45/38

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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
Open this interval in xen-calc

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.

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