User:MisterShafXen/10edo
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Prime factorization
2 × 5
Step size
120 ¢
Fifth
6\10 (720 ¢) (→ 3\5)
Semitones (A1:m2)
2:0 (240 ¢ : 0 ¢)
Consistency limit
7
Distinct consistency limit
3
| ← 9edo | 10edo | 11edo → |
10 equal divisions of the octave (abbreviated 10edo or 10ed2), also called 10-tone equal temperament (10tet) or 10 equal temperament (10et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 10 equal parts of exactly 120 ¢ each. Each step represents a frequency ratio of 21/10, or the 10th root of 2.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation | Pseudo-diatonic note names |
|---|---|---|---|---|
| 0 | 0 | 1/1 | D | A |
| 1 | 120 | 12/11, 13/12, 14/13, 15/14, 16/15, 17/16, 18/17, 20/19 | ^D, vE, vF | A#/Bb |
| 2 | 240 | 7/6, 8/7, 15/13, 17/15 | E, F | B |
| 3 | 360 | 5/4, 11/9, 16/13, 17/14, 21/17 | ^E, ^F, vG | C |
| 4 | 480 | 4/3, 13/10, 17/13, 21/16, 22/17 | G | D |
| 5 | 600 | 7/5, 10/7, 17/12 | ^G, vA | D#/Eb |
| 6 | 720 | 3/2, 17/11, 20/13 | A | E |
| 7 | 840 | 8/5, 13/8, 18/11, 21/13 | ^A, vB, vC | F |
| 8 | 960 | 7/4, 12/7 | B, C | G |
| 9 | 1080 | 11/6, 13/7, 15/8, 17/9, 19/10 | ^B, ^C, vD | G#/Ab |
| 10 | 1200 | 2/1 | D | A |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | +18.0 | -26.3 | -8.8 | +48.7 | -0.5 | +15.0 | -57.5 | -28.3 | +50.4 | +55.0 |
| Relative (%) | +0.0 | +15.0 | -21.9 | -7.4 | +40.6 | -0.4 | +12.5 | -47.9 | -23.6 | +42.0 | +45.8 | |
| Steps (reduced) |
10 (0) |
16 (6) |
23 (3) |
28 (8) |
35 (5) |
37 (7) |
41 (1) |
42 (2) |
45 (5) |
49 (9) |
50 (0) | |