9ed7/4
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Prime factorization
32
Step size
107.647¢
Octave
11\9ed7/4 (1184.12¢)
(semiconvergent)
Twelfth
18\9ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit
3
Distinct consistency limit
2
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| ← 8ed7/4 | 9ed7/4 | 10ed7/4 → |
(semiconvergent)
9 equal divisions of 7/4 (abbreviated 9ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 9 equal parts of about 108 ¢ each. Each step represents a frequency ratio of (7/4)1/9, or the 9th root of 7/4.
Theory
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -15.9 | +35.7 | -31.8 | +12.5 | +19.8 | -31.8 | -47.6 | -36.3 | -3.4 | +46.9 | +3.9 |
| Relative (%) | -14.8 | +33.2 | -29.5 | +11.6 | +18.4 | -29.5 | -44.3 | -33.7 | -3.1 | +43.6 | +3.7 | |
| Steps (reduced) |
11 (2) |
18 (0) |
22 (4) |
26 (8) |
29 (2) |
31 (4) |
33 (6) |
35 (8) |
37 (1) |
39 (3) |
40 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -27.0 | -47.6 | +48.2 | +44.1 | +46.8 | -52.1 | -38.1 | -19.2 | +3.9 | +31.0 | -45.9 | -11.9 |
| Relative (%) | -25.1 | -44.3 | +44.8 | +41.0 | +43.5 | -48.4 | -35.4 | -17.9 | +3.7 | +28.8 | -42.6 | -11.1 | |
| Steps (reduced) |
41 (5) |
42 (6) |
44 (8) |
45 (0) |
46 (1) |
46 (1) |
47 (2) |
48 (3) |
49 (4) |
50 (5) |
50 (5) |
51 (6) | |
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 107.6 | 13/12, 14/13, 18/17, 20/19, 21/20, 22/21 |
| 2 | 215.3 | 8/7, 17/15 |
| 3 | 322.9 | 6/5, 11/9, 16/13, 19/16 |
| 4 | 430.6 | 13/10, 22/17 |
| 5 | 538.2 | 15/11, 19/14 |
| 6 | 645.9 | 10/7, 19/13, 22/15 |
| 7 | 753.5 | 17/11, 20/13 |
| 8 | 861.2 | 5/3, 13/8, 18/11, 21/13 |
| 9 | 968.8 | 7/4, 12/7 |