User:MisterShafXen/32edo: Difference between revisions
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Prime factorization
25
Step size
37.5 ¢
Fifth
19\32 (712.5 ¢)
Semitones (A1:m2)
5:1 (187.5 ¢ : 37.5 ¢)
Consistency limit
3
Distinct consistency limit
3
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Latest revision as of 14:44, 1 August 2025
| ← 31edo | 32edo | 33edo → |
32 equal divisions of the octave (abbreviated 32edo or 32ed2), also called 32-tone equal temperament (32tet) or 32 equal temperament (32et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 32 equal parts of exactly 37.5 ¢ each. Each step represents a frequency ratio of 21/32, or the 32nd root of 2.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1 | D |
| 1 | 37.5 | ^D, E♭ | |
| 2 | 75 | 22/21, 23/22, 24/23, 26/25 | ^^D, ^E♭ |
| 3 | 112.5 | 15/14, 16/15, 17/16 | vvD♯, ^^E♭ |
| 4 | 150 | 12/11, 23/21 | vD♯, vvE |
| 5 | 187.5 | 19/17 | D♯, vE |
| 6 | 225 | 8/7, 17/15 | E |
| 7 | 262.5 | 7/6, 22/19 | F |
| 8 | 300 | 19/16 | ^F, G♭ |
| 9 | 337.5 | 17/14, 23/19, 28/23 | ^^F, ^G♭ |
| 10 | 375 | 21/17 | vvF♯, ^^G♭ |
| 11 | 412.5 | 14/11, 19/15, 24/19 | vF♯, vvG |
| 12 | 450 | 13/10, 22/17 | F♯, vG |
| 13 | 487.5 | G | |
| 14 | 525 | 19/14, 23/17 | ^G, A♭ |
| 15 | 562.5 | ^^G, ^A♭ | |
| 16 | 600 | 17/12, 24/17 | vvG♯, ^^A♭ |
| 17 | 637.5 | 23/16 | vG♯, vvA |
| 18 | 675 | 28/19 | G♯, vA |
| 19 | 712.5 | A | |
| 20 | 750 | 17/11, 20/13 | ^A, B♭ |
| 21 | 787.5 | 11/7, 19/12 | ^^A, ^B♭ |
| 22 | 825 | vvA♯, ^^B♭ | |
| 23 | 862.5 | 23/14, 28/17 | vA♯, vvB |
| 24 | 900 | A♯, vB | |
| 25 | 937.5 | 12/7, 19/11 | B |
| 26 | 975 | 7/4 | C |
| 27 | 1012.5 | ^C, D♭ | |
| 28 | 1050 | 11/6 | ^^C, ^D♭ |
| 29 | 1087.5 | 15/8, 28/15 | vvC♯, ^^D♭ |
| 30 | 1125 | 21/11, 23/12, 25/13 | vC♯, vvD |
| 31 | 1162.5 | C♯, vD | |
| 32 | 1200 | 2/1 | D |