just intervals