74edo: Difference between revisions

(6 intermediate revisions by 5 users not shown)

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 17:

== Notation ==

=== Ups and downs notation ===

===Ups and downs notation===

[[~~Ups~~ and downs notation]] uses ~~free-standing~~ arrows, ~~but the arrows can be connected to conventional accidentals using~~ [[Helmholtz–Ellis notation~~|Helmholtz–Ellis~~]] ~~accidentals~~:

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]]:

Here, a sharp raises by five steps, and a flat lowers by five steps, so single and double arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, then in some cases certain notes may be best spelled with triple arrows.

=== Sagittal notation ===

==== Evo flavor ====

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]]

@@ 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 17: / Line 17: @@
 == Notation ==
-=== Ups and downs notation ===
+===Ups and downs notation===
-[[Ups and downs notation]] uses free-standing arrows, but the arrows can be connected to conventional accidentals using [[Helmholtz–Ellis notation|Helmholtz–Ellis]] accidentals:
+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]]:
 {{Sharpness-sharp5}}
-Here, a sharp raises by five steps, and a flat lowers by five steps, so single and double arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, then in some cases certain notes may be best spelled with triple arrows.
 === Sagittal notation ===
 ==== Evo flavor ====
@@ 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]]