22ed5/3

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22ed5/3

23ed5/3 →

Prime factorization	2 × 11
Step size	40.1981¢
Octave	30\22ed5/3 (1205.94¢) (→15\11ed5/3)
Twelfth	47\22ed5/3 (1889.31¢)
Consistency limit	3
Distinct consistency limit	3

22 equal divisions of 5/3 (abbreviated 22ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 22 equal parts of about 40.2 ¢ each. Each step represents a frequency ratio of (5/3)^1/22, or the 22nd root of 5/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	40.198
2	80.396	20/19, 21/20, 22/21, 23/22, 24/23
3	120.594
4	160.792	11/10, 12/11, 21/19, 23/21
5	200.991	19/17
6	241.189	8/7, 15/13, 22/19, 23/20
7	281.387	13/11, 20/17
8	321.585	6/5, 23/19
9	361.783	11/9, 21/17
10	401.981	24/19
11	442.179	13/10, 22/17
12	482.377
13	522.576	15/11, 19/14, 23/17
14	562.774	18/13, 25/18
15	602.972	17/12, 24/17
16	643.17	13/9
17	683.368
18	723.566
19	763.764	17/11
20	803.962	19/12
21	844.161	18/11, 21/13
22	884.359	5/3

Harmonics

Approximation of harmonics in 22ed5/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+5.9	-12.6	+11.9	-12.6	-6.7	+7.8	+17.8	+14.9	-6.7	-10.9	-0.8
	Relative (%)	+14.8	-31.5	+29.6	-31.5	-16.7	+19.4	+44.4	+37.1	-16.7	-27.1	-1.9
Steps (reduced)		30 (8)	47 (3)	60 (16)	69 (3)	77 (11)	84 (18)	90 (2)	95 (7)	99 (11)	103 (15)	107 (19)

Approximation of harmonics in 22ed5/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-18.7	+13.8	+14.9	-16.4	-0.8	-19.3	+7.6	-0.8	-4.8	-5.0	-1.5
	Relative (%)	-46.6	+34.2	+37.1	-40.9	-2.0	-48.1	+19.0	-1.9	-12.0	-12.4	-3.8
Steps (reduced)		110 (0)	114 (4)	117 (7)	119 (9)	122 (12)	124 (14)	127 (17)	129 (19)	131 (21)	133 (1)	135 (3)