User:MisterShafXen/7ed13
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Prime factorization
7 (prime)
Step size
634.361 ¢
Octave
2\7ed13 (1268.72 ¢)
(semiconvergent)
Twelfth
3\7ed13 (1903.08 ¢)
(convergent)
Consistency limit
4
Distinct consistency limit
3
| ← 6ed13 | 7ed13 | 8ed13 → |
(semiconvergent)
(convergent)
7 equal divisions of the 13th harmonic (abbreviated 7ed13) is a nonoctave tuning system that divides the interval of 13/1 into 7 equal parts of about 634 ¢ each. Each step represents a frequency ratio of 131/7, or the 7th root of 13.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1 | D |
| 1 | 100 | 15/14, 16/15, 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 | D♯, E♭ |
| 2 | 200 | 9/8, 10/9, 17/15, 19/17, 21/19 | E |
| 3 | 300 | 6/5, 19/16, 20/17 | F |
| 4 | 400 | 5/4, 14/11, 19/15, 23/18 | F♯, G♭ |
| 5 | 500 | 4/3, 23/17 | G |
| 6 | 600 | 7/5, 10/7, 17/12, 23/16 | G♯, A♭ |
| 7 | 700 | 3/2 | A |
| 8 | 800 | 8/5, 11/7, 19/12 | A♯, B♭ |
| 9 | 900 | 5/3, 17/10 | B |
| 10 | 1000 | 9/5, 16/9, 23/13 | C |
| 11 | 1100 | 15/8, 17/9, 19/10, 21/11, 23/12 | C♯, D♭ |
| 12 | 1200 | 2/1 | D |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +69 | +1 | +137 | -249 | +70 | -197 | +206 | +2 | -180 | +289 | +139 |
| Relative (%) | +10.8 | +0.2 | +21.7 | -39.2 | +11.0 | -31.1 | +32.5 | +0.4 | -28.4 | +45.6 | +21.8 | |
| Steps (reduced) |
2 (2) |
3 (3) |
4 (4) |
4 (4) |
5 (5) |
5 (5) |
6 (6) |
6 (6) |
6 (6) |
7 (0) |
7 (0) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0 | -128 | -248 | +275 | +170 | +71 | -23 | -111 | -196 | -276 | +281 |
| Relative (%) | +0.0 | -20.2 | -39.1 | +43.3 | +26.8 | +11.2 | -3.6 | -17.6 | -30.9 | -43.6 | +44.3 | |
| Steps (reduced) |
7 (0) |
7 (0) |
7 (0) |
8 (1) |
8 (1) |
8 (1) |
8 (1) |
8 (1) |
8 (1) |
8 (1) |
9 (2) | |