55/48

Interval information

Ratio	55/48
Factorization	2-4 × 3-1 × 5 × 11
Monzo	[-4 -1 1 0 1⟩
Size in cents	235.6767¢
Name	keenanismic supermajor second
Color name	1oy2, loyo 2nd
FJS name	[math]\displaystyle{ \text{M2}^{5,11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	11.3663
Weil norm (log2 max(n, d))	11.5627
Wilson norm (sopfr(nd))	27
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55/48, the keenanismic supermajor second, is 385/384 (4.5 ¢) sharper than 8/7. It arises in 11-limit JI scales as the interval between 16/15 and 11/9, 12/11 and 5/4, 6/5 and 11/8, and their inversions.

Approximation

It is 0.038 ¢ flatter than the 11\56 supermajor second of 56edo.

Edo approximations for 55/48 (235.68 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
5	1\5	240.00	+4.32	+1.80
10	2\10	240.00	+4.32	+3.60
15	3\15	240.00	+4.32	+5.40
20	4\20	240.00	+4.32	+7.21
25	5\25	240.00	+4.32	+9.01
31	6\31	232.26	-3.42	-8.83
36	7\36	233.33	-2.34	-7.03
41	8\41	234.15	-1.53	-5.23
46	9\46	234.78	-0.89	-3.43
51	10\51	235.29	-0.38	-1.63
56	11\56	235.71	+0.04	+0.18
61	12\61	236.07	+0.39	+1.98
66	13\66	236.36	+0.69	+3.78
71	14\71	236.62	+0.94	+5.58
76	15\76	236.84	+1.17	+7.38

Usage

This interval is prominent in Johannes Dahle's playing, as he uses it to harmonize with a 11/8.

See also

• 96/55 – its octave complement
• 144/110 – its fifth complement
• Gallery of just intervals