7ed9/5
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Prime factorization
7 (prime)
Step size
145.371¢
Octave
8\7ed9/5 (1162.97¢)
Twelfth
13\7ed9/5 (1889.82¢)
(convergent)
Consistency limit
3
Distinct consistency limit
2
 |
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| ← 6ed9/5 | 7ed9/5 | 8ed9/5 → |
(convergent)
7 equal divisions of 9/5 (abbreviated 7ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 7 equal parts of about 145 ¢ each. Each step represents a frequency ratio of (9/5)1/7, or the 7th root of 9/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 145.371 | 10/9, 15/14, 19/17, 21/19 |
| 2 | 290.742 | 6/5, 7/6, 13/11 |
| 3 | 436.113 | 5/4, 9/7, 17/13, 19/15 |
| 4 | 581.484 | 7/5, 10/7 |
| 5 | 726.854 | 3/2, 14/9, 17/11 |
| 6 | 872.225 | 5/3 |
| 7 | 1017.596 | 7/4, 9/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -37.0 | -12.1 | +71.3 | -24.3 | -49.2 | -25.3 | +34.3 | -24.3 | -61.3 | +64.4 | +59.2 |
| Relative (%) | -25.5 | -8.3 | +49.1 | -16.7 | -33.8 | -17.4 | +23.6 | -16.7 | -42.2 | +44.3 | +40.7 | |
| Steps (reduced) |
8 (1) |
13 (6) |
17 (3) |
19 (5) |
21 (0) |
23 (2) |
25 (4) |
26 (5) |
27 (6) |
29 (1) |
30 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +66.0 | -62.3 | -36.4 | -2.8 | +37.7 | -61.3 | -9.5 | +47.0 | -37.4 | +27.4 | -49.6 |
| Relative (%) | +45.4 | -42.9 | -25.0 | -1.9 | +25.9 | -42.2 | -6.6 | +32.4 | -25.7 | +18.9 | -34.1 | |
| Steps (reduced) |
31 (3) |
31 (3) |
32 (4) |
33 (5) |
34 (6) |
34 (6) |
35 (0) |
36 (1) |
36 (1) |
37 (2) |
37 (2) | |