22ed5/4

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22ed5/4

23ed5/4 →

Prime factorization	2 × 11
Step size	17.5597¢
Octave	68\22ed5/4 (1194.06¢) (→34\11ed5/4)
Twelfth	108\22ed5/4 (1896.45¢) (→54\11ed5/4)
Consistency limit	3
Distinct consistency limit	2

22 equal divisions of 5/4 (abbreviated 22ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 22 equal parts of about 17.6 ¢ each. Each step represents a frequency ratio of (5/4)^1/22, or the 22nd root of 5/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.6
2	35.1
3	52.7
4	70.2	22/21
5	87.8	18/17, 20/19, 21/20, 23/22
6	105.4	19/18
7	122.9	14/13, 15/14
8	140.5	12/11
9	158	11/10, 23/21, 25/23
10	175.6	21/19
11	193.2	10/9, 19/17
12	210.7	9/8, 17/15
13	228.3
14	245.8	15/13, 22/19, 23/20
15	263.4
16	281	7/6, 20/17
17	298.5	13/11
18	316.1	25/21
19	333.6	17/14, 23/19
20	351.2	11/9
21	368.8	21/17
22	386.3

Harmonics

Approximation of harmonics in 22ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.94	-5.51	+5.68	+5.68	+6.11	+2.64	-0.26	+6.55	-0.26	-7.23	+0.17
	Relative (%)	-33.8	-31.4	+32.4	+32.4	+34.8	+15.0	-1.5	+37.3	-1.5	-41.1	+1.0
Steps (reduced)		68 (2)	108 (20)	137 (5)	159 (5)	177 (1)	192 (16)	205 (7)	217 (19)	227 (7)	236 (16)	245 (3)

Approximation of harmonics in 22ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.08	-3.30	+0.17	-6.20	-5.80	+0.61	-5.20	-6.20	-2.87	+4.39	-2.32
	Relative (%)	+11.8	-18.8	+1.0	-35.3	-33.0	+3.5	-29.6	-35.3	-16.3	+25.0	-13.2
Steps (reduced)		253 (11)	260 (18)	267 (3)	273 (9)	279 (15)	285 (21)	290 (4)	295 (9)	300 (14)	305 (19)	309 (1)