10 equal divisions of 19/10 (abbreviated 10ed19/10) is a nonoctave tuning system that divides the interval of 19/10 into 10 equal parts of about 111 ¢ each. Each step represents a frequency ratio of (19/10)1/10, or the 10th root of 19/10.
Intervals
| #
|
Cents
|
Approximate JI ratios (direct)
|
Approximate JI ratios (val)
|
| 0
|
0.0
|
exact 1/1
|
exact 1/1
|
| 1
|
111.1
|
16/15
|
11/10
|
| 2
|
222.2
|
25/22
|
7/6, 8/7, 9/8, 10/9, 12/11
|
| 3
|
333.4
|
40/33
|
5/4, 6/5, 11/9
|
| 4
|
444.5
|
31/24
|
4/3, 9/7, 5/4
|
| 5
|
555.6
|
11/8
|
4/3, 7/5, 11/8
|
| 6
|
666.7
|
72/49, 47/32
|
3/2, 10/7
|
| 7
|
777.8
|
36/23
|
11/7, 3/2
|
| 8
|
889.0
|
5/3
|
5/3
|
| 9
|
1000.1
|
16/9, 57/32
|
9/5, 11/6, 12/7
|
| 10
|
1111.2
|
exact 19/10
|
2/1
|
Harmonics
| x
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
| Absolute error (cents)
|
22
|
-13
|
45
|
-8
|
9
|
-35
|
-44
|
-26
|
14
|
-40
|
32
|
| Steps
|
11
|
17
|
22
|
25
|
28
|
30
|
32
|
34
|
36
|
37
|
39
|
| Steps (reduced)
|
1
|
7
|
2
|
5
|
8
|
0
|
2
|
4
|
6
|
7
|
9
|