22ed5/3
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Prime factorization
2 × 11
Step size
40.1981¢
Octave
30\22ed5/3 (1205.94¢) (→15\11ed5/3)
Twelfth
47\22ed5/3 (1889.31¢)
Consistency limit
3
Distinct consistency limit
3
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← 21ed5/3 | 22ed5/3 | 23ed5/3 → |
22 equal divisions of 5/3 (abbreviated 22ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 22 equal parts of about 40.2 ¢ each. Each step represents a frequency ratio of (5/3)1/22, or the 22nd root of 5/3.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 40.198 | |
2 | 80.396 | 20/19, 21/20, 22/21, 23/22, 24/23 |
3 | 120.594 | |
4 | 160.792 | 11/10, 12/11, 21/19, 23/21 |
5 | 200.991 | 19/17 |
6 | 241.189 | 8/7, 15/13, 22/19, 23/20 |
7 | 281.387 | 13/11, 20/17 |
8 | 321.585 | 6/5, 23/19 |
9 | 361.783 | 11/9, 21/17 |
10 | 401.981 | 24/19 |
11 | 442.179 | 13/10, 22/17 |
12 | 482.377 | |
13 | 522.576 | 15/11, 19/14, 23/17 |
14 | 562.774 | 18/13, 25/18 |
15 | 602.972 | 17/12, 24/17 |
16 | 643.17 | 13/9 |
17 | 683.368 | |
18 | 723.566 | |
19 | 763.764 | 17/11 |
20 | 803.962 | 19/12 |
21 | 844.161 | 18/11, 21/13 |
22 | 884.359 | 5/3 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +5.9 | -12.6 | +11.9 | -12.6 | -6.7 | +7.8 | +17.8 | +14.9 | -6.7 | -10.9 | -0.8 |
Relative (%) | +14.8 | -31.5 | +29.6 | -31.5 | -16.7 | +19.4 | +44.4 | +37.1 | -16.7 | -27.1 | -1.9 | |
Steps (reduced) |
30 (8) |
47 (3) |
60 (16) |
69 (3) |
77 (11) |
84 (18) |
90 (2) |
95 (7) |
99 (11) |
103 (15) |
107 (19) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -18.7 | +13.8 | +14.9 | -16.4 | -0.8 | -19.3 | +7.6 | -0.8 | -4.8 | -5.0 | -1.5 |
Relative (%) | -46.6 | +34.2 | +37.1 | -40.9 | -2.0 | -48.1 | +19.0 | -1.9 | -12.0 | -12.4 | -3.8 | |
Steps (reduced) |
110 (0) |
114 (4) |
117 (7) |
119 (9) |
122 (12) |
124 (14) |
127 (17) |
129 (19) |
131 (21) |
133 (1) |
135 (3) |