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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.  
Line 24: Line 24:


== Intervals ==
== Intervals ==
{| class="wikitable center-all right-2 left-3 left-4 left-5 right-9 right-10"
As 39edo is a rare case where a non-patent val does significantly better than the patent val, we provide two tables, for those who look for the most accurate temperament available and for those who would like to explore the potential utilities in this edo.
 
{| class="wikitable center-1 right-2"
|+ Table of intervals, 39df val
|-
! #
! Cents
! Approximate ratios*
|-
| 0
| 0.0
| [[1/1]]
|-
| 1
| 30.8
| ''[[36/35]]'', [[50/49]], [[55/54]], [[56/55]], [[81/80]]
|-
| 2
| 61.5
| ''[[22/21]]'', [[28/27]], [[33/32]], ''[[49/48]]''
|-
| 3
| 92.3
| ''[[16/15]]'', [[21/20]], ''[[25/24]]''
|-
| 4
| 123.1
| [[14/13]], [[15/14]]
|-
| 5
| 153.8
| [[11/10]], [[12/11]], [[13/12]]
|-
| 6
| 184.6
| [[10/9]]
|-
| 7
| 215.4
| [[9/8]], ''[[8/7]]''
|-
| 8
| 246.2
| [[15/13]]
|-
| 9
| 276.9
| [[7/6]]
|-
| 10
| 307.7
| [[6/5]]
|-
| 11
| 338.5
| [[11/9]], ''[[16/13]]''
|-
| 12
| 369.2
| [[26/21]], [[27/22]]
|-
| 13
| 400.0
| [[5/4]]
|-
| 14
| 430.8
| [[9/7]], [[14/11]]
|-
| 15
| 461.5
| [[13/10]]
|-
| 16
| 492.3
| [[4/3]]
|-
| 17
| 523.1
| [[27/20]]
|-
| 18
| 553.8
| [[11/8]], [[18/13]], ''[[15/11]]''
|-
| 19
| 584.6
| [[7/5]]
|-
| 20
| 615.4
| [[10/7]]
|-
| 21
| 646.2
| [[13/9]], [[16/11]], ''[[22/15]]''
|-
| 22
| 676.9
| [[40/27]]
|-
| 23
| 707.7
| [[3/2]]
|-
| 24
| 738.5
| [[20/13]]
|-
| 25
| 769.2
| [[11/7]], [[14/9]]
|-
| 26
| 800.0
| [[8/5]]
|-
| 27
| 830.8
| [[21/13]], [[44/27]]
|-
| 28
| 861.5
| [[18/11]], ''[[13/8]]''
|-
| 29
| 892.3
| [[5/3]]
|-
| 30
| 923.1
| [[12/7]]
|-
| 31
| 953.8
| [[26/15]]
|-
| 32
| 984.6
| [[16/9]], ''[[7/4]]''
|-
| 33
| 1015.4
| [[9/5]]
|-
| 34
| 1046.2
| [[11/6]], [[20/11]], [[24/13]]
|-
| 35
| 1076.9
| [[13/7]], [[28/15]]
|-
| 36
| 1107.7
| ''[[15/8]]'', [[40/21]], ''[[48/25]]''
|-
| 37
| 1138.5
| ''[[21/11]]'', [[27/14]], [[64/33]], ''[[96/49]]''
|-
| 38
| 1169.2
| ''[[35/18]]'', [[49/25]], [[108/55]], [[160/81]]
|-
| 39
| 1200.0
| [[2/1]]
|}
<nowiki/>* As a 13-limit temperament
 
{| class="wikitable center-1 right-2"
|+ Table of intervals, various vals
|-
|-
! rowspan="2" | #
! rowspan="2" | #
! rowspan="2" | Cents
! rowspan="2" | Cents
! rowspan="2" | Ratios of the<br>[[2.3.5.11 subgroup]]
! rowspan="2" | Ratios of the<br>[[2.3.11 subgroup]]
! colspan="2" | Intervals of 7
! colspan="3" | Intervals of 5 and 7
|-
|-
! Patent val
! 39c val
! 39 val
! 39d val
! 39d val
|-
|-
| 0
| 0
| 0.0
| 0.0
| colspan=3 | [[1/1]]
| [[1/1]]
|
|
|
|-
|-
| 1
| 1
| 30.8
| 30.8
| [[55/54]], [[81/80]]
|  
| ''[[28/27]]'', [[64/63]]
| ''[[28/27]]'', [[50/49]], [[64/63]]
| ''[[36/35]]'', [[50/49]], ''[[56/55]]''
| ''[[28/27]]'', [[64/63]], [[81/80]]
| ''[[36/35]]'', [[50/49]], [[81/80]]
|-
|-
| 2
| 2
| 61.5
| 61.5
| [[33/32]]
| [[33/32]], ''[[256/243]]''
|
| ''[[21/20]]'', [[36/35]]
| ''[[21/20]]'', [[36/35]]
| [[28/27]], ''[[49/48]]''
| ''[[22/21]]'', [[28/27]], ''[[49/48]]''
|-
|-
| 3
| 3
| 92.3
| 92.3
| ''[[16/15]]'', ''[[25/24]]''
|
| ''[[50/49]]''
| [[21/20]], [[22/21]], ''[[36/35]]''
| [[21/20]]
| ''[[16/15]]'', [[22/21]], ''[[25/24]]''
| ''[[16/15]]'', [[21/20]], ''[[25/24]]''
|-
|-
| 4
| 4
| 123.1
| 123.1
|
|  
|
| [[15/14]], [[16/15]]
|  
| [[15/14]]
| [[15/14]]
|-
|-
| 5
| 5
| 153.8
| 153.8
| [[11/10]], [[12/11]]
| [[12/11]]
| ''[[15/14]]''
| ''[[10/9]]''
|
| [[11/10]], ''[[15/14]]''
| [[11/10]]
|-
|-
| 6
| 6
| 184.6
| 184.6
|
| ''[[11/10]]''
| [[10/9]]
| [[10/9]]
| [[10/9]]
|
|
|-
|-
| 7
| 7
| 215.4
| 215.4
| [[9/8]]
| [[9/8]]
|
|
|  
| ''[[8/7]]''
| ''[[8/7]]''
|-
|-
| 8
| 8
| 246.2
| 246.2
|
|  
| [[8/7]], ''[[7/6]]''
| ''[[7/6]]'', [[8/7]]
| ''[[7/6]]'', [[8/7]]
| [[81/70]]
| [[81/70]]
|-
|-
| 9
| 9
| 276.9
| 276.9
|
| ''[[32/27]]''
| ''[[81/70]]''
|
|
| [[7/6]]
| [[7/6]]
|-
|-
| 10
| 10
| 307.7
| 307.7
|
|
| [[6/5]]
| [[6/5]]
| [[6/5]]
|
|
|-
|-
| 11
| 11
| 338.5
| 338.5
| [[11/9]]
| [[11/9]]
|
| ''[[6/5]]''
|
|  
|  
|-
|-
| 12
| 12
| 369.2
| 369.2
| [[27/22]]
| [[27/22]]
|
| ''[[5/4]]''
|
|  
|  
|-
|-
| 13
| 13
| 400.0
| 400.0
|
| ''[[14/11]]''
| [[5/4]], ''[[14/11]]''
| [[5/4]]
| [[5/4]]
| ''[[14/11]]''
|
|-
|-
| 14
| 14
| 430.8
| 430.8
|
| ''[[81/64]]''
|  
| ''[[35/27]]''
| ''[[35/27]]''
| [[9/7]], [[14/11]]
| [[9/7]], [[14/11]]
Line 124: Line 314:
| 15
| 15
| 461.5
| 461.5
|
|  
| ''[[9/7]]''
| ''[[9/7]]'', [[21/16]]
| ''[[9/7]]'', [[21/16]]
| [[35/27]]
| [[35/27]]
|-
|-
Line 131: Line 322:
| 492.3
| 492.3
| [[4/3]]
| [[4/3]]
|
|
|
|  
|  
|-
|-
| 17
| 17
| 523.1
| 523.1
|
| [[15/11]]
| [[27/20]]
| [[27/20]]
| [[27/20]]
|
|
|-
|-
| 18
| 18
| 553.8
| 553.8
| [[11/8]]
| [[11/8]]
| ''[[7/5]]''
| ''[[27/20]]''
|
| ''[[7/5]]'', ''[[15/11]]''
| ''[[15/11]]''
|-
|-
| 19
| 19
| 584.6
| 584.6
|
|  
|
| [[7/5]]
|  
| [[7/5]]
| [[7/5]]
|-
|-
| 20
| 20
| 615.4
| 615.4
|
|  
|
| [[10/7]]
|  
| [[10/7]]
| [[10/7]]
|-
|-
Line 161: Line 357:
| 646.2
| 646.2
| [[16/11]]
| [[16/11]]
| ''[[10/7]]''
| ''[[40/27]]''
|
| ''[[10/7]]'', ''[[22/15]]''
| ''[[22/15]]''
|-
|-
| 22
| 22
| 676.9
| 676.9
|
| [[22/15]]
| [[40/27]]
| [[40/27]]
| [[40/27]]
|
|
|-
|-
| 23
| 23
| 707.7
| 707.7
| [[3/2]]
| [[3/2]]
|
|
|
|  
|  
|-
|-
| 24
| 24
| 738.5
| 738.5
|
|  
| ''[[14/9]]''
| ''[[14/9]]'', [[32/21]]
| ''[[14/9]]'', [[32/21]]
| [[54/35]]
| [[54/35]]
|-
|-
| 25
| 25
| 769.2
| 769.2
|
| ''[[128/81]]''
|  
| ''[[54/35]]''
| ''[[54/35]]''
| [[11/7]], [[14/9]]
| [[11/7]], [[14/9]]
Line 190: Line 391:
| 26
| 26
| 800.0
| 800.0
|
| ''[[11/7]]''
| [[8/5]], ''[[11/7]]''
| [[8/5]]
| [[8/5]]
| ''[[11/7]]''
|
|-
|-
| 27
| 27
| 830.8
| 830.8
| [[44/27]]
| [[44/27]]
|
| ''[[8/5]]''
|
|  
|  
|-
|-
| 28
| 28
| 861.5
| 861.5
| [[18/11]]
| [[18/11]]
|
| ''[[5/3]]''
|
|  
|  
|-
|-
| 29
| 29
| 892.3
| 892.3
|
|
| [[5/3]]
| [[5/3]]
| [[5/3]]
|
|
|-
|-
| 30
| 30
| 923.1
| 923.1
|
| ''[[27/16]]''
| ''[[140/81]]''
|
|
| [[12/7]]
| [[12/7]]
|-
|-
| 31
| 31
| 953.8
| 953.8
|
|  
| [[7/4]], ''[[12/7]]''
| [[7/4]], ''[[12/7]]''
| [[7/4]], ''[[12/7]]''
| [[140/81]]
| [[140/81]]
Line 227: Line 434:
| 984.6
| 984.6
| [[16/9]]
| [[16/9]]
|
|
|  
| ''[[7/4]]''
| ''[[7/4]]''
|-
|-
| 33
| 33
| 1015.4
| 1015.4
|
| ''[[20/11]]''
| [[9/5]]
| [[9/5]]
| [[9/5]]
|
|
|-
|-
| 34
| 34
| 1046.2
| 1046.2
| [[11/6]], [[20/11]]
| [[11/6]]
| ''[[28/15]]''
| ''[[9/5]]''
|
| [[20/11]], ''[[28/15]]''
| [[20/11]]
|-
|-
| 35
| 35
| 1076.9
| 1076.9
|
|  
|
| [[15/8]], [[28/15]]
|  
| [[28/15]]
| [[28/15]]
|-
|-
| 36
| 36
| 1107.7
| 1107.7
| ''[[15/8]]'', ''[[48/25]]''
|
| ''[[49/25]]''
| [[21/11]], ''[[35/18]]'', [[40/21]]
| [[40/21]]
| ''[[15/8]]'', [[21/11]], ''[[48/25]]''
| ''[[15/8]]'', [[40/21]], ''[[48/25]]''
|-
|-
| 37
| 37
| 1138.5
| 1138.5
| [[64/33]]
| [[64/33]], ''[[243/128]]''
|
| [[35/18]], ''[[40/21]]''
| [[35/18]], ''[[40/21]]''
| [[27/14]], ''[[96/49]]''
| [[27/14]], ''[[96/49]]''
Line 262: Line 475:
| 38
| 38
| 1169.2
| 1169.2
| [[108/55]], [[160/81]]
|  
| [[63/32]], ''[[27/14]]''
| ''[[27/14]]'', [[49/25]], [[63/32]]
| ''[[35/18]]'', [[49/25]]
| ''[[27/14]]'', [[63/32]], [[160/81]]
| ''[[35/18]]'', [[49/25]], [[160/81]]
|-
|-
| 39
| 39
| 1200.0
| 1200.0
| colspan=3 | [[2/1]]
| [[2/1]]
|
|
|
|}
|}


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