22ed5/2

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22ed5/2

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Prime factorization	2 × 11
Step size	72.1052¢
Octave	17\22ed5/2 (1225.79¢)
Twelfth	26\22ed5/2 (1874.73¢) (→13\11ed5/2)
Consistency limit	2
Distinct consistency limit	2

22 equal divisions of 5/2 (abbreviated 22ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 22 equal parts of about 72.1 ¢ each. Each step represents a frequency ratio of (5/2)^1/22, or the 22nd root of 5/2.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	72.105	25/24
2	144.21	12/11, 13/12, 23/21
3	216.316	17/15, 25/22
4	288.421	13/11
5	360.526	21/17
6	432.631	23/18
7	504.736
8	576.841	7/5
9	648.947	19/13
10	721.052
11	793.157	11/7, 19/12
12	865.262
13	937.367	12/7, 19/11
14	1009.472	25/14
15	1081.578	13/7
16	1153.683
17	1225.788
18	1297.893
19	1369.998	11/5
20	1442.103
21	1514.209	12/5
22	1586.314	5/2

Harmonics

Approximation of harmonics in 22ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+25.8	-27.2	-20.5	+25.8	-1.4	+20.1	+5.3	+17.7	-20.5	+30.8	+24.4
	Relative (%)	+35.8	-37.8	-28.5	+35.8	-2.0	+27.9	+7.3	+24.5	-28.5	+42.7	+33.8
Steps (reduced)		17 (17)	26 (4)	33 (11)	39 (17)	43 (21)	47 (3)	50 (6)	53 (9)	55 (11)	58 (14)	60 (16)

Approximation of harmonics in 22ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+30.0	-26.2	-1.4	+31.0	-1.8	-28.7	+22.0	+5.3	-7.1	-15.5	-20.4
	Relative (%)	+41.6	-36.3	-2.0	+43.1	-2.5	-39.7	+30.4	+7.3	-9.9	-21.5	-28.3
Steps (reduced)		62 (18)	63 (19)	65 (21)	67 (1)	68 (2)	69 (3)	71 (5)	72 (6)	73 (7)	74 (8)	75 (9)