10ed5/3
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Prime factorization
2 × 5
Step size
88.4359¢
Octave
14\10ed5/3 (1238.1¢) (→7\5ed5/3)
Twelfth
22\10ed5/3 (1945.59¢) (→11\5ed5/3)
Consistency limit
3
Distinct consistency limit
2
| ← 9ed5/3 | 10ed5/3 | 11ed5/3 → |
10 equal divisions of 5/3 (abbreviated 10ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 10 equal parts of about 88.4 ¢ each. Each step represents a frequency ratio of (5/3)1/10, or the 10th root of 5/3.
Intervals
| Step | Interval (¢) | JI approximated | Simplified ratios |
|---|---|---|---|
| 1 | 88.44 | 81/77 | |
| 2 | 176.87 | 10/9, 11/10 | |
| 3 | 265.31 | 7/6, 29/25 | |
| 4 | 353.74 | 11/9, 29/24, 36/29 | |
| 5 | 442.18 | 9/7 | |
| 6 | 530.62 | 15/11, 40/29 | |
| 7 | 619.05 | 10/7, 63/44 | |
| 8 | 707.49 | 6/4, 44/29 | 3/2 |
| 9 | 795.92 | 16/10, 11/7, 46/29 | 8/5 |
| 10 | 884.36 | 5/3, 42/25 | |
| 11 | 972.80 | 7/4, 44/25 | |
| 12 | 1061.23 | 11/6, 54/29 | |
| 13 | 1149.67 | 29/15 | |
| 14 | 1238.10 | 66/32 | 33/16 |
| 15 | 1326.54 | 15/7 | |
| 16 | 1414.97 | 9/4, 16/7, 25/11 | |
| 17 | 1503.41 | 24/10 | 12/5 |
| 18 | 1591.85 | 10/4, 63/25 | 5/2 |
| 19 | 1680.28 | 16/6, 29/11, 66/25 | 8/3 |
| 20 | 1768.72 | 11/4, 28/10 | 14/5 |
The subgroup interpretation used is 5/3.4.6.7.9.10.11.29. Other interpretations are possible. Don't forget that fractions can multiply, e.g. 9*5/3=15, 15*5/3=25.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +38.1 | +43.6 | -12.2 | +43.6 | -6.7 | -8.3 | +25.9 | -1.2 | -6.7 | +5.2 | +31.4 |
| Relative (%) | +43.1 | +49.3 | -13.8 | +49.3 | -7.6 | -9.3 | +29.3 | -1.3 | -7.6 | +5.8 | +35.5 | |
| Steps (reduced) |
14 (4) |
22 (2) |
27 (7) |
32 (2) |
35 (5) |
38 (8) |
41 (1) |
43 (3) |
45 (5) |
47 (7) |
49 (9) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.7 | +29.8 | -1.2 | -24.5 | -41.0 | +36.9 | +31.8 | +31.4 | +35.4 | +43.3 | -33.7 |
| Relative (%) | -21.2 | +33.7 | -1.3 | -27.7 | -46.3 | +41.8 | +35.9 | +35.5 | +40.0 | +48.9 | -38.1 | |
| Steps (reduced) |
50 (0) |
52 (2) |
53 (3) |
54 (4) |
55 (5) |
57 (7) |
58 (8) |
59 (9) |
60 (0) |
61 (1) |
61 (1) | |
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