15ed7/3
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15 equal divisions of 7/3 (abbreviated 15ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 15 equal parts of about 97.8 ¢ each. Each step represents a frequency ratio of (7/3)1/15, or the 15th root of 7/3.
Theory
The chord [0 5 9]\15ed7/3, closely resembling the 5-limit major triad of 15edo, is a close approximation in this tuning system to 3:4:5. A potentially tempered 15ed7/3 chain with octaves as the equivalence results in passion temperament, with 3:4:5:7 located on the same position that it is in 15ed7/3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -26.5 | -43.9 | +44.8 | -48.2 | +27.4 | -43.9 | +18.3 | +10.0 | +23.1 | -44.1 | +0.9 |
| Relative (%) | -27.1 | -44.9 | +45.8 | -49.2 | +28.0 | -44.9 | +18.7 | +10.2 | +23.7 | -45.1 | +0.9 | |
| Steps (reduced) |
12 (12) |
19 (4) |
25 (10) |
28 (13) |
32 (2) |
34 (4) |
37 (7) |
39 (9) |
41 (11) |
42 (12) |
44 (14) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -39.9 | +27.4 | +5.7 | -8.2 | -15.4 | -16.5 | -12.4 | -3.4 | +10.0 | +27.2 | +48.0 | -25.6 |
| Relative (%) | -40.8 | +28.0 | +5.8 | -8.4 | -15.7 | -16.9 | -12.6 | -3.4 | +10.2 | +27.8 | +49.1 | -26.2 | |
| Steps (reduced) |
45 (0) |
47 (2) |
48 (3) |
49 (4) |
50 (5) |
51 (6) |
52 (7) |
53 (8) |
54 (9) |
55 (10) |
56 (11) |
56 (11) | |
Intervals
| # | Cents |
|---|---|
| 1 | 97.8 |
| 2 | 195.6 |
| 3 | 293.4 |
| 4 | 391.2 |
| 5 | 489.0 |
| 6 | 586.7 |
| 7 | 684.5 |
| 8 | 782.3 |
| 9 | 880.1 |
| 10 | 977.9 |
| 11 | 1075.7 |
| 12 | 1173.5 |
| 13 | 1271.3 |
| 14 | 1369.1 |
| 15 | 1466.9 |