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104edo divides the octave into 104 parts of size 11.54 cents each. It has two different equally viable 5-limit vals, and both are useful. The flat major third val, <104 165 241|, tempers out 3125/3072, and supports magic temperament. The sharp major third val, <104 165 242|, tempers out 2048/2025 and supports diaschismic temperament.

104edo with the flat third is especially notable as an excellent tuning for magic temperament, providing the optimal patent val for 11-limit magic and the 13-limit magic extension necromancy. In the 5-limit it tempers out the magic comma, 3125/3072; in the 7-limit, it tempers out 225/224, 245/243 and 875/864; and in the 11-limit, 100/99, 896/891, 385/384 and 540/539. It provides an excellent tuning also for the rank three temperaments pairing 100/99 with 225/224 (apollo temperament), 245/243 or 875/864, or the rank four temperament tempering out 100/99, for which it gives the optimal patent val.

104 with the sharp third is excellent for 11, 13, or 17 limit diaschismic. It tempers out 2048/2025 in the 5-limit, 126/125 and 5120/5103 in the 7-limit, 176/175 and 896/891 in the 11-limit, 196/195 and 364/363 in the 13-limit and 136/135 and 256/255 in the 17-limit.

104 is also notable as a no-fives system; on 2.3.7.11.13, it tempers out 352/351, 364/363, 896/891, 2197/2187, 16807/16731, 20449/20412, 21632/21609, 26411/26364 and 10648/10647. It is the optimal patent val for the 17&87 2.3.7.11.13 subgroup temperament tempering out 352/351, 364/363 and 2197/2187, which has a 13/9 generator, three of which give a 3.

17-limit Regular Temperaments
Degree
Cents
2
23.08
3
34.615
4
46.15
5
57.69
7
80.77
8
92.31
9
103.85
10
115.385
11
126.92
12
138.46
13
150
14
161.54
15
173.08
16
184.615
17
196.15
18
207.69
20
230.77
21
242.31
22
253.85
23
265.385
25
288.46
26
300
27
311.54
28
323.08
29
334.615
30
346.15
31
357.69
32
369.23
33
380.77
34
392.31
35
403.85
36
415.385
38
438.46
39
450
40
461.54
41
473.08
43
496.15
45
519.23
46
530.77
47
542.31
48
553.85
50
576.92
51
588.45
52
600
53
611.54
54
623.08
56
646.15
57
657.69
58
669.23
59
680.77
61
703.85
63
726.92
64
738.46
65
750
66
761.54
67
773.08
68
784.615
69
796.15
70
807.69
71
819.23
72
830.77
73
842.31
74
853.85
75
865.385
76
876.92
77
888.46
78
900
79
911.54
81
934.615
82
946.15
83
957.69
84
969.23
86
992.31
87
1003.85
88
1015.385
89
1026.92
90
1038.46
91
1050
92
1061.54
93
1073.08
95
1096.15
96
1107.69
97
1119.23
99
1142.31
100
1153.85
101
1165.385
102
1176.92