22ed7/3

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22ed7/3

23ed7/3 →

Prime factorization	2 × 11
Step size	66.676¢
Octave	18\22ed7/3 (1200.17¢) (→9\11ed7/3)
Twelfth	29\22ed7/3 (1933.6¢)
Consistency limit	8
Distinct consistency limit	2

22 equal divisions of 7/3 (abbreviated 22ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 22 equal parts of about 66.7 ¢ each. Each step represents a frequency ratio of (7/3)^1/22, or the 22nd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	66.676	23/22, 25/24
2	133.352	13/12, 14/13, 15/14
3	200.028
4	266.704	7/6, 22/19
5	333.38	17/14, 23/19
6	400.056	5/4
7	466.732	13/10, 17/13
8	533.408
9	600.084	17/12, 24/17
10	666.76	25/17
11	733.435	20/13
12	800.111	8/5
13	866.787
14	933.463	12/7, 19/11
15	1000.139	25/14
16	1066.815	13/7, 24/13
17	1133.491	25/13
18	1200.167	2/1
19	1266.843	23/11, 25/12
20	1333.519	13/6, 15/7
21	1400.195
22	1466.871	7/3

Harmonics

Approximation of harmonics in 22ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.2	+31.6	+0.3	+14.1	+31.8	+31.6	+0.5	-3.4	+14.2	-17.4	+32.0
	Relative (%)	+0.3	+47.5	+0.5	+21.1	+47.7	+47.5	+0.8	-5.1	+21.4	-26.1	+48.0
Steps (reduced)		18 (18)	29 (7)	36 (14)	42 (20)	47 (3)	51 (7)	54 (10)	57 (13)	60 (16)	62 (18)	65 (21)

Approximation of harmonics in 22ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+26.8	+31.8	-21.0	+0.7	+29.1	-3.2	-30.1	+14.4	-3.4	-17.2	-27.5
	Relative (%)	+40.1	+47.7	-31.4	+1.0	+43.6	-4.8	-45.2	+21.6	-5.1	-25.9	-41.3
Steps (reduced)		67 (1)	69 (3)	70 (4)	72 (6)	74 (8)	75 (9)	76 (10)	78 (12)	79 (13)	80 (14)	81 (15)