User:MisterShafXen/1edo
| ← 0edo | 1edo | 2edo → |
1 equal division of the octave (abbreviated 1edo or 1ed2), also called 1-tone equal temperament (1tet) or 1 equal temperament (1et) when viewed under a regular temperament perspective, is the tuning system that uses equal steps of 2/1 (one octave), or exactly 1200 ¢.
Notation
A. All A.
Theory
All intervals are either tempered out or mapped to the octave.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation (Dual flat fifth 0\1) |
Ups and downs notation (Dual sharp fifth 1\1) |
|---|---|---|---|---|
| 0 | 0 | 1/1, 4/3, 5/3, 5/4, 7/6, 8/7, 10/7, 11/6, 11/7, 11/8, 11/10, 13/9, 13/12, 14/9, 14/13, 15/13, 15/14, 16/9, 16/13, 16/15, 17/9, 17/12, 17/13, 17/14, 17/15, 17/16, 19/9, 19/12, 19/13, 19/14, 19/15, 19/16, 19/17, 20/9, 20/13, 20/17, 20/19 | D, E, F, A, B, C | D, E, F, G, B, C |
| 1 | 1200 | 2/1, 3/2, 5/2, 6/5, 7/3, 7/4, 7/5, 8/3, 8/5, 9/7, 9/8, 10/3, 11/3, 11/4, 11/5, 12/7, 12/11, 13/6, 13/7, 13/8, 13/10, 13/11, 14/11, 15/7, 15/8, 15/11, 16/7, 16/11, 17/6, 17/7, 17/8, 17/10, 17/11, 18/13, 18/17, 19/6, 19/7, 19/8, 19/10, 19/11, 20/7, 20/11 | G, D | A, D |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0 | +498 | -386 | +231 | -551 | +359 | -105 | -298 | +572 | +170 | +55 | -251 | -429 | -512 | +534 | +326 | +141 | +83 | -79 | -180 |
| Relative (%) | +0.0 | +41.5 | -32.2 | +19.3 | -45.9 | +30.0 | -8.7 | -24.8 | +47.6 | +14.2 | +4.6 | -20.9 | -35.8 | -42.6 | +44.5 | +27.2 | +11.7 | +6.9 | -6.6 | -15.0 | |
| Step | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 6 | 6 | 6 | 6 | 6 | 6 | |
| Harmonic | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | 127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -228 | -365 | -450 | -571 | +480 | +410 | +376 | +310 | +278 | +216 | +14 | -40 | -118 | -143 | -263 | -286 | -354 | -418 | -460 | -522 |
| Relative (%) | -19.0 | -30.4 | -37.5 | -47.6 | +40.0 | +34.2 | +31.3 | +25.9 | +23.2 | +18.0 | +1.1 | -3.3 | -9.8 | -11.9 | -21.9 | -23.8 | -29.5 | -34.9 | -38.4 | -43.5 | |
| Step | 6 | 6 | 6 | 6 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | |