| 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
|
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
|