22ed5/3

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← 21ed5/322ed5/323ed5/3 →
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)