74edo: Difference between revisions

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'''74edo''' divides the [[octave]] into 74 equal parts of size 16.216 [[cent]]s each. It is most notable as a [[meantone]] tuning, tempering out [[81/80]] in the [[5-limit]]; 81/80 and [[126/125]] (and hence [[225/224]]) in the [[7-limit]]; [[99/98]], 176/175 and 441/440 in the [[11-limit]]; and [[144/143]] and 847/845 in the [[13-limit]]. Discarding 847/845 from that gives [[Meantone_family|13-limit meantone]], aka 13-limit [[huygens]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone.

== Theory ==

74edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[225/224]] in the [[7-limit]]; [[99/98]], [[176/175]] and [[441/440]] in the [[11-limit]]; and [[144/143]] and [[847/845]] in the [[13-limit]]. Discarding 847/845 from that gives the 13-limit meantone extension [[grosstone]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives [[semimeantone]], a 13-limit 62 & 74 temperament with half-octave period and two parallel tracks of meantone.

74edo tunes [[harmonic]] [[11/1|11]] only 1/30 of a cent sharp, and [[13/1|13]] 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.

=== Odd harmonics ===

74 ~~tunes 11 only 1/30~~ of ~~a cent sharp~~, ~~and~~ 13 ~~2.7 cents sharp, making it a distinctly interesting choice for higher~~-limit ~~meantone~~.

=== Subsets and supersets ===

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 ==

== Notation ==

===Ups and downs notation===

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]]:

=== Sagittal notation ===

==== Evo flavor ====

File:74-EDO_Evo_Sagittal.svg

desc none

rect 80 0 300 50 [[Sagittal_notation]]

rect 300 0 685 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]

rect 20 80 180 106 [[1701/1664]]

rect 180 80 300 106 [[36/35]]

rect 300 80 460 106 [[1053/1024]]

default [[File:74-EDO_Evo_Sagittal.svg]]

</imagemap>

==== Revo flavor ====

File:74-EDO_Revo_Sagittal.svg

desc none

rect 80 0 300 50 [[Sagittal_notation]]

rect 300 0 631 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]

rect 20 80 180 106 [[1701/1664]]

rect 180 80 300 106 [[36/35]]

rect 300 80 460 106 [[1053/1024]]

default [[File:74-EDO_Revo_Sagittal.svg]]

</imagemap>

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 ==

* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 ~~Twinkle canon – 74 edo~~] by [~~http~~://~~soonlabel~~.com/~~xenharmonic/archives~~/~~573 Claudi Meneghin~~] ~~{{dead link}}~~

=== Modern renderings ===

; {{W|Scott Joplin}}

* [https://www.youtube.com/watch?v=QBqzUWr6gXk ''Maple Leaf Rag''] (1899) – rendered by Francium (2024)

* [https://www.youtube.com/watch?v=oDTF5h9tsSU ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by Claudi Meneghin (2024)

=== 21st century ===

; [[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:74edo| ]] ~~

~~[[Category:Equal divisions of the octave|##]] ~~

[[Category:Meantone]]

[[Category:Listen]]

[[Category:Historical]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''74edo''' divides the [[octave]] into 74 equal parts of size 16.216 [[cent]]s each. It is most notable as a [[meantone]] tuning, tempering out [[81/80]] in the [[5-limit]]; 81/80 and [[126/125]] (and hence [[225/224]]) in the [[7-limit]]; [[99/98]], 176/175 and 441/440 in the [[11-limit]]; and [[144/143]] and 847/845 in the [[13-limit]]. Discarding 847/845 from that gives [[Meantone_family|13-limit meantone]], aka 13-limit [[huygens]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives a 13-limit 62&amp;74 temperament with half-octave period and two parallel tracks of meantone.
+{{ED intro}}
+== Theory ==
+edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[225/224]] in the [[7-limit]]; [[99/98]], [[176/175]] and [[441/440]] in the [[11-limit]]; and [[144/143]] and [[847/845]] in the [[13-limit]]. Discarding 847/845 from that gives the 13-limit meantone extension [[grosstone]], for which 74edo gives the [[optimal patent val]]; and discarding 144/143 gives [[semimeantone]], a 13-limit 62 &amp; 74 temperament with half-octave period and two parallel tracks of meantone.
+edo tunes [[harmonic]] [[11/1|11]] only 1/30 of a cent sharp, and [[13/1|13]] 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.
+=== Odd harmonics ===
 {{Harmonics in equal|74}}
-tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.
+=== Subsets and supersets ===
+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 ==
 {{Interval table}}
+== 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]]:
+{{Sharpness-sharp5}}
+=== Sagittal notation ===
+==== Evo flavor ====
+<imagemap>
+File:74-EDO_Evo_Sagittal.svg
+desc none
+rect 80 0 300 50 [[Sagittal_notation]]
+rect 300 0 685 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
+rect 20 80 180 106 [[1701/1664]]
+rect 180 80 300 106 [[36/35]]
+rect 300 80 460 106 [[1053/1024]]
+default [[File:74-EDO_Evo_Sagittal.svg]]
+</imagemap>
+==== Revo flavor ====
+<imagemap>
+File:74-EDO_Revo_Sagittal.svg
+desc none
+rect 80 0 300 50 [[Sagittal_notation]]
+rect 300 0 631 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
+rect 20 80 180 106 [[1701/1664]]
+rect 180 80 300 106 [[36/35]]
+rect 300 80 460 106 [[1053/1024]]
+default [[File:74-EDO_Revo_Sagittal.svg]]
+</imagemap>
+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 ==
-* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 Twinkle canon – 74 edo] by  [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] {{dead link}}
+=== Modern renderings ===
+; {{W|Scott Joplin}}
+* [https://www.youtube.com/watch?v=QBqzUWr6gXk ''Maple Leaf Rag''] (1899) – rendered by Francium (2024)
+* [https://www.youtube.com/watch?v=oDTF5h9tsSU ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by Claudi Meneghin (2024)
+=== 21st century ===
+; [[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:74edo| ]] <!-- main article -->
-[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
 [[Category:Meantone]]
 [[Category:Listen]]
 [[Category:Historical]]