User:MisterShafXen/4edo
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Prime factorization
22 (highly composite)
Step size
300 ¢
Fifth
2\4 (600 ¢) (→ 1\2)
Semitones (A1:m2)
-2:2 (-600 ¢ : 600 ¢)
Dual sharp fifth
3\4 (900 ¢)
Dual flat fifth
2\4 (600 ¢) (→ 1\2)
Dual major 2nd
1\4 (300 ¢)
Consistency limit
7
Distinct consistency limit
1
| ← 3edo | 4edo | 5edo → |
4 equal divisions of the octave (abbreviated 4edo or 4ed2), also called 4-tone equal temperament (4tet) or 4 equal temperament (4et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4 equal parts of exactly 300 ¢ each. Each step represents a frequency ratio of 21/4, or the 4th root of 2.
Theory
4edo is commonly known as the diminished 7th chord in 12edo. It is also a form of diminished temperament, as 6/5 is mapped to 1\4.
Notation
A B C D
The tritone is A-C.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation (Dual flat fifth 2\4) |
Ups and downs notation (Dual sharp fifth 3\4) |
Tetratonic note names |
|---|---|---|---|---|---|
| 0 | 0 | 1/1, 20/19, 21/20 | D, E, C | D | A |
| 1 | 300 | 5/4, 6/5, 7/6, 8/7, 13/11, 16/13, 17/14, 17/15, 19/16, 20/17, 21/17 | ^D, ^E, ^C, vF, vG, vA, vB | G, B | B |
| 2 | 600 | 7/5, 10/7, 11/8, 16/11, 17/12, 19/13, 19/14 | F, G, A, B | E, C | C |
| 3 | 900 | 5/3, 7/4, 8/5, 12/7, 13/8, 17/10, 19/11 | ^F, ^G, ^A, ^B, vD | F, A | D |
| 4 | 1200 | 2/1, 19/10, 21/10 | D | D | A |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0 | -102 | -86 | -69 | +49 | +59 | -105 | +2 | -28 | -130 | +55 | +49 | -129 | +88 | -66 | +26 | +141 | +83 | -79 | +120 | +72 | -65 | +150 | +29 | -120 | +110 | +76 | +10 | -22 | -84 |
| Relative (%) | +0.0 | -34.0 | -28.8 | -22.9 | +16.2 | +19.8 | -35.0 | +0.8 | -9.4 | -43.2 | +18.3 | +16.2 | -43.0 | +29.5 | -21.8 | +8.8 | +46.9 | +27.7 | -26.4 | +40.1 | +24.1 | -21.5 | +50.0 | +9.7 | -40.0 | +36.7 | +25.4 | +3.4 | -7.3 | -28.1 | |
| Steps (reduced) |
4 (0) |
6 (2) |
9 (1) |
11 (3) |
14 (2) |
15 (3) |
16 (0) |
17 (1) |
18 (2) |
19 (3) |
20 (0) |
21 (1) |
21 (1) |
22 (2) |
22 (2) |
23 (3) |
24 (0) |
24 (0) |
24 (0) |
25 (1) |
25 (1) |
25 (1) |
26 (2) |
26 (2) |
26 (2) |
27 (3) |
27 (3) |
27 (3) |
27 (3) |
27 (3) | |