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]]''