| Prime factorization
|
5 × 13
|
| Step size
|
111.589 ¢
|
| Octave
|
11\65ed66 (1227.48 ¢)
|
| Twelfth
|
17\65ed66 (1897.01 ¢)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
65 equal divisions of the 66th harmonic (abbreviated 65ed66) is a nonoctave tuning system that divides the interval of 66/1 into 65 equal parts of about 112 ¢ each. Each step represents a frequency ratio of 661/65, or the 65th root of 66.
Intervals
| Steps
|
Cents
|
Approximate ratios
|
| 0
|
0
|
1/1
|
| 1
|
111.6
|
31/29, 33/31
|
| 2
|
223.2
|
25/22, 33/29
|
| 3
|
334.8
|
17/14, 23/19
|
| 4
|
446.4
|
22/17, 35/27
|
| 5
|
557.9
|
29/21
|
| 6
|
669.5
|
25/17, 28/19
|
| 7
|
781.1
|
11/7
|
| 8
|
892.7
|
|
| 9
|
1004.3
|
25/14, 34/19
|
| 10
|
1115.9
|
21/11
|
| 11
|
1227.5
|
|
| 12
|
1339.1
|
13/6
|
| 13
|
1450.7
|
30/13
|
| 14
|
1562.2
|
|
| 15
|
1673.8
|
|
| 16
|
1785.4
|
14/5
|
| 17
|
1897
|
|
| 18
|
2008.6
|
|
| 19
|
2120.2
|
17/5
|
| 20
|
2231.8
|
|
| 21
|
2343.4
|
|
| 22
|
2455
|
|
| 23
|
2566.5
|
22/5
|
| 24
|
2678.1
|
|
| 25
|
2789.7
|
5/1
|
| 26
|
2901.3
|
|
| 27
|
3012.9
|
|
| 28
|
3124.5
|
|
| 29
|
3236.1
|
|
| 30
|
3347.7
|
|
| 31
|
3459.3
|
|
| 32
|
3570.8
|
|
| 33
|
3682.4
|
|
| 34
|
3794
|
|
| 35
|
3905.6
|
|
| 36
|
4017.2
|
|
| 37
|
4128.8
|
|
| 38
|
4240.4
|
|
| 39
|
4352
|
|
| 40
|
4463.6
|
|
| 41
|
4575.1
|
|
| 42
|
4686.7
|
|
| 43
|
4798.3
|
|
| 44
|
4909.9
|
|
| 45
|
5021.5
|
|
| 46
|
5133.1
|
|
| 47
|
5244.7
|
|
| 48
|
5356.3
|
|
| 49
|
5467.9
|
|
| 50
|
5579.4
|
|
| 51
|
5691
|
|
| 52
|
5802.6
|
|
| 53
|
5914.2
|
|
| 54
|
6025.8
|
|
| 55
|
6137.4
|
|
| 56
|
6249
|
|
| 57
|
6360.6
|
|
| 58
|
6472.2
|
|
| 59
|
6583.7
|
|
| 60
|
6695.3
|
|
| 61
|
6806.9
|
|
| 62
|
6918.5
|
|
| 63
|
7030.1
|
|
| 64
|
7141.7
|
|
| 65
|
7253.3
|
|