User:MisterShafXen/21ed8/7

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← 20ed8/7 21ed8/7 22ed8/7 →
Prime factorization 3 × 7
Step size 11.0083 ¢ 
Octave 109\21ed8/7 (1199.9 ¢)
(convergent)
Twelfth 173\21ed8/7 (1904.43 ¢)
Consistency limit 8
Distinct consistency limit 8

21 equal divisions of 8/7 (abbreviated 21ed8/7) is a nonoctave tuning system that divides the interval of 8/7 into 21 equal parts of about 11 ¢ each. Each step represents a frequency ratio of (8/7)1/21, or the 21st root of 8/7.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 11
2 22
3 33
4 44
5 55 30/29, 31/30, 32/31, 33/32, 34/33
6 66 26/25
7 77.1 22/21, 23/22, 24/23
8 88.1 20/19, 21/20
9 99.1 18/17, 35/33
10 110.1 16/15, 33/31
11 121.1 15/14, 29/27
12 132.1 14/13
13 143.1 25/23
14 154.1 12/11, 23/21, 35/32
15 165.1 11/10
16 176.1 21/19, 31/28
17 187.1
18 198.1 28/25
19 209.2 26/23, 35/31
20 220.2 17/15, 25/22, 33/29
21 231.2 8/7
22 242.2 23/20
23 253.2 22/19
24 264.2 7/6
25 275.2 34/29
26 286.2 13/11, 33/28
27 297.2 19/16
28 308.2 31/26
29 319.2 6/5
30 330.2 23/19, 29/24
31 341.3 28/23
32 352.3
33 363.3 16/13, 21/17
34 374.3 31/25
35 385.3 5/4
36 396.3 34/27
37 407.3 19/15, 24/19
38 418.3 14/11
39 429.3 32/25
40 440.3 31/24
41 451.3 13/10
42 462.3 30/23
43 473.4 21/16, 25/19
44 484.4 33/25
45 495.4 4/3
46 506.4
47 517.4 31/23, 35/26
48 528.4 19/14
49 539.4 15/11, 26/19
50 550.4 11/8
51 561.4 29/21
52 572.4 32/23
53 583.4 7/5
54 594.4 24/17, 31/22
55 605.5 17/12
56 616.5 10/7
57 627.5 23/16, 33/23
58 638.5
59 649.5 16/11, 35/24
60 660.5 19/13, 22/15
61 671.5 28/19, 31/21
62 682.5
63 693.5