User:MisterShafXen/8ed13/4: Difference between revisions
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| Line 10: | Line 10: | ||
| steps = 8 | | steps = 8 | ||
| intervals = prime | | intervals = prime | ||
| columns = | | columns = 8}} | ||
{{Harmonics in equal | {{Harmonics in equal | ||
| num = 13 | | num = 13 | ||
| Line 16: | Line 16: | ||
| steps = 8 | | steps = 8 | ||
| intervals = prime | | intervals = prime | ||
| start = | | start = 9 | ||
| columns = | | columns = 8}} | ||
{{Harmonics in equal | |||
| num = 13 | |||
| denom = 4 | |||
| steps = 8 | |||
| intervals = prime | |||
| start = 18 | |||
| columns = 8}} | |||
Revision as of 12:35, 24 June 2025
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 | |
|---|---|---|---|---|---|---|---|---|---|
| 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) | |