8ed4/3
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Prime factorization
23
Step size
62.2556¢
Octave
19\8ed4/3 (1182.86¢)
Twelfth
31\8ed4/3 (1929.92¢)
Consistency limit
2
Distinct consistency limit
2
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| ← 7ed4/3 | 8ed4/3 | 9ed4/3 → |
8 equal divisions of 4/3 (abbreviated 8ed4/3) is a nonoctave tuning system that divides the interval of 4/3 into 8 equal parts of about 62.3 ¢ each. Each step represents a frequency ratio of (4/3)1/8, or the 8th root of 4/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 62.256 | 19/18, 20/19, 22/21 |
| 2 | 124.511 | 12/11, 13/12, 14/13, 18/17, 21/20 |
| 3 | 186.767 | 11/10, 17/15, 19/17, 21/19 |
| 4 | 249.022 | 7/6, 13/11, 20/17, 22/19 |
| 5 | 311.278 | 6/5, 11/9 |
| 6 | 373.534 | 14/11, 17/14, 19/15, 21/17 |
| 7 | 435.789 | 13/10, 22/17 |
| 8 | 498.045 | 17/13 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.1 | +28.0 | +28.0 | +15.2 | +10.8 | -7.0 | +10.8 | -6.3 | -2.0 | +19.8 | -6.3 |
| Relative (%) | -27.5 | +44.9 | +44.9 | +24.4 | +17.4 | -11.3 | +17.4 | -10.1 | -3.1 | +31.8 | -10.1 | |
| Steps (reduced) |
19 (3) |
31 (7) |
39 (7) |
45 (5) |
50 (2) |
54 (6) |
58 (2) |
61 (5) |
64 (0) |
67 (3) |
69 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -20.4 | -24.2 | -19.1 | -6.3 | +13.2 | -23.5 | +7.4 | -19.1 | +20.9 | +2.7 | -12.0 |
| Relative (%) | -32.7 | -38.8 | -30.7 | -10.1 | +21.3 | -37.7 | +12.0 | -30.7 | +33.6 | +4.3 | -19.3 | |
| Steps (reduced) |
71 (7) |
73 (1) |
75 (3) |
77 (5) |
79 (7) |
80 (0) |
82 (2) |
83 (3) |
85 (5) |
86 (6) |
87 (7) | |