26ed5/2

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← 25ed5/226ed5/227ed5/2 →
Prime factorization 2 × 13
Step size 61.0121¢ 
Octave 20\26ed5/2 (1220.24¢) (→10\13ed5/2)
Twelfth 31\26ed5/2 (1891.37¢)
(semiconvergent)
Consistency limit 2
Distinct consistency limit 2

26 equal divisions of 5/2 (abbreviated 26ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 26 equal parts of about 61 ¢ each. Each step represents a frequency ratio of (5/2)1/26, or the 26th root of 5/2.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 61.012 25/24, 26/25
2 122.024 14/13, 15/14
3 183.036
4 244.048 15/13, 22/19
5 305.06 6/5
6 366.072 21/17
7 427.084 9/7, 14/11, 23/18
8 488.097
9 549.109 26/19
10 610.121
11 671.133 22/15
12 732.145 23/15
13 793.157 11/7, 19/12
14 854.169 18/11, 23/14
15 915.181 22/13
16 976.193 23/13
17 1037.205
18 1098.217 17/9
19 1159.229
20 1220.241
21 1281.253 23/11, 25/12
22 1342.265 13/6
23 1403.278
24 1464.29 7/3
25 1525.302 12/5, 17/7
26 1586.314 5/2

Harmonics

Approximation of harmonics in 26ed5/2
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +20.2 -10.6 -20.5 +20.2 +9.7 -13.2 -0.3 -21.2 -20.5 -2.5 +29.9
Relative (%) +33.2 -17.3 -33.6 +33.2 +15.8 -21.6 -0.5 -34.7 -33.6 -4.1 +49.0
Steps
(reduced)
20
(20)
31
(5)
39
(13)
46
(20)
51
(25)
55
(3)
59
(7)
62
(10)
65
(13)
68
(16)
71
(19)
Approximation of harmonics in 26ed5/2
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +13.4 +7.1 +9.7 +20.0 -24.0 -0.9 +27.5 -0.3 -23.7 +17.7 +1.8
Relative (%) +21.9 +11.6 +15.8 +32.7 -39.3 -1.5 +45.1 -0.5 -38.9 +29.1 +2.9
Steps
(reduced)
73
(21)
75
(23)
77
(25)
79
(1)
80
(2)
82
(4)
84
(6)
85
(7)
86
(8)
88
(10)
89
(11)