27/16

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The Pythagorean major sixth, 27/16, may be reached by stacking three perfect fifths (3/2) and reducing by one octave. Compared to the more typical 5/3 which is narrower by 81/80, this interval is more dissonant, with a harmonic entropy level roughly on par with that of 6/5.

Interval information
Ratio 27/16
Factorization 2-4 × 33
Monzo [-4 3
Size in cents 905.865¢
Name Pythagorean major sixth
Color name w6, wa 6th
FJS name [math]\displaystyle{ \text{M6} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 8.75489
Weil norm (log2 max(n, d)) 9.50978
Wilson norm (sopfr(nd)) 17

[sound info]
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Approximation

Edo approximations for 27/16 (905.87 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
4 3\4 900.00 -5.87 -1.96
8 6\8 900.00 -5.87 -3.91
12 9\12 900.00 -5.87 -5.87
16 12\16 900.00 -5.87 -7.82
20 15\20 900.00 -5.87 -9.78
33 25\33 909.09 +3.23 +8.87
37 28\37 908.11 +2.24 +6.92
41 31\41 907.32 +1.45 +4.96
45 34\45 906.67 +0.80 +3.01
49 37\49 906.12 +0.26 +1.05
53 40\53 905.66 -0.20 -0.90
57 43\57 905.26 -0.60 -2.86
61 46\61 904.92 -0.95 -4.81
65 49\65 904.62 -1.25 -6.77
69 52\69 904.35 -1.52 -8.72

See also