User:MisterShafXen/8ed13/4
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8 equal divisions of 13/4 (abbreviated 8ed13/4) is a nonoctave tuning system that divides the interval of 13/4 into 8 equal parts of about 255 ¢ each. Each step represents a frequency ratio of (13/4)1/8, or the 8th root of 13/4.
Theory
This tuning tempers out 11/10 in the 11-limit, 23/20 and 23/22 in the 23-limit
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +75 | -116 | +19 | -53 | -70 | -104 | -59 | +4 | -72 | +37 | -79 | +125 | -52 | +120 | -34 | +13 | +83 | +25 | +118 | +17 |
| Relative (%) | +29.5 | -45.7 | +7.6 | -20.8 | -27.5 | -40.9 | -23.0 | +1.5 | -28.2 | +14.5 | -30.8 | +49.1 | -20.5 | +47.1 | -13.2 | +5.2 | +32.4 | +9.8 | +46.1 | +6.7 | |
| Steps (reduced) |
5 (5) |
7 (7) |
11 (3) |
13 (5) |
16 (0) |
17 (1) |
19 (3) |
20 (4) |
21 (5) |
23 (7) |
23 (7) |
25 (1) |
25 (1) |
26 (2) |
26 (2) |
27 (3) |
28 (4) |
28 (4) |
29 (5) |
29 (5) | |
| Harmonic | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | 127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -31 | +87 | +2 | -119 | -13 | -83 | -117 | +72 | +40 | -22 | +31 | -23 | -100 | -126 | +9 | -14 | -81 | +109 | +67 | +6 |
| Relative (%) | -12.1 | +34.3 | +0.8 | -46.6 | -5.0 | -32.5 | -45.8 | +28.4 | +15.8 | -8.7 | +12.1 | -9.0 | -39.4 | -49.2 | +3.6 | -5.4 | -31.9 | +42.7 | +26.2 | +2.3 | |
| Steps (reduced) |
29 (5) |
30 (6) |
30 (6) |
30 (6) |
31 (7) |
31 (7) |
31 (7) |
32 (0) |
32 (0) |
32 (0) |
33 (1) |
33 (1) |
33 (1) |
33 (1) |
34 (2) |
34 (2) |
34 (2) |
35 (3) |
35 (3) |
35 (3) | |