| Prime factorization
|
23 (prime)
|
| Step size
|
10.051 ¢
|
| Octave
|
119\23ed8/7 (1196.07 ¢)
|
| Twelfth
|
189\23ed8/7 (1899.65 ¢)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
23 equal divisions of 8/7 (abbreviated 23ed8/7) is a nonoctave tuning system that divides the interval of 8/7 into 23 equal parts of about 10.1 ¢ each. Each step represents a frequency ratio of (8/7)1/23, or the 23rd root of 8/7. This tuning is almost exactly every 5th step of 597edo.
Intervals
| Steps
|
Cents
|
Approximate ratios
|
| 0
|
0
|
1/1
|
| 1
|
10.1
|
|
| 2
|
20.1
|
|
| 3
|
30.2
|
|
| 4
|
40.2
|
|
| 5
|
50.3
|
|
| 6
|
60.3
|
24/23
|
| 7
|
70.4
|
|
| 8
|
80.4
|
20/19, 22/21, 23/22, 25/24
|
| 9
|
90.5
|
18/17, 21/20
|
| 10
|
100.5
|
16/15, 19/18
|
| 11
|
110.6
|
|
| 12
|
120.6
|
14/13, 15/14
|
| 13
|
130.7
|
|
| 14
|
140.7
|
12/11, 25/23
|
| 15
|
150.8
|
13/12
|
| 16
|
160.8
|
23/21
|
| 17
|
170.9
|
11/10, 21/19
|
| 18
|
180.9
|
10/9
|
| 19
|
191
|
19/17
|
| 20
|
201
|
|
| 21
|
211.1
|
9/8
|
| 22
|
221.1
|
8/7, 17/15, 25/22
|
| 23
|
231.2
|
|