6ed4/3
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Prime factorization
2 × 3
Step size
83.0075¢
Octave
14\6ed4/3 (1162.1¢) (→7\3ed4/3)
Twelfth
23\6ed4/3 (1909.17¢)
(convergent)
Consistency limit
2
Distinct consistency limit
2
Special properties
 |
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| ← 5ed4/3 | 6ed4/3 | 7ed4/3 → |
(convergent)
6 equal divisions of 4/3 (abbreviated 6ed4/3) is a nonoctave tuning system that divides the interval of 4/3 into 6 equal parts of about 83 ¢ each. Each step represents a frequency ratio of (4/3)1/6, or the 6th root of 4/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 83.007 | 18/17, 19/18, 20/19 |
| 2 | 166.015 | 10/9, 11/10, 13/12, 14/13, 15/14, 17/15, 19/17 |
| 3 | 249.022 | 13/11, 20/17 |
| 4 | 332.03 | 11/9, 17/14 |
| 5 | 415.037 | 9/7, 13/10, 14/11, 21/17 |
| 6 | 498.045 | 17/13, 19/14 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -37.9 | +7.2 | +7.2 | +35.9 | -30.7 | +34.5 | -30.7 | +14.4 | -2.0 | -0.9 | +14.4 |
| Relative (%) | -45.7 | +8.7 | +8.7 | +43.3 | -37.0 | +41.5 | -37.0 | +17.4 | -2.4 | -1.1 | +17.4 | |
| Steps (reduced) |
14 (2) |
23 (5) |
29 (5) |
34 (4) |
37 (1) |
41 (5) |
43 (1) |
46 (4) |
48 (0) |
50 (2) |
52 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -41.1 | -3.4 | -39.8 | +14.4 | -7.5 | -23.5 | -34.1 | -39.8 | -41.3 | -38.8 | -32.8 |
| Relative (%) | -49.5 | -4.1 | -48.0 | +17.4 | -9.1 | -28.3 | -41.0 | -48.0 | -49.8 | -46.8 | -39.5 | |
| Steps (reduced) |
53 (5) |
55 (1) |
56 (2) |
58 (4) |
59 (5) |
60 (0) |
61 (1) |
62 (2) |
63 (3) |
64 (4) |
65 (5) | |
Music
- Funny Snakecharmer - Sven Karma (Dec 2023) - uses the 8edf Kartvelian tetradecatonic scale, alternating blocks of 8edf and 6ed4/3