19ed5/2

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← 18ed5/219ed5/220ed5/2 →
Prime factorization 19 (prime)
Step size 83.4902¢ 
Octave 14\19ed5/2 (1168.86¢)
Twelfth 23\19ed5/2 (1920.27¢)
Consistency limit 2
Distinct consistency limit 2

19 equal divisions of 5/2 (abbreviated 19ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 19 equal parts of about 83.5 ¢ each. Each step represents a frequency ratio of (5/2)1/19, or the 19th root of 5/2.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 83.49 18/17, 19/18, 22/21, 23/22
2 166.98 21/19, 23/21
3 250.471 7/6, 15/13, 22/19
4 333.961 11/9, 23/19
5 417.451 19/15, 23/18
6 500.941
7 584.431 7/5
8 667.922 19/13, 22/15
9 751.412 17/11, 23/15
10 834.902 21/13
11 918.392 12/7, 22/13
12 1001.882 23/13
13 1085.373 13/7, 17/9
14 1168.863
15 1252.353
16 1335.843 13/6, 15/7
17 1419.333
18 1502.824 12/5
19 1586.314 5/2

Harmonics

Approximation of harmonics in 19ed5/2
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -31.1 +18.3 +21.2 -31.1 -12.8 -29.2 -9.9 +36.6 +21.2 +23.2 +39.5
Relative (%) -37.3 +21.9 +25.4 -37.3 -15.4 -35.0 -11.9 +43.9 +25.4 +27.8 +47.4
Steps
(reduced)
14
(14)
23
(4)
29
(10)
33
(14)
37
(18)
40
(2)
43
(5)
46
(8)
48
(10)
50
(12)
52
(14)
Approximation of harmonics in 19ed5/2
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -15.5 +23.1 -12.8 -41.1 +21.0 +5.5 -4.6 -9.9 -10.9 -7.9 -1.4
Relative (%) -18.6 +27.7 -15.4 -49.2 +25.1 +6.6 -5.5 -11.9 -13.1 -9.5 -1.7
Steps
(reduced)
53
(15)
55
(17)
56
(18)
57
(0)
59
(2)
60
(3)
61
(4)
62
(5)
63
(6)
64
(7)
65
(8)