87edo: Difference between revisions

(5 intermediate revisions by 4 users not shown)

Line 18:

=== Subsets and supersets ===

87edo contains [[3edo]] and [[29edo]] as subset edos.

[[348edo]], which slices the edostep in four, provides a good correction of the 7th harmonic.

== Intervals ==

Line 350:

Line 352:

87edo can be written using [[Kite's ups and downs notation]]. Note that quudsharp (quadruple-down sharp) is equivalent to quip (quintuple-up) and that quupflat (quadruple-up flat) is equivalent to quid (quintuple-down):

Mapping an arrow to 2\87 rather than 1\87 is an alternative approach which takes advantage of 87edo being a tuning of akea temperament. This way, one arrow is equivalent to 81/80~64/63, and two arrows are equivalent to 33/32~1053/1024.

== Approximation to JI ==

Line 513:

Line 516:

| [[Mystery]]

|}

<nowiki/>* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if distinct

<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

87 can serve as a mos in these:

Line 681:

Line 684:

== Music ==

; [[ALLY195]]

* [https://www.bilibili.com/video/BV16h411g7QM/ ''Root note and subharmonic series cadence - 103EDO, 87EDO, 94EDO''] (2023)

* [https://www.bilibili.com/video/BV1N84y1T792/ ''A comparison between 87edo and 12edo''] (2023)

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/ecxELXmkYAs ''microtonal improvisation in 87edo''] (2025)

@@ Line 18: / Line 18: @@
 === Subsets and supersets ===
 edo contains [[3edo]] and [[29edo]] as subset edos.
+[[348edo]], which slices the edostep in four, provides a good correction of the 7th harmonic.
 == Intervals ==
@@ Line 350: / Line 352: @@
 edo can be written using [[Kite's ups and downs notation]]. Note that quudsharp (quadruple-down sharp) is equivalent to quip (quintuple-up) and that quupflat (quadruple-up flat) is equivalent to quid (quintuple-down):
 {{Ups and downs sharpness}}
+Mapping an arrow to 2\87 rather than 1\87 is an alternative approach which takes advantage of 87edo being a tuning of akea temperament. This way, one arrow is equivalent to 81/80~64/63, and two arrows are equivalent to 33/32~1053/1024.
 == Approximation to JI ==
@@ Line 513: / Line 516: @@
 | [[Mystery]]
 |}
-<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 can serve as a mos in these:
@@ Line 681: / Line 684: @@
 == Music ==
+; [[ALLY195]]
+* [https://www.bilibili.com/video/BV16h411g7QM/ ''Root note and subharmonic series cadence - 103EDO, 87EDO, 94EDO''] (2023)
+* [https://www.bilibili.com/video/BV1N84y1T792/ ''A comparison between 87edo and 12edo''] (2023)
 ; [[Bryan Deister]]
 * [https://www.youtube.com/shorts/ecxELXmkYAs ''microtonal improvisation in 87edo''] (2025)