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39edo: Difference between revisions

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→Intervals: break off the tri-column of color notation for a clean table
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== 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
| [[28/27]], [[33/32]], ''[[49/48]]''
|-
| 3
| 92.3
| ''[[16/15]]'', [[21/20]], ''[[25/24]]''
|-
| 4
| 123.1
| [[15/14]]
|-
| 5
| 153.8
| [[11/10]], [[12/11]]
|-
| 6
| 184.6
| [[10/9]]
|-
| 7
| 215.4
| [[9/8]], ''[[8/7]]''
|-
| 8
| 246.2
| [[81/70]]
|-
| 9
| 276.9
| [[7/6]]
|-
| 10
| 307.7
| [[6/5]]
|-
| 11
| 338.5
| [[11/9]]
|-
| 12
| 369.2
| [[27/22]]
|-
| 13
| 400.0
| [[5/4]]
|-
| 14
| 430.8
| [[9/7]], [[14/11]]
|-
| 15
| 461.5
| [[35/27]]
|-
| 16
| 492.3
| [[4/3]]
|-
| 17
| 523.1
| [[27/20]]
|-
| 18
| 553.8
| [[11/8]]
|-
| 19
| 584.6
| [[7/5]]
|-
| 20
| 615.4
| [[10/7]]
|-
| 21
| 646.2
| [[16/11]]
|-
| 22
| 676.9
| [[40/27]]
|-
| 23
| 707.7
| [[3/2]]
|-
| 24
| 738.5
| [[54/35]]
|-
| 25
| 769.2
| [[11/7]], [[14/9]]
|-
| 26
| 800.0
| [[8/5]]
|-
| 27
| 830.8
| [[44/27]]
|-
| 28
| 861.5
| [[18/11]]
|-
| 29
| 892.3
| [[5/3]]
|-
| 30
| 923.1
| [[12/7]]
|-
| 31
| 953.8
| [[140/81]]
|-
| 32
| 984.6
| [[16/9]], ''[[7/4]]''
|-
| 33
| 1015.4
| [[9/5]]
|-
| 34
| 1046.2
| [[11/6]], [[20/11]]
|-
| 35
| 1076.9
| [[28/15]]
|-
| 36
| 1107.7
| ''[[15/8]]'', [[40/21]], ''[[48/25]]''
|-
| 37
| 1138.5
| [[27/14]], [[64/33]], ''[[96/49]]''
|-
| 38
| 1169.2
| ''[[35/18]]'', [[49/25]], [[108/55]], [[160/81]]
|-
| 39
| 1200.0
| [[2/1]]
|}
 
{| 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]]
|
| ''[[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
|
|  
| ''[[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
|
|
|  
| ''[[35/27]]''
| ''[[35/27]]''
| [[9/7]], [[14/11]]
| [[9/7]], [[14/11]]
Line 124: Line 313:
| 15
| 15
| 461.5
| 461.5
|
|  
| ''[[9/7]]''
| ''[[9/7]]'', [[21/16]]
| ''[[9/7]]'', [[21/16]]
| [[35/27]]
| [[35/27]]
|-
|-
Line 131: Line 321:
| 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 356:
| 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
|
|
|  
| ''[[54/35]]''
| ''[[54/35]]''
| [[11/7]], [[14/9]]
| [[11/7]], [[14/9]]
Line 190: Line 390:
| 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
|
|  
| ''[[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 433:
| 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]]
|
| [[35/18]], ''[[40/21]]''
| [[35/18]], ''[[40/21]]''
| [[27/14]], ''[[96/49]]''
| [[27/14]], ''[[96/49]]''
Line 262: Line 474:
| 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]]
|
|
|
|}
|}


Retrieved from "https://en.xen.wiki/w/39edo"