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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]]
Retrieved from "https://en.xen.wiki/w/98edo"