| Prime factorization
|
3 × 13
|
| Step size
|
198.244 ¢
|
| Octave
|
6\39ed87 (1189.47 ¢) (→ 2\13ed87)
|
| Twelfth
|
10\39ed87 (1982.44 ¢)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
39 equal divisions of the 87th harmonic (abbreviated 39ed87) is a nonoctave tuning system that divides the interval of 87/1 into 39 equal parts of about 198 ¢ each. Each step represents a frequency ratio of 871/39, or the 39th root of 87.
Intervals
| Steps
|
Cents
|
Approximate ratios
|
| 0
|
0
|
1/1
|
| 1
|
198.2
|
19/17, 28/25
|
| 2
|
396.5
|
29/23
|
| 3
|
594.7
|
24/17
|
| 4
|
793
|
19/12
|
| 5
|
991.2
|
23/13
|
| 6
|
1189.5
|
|
| 7
|
1387.7
|
29/13
|
| 8
|
1586
|
5/2
|
| 9
|
1784.2
|
14/5
|
| 10
|
1982.4
|
22/7
|
| 11
|
2180.7
|
|
| 12
|
2378.9
|
|
| 13
|
2577.2
|
|
| 14
|
2775.4
|
|
| 15
|
2973.7
|
|
| 16
|
3171.9
|
25/4
|
| 17
|
3370.2
|
7/1
|
| 18
|
3568.4
|
|
| 19
|
3766.6
|
|
| 20
|
3964.9
|
|
| 21
|
4163.1
|
|
| 22
|
4361.4
|
|
| 23
|
4559.6
|
|
| 24
|
4757.9
|
|
| 25
|
4956.1
|
|
| 26
|
5154.4
|
|
| 27
|
5352.6
|
|
| 28
|
5550.8
|
|
| 29
|
5749.1
|
|
| 30
|
5947.3
|
|
| 31
|
6145.6
|
|
| 32
|
6343.8
|
|
| 33
|
6542.1
|
|
| 34
|
6740.3
|
|
| 35
|
6938.6
|
|
| 36
|
7136.8
|
|
| 37
|
7335
|
|
| 38
|
7533.3
|
|
| 39
|
7731.5
|
|