8ed9/5
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Prime factorization
23
Step size
127.2¢
Octave
9\8ed9/5 (1144.8¢)
Twelfth
15\8ed9/5 (1907.99¢)
(convergent)
Consistency limit
3
Distinct consistency limit
2
 |
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| ← 7ed9/5 | 8ed9/5 | 9ed9/5 → |
(convergent)
8 equal divisions of 9/5 (abbreviated 8ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 8 equal parts of about 127 ¢ each. Each step represents a frequency ratio of (9/5)1/8, or the 8th root of 9/5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 127.2 | 19/18, 21/20 |
| 2 | 254.399 | 7/6, 13/11, 15/13, 17/15, 22/19 |
| 3 | 381.599 | 11/9, 19/15 |
| 4 | 508.798 | 15/11, 17/13 |
| 5 | 635.998 | 10/7, 13/9, 19/13, 22/15 |
| 6 | 763.197 | 17/11 |
| 7 | 890.397 | 5/3, 12/7, 22/13 |
| 8 | 1017.596 | 9/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -55.2 | +6.0 | +16.8 | +12.1 | -49.2 | -61.6 | -38.4 | +12.1 | -43.1 | +46.3 | +22.8 |
| Relative (%) | -43.4 | +4.7 | +13.2 | +9.5 | -38.7 | -48.5 | -30.2 | +9.5 | -33.9 | +36.4 | +17.9 | |
| Steps (reduced) |
9 (1) |
15 (7) |
19 (3) |
22 (6) |
24 (0) |
26 (2) |
28 (4) |
30 (6) |
31 (7) |
33 (1) |
34 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +11.5 | +10.4 | +18.1 | +33.6 | +55.8 | -43.1 | -9.5 | +28.9 | -55.6 | -8.9 | +41.3 |
| Relative (%) | +9.0 | +8.1 | +14.2 | +26.4 | +43.9 | -33.9 | -7.5 | +22.7 | -43.7 | -7.0 | +32.5 | |
| Steps (reduced) |
35 (3) |
36 (4) |
37 (5) |
38 (6) |
39 (7) |
39 (7) |
40 (0) |
41 (1) |
41 (1) |
42 (2) |
43 (3) | |