87edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
87edo contains [[3edo]] and [[29edo]] as subset edos. | 87edo contains [[3edo]] and [[29edo]] as subset edos. | ||
[[348edo]], which slices the edostep in four, provides a good correction of the 7th harmonic. | |||
== Intervals == | == Intervals == | ||
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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): | 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): | ||
{{Ups and downs sharpness}} | {{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 == | == Approximation to JI == | ||
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| [[Mystery]] | | [[Mystery]] | ||
|} | |} | ||
<nowiki/>* [[Normal | <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: | 87 can serve as a mos in these: | ||
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== Music == | == Music == | ||
=== Modern renderings === | |||
; {{W|Stomach Book}} | |||
* [https://www.youtube.com/shorts/rINJKiMQE78 ''Circuit Bent''] (2024) – microtonal cover in 87edo by [[Bryan Deister]] (2025) | |||
=== 21st century === | |||
; [[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]] | ; [[Bryan Deister]] | ||
* [https://www.youtube.com/shorts/ecxELXmkYAs ''microtonal improvisation in 87edo''] (2025) | * [https://www.youtube.com/shorts/ecxELXmkYAs ''microtonal improvisation in 87edo''] (2025) | ||
* [https://www.youtube.com/shorts/5OH9OOGeuX4 ''87edo waltz''] (2025) | * [https://www.youtube.com/shorts/5OH9OOGeuX4 ''87edo waltz''] (2025) | ||
* [https://www.youtube.com/shorts/ | * [https://www.youtube.com/shorts/8mHBYBfRjy4 ''87edo improv''] (2026) | ||
; [[Gene Ward Smith]] | ; [[Gene Ward Smith]] | ||