98edo: Difference between revisions

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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]].
+{{Infobox ET}}
+{{ED intro}}
-[[Category:edo]]
+== Theory ==
-[[Category:meantone]]
+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.
+=== Odd harmonics ===
+{{Harmonics in equal|98}}
+=== Subsets and supersets ===
+Since 98 factors into {{factorization|98}}, 98edo has subset edos {{EDOs| 2, 7, 14, and 49 }}.
+== Intervals ==
+{{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: string 2 open
+/1: string 6 fret 6
+/2: string 3 fret 16
+/4: string 4 fret 12
+/4: string 1 fret 10
+/8: string 1 fret 14
+/8: string 2 fret 5 and string 6 fret 11
+/8: string 5 fret 4
+/8: string 6 fret 5
+/16: string 2 fret 1
+/16: string 4 fret 22
+/16: string 3 fret 3
+/16: string 5 fret 2
+/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]]