10ed5/4
Jump to navigation
Jump to search
Prime factorization
2 × 5
Step size
38.6314¢
Octave
31\10ed5/4 (1197.57¢)
(semiconvergent)
Twelfth
49\10ed5/4 (1892.94¢)
(semiconvergent)
Consistency limit
12
Distinct consistency limit
2
| ← 9ed5/4 | 10ed5/4 | 11ed5/4 → |
(semiconvergent)
(semiconvergent)
Division of the just major third into 10 equal parts (10ED5/4) is related to 31 edo, but with the 5/4 rather than the 2/1 being just. The octave is about 2.43 cents compressed and the step size is 38.63 cents.
Lookalikes: 31edo, 49edt, 72ed5, 18edf
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 38.6 | |
| 2 | 77.3 | 18/17, 20/19, 21/20, 22/21 |
| 3 | 115.9 | 14/13, 15/14, 16/15, 17/16, 19/18 |
| 4 | 154.5 | 11/10, 12/11, 13/12, 21/19 |
| 5 | 193.2 | 9/8, 10/9, 19/17 |
| 6 | 231.8 | 8/7, 15/13, 17/15, 22/19 |
| 7 | 270.4 | 7/6, 20/17 |
| 8 | 309.1 | 6/5, 13/11, 19/16 |
| 9 | 347.7 | 11/9, 16/13, 17/14, 21/17 |
| 10 | 386.3 | 5/4 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.4 | -9.0 | -4.9 | -4.9 | -11.4 | -7.9 | -7.3 | -18.0 | -7.3 | -17.8 | -13.9 |
| Relative (%) | -6.3 | -23.3 | -12.6 | -12.6 | -29.6 | -20.4 | -18.9 | -46.7 | -18.9 | -46.0 | -35.9 | |
| Steps (reduced) |
31 (1) |
49 (9) |
62 (2) |
72 (2) |
80 (0) |
87 (7) |
93 (3) |
98 (8) |
103 (3) |
107 (7) |
111 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.1 | -10.3 | -13.9 | -9.7 | +1.2 | +18.2 | +1.8 | -9.7 | -16.9 | +18.4 | +18.7 |
| Relative (%) | +5.4 | -26.7 | -35.9 | -25.1 | +3.2 | +47.0 | +4.7 | -25.1 | -43.8 | +47.7 | +48.5 | |
| Steps (reduced) |
115 (5) |
118 (8) |
121 (1) |
124 (4) |
127 (7) |
130 (0) |
132 (2) |
134 (4) |
136 (6) |
139 (9) |
141 (1) | |