88edo: Difference between revisions

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-In music, '''88 equal temperament''' is the scale derived by dividing the octave into 88 equally large steps, 13.6363 [[cent|cent]]s in size. Using two different approximations to the perfect fifth (one of 51 steps and one of 52 steps), it is compatible with both [[Meantone|meantone temperament]] and the particular variety of [[Superpyth|superpyth]] temperament(s) supported by [[22edo|22 equal temperament]], respectively. The meantone fifth is 0.0384 cents flatter than that of [[Lucy_Tuning|Lucy Tuning]] and, thus, audibly indistinguishable from it. It also gives the [[Optimal_patent_val|optimal patent val]] for the 11-limit [[Meantone_family|mothra]] and [[Didymus_rank_three_family|euterpe]] temperaments.
+{{Infobox ET}}
-{{harmonics in equal|88}}
+{{ED intro}}
-[[Category:Equal divisions of the octave]]
-[[Category:Euterpe]]
+== Theory ==
+Using two different approximations to the [[3/2|perfect fifth]] (one of 51 steps and one of 52 steps), 88edo is compatible with both [[meantone]] and the particular variety of [[superpyth]] supported by [[22edo|22 equal temperament]], respectively. The meantone fifth is 0.0384 cents flatter than that of [[Lucy Tuning]] and, thus, audibly indistinguishable from it. It also gives the [[optimal patent val]] for the 11-limit [[mothra]] and [[euterpe]] temperaments.
+=== Odd harmonics ===
+{{Harmonics in equal|88}}
+=== Subsets and supersets ===
+Since 88 factors into {{factorization|88}}, 88edo has subset edos {{EDOs| 2, 4, 8, 11, 22, and 44 }}. [[176edo]], which doubles it, provides correction for the approximation to harmonic 3.
+== Intervals ==
+{{Interval table}}
+== Instruments ==
+=== Lumatone ===
+[[Lumatone mapping for 88edo]]
+=== Skip fretting ===
+'''Skip fretting system 88 6 13''' is a [[skip fretting]] system for [[88edo]]. All examples on this page are for 7-string [[guitar]].
+; Prime intervals
+/1: string 2 open
+/1: string 6 fret 6
+/2: string 5 fret 2
+/4: not easily accessible
+/4: string 7 fret 1
+/8: not easily accessible
+/8: string 4 fret 6
+/16: not easily accessible
+/16: not easily accessible
+== Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/watch?v=JQly-kX6kcM ''microtonal improvisation in 88edo''] (2025)
 [[Category:Lucy tuning]]
 [[Category:Meantone]]
 [[Category:Mothra]]