8ed5/4
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Prime factorization
23
Step size
48.2892¢
Octave
25\8ed5/4 (1207.23¢)
Twelfth
39\8ed5/4 (1883.28¢)
(semiconvergent)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 7ed5/4 | 8ed5/4 | 9ed5/4 → |
(semiconvergent)
8 equal divisions of 5/4 (abbreviated 8ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 8 equal parts of about 48.3 ¢ each. Each step represents a frequency ratio of (5/4)1/8, or the 8th root of 5/4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 48.289 | 21/20 |
| 2 | 96.578 | 15/14, 17/16, 20/19, 22/21 |
| 3 | 144.868 | 11/10, 12/11, 13/12, 14/13, 16/15, 21/19 |
| 4 | 193.157 | 19/17 |
| 5 | 241.446 | 8/7, 15/13, 17/15, 22/19 |
| 6 | 289.735 | 6/5, 7/6, 13/11, 19/16, 20/17 |
| 7 | 338.024 | 17/14, 21/17 |
| 8 | 386.314 | 5/4, 11/9, 16/13 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.2 | -18.7 | +14.5 | +14.5 | -11.4 | +11.4 | +21.7 | +10.9 | +21.7 | +1.6 | -4.2 |
| Relative (%) | +15.0 | -38.7 | +29.9 | +29.9 | -23.7 | +23.6 | +44.9 | +22.7 | +44.9 | +3.2 | -8.7 | |
| Steps (reduced) |
25 (1) |
39 (7) |
50 (2) |
58 (2) |
64 (0) |
70 (6) |
75 (3) |
79 (7) |
83 (3) |
86 (6) |
89 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.1 | +18.6 | -4.2 | -19.4 | +20.5 | +18.2 | +21.1 | -19.4 | -7.3 | +8.8 | -19.9 |
| Relative (%) | +4.3 | +38.6 | -8.7 | -40.1 | +42.5 | +37.6 | +43.8 | -40.1 | -15.0 | +18.2 | -41.2 | |
| Steps (reduced) |
92 (4) |
95 (7) |
97 (1) |
99 (3) |
102 (6) |
104 (0) |
106 (2) |
107 (3) |
109 (5) |
111 (7) |
112 (0) | |