23ed5/2
Jump to navigation
Jump to search
Prime factorization
23 (prime)
Step size
68.9702¢
Octave
17\23ed5/2 (1172.49¢)
Twelfth
28\23ed5/2 (1931.16¢)
Consistency limit
2
Distinct consistency limit
2
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
← 22ed5/2 | 23ed5/2 | 24ed5/2 → |
23 equal divisions of 5/2 (abbreviated 23ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 23 equal parts of about 69 ¢ each. Each step represents a frequency ratio of (5/2)1/23, or the 23rd root of 5/2.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 68.97 | 25/24 |
2 | 137.94 | 12/11, 13/12, 14/13 |
3 | 206.91 | 17/15 |
4 | 275.881 | 7/6, 13/11 |
5 | 344.851 | 17/14 |
6 | 413.821 | 14/11, 19/15, 23/18 |
7 | 482.791 | |
8 | 551.761 | |
9 | 620.731 | |
10 | 689.702 | |
11 | 758.672 | 17/11 |
12 | 827.642 | |
13 | 896.612 | |
14 | 965.582 | |
15 | 1034.552 | |
16 | 1103.523 | |
17 | 1172.493 | |
18 | 1241.463 | |
19 | 1310.433 | 15/7 |
20 | 1379.403 | |
21 | 1448.373 | |
22 | 1517.344 | 12/5 |
23 | 1586.314 | 5/2 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -27.5 | +29.2 | +14.0 | -27.5 | +1.7 | +10.7 | -13.6 | -10.6 | +14.0 | -13.1 | -25.8 |
Relative (%) | -39.9 | +42.4 | +20.2 | -39.9 | +2.5 | +15.5 | -19.6 | -15.3 | +20.2 | -19.0 | -37.4 | |
Steps (reduced) |
17 (17) |
28 (5) |
35 (12) |
40 (17) |
45 (22) |
49 (3) |
52 (6) |
55 (9) |
58 (12) |
60 (14) |
62 (16) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -26.4 | -16.8 | +1.7 | +27.9 | -8.1 | +30.9 | +6.3 | -13.6 | -29.0 | +28.4 | +20.4 |
Relative (%) | -38.3 | -24.4 | +2.5 | +40.5 | -11.7 | +44.8 | +9.1 | -19.6 | -42.1 | +41.1 | +29.5 | |
Steps (reduced) |
64 (18) |
66 (20) |
68 (22) |
70 (1) |
71 (2) |
73 (4) |
74 (5) |
75 (6) |
76 (7) |
78 (9) |
79 (10) |