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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 [[Meantone_family#Mothra-Mosura-13-limit|mosura temperament]].
'''98 EDO''', the 98 equal temperament divides the octave into 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-family]] 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.


{{Primes in edo|98|prec=2}}


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 km<sup>n</sup> edo which does this and the first edo which allows one to use a Magic MOS scale as a circulating temperament.
Since 98 EDO 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 ''km<sup>n</sup>'' EDO which does this and the first EDO which allows one to use a Magic MOS scale as a circulating temperament.
{| class="wikitable"
 
|+Circulating temperaments in 98edo
{| class="wikitable center-all"
!Tones
|+ Circulating temperaments in 98 EDO
!Pattern
!L:s
|-
|-
|5
! Tones
|[[3L 2s]]
! Pattern
|20:19
! L:s
|-
|-
|6
| 5
|[[2L 4s]]
| [[3L 2s]]
|17:16
| 20:19
|-
|-
|7
| 6
|[[7edo]]
| [[2L 4s]]
|equal
| 17:16
|-
|-
|8
| 7
|[[2L 6s]]
| ''[[7 EDO]]''
|13:12
| ''equal''
|-
|-
|9
| 8
|[[8L 1s]]
| [[2L 6s]]
|11:10
| 13:12
|-
|-
|10
| 9
|[[8L 2s]]
| [[8L 1s]]
|10:9
| 11:10
|-
|-
|11
| 10
|[[10L 1s]]
| [[8L 2s]]
| rowspan="2" |9:8
| 10:9
|-
|-
|12
| 11
|[[2L 10s]]
| [[10L 1s]]
| rowspan="2" | 9:8
|-
|-
|13
| 12
|[[7L 6s]]
| [[2L 10s]]
|8:7
|-
|-
|14
| 13
|[[14edo]]
| [[7L 6s]]
|equal
| 8:7
|-
|-
|15
| 14
|[[8L 7s]]
| ''[[14 EDO]]''
| rowspan="2" |7:6
| ''equal''
|-
|-
|16
| 15
|2L 14s
| [[8L 7s]]
| rowspan="2" | 7:6
|-
|-
|17
| 16
|13L 4s
| 2L 14s
| rowspan="3" |6:5
|-
|-
|18
| 17
|8L 10s
| 13L 4s
| rowspan="3" | 6:5
|-
|-
|19
| 18
|[[3L 16s]]
| 8L 10s
|-
|-
|20
| 19
|18L 2s
| [[3L 16s]]
| rowspan="5" |5:4
|-
|-
|21
| 20
|14L 7s
| 18L 2s
| rowspan="5" | 5:4
|-
|-
|22
| 21
|10L 12s
| 14L 7s
|-
|-
|23
| 22
|6L 17s
| 10L 12s
|-
|-
|24
| 23
|2L 22s
| 6L 17s
|-
|-
|25
| 24
|23L 2s
| 2L 22s
| rowspan="8" |4:3
|-
|-
|26
| 25
|20L 6s
| 23L 2s
| rowspan="8" | 4:3
|-
|-
|27
| 26
|17L 10s
| 20L 6s
|-
|-
|28
| 27
|14L 14s
| 17L 10s
|-
|-
|29
| 28
|11L 18s
| 14L 14s
|-
|-
|30
| 29
|8L 22s
| 11L 18s
|-
|-
|31
| 30
|5L 26s
| 8L 22s
|-
|-
|32
| 31
|2L 30s
| 5L 26s
|-
|-
|33
| 32
|32L 1s
| 2L 30s
| rowspan="16" |3:2
|-
|-
|34
| 33
|30L 4s
| 32L 1s
| rowspan="16" | 3:2
|-
|-
|35
| 34
|28L 7s
| 30L 4s
|-
|-
|36
| 35
|26L 10s
| 28L 7s
|-
|-
|37
| 36
|24L 13s
| 26L 10s
|-
|-
|38
| 37
|22L 16s
| 24L 13s
|-
|-
|39
| 38
|20L 19s
| 22L 16s
|-
|-
|40
| 39
|18L 22s
| 20L 19s
|-
|-
|41
| 40
|16L 25s
| 18L 22s
|-
|-
|42
| 41
|14L 28s
| 16L 25s
|-
|-
|43
| 42
|12L 31s
| 14L 28s
|-
|-
|44
| 43
|10L 34s
| 12L 31s
|-
|-
|45
| 44
|8L 37s
| 10L 34s
|-
|-
|46
| 45
|6L 40s
| 8L 37s
|-
|-
|47
| 46
|4L 43s
| 6L 40s
|-
|-
|48
| 47
|2L 46s
| 4L 43s
|-
|-
|49
| 48
|[[49edo]]
| 2L 46s
|equal
|-
|-
|50
| 49
|48L 2s
| ''[[49 EDO]]''
| rowspan="29" |2:1
| ''equal''
|-
|-
|51
| 50
|47L 4s
| 48L 2s
| rowspan="29" | 2:1
|-
|-
|52
| 51
|46L 6s
| 47L 4s
|-
|-
|53
| 52
|45L 8s
| 46L 6s
|-
|-
|54
| 53
|44L 10s
| 45L 8s
|-
|-
|55
| 54
|43L 12s
| 44L 10s
|-
|-
|56
| 55
|42L 14s
| 43L 12s
|-
|-
|57
| 56
|41L 16s
| 42L 14s
|-
|-
|58
| 57
|40L 18s
| 41L 16s
|-
|-
|59
| 58
|39L 20s
| 40L 18s
|-
|-
|60
| 59
|38L 22s
| 39L 20s
|-
|-
|61
| 60
|37L 24s
| 38L 22s
|-
|-
|62
| 61
|36L 26s
| 37L 24s
|-
|-
|63
| 62
|35L 28s
| 36L 26s
|-
|-
|64
| 63
|34L 30s
| 35L 28s
|-
|-
|65
| 64
|33L 32s
| 34L 30s
|-
|-
|66
| 65
|32L 34s
| 33L 32s
|-
|-
|67
| 66
|31L 36s
| 32L 34s
|-
|-
|68
| 67
|30L 38s
| 31L 36s
|-
|-
|69
| 68
|29L 40s
| 30L 38s
|-
|-
|70
| 69
|28L 42s
| 29L 40s
|-
|-
|71
| 70
|27L 44s
| 28L 42s
|-
|-
|72
| 71
|26L 46s
| 27L 44s
|-
|-
|73
| 72
|25L 48s
| 26L 46s
|-
|-
|74
| 73
|24L 50s
| 25L 48s
|-
|-
|75
| 74
|23L 52s
| 24L 50s
|-
|-
|76
| 75
|22L 54s
| 23L 52s
|-
|-
|77
| 76
|21L 56s
| 22L 54s
|-
|-
|78
| 77
|20L 58s
| 21L 56s
|-
| 78
| 20L 58s
|}
|}
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:meantone]]
[[Category:Meantone]]

Revision as of 08:21, 10 June 2021

98 EDO, the 98 equal temperament divides the octave into 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-family 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.

Script error: No such module "primes_in_edo".

Since 98 EDO 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 kmn EDO which does this and the first EDO which allows one to use a Magic MOS scale as a circulating temperament.

Circulating temperaments in 98 EDO
Tones Pattern L:s
5 3L 2s 20:19
6 2L 4s 17:16
7 7 EDO equal
8 2L 6s 13:12
9 8L 1s 11:10
10 8L 2s 10:9
11 10L 1s 9:8
12 2L 10s
13 7L 6s 8:7
14 14 EDO 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 17s
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 49 EDO 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
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