98edo

The 98 equal temperament divides the octave into 98 equal parts of 12.245 cents each. The patent val has a flat 3, a sharp 5 and a slightly flat 7, and tempers out 81/80 in the 5-limit, making it a meantone system with a 4 cent flat fifth. In the 7-limit it tempers out 1029/1024, 1728/1715, supporting mothra temperament, in the 11-limit 176/175 and 540/539, supporting mosura, and in the 13-limit 144/143 and 196/195. It provides the optimal patent val for 13-limit mosura temperament.

Since 98edo has a step of 12.245 cents, it also allows one to use its MOS scales as circulating temperaments. As 2*7*7edo, It is the first kn² edo which does this and the first edo which allows one to use a Magic MOS scale as a circulating temperament.

Circulating temperaments in 98edo

Tones	Pattern	L:s
5	3L 2s	20:19
6	2L 4s	17:16
7	7edo	equal
8	2L 6s	13:12
9	8L 1s	11:10
10	8L 2s	10:9
11	10L 1s	9:8
12	1L 11s
13	7L 6s	8:7
14	14edo	equal
15	8L 7s	7:6
16	2L 14s
17	13L 4s	6:5
18	8L 10s
19	3L 16s
20	18L 2s	5:4
21	14L 7s
22	10L 12s
23	6L 14s
24	2L 22s
25	23L 2s	4:3
26	20L 6s
27	17L 10s
28	14L 14s
29	11L 18s
30	8L 22s
31	5L 26s
32	2L 30s
33	32L 1s	3:2
34	30L 4s
35	28L 7s
36	26L 10s
37	24L 13s
38	22L 16s
39	20L 19s
40	18L 22s
41	16L 25s
42	14L 28s
43	12L 31s
44	10L 34s
45	8L 37s
46	6L 40s
47	4L 43s
48	2L 46s
49	49edo	equal
50	48L 2s	2:1
51	47L 4s
52	46L 6s
53	45L 8s
54	44L 10s
55	43L 12s
56	42L 14s
57	41L 16s
58	40L 18s
59	39L 20s
60	38L 22s
61	37L 24s
62	36L 26s
63	35L 28s
64	34L 30s
65	33L 32s
66	32L 34s
67	31L 36s
68	30L 38s
69	29L 40s
70	28L 42s
71	27L 44s
72	26L 46s
73	25L 48s
74	24L 50s
75	23L 52s
76	22L 54s
77	21L 56s
78	20L 58s