102ed7/3

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← 101ed7/3 102ed7/3 103ed7/3 →
Prime factorization 2 × 3 × 17
Step size 14.3811¢ 
Octave 83\102ed7/3 (1193.63¢)
Twelfth 132\102ed7/3 (1898.3¢) (→22\17ed7/3)
Consistency limit 3
Distinct consistency limit 3

102 equal divisions of 7/3 (abbreviated 102ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 102 equal parts of about 14.4⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)1/102, or the 102nd root of 7/3.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 14.4
2 28.8
3 43.1
4 57.5 30/29, 31/30
5 71.9
6 86.3 21/20, 41/39
7 100.7 35/33
8 115 31/29
9 129.4
10 143.8
11 158.2 23/21, 34/31
12 172.6 21/19
13 187 29/26, 39/35
14 201.3
15 215.7 17/15
16 230.1
17 244.5
18 258.9 43/37
19 273.2 34/29, 41/35
20 287.6 13/11
21 302
22 316.4
23 330.8 23/19
24 345.1
25 359.5
26 373.9 41/33
27 388.3
28 402.7 29/23
29 417.1
30 431.4
31 445.8 22/17
32 460.2 30/23, 43/33
33 474.6
34 489
35 503.3
36 517.7 27/20, 31/23
37 532.1
38 546.5
39 560.9 29/21
40 575.2
41 589.6 38/27
42 604 44/31
43 618.4 10/7
44 632.8
45 647.1 45/31
46 661.5 22/15
47 675.9 31/21, 34/23
48 690.3
49 704.7
50 719.1
51 733.4 26/17, 29/19
52 747.8
53 762.2 45/29
54 776.6
55 791 30/19
56 805.3 35/22
57 819.7
58 834.1 34/21
59 848.5 31/19
60 862.9
61 877.2
62 891.6
63 906
64 920.4 17/10
65 934.8
66 949.2 45/26
67 963.5
68 977.9
69 992.3 39/22
70 1006.7 34/19
71 1021.1
72 1035.4
73 1049.8
74 1064.2
75 1078.6 41/22
76 1093
77 1107.3
78 1121.7 44/23
79 1136.1 27/14
80 1150.5 33/17
81 1164.9
82 1179.2
83 1193.6
84 1208
85 1222.4
86 1236.8 45/22
87 1251.2 35/17
88 1265.5
89 1279.9 44/21
90 1294.3 19/9
91 1308.7
92 1323.1
93 1337.4
94 1351.8
95 1366.2 11/5
96 1380.6 20/9
97 1395
98 1409.3
99 1423.7 25/11
100 1438.1 39/17
101 1452.5 44/19
102 1466.9 7/3

Harmonics

Approximation of harmonics in 102ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -6.37 -3.65 +1.64 +3.62 +4.36 -3.65 -4.73 +7.08 -2.75 +4.82 -2.01
Relative (%) -44.3 -25.4 +11.4 +25.2 +30.3 -25.4 -32.9 +49.2 -19.1 +33.5 -14.0
Steps
(reduced)
83
(83)
132
(30)
167
(65)
194
(92)
216
(12)
234
(30)
250
(46)
265
(61)
277
(73)
289
(85)
299
(95)
Approximation of harmonics in 102ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +3.23 +4.36 -0.03 +3.28 -1.00 +0.71 -6.61 +5.26 +7.08 -1.55 -6.60
Relative (%) +22.4 +30.3 -0.2 +22.8 -7.0 +4.9 -45.9 +36.6 +49.2 -10.8 -45.9
Steps
(reduced)
309
(3)
318
(12)
326
(20)
334
(28)
341
(35)
348
(42)
354
(48)
361
(55)
367
(61)
372
(66)
377
(71)