User:MisterShafXen/2edo
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Prime factorization
2 (prime)
Step size
600 ¢
Fifth
1\2 (600 ¢)
(convergent)
Semitones (A1:m2)
-1:1 (-600 ¢ : 600 ¢)
Consistency limit
3
Distinct consistency limit
1
Special properties
| ← 1edo | 2edo | 3edo → |
(convergent)
2 equal divisions of the octave (abbreviated 2edo or 2ed2), also called 2-tone equal temperament (2tet) or 2 equal temperament (2et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2 equal parts of exactly 600 ¢ each. Each step represents a frequency ratio of 21/2, or the 2nd root of 2.
Theory
This tuning tempers out 9/8, supporting antitonic.
Notation
A B. All As and Bs.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1, 8/7, 9/8, 11/10, 12/11, 13/12, 15/14, 16/15, 17/15, 17/16, 18/17, 19/17, 19/18 | D, E, C |
| 1 | 600 | 3/2, 4/3, 5/4, 7/5, 8/5, 10/7, 11/7, 11/8, 13/8, 13/9, 14/11, 15/11, 16/11, 16/13, 17/11, 17/12, 17/13, 18/13, 19/12, 19/13 | F, G, A, B |
| 2 | 1200 | 2/1, 7/4, 9/4, 11/5, 11/6, 13/6, 15/7, 15/8, 16/7, 16/9, 17/8, 17/9, 19/9, 20/11 | D |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0 | -102 | +214 | +231 | +49 | -241 | -105 | -298 | -28 | +170 | +55 | -251 | +171 | +88 | -66 |
| Relative (%) | +0.0 | -17.0 | +35.6 | +38.5 | +8.1 | -40.1 | -17.5 | -49.6 | -4.7 | +28.4 | +9.2 | -41.9 | +28.5 | +14.7 | -10.9 | |
| Steps (reduced) |
2 (0) |
3 (1) |
5 (1) |
6 (0) |
7 (1) |
7 (1) |
8 (0) |
8 (0) |
9 (1) |
10 (0) |
10 (0) |
10 (0) |
11 (1) |
11 (1) |
11 (1) | |
| Harmonic | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -274 | +141 | +83 | -79 | -180 | -228 | +235 | +150 | +29 | -120 | -190 | -224 | -290 | +278 | +216 |
| Relative (%) | -45.6 | +23.5 | +13.9 | -13.2 | -29.9 | -38.0 | +39.2 | +25.0 | +4.9 | -20.0 | -31.6 | -37.3 | -48.3 | +46.4 | +36.0 | |
| Steps (reduced) |
11 (1) |
12 (0) |
12 (0) |
12 (0) |
12 (0) |
12 (0) |
13 (1) |
13 (1) |
13 (1) |
13 (1) |
13 (1) |
13 (1) |
13 (1) |
14 (0) |
14 (0) | |
| Harmonic | 127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 | 179 | 181 | 191 | 193 | 197 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +14 | -40 | -118 | -143 | -263 | -286 | +246 | +182 | +140 | +78 | +19 | +0 | -93 | -111 | -146 |
| Relative (%) | +2.3 | -6.7 | -19.6 | -23.8 | -43.8 | -47.7 | +41.1 | +30.3 | +23.3 | +13.1 | +3.2 | +0.0 | -15.5 | -18.5 | -24.4 | |
| Steps (reduced) |
14 (0) |
14 (0) |
14 (0) |
14 (0) |
14 (0) |
14 (0) |
15 (1) |
15 (1) |
15 (1) |
15 (1) |
15 (1) |
15 (1) |
15 (1) |
15 (1) |
15 (1) | |