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| '''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 system of [[meantone family]] 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.
| | {{Infobox ET}} |
| | {{ED intro}} |
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| {{Primes in edo|98}}
| | == Theory == |
| | The [[patent val]] of 98edo has a flat [[3/1|3]], a sharp [[5/1|5]] and a slightly flat [[7/1|7]], and [[tempering out|tempers out]] [[81/80]] in the 5-limit, making it a system of [[meantone family]] with a 4-cent-flat fifth. In the 7-limit it tempers out [[1029/1024]], [[1728/1715]], [[support]]ing [[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. |
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| 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.
| | === Odd harmonics === |
| | {{Harmonics in equal|98}} |
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| {| class="wikitable center-all"
| | === Subsets and supersets === |
| |+ Circulating temperaments in 98 EDO
| | Since 98 factors into {{factorization|98}}, 98edo has subset edos {{EDOs| 2, 7, 14, and 49 }}. |
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| ! Tones
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| ! Pattern
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| ! L:s
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| |-
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| | 5
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| | [[3L 2s]]
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| | 20:19
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| |-
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| | 6
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| | [[2L 4s]]
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| | 17:16
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| |-
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| | 7
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| | ''[[7 EDO]]''
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| | ''equal''
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| |-
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| | 8
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| | [[2L 6s]]
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| | 13:12
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| |-
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| | 9
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| | [[8L 1s]]
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| | 11:10
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| |-
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| | 10
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| | [[8L 2s]]
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| | 10:9
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| |-
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| | 11
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| | [[10L 1s]]
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| | rowspan="2" | 9:8
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| |-
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| | 12
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| | [[2L 10s]]
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| |-
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| | 13
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| | [[7L 6s]]
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| | 8:7
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| |-
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| | 14
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| | ''[[14 EDO]]''
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| | ''equal''
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| |-
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| | 15
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| | [[8L 7s]]
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| | rowspan="2" | 7:6
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| |-
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| | 16
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| | 2L 14s
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| |-
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| | 17
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| | 13L 4s
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| | rowspan="3" | 6:5
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| |-
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| | 18
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| | 8L 10s
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| |-
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| | 19
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| | [[3L 16s]]
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| |-
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| | 20
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| | 18L 2s
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| | rowspan="5" | 5:4
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| |-
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| | 21
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| | 14L 7s
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| |-
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| | 22
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| | 10L 12s
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| |-
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| | 23
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| | 6L 17s
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| |-
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| | 24
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| | 2L 22s
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| |-
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| | 25
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| | 23L 2s
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| | rowspan="8" | 4:3
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| |- | |
| | 26
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| | 20L 6s
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| |-
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| | 27
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| | 17L 10s
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| |- | |
| | 28
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| | 14L 14s
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| |-
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| | 29
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| | 11L 18s
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| |-
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| | 30
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| | 8L 22s
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| |-
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| | 31
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| | 5L 26s
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| |-
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| | 32
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| | 2L 30s
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| |-
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| | 33
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| | 32L 1s
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| | rowspan="16" | 3:2
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| |-
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| | 34
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| | 30L 4s
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| |-
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| | 35
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| | 28L 7s
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| |-
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| | 36
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| | 26L 10s
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| |-
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| | 37
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| | 24L 13s
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| |-
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| | 38
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| | 22L 16s
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| |-
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| | 39
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| | 20L 19s
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| |-
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| | 40
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| | 18L 22s
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| |-
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| | 41
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| | 16L 25s
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| |-
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| | 42
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| | 14L 28s
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| |-
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| | 43
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| | 12L 31s
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| |-
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| | 44
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| | 10L 34s
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| |-
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| | 45
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| | 8L 37s
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| |-
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| | 46
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| | 6L 40s
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| |-
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| | 47
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| | 4L 43s
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| |-
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| | 48
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| | 2L 46s
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| |-
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| | 49
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| | ''[[49 EDO]]''
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| | ''equal''
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| |-
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| | 50
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| | 48L 2s
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| | rowspan="29" | 2:1
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| |-
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| | 51
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| | 47L 4s
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| |-
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| | 52
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| | 46L 6s
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| |-
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| | 53
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| | 45L 8s
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| |-
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| | 54
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| | 44L 10s
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| |-
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| | 55
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| | 43L 12s
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| |-
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| | 56
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| | 42L 14s
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| |-
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| | 57
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| | 41L 16s
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| |-
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| | 58
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| | 40L 18s
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| |-
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| | 59
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| | 39L 20s
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| |-
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| | 60
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| | 38L 22s
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| |-
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| | 61
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| | 37L 24s
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| |-
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| | 62
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| | 36L 26s
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| |-
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| | 63
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| | 35L 28s
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| |-
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| | 64
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| | 34L 30s
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| |-
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| | 65
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| | 33L 32s
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| |-
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| | 66
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| | 32L 34s
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| |-
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| | 67
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| | 31L 36s
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| |-
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| | 68
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| | 30L 38s
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| |-
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| | 69
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| | 29L 40s
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| |-
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| | 70
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| | 28L 42s
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| |-
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| | 71
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| | 27L 44s
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| |-
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| | 72
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| | 26L 46s
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| |-
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| | 73
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| | 25L 48s
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| |-
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| | 74
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| | 24L 50s
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| |-
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| | 75
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| | 23L 52s
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| |-
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| | 76
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| | 22L 54s
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| |-
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| | 77
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| | 21L 56s
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| |-
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| | 78
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| | 20L 58s
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| |}
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| [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> | | == Intervals == |
| [[Category:Meantone]] | | {{Interval table}} |
| | |
| | == Instruments == |
| | === Keyboards === |
| | [[Lumatone mapping for 98edo|Lumatone mappings for 98edo]] are available. |
| | |
| | === Skip fretting === |
| | '''Skip fretting system 98 9 11''' is a [[skip fretting]] system for [[98edo]]. All examples on this page are for 7-string [[guitar]]. |
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| | ; Odd harmonics |
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| | 1/1: string 2 open |
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| | 2/1: string 6 fret 6 |
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| | 3/2: string 3 fret 16 |
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| | 5/4: string 4 fret 12 |
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| | 7/4: string 1 fret 10 |
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| | 9/8: string 1 fret 14 |
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| | 11/8: string 2 fret 5 and string 6 fret 11 |
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| | 13/8: string 5 fret 4 |
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| | 15/8: string 6 fret 5 |
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| | 17/16: string 2 fret 1 |
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| | 19/16: string 4 fret 22 |
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| | 21/16: string 3 fret 3 |
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| | 23/16: string 5 fret 2 |
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| | 25/16: string 2 fret 7 |
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| | == Music == |
| | ; [[Bryan Deister]] |
| | * [https://www.youtube.com/watch?v=pR4li7aIUZE ''microtonal improvisation in 98edo''] (2023) |
| | * [https://www.youtube.com/shorts/4NR3KFBd720 ''98edo waltz''] (2025) |
| | * [https://www.youtube.com/shorts/EUR8t8ynORg ''98edo prelude''] (2025) |
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| | [[Category:Mothra]] |
| | [[Category:Listen]] |