22/15

Interval information

Ratio	22/15
Factorization	2 × 3-1 × 5-1 × 11
Monzo	[1 -1 -1 0 1⟩
Size in cents	663.0492¢
Names	undecimal diminished fifth, undecimal acute ultra-diminished fifth
Color name	1og5, logu 5th
FJS name	[math]\displaystyle{ \text{d5}^{11}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.36632
Weil norm (log2 max(n, d))	8.91886
Wilson norm (sopfr(nd))	21
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The undecimal diminished fifth of 22/15 is flat of 3/2 by 45/44, and is the interval between 5/4 and 11/6. It is wider than 16/11 by exactly 121/120 and narrower than 40/27 by exactly 100/99. Additionally, it is wider than 352/243 by exactly 81/80, which lends to it being called the undecimal acute ultra-diminished fifth. 5 steps of 9edo is a good approximation of this interval.

Approximation

Edo approximations for 22/15 (663.05 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
9	5\9	666.67	+3.62	+2.71
11	6\11	654.55	-8.50	-7.80
18	10\18	666.67	+3.62	+5.43
20	11\20	660.00	-3.05	-5.08
27	15\27	666.67	+3.62	+8.14
29	16\29	662.07	-0.98	-2.37
38	21\38	663.16	+0.11	+0.34
47	26\47	663.83	+0.78	+3.06
49	27\49	661.22	-1.82	-7.45
56	31\56	664.29	+1.24	+5.77
58	32\58	662.07	-0.98	-4.74
65	36\65	664.62	+1.57	+8.48
67	37\67	662.69	-0.36	-2.02
76	42\76	663.16	+0.11	+0.69
78	43\78	661.54	-1.51	-9.82

See also

• 15/11 – its octave complement
• 45/44 – its fifth complement
• Gallery of just intervals