15/11

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Interval information
Ratio 15/11
Factorization 3 × 5 × 11-1
Monzo [0 1 1 0 -1
Size in cents 536.9508¢
Names undecimal augmented fourth,
undecimal grave infra-augmented fourth
Color name 1uy4, luyo 4th
FJS name [math]\displaystyle{ \text{A4}^{5}_{11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.36632
Weil norm (log2 max(n, d)) 7.81378
Wilson norm (sopfr(nd)) 19

[sound info]
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The interval 15/11, known most frequently as the undecimal augmented fourth, is the difference between the 11th and 15th partials of the harmonic series. It is 536.95 cents wide, exactly 45/44 larger than a perfect fourth, and almost exactly a sixth-tone sharper than a 12edo fourth. It is narrower than 11/8 by exactly 121/120, and is wider than 27/20 by exactly 100/99. Additionally, it is narrower than 243/176 by exactly 81/80, which lends to it being called the undecimal grave infra-augmented fourth. 15/11 can be called a superfourth, as it falls between the interval categories of perfect fourth and tritone. 4 steps of 9edo is an excellent approximation for 15/11.

Approximation

Edo approximations for 15/11 (536.95 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
9 4\9 533.33 -3.62 -2.71
11 5\11 545.45 +8.50 +7.80
18 8\18 533.33 -3.62 -5.43
20 9\20 540.00 +3.05 +5.08
27 12\27 533.33 -3.62 -8.14
29 13\29 537.93 +0.98 +2.37
38 17\38 536.84 -0.11 -0.34
47 21\47 536.17 -0.78 -3.06
49 22\49 538.78 +1.82 +7.45
56 25\56 535.71 -1.24 -5.77
58 26\58 537.93 +0.98 +4.74
65 29\65 535.38 -1.57 -8.48
67 30\67 537.31 +0.36 +2.02
76 34\76 536.84 -0.11 -0.69
78 35\78 538.46 +1.51 +9.82

See also