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39edo: Difference between revisions

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39edo, with its 400{{c}} major third, [[tempering out|tempers out]] the [[128/125|diesis]] (128/125), and using the 39d val, the septimal comma, [[64/63]], as well as [[126/125]] are added to the comma list. In the 11-limit we find that the equal temperament tempers out [[99/98]] and [[121/120]]. Tempering out both 128/125 and 64/63 makes 39et, in some few ways, allied to [[12edo|12et]] in [[support]]ing [[augene]], and is in fact, an excellent choice for a 7-limit augene tuning. It also tempers out the [[amity comma]] (1600000/1594323), and supports the variant of amity known as [[accord]].  
39edo, with its 400{{c}} major third, [[tempering out|tempers out]] the [[128/125|diesis]] (128/125), and using the 39d val, the septimal comma, [[64/63]], as well as [[126/125]] are added to the comma list. In the 11-limit we find that the equal temperament tempers out [[99/98]] and [[121/120]]. Tempering out both 128/125 and 64/63 makes 39et, in some few ways, allied to [[12edo|12et]] in [[support]]ing [[augene]], and is in fact, an excellent choice for a 7-limit augene tuning. It also tempers out the [[amity comma]] (1600000/1594323), and supports the variant of amity known as [[accord]].  


Alternatively, the patent val tempers out [[49/48]] to yield [[semaphore]], and provides a reasonable tuning of [[triforce]] beyond [[15edo]], and optimizes both its semaphore and augmented components by tuning the fifth sharp. The 39c val supports [[negri]].  
Alternatively, the patent val tempers out [[49/48]] to yield [[semaphore]], and provides a reasonable tuning of [[triforce]] beyond [[15edo]], and optimizes both its semaphore and augmented components by tuning the fifth sharp. The 39c val supports [[negri]] and 5-limit [[Syntonic–chromatic_equivalence_continuum#Sixix_(5-limit)|sixix]].  


If we take 22\39 as a fifth, 39edo can be used as a tuning of [[mavila]] through the 39bc val, and from that point of view it seems to have attracted the attention of the [[Armodue]] school, an Italian group that use the scheme of [[7L 2s|superdiatonic]] LLLsLLLLs like a base scale for notation and theory, suited in [[16edo]] and allied systems: [[25edo]] [1/3-tone 3;2]; [[41edo]] [1/5-tone 5;3]; and [[57edo]] [1/7-tone 7;4]. The [[hornbostel]] temperament is included too with: [[23edo]] [1/3-tone 3;1]; 39edo [1/5-tone 5;2] & [[62edo]] [1/8-tone 8;3]. The mavila fifth in 39edo like all mavila fifths is very, very flat, in this case, 25{{c}} flat.  
If we take 22\39 as a fifth, 39edo can be used as a tuning of [[mavila]] through the 39bc val, and from that point of view it seems to have attracted the attention of the [[Armodue]] school, an Italian group that use the scheme of [[7L 2s|superdiatonic]] LLLsLLLLs like a base scale for notation and theory, suited in [[16edo]] and allied systems: [[25edo]] [1/3-tone 3;2]; [[41edo]] [1/5-tone 5;3]; and [[57edo]] [1/7-tone 7;4]. The [[hornbostel]] temperament is included too with: [[23edo]] [1/3-tone 3;1]; 39edo [1/5-tone 5;2] & [[62edo]] [1/8-tone 8;3]. The mavila fifth in 39edo like all mavila fifths is very, very flat, in this case, 25{{c}} flat.  
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! #
! #
! Cents
! Cents
! Approximate ratios
! Approximate ratios*
|-
|-
| 0
| 0
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| 2
| 2
| 61.5
| 61.5
| [[28/27]], [[33/32]], ''[[49/48]]''
| ''[[22/21]]'', [[28/27]], [[33/32]], ''[[49/48]]''
|-
|-
| 3
| 3
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| 4
| 4
| 123.1
| 123.1
| [[15/14]]
| [[14/13]], [[15/14]]
|-
|-
| 5
| 5
| 153.8
| 153.8
| [[11/10]], [[12/11]]
| [[11/10]], [[12/11]], [[13/12]]
|-
|-
| 6
| 6
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| 8
| 8
| 246.2
| 246.2
| [[81/70]]
| [[15/13]]
|-
|-
| 9
| 9
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| 11
| 11
| 338.5
| 338.5
| [[11/9]]
| [[11/9]], ''[[16/13]]''
|-
|-
| 12
| 12
| 369.2
| 369.2
| [[27/22]]
| [[26/21]], [[27/22]]
|-
|-
| 13
| 13
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| 15
| 15
| 461.5
| 461.5
| [[35/27]]
| [[13/10]]
|-
|-
| 16
| 16
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| 18
| 18
| 553.8
| 553.8
| [[11/8]]
| [[11/8]], [[18/13]], ''[[15/11]]''
|-
|-
| 19
| 19
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| 21
| 21
| 646.2
| 646.2
| [[16/11]]
| [[13/9]], [[16/11]], ''[[22/15]]''
|-
|-
| 22
| 22
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| 24
| 24
| 738.5
| 738.5
| [[54/35]]
| [[20/13]]
|-
|-
| 25
| 25
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| 27
| 27
| 830.8
| 830.8
| [[44/27]]
| [[21/13]], [[44/27]]
|-
|-
| 28
| 28
| 861.5
| 861.5
| [[18/11]]
| [[18/11]], ''[[13/8]]''
|-
|-
| 29
| 29
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| 31
| 31
| 953.8
| 953.8
| [[140/81]]
| [[26/15]]
|-
|-
| 32
| 32
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| 34
| 34
| 1046.2
| 1046.2
| [[11/6]], [[20/11]]
| [[11/6]], [[20/11]], [[24/13]]
|-
|-
| 35
| 35
| 1076.9
| 1076.9
| [[28/15]]
| [[13/7]], [[28/15]]
|-
|-
| 36
| 36
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| 37
| 37
| 1138.5
| 1138.5
| [[27/14]], [[64/33]], ''[[96/49]]''
| ''[[21/11]]'', [[27/14]], [[64/33]], ''[[96/49]]''
|-
|-
| 38
| 38
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| [[2/1]]
| [[2/1]]
|}
|}
<nowiki/>* As a 13-limit temperament


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
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| 2
| 2
| 61.5
| 61.5
| [[33/32]]
| [[33/32]], ''[[256/243]]''
|  
|  
| ''[[21/20]]'', [[36/35]]
| ''[[21/20]]'', [[36/35]]
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| 9
| 9
| 276.9
| 276.9
|  
| ''[[32/27]]''
|  
|  
|  
|  
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| 14
| 14
| 430.8
| 430.8
|  
| ''[[81/64]]''
|  
|  
| ''[[35/27]]''
| ''[[35/27]]''
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| 25
| 25
| 769.2
| 769.2
|  
| ''[[128/81]]''
|  
|  
| ''[[54/35]]''
| ''[[54/35]]''
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| 30
| 30
| 923.1
| 923.1
|  
| ''[[27/16]]''
|  
|  
|  
|  
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| 37
| 37
| 1138.5
| 1138.5
| [[64/33]]
| [[64/33]], ''[[243/128]]''
|  
|  
| [[35/18]], ''[[40/21]]''
| [[35/18]], ''[[40/21]]''
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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods <br />per 8ve
! Periods <br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
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| 5\39
| 5\39
| 153.8
| 153.8
|  
| [[Nusecond]] (39df)
| [[1L&nbsp;6s]], [[7L&nbsp;1s]], [[8L&nbsp;7s]], [[8L&nbsp;15s]], [[8L&nbsp;23s]]
| [[1L&nbsp;6s]], [[7L&nbsp;1s]], [[8L&nbsp;7s]], [[8L&nbsp;15s]], [[8L&nbsp;23s]]
|-
|-
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| 10\39
| 10\39
| 307.7
| 307.7
| [[Familia]] (39df)
|  
| [[3L&nbsp;1s]], [[4L&nbsp;3s]], [[4L&nbsp;7s]], [[4L&nbsp;11s]], [[4L&nbsp;15s]], [[4L&nbsp;19s]], [[4L&nbsp;23s]], [[4L&nbsp;27s]], [[4L&nbsp;31s]]
| [[3L&nbsp;1s]], [[4L&nbsp;3s]], [[4L&nbsp;7s]], [[4L&nbsp;11s]], [[4L&nbsp;15s]], [[4L&nbsp;19s]], [[4L&nbsp;23s]], [[4L&nbsp;27s]], [[4L&nbsp;31s]]
|-
|-
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|-
|-
| 3
| 3
| 6\39
| 3\39
| 184.6
| 92.3
| [[Terrain]] / [[mirkat]] (39df)
| [[Augene]] (39d)
| [[3L&nbsp;3s]], [[6L&nbsp;3s]], [[6L&nbsp;9s]], [[6L 15]], [[6L&nbsp;21s]], [[6L&nbsp;27s]]
| [[3L&nbsp;3s]], [[3L&nbsp;6s]], [[3L&nbsp;9s]], [[12L&nbsp;3s]], [[12L&nbsp;15s]]
|-
| 3
| 4\39
| 123.0
| [[Deflated]] (39bd)
| [[3L&nbsp;3s]], [[3L&nbsp;6s]], [[9L&nbsp;3s]], [[9L&nbsp;12s]], [[9L&nbsp;21s]]
|-
|-
| 3
| 3
| 8\39 <br>(5\39)
| 5\39
| 246.2 <br>(153.8)
| 153.8
| [[Triforce]] (39)
| [[Triforce]] (39)
| [[3L&nbsp;3s]], [[6L&nbsp;3s]], [[9L&nbsp;6s]], [[15L&nbsp;9s]]
| [[3L&nbsp;3s]], [[6L&nbsp;3s]], [[9L&nbsp;6s]], [[15L&nbsp;9s]]
|-
|-
| 3
| 3
| 16\39 <br>(3\39)
| 6\39
| 492.3 <br>(92.3)
| 184.6
| [[Augene]] (39d)
| [[Terrain]]
| [[3L&nbsp;3s]], [[3L&nbsp;6s]], [[3L&nbsp;9s]], [[12L&nbsp;3s]], [[12L&nbsp;15s]]
| [[3L&nbsp;3s]], [[6L&nbsp;3s]], [[6L&nbsp;9s]], [[6L 15]], [[6L&nbsp;21s]], [[6L&nbsp;27s]]
|-
| 3
| 17\39 <br>(4\39)
| 523.1 <br>(123.0)
| [[Deflated]] (39bd)
| [[3L&nbsp;3s]], [[3L&nbsp;6s]], [[9L&nbsp;3s]], [[9L&nbsp;12s]], [[9L&nbsp;21s]]
|-
|-
| 13
| 13
| 16\39 <br>(1\39)
| 1\39
| 492.3 <br>(30.8)
| 30.8
| [[Tridecatonic]]
| [[Tridecatonic]]
| [[13L&nbsp;13s]]
| [[13L&nbsp;13s]]
|}
|}
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]
 
39et can be detempered to [[mirkat]] (39df & 72) and [[familia]] (39df & 113).


== Octave stretch or compression ==
== Octave stretch or compression ==
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It also offers ''many'' possible [[pentatonic]] scales, including the [[2L 3s]] mos (which is 9 7 7 9 7). [[Slendro]] can be approximated using that scale or using something like the [[quasi-equal]] 8 8 8 8 7 or 8 8 7 8 8.  
It also offers ''many'' possible [[pentatonic]] scales, including the [[2L 3s]] mos (which is 9 7 7 9 7). [[Slendro]] can be approximated using that scale or using something like the [[quasi-equal]] 8 8 8 8 7 or 8 8 7 8 8.  


One expressive [[pentatonic]] scale is the oneirotonic subset 9 6 9 9 6.  
An expressive [[pentatonic]] subset of [[oneirotonic]] - 9 6 9 9 6 - is available because 39edo contains [[13edo]].


Many Asian{{clarify|which ones specifically}} and [[African music|African]] {{clarify|which ones specifically}} musical styles can thus be accommodated.
Many Asian{{clarify|which ones specifically}} and [[African music|African]] {{clarify|which ones specifically}} musical styles can thus be accommodated.


== Scales ==
== Scales ==
* [[Quasisuper]][7] [[MOS scale]]: 7 7 2 7 7 7 2
; [[Augene]] scales
* Quasisuper[7] [[5-limit|pental]] [[modmos]]: 7 6 3 7 6 7 3
* Augene[6] [[MOS scale]]: 10 3 10 3 10 3
* [[3L 6s]] modmos: 7 3 3 3 7 3 3 7 3
* Augene[9] MOS: 3 7 3 3 7 3 3 7 3
* [[3L 6s]] (augene9) [[modmos]]: 7 3 3 3 7 3 3 7 3
* Augene[12] MOS: 3 3 4 3 3 3 4 3 3 3 4 3
* Augene[15] MOS: 3 3 1 3 3 3 3 1 3 3 3 3 1 3 3
 
; [[Quasisuper]] scales
* Quasisuper[7] MOS: 7 7 2 7 7 7 2
* Quasisuper[7] [[5-limit|pental]] modmos: 7 6 3 7 6 7 33
* Extended quasisuper: 4 3 6 3 4 3 6 4 3 3
* Extended quasisuper: 4 3 6 3 4 3 6 4 3 3
* Quasisuper[22] MOS scale (resembles [[Indian]] [[sruti]]): 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2
* Quasisuper[22] MOS (resembles [[Indian]] [[sruti]]): 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2
* Slendro approximations: 9 7 7 9 7 or 8 8 8 8 7 or 8 8 7 8 8
 
* An expressive [[oneirotonic]] subset: 9 6 9 9 6
; [[Amity]] scales
* Amity[7] MOS: 6 6 5 6 5 6 5
* Amity[11] MOS: 5 1 5 5 1 5 1 5 5 1 5
* Amity[18] MOS: 1 4 1 4 1 1 4 1 1 4 1 4 1 1 4 1 4 1
* Amity[25] MOS: 1 3 1 1 1 3 1 1 3 1 1 1 3 1 1 1 3 1 1 3 1 1 1 3 1
* Amity[32] MOS: 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1
 
; Others
* Pelog approximation: 4 5 13 4 13
* Slendro/[[equipentatonic]] approximations: 9 7 7 9 7 ''or'' 8 8 8 8 7 ''or'' 8 8 7 8 8
* ''The scales listed in: [[User:BudjarnLambeth/Quasipelog theory]]''
* ''The scales listed in: [[User:BudjarnLambeth/Quasipelog theory]]''


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; {{W|HOYO-MiX}}
; {{W|HOYO-MiX}}
* [https://www.youtube.com/shorts/4y11CWLIHNA "Sinner's Finale" from ''Genshin Impact OST''] (2023) – covered by [[Bryan Deister]] (2025)
* [https://www.youtube.com/shorts/4y11CWLIHNA "Sinner's Finale" from ''Genshin Impact OST''] (2023) – covered by [[Bryan Deister]] (2025)
; KzX
* [https://www.youtube.com/shorts/IRt0SqDSLbo ''Stalemate''] (2012 — microtonal cover in 39edo by [[Bryan Deister]] (2026)


=== 21st century ===
=== 21st century ===
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[[Category:Listen]]
[[Category:Listen]]
{{Todo|add scales list}}
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