33ed7/4
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Prime factorization
3 × 11
Step size
29.3584¢
Octave
41\33ed7/4 (1203.69¢)
Twelfth
65\33ed7/4 (1908.29¢)
Consistency limit
10
Distinct consistency limit
3
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← 32ed7/4 | 33ed7/4 | 34ed7/4 → |
33 equal divisions of 7/4 (abbreviated 33ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 33 equal parts of about 29.4 ¢ each. Each step represents a frequency ratio of (7/4)1/33, or the 33rd root of 7/4.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 29.358 | |
2 | 58.717 | 28/27 |
3 | 88.075 | 19/18, 20/19, 21/20 |
4 | 117.433 | 15/14, 16/15 |
5 | 146.792 | 25/23 |
6 | 176.15 | 10/9, 21/19 |
7 | 205.509 | 9/8, 26/23 |
8 | 234.867 | 8/7, 23/20 |
9 | 264.225 | 7/6 |
10 | 293.584 | 13/11, 19/16, 25/21 |
11 | 322.942 | 6/5, 23/19 |
12 | 352.3 | |
13 | 381.659 | 5/4 |
14 | 411.017 | 19/15, 24/19 |
15 | 440.375 | 9/7, 22/17 |
16 | 469.734 | 17/13, 21/16, 25/19 |
17 | 499.092 | 4/3 |
18 | 528.45 | 19/14, 23/17, 27/20 |
19 | 557.809 | |
20 | 587.167 | 7/5 |
21 | 616.526 | 10/7, 27/19 |
22 | 645.884 | |
23 | 675.242 | 25/17, 28/19 |
24 | 704.601 | 3/2 |
25 | 733.959 | 23/15, 26/17 |
26 | 763.317 | 14/9 |
27 | 792.676 | 19/12 |
28 | 822.034 | 8/5 |
29 | 851.392 | 23/14 |
30 | 880.751 | 5/3 |
31 | 910.109 | 17/10, 22/13, 27/16 |
32 | 939.468 | 12/7 |
33 | 968.826 | 7/4 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +3.7 | +6.3 | +7.4 | +2.7 | +10.0 | +7.4 | +11.1 | +12.7 | +6.4 | -11.8 | +13.7 |
Relative (%) | +12.6 | +21.6 | +25.2 | +9.3 | +34.2 | +25.2 | +37.7 | +43.2 | +21.9 | -40.2 | +46.7 | |
Steps (reduced) |
41 (8) |
65 (32) |
82 (16) |
95 (29) |
106 (7) |
115 (16) |
123 (24) |
130 (31) |
136 (4) |
141 (9) |
147 (15) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -7.4 | +11.1 | +9.1 | -14.6 | -2.1 | -13.0 | +10.8 | +10.1 | +13.7 | -8.1 | +3.0 |
Relative (%) | -25.3 | +37.7 | +30.9 | -49.7 | -7.2 | -44.2 | +36.9 | +34.5 | +46.7 | -27.6 | +10.3 | |
Steps (reduced) |
151 (19) |
156 (24) |
160 (28) |
163 (31) |
167 (2) |
170 (5) |
174 (9) |
177 (12) |
180 (15) |
182 (17) |
185 (20) |