|
|
| (12 intermediate revisions by 7 users not shown) |
| Line 1: |
Line 1: |
| {{Infobox ET}} | | {{Infobox ET}} |
| '''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.
| | {{ED intro}} |
|
| |
|
| {{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. |
|
| |
|
| 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}} |
|
| |
|
| {| 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 }}. |
| |-
| |
| ! 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]]
| |
| | rowspan="2" | 9:8
| |
| |-
| |
| | 12
| |
| | [[2L 10s]]
| |
| |-
| |
| | 13
| |
| | [[7L 6s]]
| |
| | 8:7
| |
| |-
| |
| | 14
| |
| | ''[[14 EDO]]''
| |
| | ''equal''
| |
| |-
| |
| | 15
| |
| | [[8L 7s]]
| |
| | rowspan="2" | 7:6
| |
| |-
| |
| | 16
| |
| | 2L 14s
| |
| |-
| |
| | 17
| |
| | 13L 4s
| |
| | rowspan="3" | 6:5
| |
| |-
| |
| | 18
| |
| | 8L 10s
| |
| |-
| |
| | 19
| |
| | [[3L 16s]]
| |
| |-
| |
| | 20
| |
| | 18L 2s
| |
| | rowspan="5" | 5:4
| |
| |-
| |
| | 21
| |
| | 14L 7s
| |
| |-
| |
| | 22
| |
| | 10L 12s
| |
| |-
| |
| | 23
| |
| | 6L 17s
| |
| |-
| |
| | 24
| |
| | 2L 22s
| |
| |-
| |
| | 25
| |
| | 23L 2s
| |
| | rowspan="8" | 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
| |
| | rowspan="16" | 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
| |
| | rowspan="29" | 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
| |
| |}
| |
|
| |
|
| [[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]]. |
| | |
| | ; Odd harmonics |
| | |
| | 1/1: string 2 open |
| | |
| | 2/1: string 6 fret 6 |
| | |
| | 3/2: string 3 fret 16 |
| | |
| | 5/4: string 4 fret 12 |
| | |
| | 7/4: string 1 fret 10 |
| | |
| | 9/8: string 1 fret 14 |
| | |
| | 11/8: string 2 fret 5 and string 6 fret 11 |
| | |
| | 13/8: string 5 fret 4 |
| | |
| | 15/8: string 6 fret 5 |
| | |
| | 17/16: string 2 fret 1 |
| | |
| | 19/16: string 4 fret 22 |
| | |
| | 21/16: string 3 fret 3 |
| | |
| | 23/16: string 5 fret 2 |
| | |
| | 25/16: string 2 fret 7 |
| | |
| | == 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) |
| | |
| | [[Category:Mothra]] |
| | [[Category:Listen]] |