User:MisterShafXen/9edo
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Prime factorization
32
Step size
133.333 ¢
Fifth
5\9 (666.667 ¢)
Semitones (A1:m2)
-1:2 (-133.3 ¢ : 266.7 ¢)
Consistency limit
7
Distinct consistency limit
5
| ← 8edo | 9edo | 10edo → |
9 equal divisions of the octave (abbreviated 9edo or 9ed2), also called 9-tone equal temperament (9tet) or 9 equal temperament (9et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 9 equal parts of about 133 ¢ each. Each step represents a frequency ratio of 21/9, or the 9th root of 2.
Theory
9edo can be seen as the flattest mavila tuning. Its antidiatonic scale is basic, and its superdiatonic is equalized. If the fifths are flatter than 9's (e.g. 11edo's), the superdiatonic becomes balzano.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation | Tritonic note names |
|---|---|---|---|---|
| 0 | 0 | 1/1 | D | A |
| 1 | 133.3 | 11/10, 12/11, 13/12, 14/13, 15/14, 16/15, 17/16 | E | A# |
| 2 | 266.7 | 7/6, 8/7, 13/11, 15/13, 19/16, 20/17, 22/19 | E♯, F♭ | Bb |
| 3 | 400 | 5/4, 9/7, 14/11, 19/15 | F | B |
| 4 | 533.3 | 4/3, 11/8, 15/11, 18/13, 19/14 | G | B# |
| 5 | 666.7 | 3/2, 13/9, 16/11, 19/13, 22/15 | A | Cb |
| 6 | 800 | 8/5, 11/7, 14/9, 19/12, 21/13 | B | C |
| 7 | 933.3 | 7/4, 12/7, 17/10, 19/11, 22/13 | B♯, C♭ | C# |
| 8 | 1066.7 | 11/6, 13/7, 15/8, 20/11 | C | Ab |
| 9 | 1200 | 2/1 | D | A |
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -35.3 | +13.7 | -35.5 | +62.8 | -18.0 | -40.5 | -21.6 | +28.4 | -30.8 | +62.6 | +38.4 |
| Relative (%) | -26.5 | +10.3 | -26.6 | +47.1 | -13.5 | -30.4 | -16.2 | +21.3 | -23.1 | +46.9 | +28.8 | |
| Steps (reduced) |
14 (5) |
21 (3) |
25 (7) |
29 (2) |
31 (4) |
33 (6) |
35 (8) |
37 (1) |
38 (2) |
40 (4) |
41 (5) | |