User:MisterShafXen/6edo
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Prime factorization
2 × 3 (highly composite)
Step size
200 ¢
Fifth
4\6 (800 ¢) (→ 2\3)
Semitones (A1:m2)
4:-2 (800 ¢ : -400 ¢)
Dual sharp fifth
4\6 (800 ¢) (→ 2\3)
Dual flat fifth
3\6 (600 ¢) (→ 1\2)
Dual major 2nd
1\6 (200 ¢)
(convergent)
Consistency limit
7
Distinct consistency limit
3
| ← 5edo | 6edo | 7edo → |
(convergent)
6 equal divisions of the octave (abbreviated 6edo or 6ed2), also called 6-tone equal temperament (6tet) or 6 equal temperament (6et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 6 equal parts of exactly 200 ¢ each. Each step represents a frequency ratio of 21/6, or the 6th root of 2.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation (Dual flat fifth 3\6) |
Ups and downs notation (Dual sharp fifth 4\6) |
|---|---|---|---|---|
| 0 | 0 | 1/1 | D, E, C | D, F, B |
| 1 | 200 | 8/7, 11/10, 12/11, 17/15 | ^D, ^E, ^C, ^F♭, ^G♭, ^A♭, ^B♭ | ^D, ^F, ^B, vE, vG |
| 2 | 400 | 5/4, 13/10, 14/11, 16/13, 21/17 | vD♯, vE♯, vC♯, vF, vG, vA, vB | E, G |
| 3 | 600 | 7/5, 10/7, 11/8, 16/11, 17/12, 19/13 | F, G, A, B | ^E, ^G, vA, vC |
| 4 | 800 | 8/5, 11/7, 13/8, 17/11, 20/13 | ^F, ^G, ^A, ^B, ^D♭ | A, C |
| 5 | 1000 | 7/4, 11/6, 20/11 | vF♯, vG♯, vA♯, vB♯, vD | ^A, ^C, vD |
| 6 | 1200 | 2/1 | D | D |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | +98.0 | +13.7 | +31.2 | +48.7 | -40.5 | +95.0 | -97.5 | -28.3 | -29.6 | +55.0 |
| Relative (%) | +0.0 | +49.0 | +6.8 | +15.6 | +24.3 | -20.3 | +47.5 | -48.8 | -14.1 | -14.8 | +27.5 | |
| Steps (reduced) |
6 (0) |
10 (4) |
14 (2) |
17 (5) |
21 (3) |
22 (4) |
25 (1) |
25 (1) |
27 (3) |
29 (5) |
30 (0) | |