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{{Infobox ET}}
{{Infobox ET}}
'''73 EDO''' divides the octave into 73 equal parts of 16.438 [[cent]]s each. It tempers out 78732/78125 and 262144/253125 in the [[5-limit]], [[126/125]] and [[245/243]] in the [[7-limit]], 176/175, 441/440 and 4000/3993 in the [[11-limit]], and 91/90, 169/168, 196/195, [[325/324]], [[351/350]] and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[marrakesh]] temperament. 73 EDO has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see following table.
{{ED intro}}


{{Primes in edo|73|columns=9}}
== Theory ==
73edo has a very sharp tendency, with the approximations of [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[78732/78125]] and [[262144/253125]] in the [[5-limit]]; [[126/125]] and [[245/243]] in the [[7-limit]]; [[176/175]], [[441/440]] and [[4000/3993]] in the [[11-limit]]; [[91/90]], [[169/168]], [[196/195]], [[325/324]], [[351/350]], and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[marrakesh]] temperament, though [[104edo]] and [[135edo]] tune it better.


73 EDO fits in mavila scale, by the 9;5 relation in the [[7L_2s|superdiatonic]] scheme.
73edo can be used as a tuning of [[trismegistus]] or [[mavila]], by the 9:5 relation in the [[7L 2s|superdiatonic]] scheme, though neither of these use the most accurate 3/2. It is also notable for supporting the 2.3.5.7.13 version of [[sensi]] entirely by patent val.


73 EDO is the 21st [[prime EDO]].
=== Prime harmonics ===
{{Harmonics in equal|73|intervals=prime}}
 
=== Subsets and supersets ===
73edo is the 21st [[prime edo]], past [[71edo]] and before [[79edo]].


== Intervals ==
== Intervals ==
{|class="wikitable"
{{Interval table}}
|-
 
!#
== Notation ==
!Cents
 
!Diatonic interval category
=== Sagittal notation ===
|-
This notation uses the same sagittal sequence as [[80edo#Sagittal notation|80-EDO]].
|0
 
|0.0
==== Evo flavor ====
|perfect unison
<imagemap>
|-
File:73-EDO_Evo_Sagittal.svg
|1
desc none
|16.4
rect 80 0 300 50 [[Sagittal_notation]]
|superunison
rect 300 0 719 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
|-
rect 20 80 120 106 [[64/63]]
|2
rect 120 80 220 106 [[81/80]]
|32.9
rect 220 80 350 106 [[45/44]]
|superunison
rect 350 80 470 106 [[33/32]]
|-
default [[File:73-EDO_Evo_Sagittal.svg]]
|3
</imagemap>
|49.3
 
|subminor second
==== Revo flavor ====
|-
<imagemap>
|4
File:73-EDO_Revo_Sagittal.svg
|65.8
desc none
|subminor second
rect 80 0 300 50 [[Sagittal_notation]]
|-
rect 300 0 679 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
|5
rect 20 80 120 106 [[64/63]]
|82.2
rect 120 80 220 106 [[81/80]]
|minor second
rect 220 80 350 106 [[45/44]]
|-
rect 350 80 470 106 [[33/32]]
|6
default [[File:73-EDO_Revo_Sagittal.svg]]
|98.6
</imagemap>
|minor second
 
|-
== Scales ==
|7
* Porky[7]: 10 10 10 13 10 10 10 ((10, 20, 30, 43, 53, 63, 73)\73)
|115.1
 
|minor second
== Instruments ==
|-
 
|8
A [[Lumatone mapping for 73edo]] is available.
|131.5
 
|supraminor second
== Music ==
|-
; [[Bryan Deister]]
|9
* [https://www.youtube.com/shorts/meZYE1Yj2pY ''microtonal improvisation in 73edo''] (2025)
|147.9
* ''Waltz in 73edo'' (2026)
|neutral second
** [https://www.youtube.com/shorts/sRZEJVBuDl0 ''<nowiki>[short]</nowiki>''] (Lumatone view)
|-
** [https://www.youtube.com/watch?v=Z-3a5LJlul8 ''<nowiki>[full version]</nowiki>'']
|10
 
|164.4
; [[Claudi Meneghin]]
|submajor second
* [https://www.youtube.com/watch?v=NuCnLVijULo ''Little Fugue on Happy Birthday''] (2020)
|-
|11
|180.8
|major second
|-
|12
|197.3
|major second
|-
|13
|213.7
|major second
|-
|14
|230.1
|supermajor second
|-
|15
|246.6
|ultramajor second
|-
|16
|263.0
|subminor third
|-
|17
|279.5
|subminor third
|-
|18
|295.9
|minor third
|-
|19
|312.3
|minor third
|-
|20
|328.8
|supraminor third
|-
|21
|345.2
|neutral third
|-
|22
|361.6
|submajor third
|-
|23
|378.1
|submajor third
|-
|24
|394.5
|major third
|-
|25
|411.0
|major third
|-
|26
|427.4
|supermajor third
|-
|27
|443.8
|ultramajor third
|-
|28
|460.3
|subfourth
|-
|29
|476.7
|subfourth
|-
|30
|493.2
|perfect fourth
|-
|31
|509.6
|perfect fourth
|-
|32
|526.0
|superfourth
|-
|33
|542.5
|superfourth
|-
|34
|558.9
|superfourth
|-
|35
|575.3
|low tritone
|-
|36
|591.8
|low tritone
|-
|37
|608.2
|high tritone
|-
|38
|624.7
|high tritone
|-
|39
|641.1
|subfifth
|-
|40
|657.5
|subfifth
|-
|41
|674.0
|subfifth
|-
|42
|690.4
|perfect fifth
|-
|43
|706.8
|perfect fifth
|-
|44
|723.3
|superfifth
|-
|45
|739.7
|superfifth
|-
|46
|756.2
|ultrafifth
|-
|47
|772.6
|subminor sixth
|-
|48
|789.0
|minor sixth
|-
|49
|805.5
|minor sixth
|-
|50
|821.9
|supraminor sixth
|-
|51
|838.4
|supraminor sixth
|-
|52
|854.8
|neutral sixth
|-
|53
|871.2
|submajor sixth
|-
|54
|887.7
|major sixth
|-
|55
|904.1
|major sixth
|-
|56
|920.5
|supermajor sixth
|-
|57
|937.0
|supermajor sixth
|-
|58
|953.4
|ultramajor sixth
|-
|59
|969.9
|subminor seventh
|-
|60
|986.3
|minor seventh
|-
|61
|1002.7
|minor seventh
|-
|62
|1019.2
|minor seventh
|-
|63
|1035.6
|supraminor seventh
|-
|64
|1052.1
|neutral seventh
|-
|65
|1068.5
|submajor seventh
|-
|66
|1084.9
|major seventh
|-
|67
|1101.4
|major seventh
|-
|68
|1117.8
|major seventh
|-
|69
|1134.2
|supermajor seventh
|-
|70
|1150.7
|ultramajor seventh
|-
|71
|1167.1
|suboctave
|-
|72
|1183.6
|suboctave
|-
|73
|1200.0
|perfect octave
|}


[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Prime EDO]]
[[Category:Marrakesh]]
[[Category:Marrakesh]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/73edo"