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{{Infobox ET}}
{{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&74 temperament with half-octave period and two parallel tracks of meantone.
{{ED intro}}
{{Primes in edo|74}}


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.
== 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 ===
{{Harmonics in equal|74}}
 
=== 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 ==
== Intervals ==
{|class="wikitable"
{{Interval table}}
|-
 
!#
== Notation ==
!Cents
===Ups and downs notation===
!Diatonic interval category
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).
|-
{{Sharpness-sharp5a}}
|0
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]]:
|0.0
{{Sharpness-sharp5}}
|perfect unison
=== Sagittal notation ===
|-
==== Evo flavor ====
|1
<imagemap>
|16.2
File:74-EDO_Evo_Sagittal.svg
|superunison
desc none
|-
rect 80 0 300 50 [[Sagittal_notation]]
|2
rect 300 0 685 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
|32.4
rect 20 80 180 106 [[1701/1664]]
|superunison
rect 180 80 300 106 [[36/35]]
|-
rect 300 80 460 106 [[1053/1024]]
|3
default [[File:74-EDO_Evo_Sagittal.svg]]
|48.6
</imagemap>
|subminor second
 
|-
==== Revo flavor ====
|4
<imagemap>
|64.9
File:74-EDO_Revo_Sagittal.svg
|subminor second
desc none
|-
rect 80 0 300 50 [[Sagittal_notation]]
|5
rect 300 0 631 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
|81.1
rect 20 80 180 106 [[1701/1664]]
|minor second
rect 180 80 300 106 [[36/35]]
|-
rect 300 80 460 106 [[1053/1024]]
|6
default [[File:74-EDO_Revo_Sagittal.svg]]
|97.3
</imagemap>
|minor second
 
|-
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.
|7
 
|113.5
== Instruments ==
|minor second
* [[Lumatone mapping for 74edo]]
|-
|8
|129.7
|supraminor second
|-
|9
|145.9
|neutral second
|-
|10
|162.2
|submajor second
|-
|11
|178.4
|submajor second
|-
|12
|194.6
|major second
|-
|13
|210.8
|major second
|-
|14
|227.0
|supermajor second
|-
|15
|243.2
|ultramajor second
|-
|16
|259.5
|ultramajor second
|-
|17
|275.7
|subminor third
|-
|18
|291.9
|minor third
|-
|19
|308.1
|minor third
|-
|20
|324.3
|supraminor third
|-
|21
|340.5
|neutral third
|-
|22
|356.8
|neutral third
|-
|23
|373.0
|submajor third
|-
|24
|389.2
|major third
|-
|25
|405.4
|major third
|-
|26
|421.6
|supermajor third
|-
|27
|437.8
|supermajor third
|-
|28
|454.1
|ultramajor third
|-
|29
|470.3
|subfourth
|-
|30
|486.5
|perfect fourth
|-
|31
|502.7
|perfect fourth
|-
|32
|518.9
|perfect fourth
|-
|33
|535.1
|superfourth
|-
|34
|551.4
|superfourth
|-
|35
|567.6
|low tritone
|-
|36
|583.8
|low tritone
|-
|37
|600.0
|high tritone
|-
|38
|616.2
|high tritone
|-
|39
|632.4
|high tritone
|-
|40
|648.6
|subfifth
|-
|41
|664.9
|subfifth
|-
|42
|681.1
|perfect fifth
|-
|43
|697.3
|perfect fifth
|-
|44
|713.5
|perfect fifth
|-
|45
|729.7
|superfifth
|-
|46
|745.9
|ultrafifth
|-
|47
|762.2
|subminor sixth
|-
|48
|778.4
|subminor sixth
|-
|49
|794.6
|minor sixth
|-
|50
|810.8
|minor sixth
|-
|51
|827.0
|supraminor sixth
|-
|52
|843.2
|neutral sixth
|-
|53
|859.5
|neutral sixth
|-
|54
|875.7
|submajor sixth
|-
|55
|891.9
|major sixth
|-
|56
|908.1
|major sixth
|-
|57
|924.3
|supermajor sixth
|-
|58
|940.5
|ultramajor sixth
|-
|59
|956.8
|ultramajor sixth
|-
|60
|973.0
|subminor seventh
|-
|61
|989.2
|minor seventh
|-
|62
|1005.4
|minor seventh
|-
|63
|1021.6
|supraminor seventh
|-
|64
|1037.8
|supraminor seventh
|-
|65
|1054.1
|neutral seventh
|-
|66
|1070.3
|submajor seventh
|-
|67
|1086.5
|major seventh
|-
|68
|1102.7
|major seventh
|-
|69
|1118.9
|major seventh
|-
|70
|1135.1
|supermajor seventh
|-
|71
|1151.4
|ultramajor seventh
|-
|72
|1167.6
|suboctave
|-
|73
|1183.8
|suboctave
|-
|74
|1200.0
|perfect octave
|}


== Music ==
== 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:Meantone]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Historical]]
Retrieved from "https://en.xen.wiki/w/74edo"