22ed11/5

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← 21ed11/5 22ed11/5 23ed11/5 →
Prime factorization 2 × 11
Step size 62.0456¢ 
Octave 19\22ed11/5 (1178.87¢)
Twelfth 31\22ed11/5 (1923.42¢)
Consistency limit 2
Distinct consistency limit 2

22 equal divisions of 11/5 (abbreviated 22ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 22 equal parts of about 62 ¢ each. Each step represents a frequency ratio of (11/5)1/22, or the 22nd root of 11/5.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 62.046 24/23
2 124.091
3 186.137 19/17, 21/19
4 248.183 15/13, 22/19, 23/20
5 310.228 6/5, 25/21
6 372.274 21/17
7 434.32 22/17
8 496.365
9 558.411 18/13, 25/18
10 620.456 10/7
11 682.502
12 744.548 17/11
13 806.593 19/12
14 868.639 23/14
15 930.685 12/7, 17/10
16 992.73
17 1054.776 11/6
18 1116.822 19/10, 21/11, 23/12
19 1178.867
20 1240.913
21 1302.959
22 1365.004 11/5

Harmonics

Approximation of harmonics in 22ed11/5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -21.1 +21.5 +19.8 +5.7 +0.3 -18.4 -1.4 -19.1 -15.4 +5.7 -20.8
Relative (%) -34.1 +34.6 +31.9 +9.3 +0.5 -29.6 -2.2 -30.8 -24.8 +9.3 -33.5
Steps
(reduced)
19
(19)
31
(9)
39
(17)
45
(1)
50
(6)
54
(10)
58
(14)
61
(17)
64
(20)
67
(1)
69
(3)
Approximation of harmonics in 22ed11/5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +26.8 +22.6 +27.2 -22.5 -3.3 +21.8 -9.8 +25.5 +3.1 -15.4 -30.3
Relative (%) +43.1 +36.3 +43.8 -36.2 -5.4 +35.1 -15.7 +41.1 +5.0 -24.8 -48.8
Steps
(reduced)
72
(6)
74
(8)
76
(10)
77
(11)
79
(13)
81
(15)
82
(16)
84
(18)
85
(19)
86
(20)
87
(21)