5ed5/2
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Prime factorization
5 (prime)
Step size
317.263¢
Octave
4\5ed5/2 (1269.05¢)
(semiconvergent)
Twelfth
6\5ed5/2 (1903.58¢)
(convergent)
Consistency limit
7
Distinct consistency limit
2
| ← 4ed5/2 | 5ed5/2 | 6ed5/2 → |
(semiconvergent)
(convergent)
5ED5/2 is the equal division of the 5/2 interval into 5 parts of 317.2627 cents each, corresponding to 3.7824 EDO. It is strongly related to the hanson temperament. Its patent val tempers out the same 7-limit commas as 4EDO, but mapping of 11 and higher prime harmonics differs to 4EDO.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 317.263 | 5/4, 6/5, 7/6, 11/9, 13/11, 15/13 |
| 2 | 634.525 | 3/2, 7/5, 10/7, 13/9, 18/13, 19/13 |
| 3 | 951.788 | 5/3, 7/4, 9/5, 12/7, 19/11 |
| 4 | 1269.051 | 2/1, 13/6, 15/7, 19/9, 21/10 |
| 5 | 1586.314 | 5/2, 12/5, 13/5, 18/7 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +69 | +2 | +138 | +69 | +71 | +121 | -110 | +3 | +138 | -27 | +140 |
| Relative (%) | +21.8 | +0.5 | +43.5 | +21.8 | +22.3 | +38.2 | -34.7 | +1.0 | +43.5 | -8.5 | +44.0 | |
| Steps (reduced) |
4 (4) |
6 (1) |
8 (3) |
9 (4) |
10 (0) |
11 (1) |
11 (1) |
12 (2) |
13 (3) |
13 (3) |
14 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1 | -127 | +71 | -41 | -146 | +72 | -21 | -110 | +123 | +42 | -35 |
| Relative (%) | +0.4 | -40.1 | +22.3 | -12.9 | -46.0 | +22.8 | -6.7 | -34.7 | +38.7 | +13.3 | -11.0 | |
| Steps (reduced) |
14 (4) |
14 (4) |
15 (0) |
15 (0) |
15 (0) |
16 (1) |
16 (1) |
16 (1) |
17 (2) |
17 (2) |
17 (2) | |