Xenharmonic Wiki

98edo: Difference between revisions

← Older edit
VisualWikitext
No edit summary
Move Music section below Instruments to conform to most other EDO pages; add Bryan Deister's ''98edo prelude'' (2025); add Lumatone mapping for 98edo page
 
(19 intermediate revisions by 11 users not shown)
Line 1: Line 1:
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]].
{{Infobox ET}}
{{ED intro}}


== 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 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 kn<sup>2</sup> edo which does this and the first edo which allows one to use a Magic MOS scale as a circulating temperament.
=== Odd harmonics ===
{| class="wikitable"
{{Harmonics in equal|98}}
|+Circulating temperaments in 98edo
 
!Tones
=== Subsets and supersets ===
!Pattern
Since 98 factors into {{factorization|98}}, 98edo has subset edos {{EDOs| 2, 7, 14, and 49 }}.
!L:s
 
|-
== Intervals ==
|5
{{Interval table}}
|[[3L 2s]]
 
|20:19
== Instruments ==
|-
=== Keyboards ===
|6
[[Lumatone mapping for 98edo|Lumatone mappings for 98edo]] are available.
|[[2L 4s]]
 
|17:16
=== 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]].
|7
 
|[[7edo]]
; Odd harmonics
|equal
 
|-
1/1: string 2 open
|8
 
|[[2L 6s]]
2/1: string 6 fret 6
|13:12
 
|-
3/2: string 3 fret 16
|9
 
|[[8L 1s]]
5/4: string 4 fret 12  
|11:10
 
|-
7/4: string 1 fret 10
|10
 
|[[8L 2s]]
9/8: string 1 fret 14
|10:9
 
|-
11/8: string 2 fret 5 and string 6 fret 11
|11
 
|[[10L 1s]]
13/8: string 5 fret 4
| rowspan="2" |9:8
 
|-
15/8: string 6 fret 5
|12
 
|[[1L 11s]]
17/16: string 2 fret 1
|-
 
|13
19/16: string 4 fret 22
|[[7L 6s]]
 
|8:7
21/16: string 3 fret 3
|-
 
|14
23/16: string 5 fret 2
|[[14edo]]
 
|equal
25/16: string 2 fret 7
|-
 
|15
== Music ==
|[[8L 7s]]
; [[Bryan Deister]]
| rowspan="2" |7:6
* [https://www.youtube.com/watch?v=pR4li7aIUZE ''microtonal improvisation in 98edo''] (2023)
|-
* [https://www.youtube.com/shorts/4NR3KFBd720 ''98edo waltz''] (2025)
|16
* [https://www.youtube.com/shorts/EUR8t8ynORg ''98edo prelude''] (2025)
|2L 14s
 
|-
[[Category:Mothra]]
|17
[[Category:Listen]]
|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 14s
|-
|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
|[[49edo]]
|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]]
[[Category:meantone]]
Retrieved from "https://en.xen.wiki/w/98edo"