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 25/24 and 27/20 in the 5-limit, 15/14 and 36/35 in the 7-limit, 11/10, 33/28, and 27/22 in the 11-limit, 13/12 and 26/25 in the 13-limit, 35/34 and 18/17 in the 17-limit, 19/18 in the 19-limit, 23/20, 27/23, and 23/22 in the 23-limit, 29/28, 33/29, and 30/29 in the 29-limit, 31/28, 33/31, 31/29, and 31/30 in the 31-limit, 37/32 and 38/37 in the 37-limit, and many more.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +75 | -116 | +19 | -53 | -70 | -104 | -59 | +4 |
| Relative (%) | +29.5 | -45.7 | +7.6 | -20.8 | -27.5 | -40.9 | -23.0 | +1.5 | |
| Steps (reduced) |
5 (5) |
7 (7) |
11 (3) |
13 (5) |
16 (0) |
17 (1) |
19 (3) |
20 (4) | |
| Harmonic | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -72 | +37 | -79 | +125 | -52 | +120 | -34 | +13 |
| Relative (%) | -28.2 | +14.5 | -30.8 | +49.1 | -20.5 | +47.1 | -13.2 | +5.2 | |
| Steps (reduced) |
21 (5) |
23 (7) |
23 (7) |
25 (1) |
25 (1) |
26 (2) |
26 (2) |
27 (3) | |
| Harmonic | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +25 | +118 | +17 | -31 | +87 | +2 | -119 | -13 |
| Relative (%) | +9.8 | +46.1 | +6.7 | -12.1 | +34.3 | +0.8 | -46.6 | -5.0 | |
| Steps (reduced) |
28 (4) |
29 (5) |
29 (5) |
29 (5) |
30 (6) |
30 (6) |
30 (6) |
31 (7) | |