64ed7/3

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← 63ed7/364ed7/365ed7/3 →
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

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

Approximation of harmonics in 64ed7/3
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)
Approximation of harmonics in 64ed7/3
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)