| Prime factorization
|
3 × 17
|
| Step size
|
13.7638 ¢
|
| Octave
|
87\51edf (1197.45 ¢) (→ 29\17edf)
|
| Twelfth
|
138\51edf (1899.41 ¢) (→ 46\17edf)
|
| Consistency limit
|
6
|
| Distinct consistency limit
|
6
|
51 equal divisions of the perfect fifth (abbreviated 51edf or 51ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 51 equal parts of about 13.8 ¢ each. Each step represents a frequency ratio of (3/2)1/51, or the 51st root of 3/2.
Intervals
| Steps
|
Cents
|
Approximate ratios
|
| 0
|
0
|
1/1
|
| 1
|
13.8
|
|
| 2
|
27.5
|
|
| 3
|
41.3
|
|
| 4
|
55.1
|
|
| 5
|
68.8
|
24/23, 25/24
|
| 6
|
82.6
|
22/21
|
| 7
|
96.3
|
18/17, 19/18
|
| 8
|
110.1
|
16/15, 17/16, 31/29
|
| 9
|
123.9
|
14/13
|
| 10
|
137.6
|
27/25
|
| 11
|
151.4
|
|
| 12
|
165.2
|
|
| 13
|
178.9
|
10/9, 31/28
|
| 14
|
192.7
|
19/17, 29/26
|
| 15
|
206.5
|
9/8
|
| 16
|
220.2
|
17/15
|
| 17
|
234
|
|
| 18
|
247.7
|
|
| 19
|
261.5
|
|
| 20
|
275.3
|
27/23
|
| 21
|
289
|
13/11, 32/27
|
| 22
|
302.8
|
19/16, 31/26
|
| 23
|
316.6
|
6/5
|
| 24
|
330.3
|
23/19
|
| 25
|
344.1
|
28/23
|
| 26
|
357.9
|
|
| 27
|
371.6
|
26/21
|
| 28
|
385.4
|
5/4
|
| 29
|
399.2
|
24/19
|
| 30
|
412.9
|
14/11, 19/15
|
| 31
|
426.7
|
23/18, 32/25
|
| 32
|
440.4
|
|
| 33
|
454.2
|
|
| 34
|
468
|
|
| 35
|
481.7
|
29/22
|
| 36
|
495.5
|
4/3
|
| 37
|
509.3
|
|
| 38
|
523
|
23/17, 27/20
|
| 39
|
536.8
|
|
| 40
|
550.6
|
|
| 41
|
564.3
|
25/18
|
| 42
|
578.1
|
|
| 43
|
591.8
|
24/17, 31/22
|
| 44
|
605.6
|
17/12, 27/19
|
| 45
|
619.4
|
|
| 46
|
633.1
|
23/16
|
| 47
|
646.9
|
|
| 48
|
660.7
|
|
| 49
|
674.4
|
28/19, 31/21
|
| 50
|
688.2
|
|
| 51
|
702
|
3/2
|