55/32

55/32, the keenanismic supermajor sixth, is 385/384 (~4.5 ¢) sharper than 12/7, making it more than a bit useful in 11-limit just intonation.

Interval information

Ratio	55/32
Factorization	2-5 × 5 × 11
Monzo	[-5 0 1 0 1⟩
Size in cents	937.6317¢
Name	keenanismic supermajor sixth
Color name	1oy6, loyo 6th
FJS name	[math]\displaystyle{ \text{M6}^{5,11} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	10.7814
Weil norm (log2 max(n, d))	11.5627
Wilson norm (sopfr(nd))	26
[sound info]
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It also happens to be the ratio between the standard A of 440Hz and the nonstandard C of 256Hz occasionally used for mathematical convenience.

Approximation

Edo approximations for 55/32 (937.63 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
5	4\5	960.00	+22.37	+9.32
9	7\9	933.33	-4.30	-3.22
14	11\14	942.86	+5.23	+6.10
18	14\18	933.33	-4.30	-6.45
23	18\23	939.13	+1.50	+2.87
27	21\27	933.33	-4.30	-9.67
32	25\32	937.50	-0.13	-0.35
37	29\37	940.54	+2.91	+8.97
41	32\41	936.59	-1.05	-3.57
46	36\46	939.13	+1.50	+5.75
50	39\50	936.00	-1.63	-6.80
55	43\55	938.18	+0.55	+2.52
64	50\64	937.50	-0.13	-0.70
69	54\69	939.13	+1.50	+8.62
73	57\73	936.99	-0.65	-3.93
78	61\78	938.46	+0.83	+5.39

See also

• 64/55 -- its octave complement
• Gallery of just intervals