74edo: Difference between revisions

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=== Subsets and supersets ===

Since 74 factors into {{factorization|74}}, 74edo contains [[2edo]] and [[37edo]] as its subsets.

Since 74 factors into {{factorization|74}}, 74edo contains [[2edo]] and [[37edo]] as its subsets; of these, 37edo has the same highly accurate prime harmonics in the no-3s [[13-limit]].

== Intervals ==

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== Notation ==

===Ups and downs notation===

~~32edo~~ can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).

74edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).

Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. It uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:

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In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

== Instruments ==

* [[Lumatone mapping for 74edo]]

== Music ==

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; [[Claudi Meneghin]]

* ''Twinkle canon'' (2012) – [https://web.archive.org/web/20171009205013/http://soonlabel.com/xenharmonic/archives/573 detail] | [https://web.archive.org/web/20201127015514/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 play]

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025)

[[Category:Meantone]]

[[Category:Listen]]

[[Category:Historical]]

@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-Since 74 factors into {{factorization|74}}, 74edo contains [[2edo]] and [[37edo]] as its subsets.
+Since 74 factors into {{factorization|74}}, 74edo contains [[2edo]] and [[37edo]] as its subsets; of these, 37edo has the same highly accurate prime harmonics in the no-3s [[13-limit]].
 == Intervals ==
@@ Line 18: / Line 18: @@
 == Notation ==
 ===Ups and downs notation===
 edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
 {{Sharpness-sharp5a}}
 Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. It uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
@@ Line 48: / Line 48: @@
 In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
+== Instruments ==
+* [[Lumatone mapping for 74edo]]
 == Music ==
@@ Line 58: / Line 61: @@
 ; [[Claudi Meneghin]]
 * ''Twinkle canon'' (2012) – [https://web.archive.org/web/20171009205013/http://soonlabel.com/xenharmonic/archives/573 detail] | [https://web.archive.org/web/20201127015514/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 play]
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025)
 [[Category:Meantone]]
 [[Category:Listen]]
 [[Category:Historical]]