User:MisterShafXen/25ed7
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Prime factorization
52
Step size
134.753 ¢
Octave
9\25ed7 (1212.78 ¢)
Twelfth
14\25ed7 (1886.54 ¢)
Consistency limit
8
Distinct consistency limit
6
| ← 24ed7 | 25ed7 | 26ed7 → |
25 equal divisions of the 7th harmonic (abbreviated 25ed7) is a nonoctave tuning system that divides the interval of 7/1 into 25 equal parts of about 135 ¢ each. Each step represents a frequency ratio of 71/25, or the 25th root of 7.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 134.8 | 13/12, 14/13 |
| 2 | 269.5 | 7/6 |
| 3 | 404.3 | 19/15, 24/19 |
| 4 | 539 | 11/8, 15/11, 19/14, 26/19 |
| 5 | 673.8 | 22/15 |
| 6 | 808.5 | 8/5 |
| 7 | 943.3 | 12/7, 19/11, 26/15 |
| 8 | 1078 | 13/7, 15/8 |
| 9 | 1212.8 | |
| 10 | 1347.5 | 13/6, 24/11 |
| 11 | 1482.3 | 26/11 |
| 12 | 1617 | 23/9 |
| 13 | 1751.8 | 11/4 |
| 14 | 1886.5 | |
| 15 | 2021.3 | 16/5 |
| 16 | 2156 | |
| 17 | 2290.8 | 15/4 |
| 18 | 2425.6 | |
| 19 | 2560.3 | 22/5 |
| 20 | 2695.1 | 19/4 |
| 21 | 2829.8 | |
| 22 | 2964.6 | |
| 23 | 3099.3 | 6/1 |
| 24 | 3234.1 | 13/2 |
| 25 | 3368.8 | 7/1 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.8 | -15.4 | +43.5 | +0.0 | +26.0 | +6.3 | -53.8 | +23.1 | -38.2 | -35.2 | -15.9 |
| Relative (%) | +9.5 | -11.4 | +32.3 | +0.0 | +19.3 | +4.7 | -40.0 | +17.1 | -28.3 | -26.1 | -11.8 | |
| Steps (reduced) |
9 (9) |
14 (14) |
21 (21) |
25 (0) |
31 (6) |
33 (8) |
36 (11) |
38 (13) |
40 (15) |
43 (18) |
44 (19) | |