22ed7/4

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22ed7/4

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Prime factorization	2 × 11
Step size	44.0375¢
Octave	27\22ed7/4 (1189.01¢)
Twelfth	43\22ed7/4 (1893.61¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	3

22 equal divisions of 7/4 (abbreviated 22ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 22 equal parts of about 44 ¢ each. Each step represents a frequency ratio of (7/4)^1/22, or the 22nd root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	44.038
2	88.075	18/17, 21/20, 22/21, 23/22
3	132.113	15/14, 25/23
4	176.15	10/9, 11/10
5	220.188	8/7, 17/15, 25/22
6	264.225	7/6
7	308.263	6/5, 25/21
8	352.3	11/9, 21/17
9	396.338	5/4
10	440.375	9/7, 22/17
11	484.413	4/3, 21/16
12	528.45	15/11, 23/17
13	572.488	7/5, 25/18
14	616.526	10/7, 17/12
15	660.563	19/13, 22/15, 25/17
16	704.601	3/2
17	748.638	17/11, 23/15
18	792.676	11/7
19	836.713
20	880.751	5/3
21	924.788	12/7, 17/10
22	968.826	7/4

Harmonics

Approximation of harmonics in 22ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11.0	-8.3	-22.0	-11.9	-19.3	-22.0	+11.1	-16.7	+21.1	-11.8	+13.7
	Relative (%)	-24.9	-18.9	-49.9	-27.1	-43.9	-49.9	+25.2	-37.9	+47.9	-26.8	+31.2
Steps (reduced)		27 (5)	43 (21)	54 (10)	63 (19)	70 (4)	76 (10)	82 (16)	86 (20)	91 (3)	94 (6)	98 (10)

Approximation of harmonics in 22ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+7.3	+11.1	-20.3	+0.1	-16.8	+16.4	+10.8	+10.1	+13.7	+21.3	-11.7
	Relative (%)	+16.5	+25.2	-46.1	+0.2	-38.1	+37.2	+24.6	+23.0	+31.2	+48.3	-26.5
Steps (reduced)		101 (13)	104 (16)	106 (18)	109 (21)	111 (1)	114 (4)	116 (6)	118 (8)	120 (10)	122 (12)	123 (13)