26ed5/2
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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
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← 25ed5/2 | 26ed5/2 | 27ed5/2 → |
(semiconvergent)
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
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) |
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) |