102ed7/3
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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
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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
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) |
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) |