40edf

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40EDF is the equal division of the just perfect fifth into 40 parts of 17.5489 cents each, corresponding to 68.3805 edo. It is related to the regular temperament which tempers out 2401/2400, 9801/9800, and 9453125/9437184 in the 11-limit, which is supported by 68edo, 274edo, 342edo, 410edo, 616edo, and 752edo among others.

Intervals

degree cents value corresponding
JI intervals
comments
0 exact 1/1
1 17.5489 100/99, 99/98, 81/80
2 35.09775 50/49, 49/48
3 52.6466 33/32
4 70.1955 25/24
5 87.7444 20/19
6 105.29325 17/16
7 122.8421 15/14
8 140.391 13/12
9 157.9399 23/21
10 175.48875 10/9
11 193.0376 19/17
12 210.5865 17/15
13 228.1354 8/7
14 245.68425 15/13
15 263.2331 7/6
16 280.782 20/17
17 298.3309 19/16
18 315.87975 6/5
19 333.4286 63/52
20 350.9775 60/49, 49/40
21 368.5264 26/21
22 386.07525 5/4
23 403.6241 24/19
24 421.173 51/40
25 438.7219 9/7
26 456.27075 13/10
27 473.8196 21/16
28 491.3685 4/3
29 508.9174 66/49
30 526.46625 200/147, 49/36, 27/20
31 544.0151 11/8
32 561.564 25/18
33 579.1129 7/5
34 596.66175 24/17
35 614.2106 10/7
36 631.7595 36/25
37 649.3084 16/11
38 666.85725 147/100, 72/49
39 684.4061 297/200, 49/33, 40/27
40 701.955 exact 3/2 just perfect fifth
41 719.5039 50/33, 297/196, 243/160, 32/21
42 737.05275 75/49, 49/32
43 754.6016 99/64
44 772.1505 25/16
45 789.6994 30/19
46 807.24825 51/32
47 824.7971 45/28
48 842.346 13/8
49 859.8949 32/14
50 877.44375 5/3
51 894.9926 57/34
52 912.5415 17/10
53 930.0904 12/7
54 947.63925 45/26
55 965.1981 7/4
56 982.737 30/17
57 1000.2859 57/32
58 1017.83275 9/5
59 1035.3836 189/104
60 1052.9325 90/49, 147/80
61 1070.4814 13/7
62 1088.03025 15/8
63 1105.4791 36/19
64 1123.128 153/80
65 1140.6769 27/14
66 1158.22575 39/20
67 1175.7746 63/32
68 1193.3235 2/1
69 1210.8724 99/49
70 1228.42125 300/147, 49/24, 81/40
71 1246.9701 33/16
72 1263.519 25/12
73 1281.0679 21/10
74 1298.61675 36/17
75 1316.1756 15/7
76 1333.7145 54/25
77 1351.2634 24/11
78 1368.81375 441/200, 108/49
79 1386.3611 891/400, 49/22, 20/9
80 1403.91 exact 9/8

Related regular temperaments

Adding one half of the octave as a generator, 40EDF leads the regular temperament which tempers out 2401/2400, 9801/9800, and 9453125/9437184 in the 11-limit.

11-limit 68&342

Commas: 2401/2400, 9801/9800, 9453125/9437184

POTE generator: ~99/98 = 17.545

Map: [<2 2 4 5 8|, <0 40 22 21 -37|]

EDOs: 68, 274, 342, 410, 616, 752

2.3.5.7.11.17 subgroup 68&342

Commas: 1089/1088, 1225/1224, 2401/2400, 24576/24565

POTE generator: ~99/98 = 17.546

Map: [<2 2 4 5 8 8|, <0 40 22 21 -37 6|]

EDOs: 68, 274, 342, 410, 616, 752

2.3.5.7.11.17.19 subgroup 68&342

Commas: 1089/1088, 1225/1224, 1445/1444, 1617/1615, 2401/2400

POTE generator: ~96/95 = 17.547

Map: [<2 2 4 5 8 8 8|, <0 40 22 21 -37 6 17|]

EDOs: 68, 274, 342, 410, 616, 752h

2.3.5.7.11.17.19.23 subgroup 68&342

Commas: 875/874, 1089/1088, 1225/1224, 1445/1444, 1617/1615, 2024/2023

POTE generator: ~96/95 = 17.546

Map: [<2 2 4 5 8 8 8 7|, <0 40 22 21 -37 6 17 70|]

EDOs: 68, 274, 342, 410, 616i, 752h