104ed7/3

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← 103ed7/3104ed7/3105ed7/3 →
Prime factorization 23 × 13
Step size 14.1045¢ 
Octave 85\104ed7/3 (1198.88¢)
(semiconvergent)
Twelfth 135\104ed7/3 (1904.11¢)
Consistency limit 4
Distinct consistency limit 4

104 equal divisions of 7/3 (abbreviated 104ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 104 equal parts of about 14.1 ¢ each. Each step represents a frequency ratio of (7/3)1/104, or the 104th root of 7/3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 14.105
2 28.209
3 42.314 40/39, 41/40, 42/41, 43/42
4 56.418 32/31
5 70.523
6 84.627 21/20, 41/39, 43/41
7 98.732 18/17
8 112.836
9 126.941 14/13, 43/40
10 141.045
11 155.15 23/21
12 169.254 32/29, 43/39
13 183.359 10/9
14 197.463 37/33, 46/41
15 211.568 26/23
16 225.672 33/29, 41/36
17 239.777 23/20, 39/34
18 253.882 22/19
19 267.986 7/6
20 282.091 20/17, 33/28
21 296.195 19/16
22 310.3
23 324.404 41/34
24 338.509 28/23
25 352.613 38/31
26 366.718 21/17
27 380.822
28 394.927
29 409.031
30 423.136 23/18, 37/29
31 437.24 9/7
32 451.345 35/27
33 465.449 17/13
34 479.554 29/22
35 493.658
36 507.763
37 521.868 23/17, 27/20
38 535.972
39 550.077 11/8
40 564.181 18/13
41 578.286
42 592.39 31/22
43 606.495 44/31
44 620.599
45 634.704 13/9
46 648.808 16/11
47 662.913
48 677.017 34/23
49 691.122
50 705.226
51 719.331
52 733.435 26/17, 29/19
53 747.54 20/13, 37/24
54 761.645
55 775.749 36/23
56 789.854 41/26
57 803.958 43/27
58 818.063
59 832.167 21/13, 34/21
60 846.272 31/19
61 860.376 23/14
62 874.481
63 888.585
64 902.69 32/19
65 916.794 17/10
66 930.899 12/7
67 945.003 19/11
68 959.108 40/23
69 973.212
70 987.317 23/13
71 1001.421 41/23
72 1015.526 9/5
73 1029.631 29/16
74 1043.735 42/23
75 1057.84
76 1071.944 13/7
77 1086.049
78 1100.153 17/9
79 1114.258 40/21
80 1128.362 23/12
81 1142.467
82 1156.571 39/20, 41/21
83 1170.676
84 1184.78
85 1198.885 2/1
86 1212.989
87 1227.094
88 1241.198 41/20, 43/21
89 1255.303 33/16
90 1269.408
91 1283.512 21/10
92 1297.617 36/17
93 1311.721
94 1325.826 43/20
95 1339.93 13/6
96 1354.035
97 1368.139
98 1382.244 20/9
99 1396.348
100 1410.453
101 1424.557 41/18
102 1438.662 39/17
103 1452.766 37/16, 44/19
104 1466.871 7/3

Harmonics

Approximation of harmonics in 104ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -1.12 +2.16 -2.23 +6.38 +1.04 +2.16 -3.35 +4.31 +5.27 -4.59 -0.07
Relative (%) -7.9 +15.3 -15.8 +45.3 +7.4 +15.3 -23.7 +30.6 +37.3 -32.5 -0.5
Steps
(reduced)
85
(85)
135
(31)
170
(66)
198
(94)
220
(12)
239
(31)
255
(47)
270
(62)
283
(75)
294
(86)
305
(97)
Approximation of harmonics in 104ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +2.40 +1.04 -5.57 -4.46 +3.42 +3.20 -5.78 +4.15 +4.31 -5.70 +1.97
Relative (%) +17.0 +7.4 -39.5 -31.6 +24.2 +22.7 -41.0 +29.4 +30.6 -40.4 +14.0
Steps
(reduced)
315
(3)
324
(12)
332
(20)
340
(28)
348
(36)
355
(43)
361
(49)
368
(56)
374
(62)
379
(67)
385
(73)