40edf

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	0.0000	exact 1/1
1	17.5489	100/99, 99/98
2	35.0978	50/49, 49/48
3	52.6466	33/32
4	70.1955	25/24
5	87.7444	20/19
6	105.2933	17/16
7	122.8421
8	140.3910
9	157.9399	23/21
10	175.4888
11	193.0376	19/17
12	210.5865
13	228.1354
14	245.6843
15	263.2331
16	280.7820	20/17
17	298.3309	19/16
18	315.8798	6/5
19	333.4286
20	350.9775	60/49, 49/40
21	368.5264
22	386.0753	5/4
23	403.6241	24/19
24	421.1730	51/40
25	438.7219
26	456.2708
27	473.8196
28	491.3685
29	508.9174
30	526.4663
31	544.0151
32	561.5640
33	579.1129
34	596.6618	24/17
35	614.2106
36	631.7595	36/25
37	649.3084	16/11
38	666.8573
39	694.4061	49/33
40	701.9550	exact 3/2	just perfect fifth

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