87ed7: Difference between revisions

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Revision as of 03:55, 17 January 2019

Division of the 7th harmonic into 87 equal parts (87ed7) is related to 31 edo, but with the 7/1 rather than the 2/1 being just. The octave is slightly stretched (about 0.3862 cents) and the step size is about 38.7221 cents.

degree cents value corresponding
JI intervals 		comments
0 0.0000 exact 1/1
1 38.7221
2 77.4443
3 116.1664 77/72, 15/14
4 154.8885
5 193.6107 19/17, 85/76
6 232.3328 8/7
7 271.0550
8 309.7771
9 348.4992 11/9, 49/40
10 387.2214 5/4
11 425.9435
12 464.6656 98/75
13 503.3878 91/68, 75/56
14 542.1099
15 580.8321 7/5
16 619.5542 10/7
17 658.2763
18 696.9985 112/75, 121/81, 136/91, 187/125
19 735.7206
20 774.4427
21 813.1649 8/5
22 851.8870
23 890.6091
24 929.3313 65/38
25 968.0534
26 1006.7756
27 1045.4977 64/35
28 1084.2198
29 1122.9420
30 1161.6641 88/45, 96/49, 49/25
31 1200.3862 2/1
32 1239.1084
33 1277.8305 44/21
34 1316.5527
35 1355.2748
36 1393.9969 38/17, 85/38
37 1432.7191
38 1471.4412
39 1510.1633
40 1548.8855
41 1587.6076
42 1626.3297 64/25
43 1665.0519
44 1703.7740
45 1742.4962 52/19
46 1781.2183
47 1819.9404
48 1858.6626 38/13
49 1897.3847
50 1936.1068
51 1974.8290 25/8
52 2013.5511
53 2052.2733
54 2090.9954
55 2129.7175
56 2168.4397
57 2207.1618 68/19
58 2245.8839
59 2284.6061
60 2323.3282 65/17
61 2362.0503
62 2400.7725
63 2439.4946 45/11
64 2478.2168
65 2516.9389
66 2555.6610 35/8
67 2594.3832
68 2633.1053
69 2671.8274
70 2710.5496
71 2749.2717
72 2787.9939 5/1
73 2826.7160
74 2865.4381
75 2904.1603 75/14
76 2942.8824
77 2981.6045
78 3020.3267 40/7, 63/11
79 3059.0488
80 3097.7709
81 3136.4931 49/8
82 3175.2152
83 3213.9374
84 3252.6595 98/15, 72/11
85 3291.3816
86 3330.1038
87 3368.8259 exact 7/1 harmonic seventh plus two octaves
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