User:MisterShafXen/7edo
Jump to navigation
Jump to search
Prime factorization
7 (prime)
Step size
171.429 ¢
Fifth
4\7 (685.714 ¢)
(semiconvergent)
Semitones (A1:m2)
0:1 (0 ¢ : 171.4 ¢)
Consistency limit
5
Distinct consistency limit
3
| ← 6edo | 7edo | 8edo → |
(semiconvergent)
7 equal divisions of the octave (abbreviated 7edo or 7ed2), also called 7-tone equal temperament (7tet) or 7 equal temperament (7et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 7 equal parts of about 171 ¢ each. Each step represents a frequency ratio of 21/7, or the 7th root of 2.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1 | D |
| 1 | 171.4 | 9/8, 10/9, 11/10, 12/11, 13/12, 14/13, 19/17, 21/19 | E |
| 2 | 342.9 | 5/4, 6/5, 11/9, 16/13, 17/14, 19/16, 21/17 | F |
| 3 | 514.3 | 4/3, 11/8, 15/11, 17/13, 18/13, 19/14, 21/16 | G |
| 4 | 685.7 | 3/2, 13/9, 16/11, 19/13 | A |
| 5 | 857.1 | 5/3, 8/5, 13/8, 18/11, 21/13 | B |
| 6 | 1028.6 | 9/5, 11/6, 13/7, 16/9, 20/11 | C |
| 7 | 1200 | 2/1 | D |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | -16.2 | -43.5 | +59.7 | -37.0 | +16.6 | +66.5 | +45.3 | +57.4 | -1.0 | +55.0 |
| Relative (%) | +0.0 | -9.5 | -25.3 | +34.9 | -21.6 | +9.7 | +38.8 | +26.5 | +33.5 | -0.6 | +32.1 | |
| Steps (reduced) |
7 (0) |
11 (4) |
16 (2) |
20 (6) |
24 (3) |
26 (5) |
29 (1) |
30 (2) |
32 (4) |
34 (6) |
35 (0) | |