64ed7/3
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Prime factorization
26
Step size
22.9199¢
Octave
52\64ed7/3 (1191.83¢) (→13\16ed7/3)
Twelfth
83\64ed7/3 (1902.35¢)
(semiconvergent)
Consistency limit
3
Distinct consistency limit
3
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← 63ed7/3 | 64ed7/3 | 65ed7/3 → |
(semiconvergent)
64 equal divisions of 7/3 (abbreviated 64ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 64 equal parts of about 22.9 ¢ each. Each step represents a frequency ratio of (7/3)1/64, or the 64th root of 7/3.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 22.92 | |
2 | 45.84 | |
3 | 68.76 | 27/26 |
4 | 91.679 | 19/18, 20/19 |
5 | 114.599 | 31/29 |
6 | 137.519 | |
7 | 160.439 | 23/21, 34/31 |
8 | 183.359 | 10/9 |
9 | 206.279 | |
10 | 229.199 | |
11 | 252.118 | 22/19 |
12 | 275.038 | 27/23, 34/29 |
13 | 297.958 | |
14 | 320.878 | |
15 | 343.798 | 11/9 |
16 | 366.718 | 21/17, 26/21 |
17 | 389.638 | |
18 | 412.557 | 33/26 |
19 | 435.477 | 9/7 |
20 | 458.397 | 30/23 |
21 | 481.317 | 29/22 |
22 | 504.237 | |
23 | 527.157 | 19/14, 23/17 |
24 | 550.077 | |
25 | 572.996 | |
26 | 595.916 | 31/22 |
27 | 618.836 | 10/7 |
28 | 641.756 | 29/20 |
29 | 664.676 | |
30 | 687.596 | |
31 | 710.516 | |
32 | 733.435 | 26/17, 29/19 |
33 | 756.355 | 17/11, 31/20 |
34 | 779.275 | 11/7 |
35 | 802.195 | 27/17 |
36 | 825.115 | 29/18 |
37 | 848.035 | 31/19 |
38 | 870.955 | 33/20 |
39 | 893.874 | |
40 | 916.794 | 17/10 |
41 | 939.714 | 31/18 |
42 | 962.634 | |
43 | 985.554 | 23/13, 30/17 |
44 | 1008.474 | 34/19 |
45 | 1031.394 | 20/11 |
46 | 1054.313 | |
47 | 1077.233 | |
48 | 1100.153 | 17/9 |
49 | 1123.073 | 21/11 |
50 | 1145.993 | 33/17 |
51 | 1168.913 | |
52 | 1191.833 | |
53 | 1214.752 | |
54 | 1237.672 | |
55 | 1260.592 | 29/14 |
56 | 1283.512 | 21/10 |
57 | 1306.432 | |
58 | 1329.352 | |
59 | 1352.272 | |
60 | 1375.191 | 31/14 |
61 | 1398.111 | |
62 | 1421.031 | |
63 | 1443.951 | 23/10, 30/13 |
64 | 1466.871 | 7/3 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -8.2 | +0.4 | +6.6 | +9.9 | -7.8 | +0.4 | -1.6 | +0.8 | +1.7 | -2.8 | +7.0 |
Relative (%) | -35.6 | +1.7 | +28.7 | +43.2 | -33.9 | +1.7 | -6.9 | +3.4 | +7.6 | -12.3 | +30.4 | |
Steps (reduced) |
52 (52) |
83 (19) |
105 (41) |
122 (58) |
135 (7) |
147 (19) |
157 (29) |
166 (38) |
174 (46) |
181 (53) |
188 (60) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +5.9 | -7.8 | +10.3 | -9.7 | -0.1 | -7.4 | -9.3 | -6.4 | +0.8 | -11.0 | +3.7 |
Relative (%) | +25.8 | -33.9 | +44.9 | -42.5 | -0.5 | -32.2 | -40.6 | -28.0 | +3.4 | -48.0 | +16.3 | |
Steps (reduced) |
194 (2) |
199 (7) |
205 (13) |
209 (17) |
214 (22) |
218 (26) |
222 (30) |
226 (34) |
230 (38) |
233 (41) |
237 (45) |