| Prime factorization
|
32 × 5
|
| Step size
|
53.3333 ¢
|
| Octave
|
23\45ed4 (1226.67 ¢)
|
| Twelfth
|
36\45ed4 (1920 ¢) (→ 4\5ed4)
|
| Consistency limit
|
1
|
| Distinct consistency limit
|
1
|
45 equal divisions of the 4th harmonic (abbreviated 45ed4) is a nonoctave tuning system that divides the interval of 4/1 into 45 equal parts of about 53.3 ¢ each. Each step represents a frequency ratio of 41/45, or the 45th root of 4.
Intervals
| Steps
|
Cents
|
Approximate ratios
|
| 0
|
0
|
1/1
|
| 1
|
53.3
|
|
| 2
|
106.7
|
|
| 3
|
160
|
11/10, 23/21
|
| 4
|
213.3
|
17/15, 26/23
|
| 5
|
266.7
|
|
| 6
|
320
|
|
| 7
|
373.3
|
26/21, 31/25
|
| 8
|
426.7
|
|
| 9
|
480
|
|
| 10
|
533.3
|
15/11, 19/14
|
| 11
|
586.7
|
7/5
|
| 12
|
640
|
|
| 13
|
693.3
|
|
| 14
|
746.7
|
|
| 15
|
800
|
|
| 16
|
853.3
|
23/14
|
| 17
|
906.7
|
|
| 18
|
960
|
|
| 19
|
1013.3
|
|
| 20
|
1066.7
|
13/7
|
| 21
|
1120
|
21/11
|
| 22
|
1173.3
|
|
| 23
|
1226.7
|
|
| 24
|
1280
|
21/10, 23/11
|
| 25
|
1333.3
|
|
| 26
|
1386.7
|
20/9, 29/13
|
| 27
|
1440
|
23/10
|
| 28
|
1493.3
|
26/11
|
| 29
|
1546.7
|
22/9
|
| 30
|
1600
|
|
| 31
|
1653.3
|
13/5
|
| 32
|
1706.7
|
|
| 33
|
1760
|
|
| 34
|
1813.3
|
|
| 35
|
1866.7
|
|
| 36
|
1920
|
|
| 37
|
1973.3
|
|
| 38
|
2026.7
|
|
| 39
|
2080
|
10/3
|
| 40
|
2133.3
|
|
| 41
|
2186.7
|
|
| 42
|
2240
|
|
| 43
|
2293.3
|
|
| 44
|
2346.7
|
|
| 45
|
2400
|
|