7ed5
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Prime factorization
7 (prime)
Step size
398.045¢
Octave
3\7ed5 (1194.13¢)
(convergent)
Twelfth
5\7ed5 (1990.22¢)
(semiconvergent)
Consistency limit
6
Distinct consistency limit
2
| ← 6ed5 | 7ed5 | 8ed5 → |
(convergent)
(semiconvergent)
Division of the 5th harmonic into 7 equal parts (7ed5) is related to 3 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 5.8656 cents compressed and the step size is about 398.0448 cents. It is related to the regular temperaments which temper out 441/440 and 244515348/244140625 in the 11-limit, which is supported by 3, 12, 15, 175, 190, 202, and/or 217 EDOs.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6 | +88 | -12 | +0 | +82 | -184 | -18 | +177 | -6 | -171 | +77 |
| Relative (%) | -1.5 | +22.2 | -2.9 | +0.0 | +20.7 | -46.3 | -4.4 | +44.4 | -1.5 | -42.9 | +19.2 | |
| Steps (reduced) |
3 (3) |
5 (5) |
6 (6) |
7 (0) |
8 (1) |
8 (1) |
9 (2) |
10 (3) |
10 (3) |
10 (3) |
11 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -62 | -190 | +88 | -23 | -128 | +171 | +77 | -12 | -96 | -177 | +144 |
| Relative (%) | -15.6 | -47.8 | +22.2 | -5.9 | -32.3 | +42.9 | +19.4 | -2.9 | -24.2 | -44.4 | +36.3 | |
| Steps (reduced) |
11 (4) |
11 (4) |
12 (5) |
12 (5) |
12 (5) |
13 (6) |
13 (6) |
13 (6) |
13 (6) |
13 (6) |
14 (0) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 398.0448 | 34/27 | pseudo-5/4 |
| 2 | 796.0896 | 19/12 | |
| 3 | 1194.1344 | 255/128 | pseudo-octave |
| 4 | 1592.1793 | 128/51 | pseudo-5/2 |
| 5 | 1990.2241 | 60/19 | |
| 6 | 2388.2689 | 135/34 | pseudo-4/1 |
| 7 | 2786.3137 | exact 5/1 | just major third plus two octaves |