23ed5/2

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← 22ed5/223ed5/224ed5/2 →
Prime factorization 23 (prime)
Step size 68.9702¢ 
Octave 17\23ed5/2 (1172.49¢)
Twelfth 28\23ed5/2 (1931.16¢)
Consistency limit 2
Distinct consistency limit 2

23 equal divisions of 5/2 (abbreviated 23ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 23 equal parts of about 69 ¢ each. Each step represents a frequency ratio of (5/2)1/23, or the 23rd root of 5/2.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 68.97 25/24
2 137.94 12/11, 13/12, 14/13
3 206.91 17/15
4 275.881 7/6, 13/11
5 344.851 17/14
6 413.821 14/11, 19/15, 23/18
7 482.791
8 551.761
9 620.731
10 689.702
11 758.672 17/11
12 827.642
13 896.612
14 965.582
15 1034.552
16 1103.523
17 1172.493
18 1241.463
19 1310.433 15/7
20 1379.403
21 1448.373
22 1517.344 12/5
23 1586.314 5/2

Harmonics

Approximation of harmonics in 23ed5/2
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -27.5 +29.2 +14.0 -27.5 +1.7 +10.7 -13.6 -10.6 +14.0 -13.1 -25.8
Relative (%) -39.9 +42.4 +20.2 -39.9 +2.5 +15.5 -19.6 -15.3 +20.2 -19.0 -37.4
Steps
(reduced)
17
(17)
28
(5)
35
(12)
40
(17)
45
(22)
49
(3)
52
(6)
55
(9)
58
(12)
60
(14)
62
(16)
Approximation of harmonics in 23ed5/2
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -26.4 -16.8 +1.7 +27.9 -8.1 +30.9 +6.3 -13.6 -29.0 +28.4 +20.4
Relative (%) -38.3 -24.4 +2.5 +40.5 -11.7 +44.8 +9.1 -19.6 -42.1 +41.1 +29.5
Steps
(reduced)
64
(18)
66
(20)
68
(22)
70
(1)
71
(2)
73
(4)
74
(5)
75
(6)
76
(7)
78
(9)
79
(10)