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.
| 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 |