User:MisterShafXen/8edo: Difference between revisions
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Prime factorization
23
Step size
150 ¢
Fifth
5\8 (750 ¢)
Semitones (A1:m2)
3:-1 (450 ¢ : -150 ¢)
Consistency limit
5
Distinct consistency limit
3
Created page with "{{Infobox ET}} {{ED intro}} == Harmonics == {{Harmonics in equal|steps=8}} == Intervals == {{Interval table|8edo|additional=Octatonic note names A B C D E F G H A}}" Tags: Visual edit Mobile edit Mobile web edit Advanced mobile edit |
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Revision as of 16:44, 1 August 2025
| ← 7edo | 8edo | 9edo → |
8 equal divisions of the octave (abbreviated 8edo or 8ed2), also called 8-tone equal temperament (8tet) or 8 equal temperament (8et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8 equal parts of exactly 150 ¢ each. Each step represents a frequency ratio of 21/8, or the 8th root of 2.
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +48.0 | +63.7 | -68.8 | -53.9 | +48.7 | +59.5 | -38.3 | +45.0 | +2.5 | -20.8 | -28.3 |
| Relative (%) | +32.0 | +42.5 | -45.9 | -35.9 | +32.5 | +39.6 | -25.5 | +30.0 | +1.7 | -13.9 | -18.8 | |
| Steps (reduced) |
13 (5) |
19 (3) |
22 (6) |
25 (1) |
28 (4) |
30 (6) |
31 (7) |
33 (1) |
34 (2) |
35 (3) |
36 (4) | |
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation | Octatonic note names |
|---|---|---|---|---|
| 0 | 0 | 1/1 | D | A |
| 1 | 150 | 10/9, 11/10, 12/11, 13/12, 19/17, 21/19 | F | B |
| 2 | 300 | 6/5, 13/11, 19/16, 20/17 | E | C |
| 3 | 450 | 13/10, 17/13, 21/16, 22/17 | G | D |
| 4 | 600 | 13/9, 17/12, 18/13 | ^G, vA | E |
| 5 | 750 | 17/11, 20/13 | A | F |
| 6 | 900 | 5/3, 17/10, 22/13 | C | G |
| 7 | 1050 | 9/5, 11/6, 20/11 | B | H |
| 8 | 1200 | 2/1 | D | A |