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Line 14: Line 14:
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]]
|-
|-
! rowspan="2" | Steps
| 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" | 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
! colspan="3" rowspan="2" | [[Ups and downs notation]]
|-
|-
! Patent val
! 39c val
! 39 val
! 39d val
! 39d val
|-
|-
| 0
| 0
| 0.0
| 0.0
| colspan=3 | [[1/1]]
| [[1/1]]
|
|
|
|-
| 1
| 30.8
|
| ''[[28/27]]'', [[50/49]], [[64/63]]
| ''[[28/27]]'', [[64/63]], [[81/80]]
| ''[[36/35]]'', [[50/49]], [[81/80]]
|-
| 2
| 61.5
| [[33/32]], ''[[256/243]]''
|
| ''[[21/20]]'', [[36/35]]
| ''[[22/21]]'', [[28/27]], ''[[49/48]]''
|-
| 3
| 92.3
|
| [[21/20]], [[22/21]], ''[[36/35]]''
| ''[[16/15]]'', [[22/21]], ''[[25/24]]''
| ''[[16/15]]'', [[21/20]], ''[[25/24]]''
|-
| 4
| 123.1
|
| [[15/14]], [[16/15]]
|
| [[15/14]]
|-
| 5
| 153.8
| [[12/11]]
| ''[[10/9]]''
| [[11/10]], ''[[15/14]]''
| [[11/10]]
|-
| 6
| 184.6
|
| ''[[11/10]]''
| [[10/9]]
| [[10/9]]
|-
| 7
| 215.4
| [[9/8]]
|
|
| ''[[8/7]]''
|-
| 8
| 246.2
|
| ''[[7/6]]'', [[8/7]]
| ''[[7/6]]'', [[8/7]]
| [[81/70]]
|-
| 9
| 276.9
| ''[[32/27]]''
|
|
| [[7/6]]
|-
| 10
| 307.7
|
|
| [[6/5]]
| [[6/5]]
|-
| 11
| 338.5
| [[11/9]]
| ''[[6/5]]''
|
|
|-
| 12
| 369.2
| [[27/22]]
| ''[[5/4]]''
|
|
|-
| 13
| 400.0
|
| ''[[14/11]]''
| [[5/4]], ''[[14/11]]''
| [[5/4]]
|-
| 14
| 430.8
| ''[[81/64]]''
|
| ''[[35/27]]''
| [[9/7]], [[14/11]]
|-
| 15
| 461.5
|
| ''[[9/7]]'', [[21/16]]
| ''[[9/7]]'', [[21/16]]
| [[35/27]]
|-
| 16
| 492.3
| [[4/3]]
|
|
|
|-
| 17
| 523.1
|
| [[15/11]]
| [[27/20]]
| [[27/20]]
|-
| 18
| 553.8
| [[11/8]]
| ''[[27/20]]''
| ''[[7/5]]'', ''[[15/11]]''
| ''[[15/11]]''
|-
| 19
| 584.6
|
| [[7/5]]
|
| [[7/5]]
|-
| 20
| 615.4
|
| [[10/7]]
|
| [[10/7]]
|-
| 21
| 646.2
| [[16/11]]
| ''[[40/27]]''
| ''[[10/7]]'', ''[[22/15]]''
| ''[[22/15]]''
|-
| 22
| 676.9
|
| [[22/15]]
| [[40/27]]
| [[40/27]]
|-
| 23
| 707.7
| [[3/2]]
|
|
|
|-
| 24
| 738.5
|
| ''[[14/9]]'', [[32/21]]
| ''[[14/9]]'', [[32/21]]
| [[54/35]]
|-
| 25
| 769.2
| ''[[128/81]]''
|
| ''[[54/35]]''
| [[11/7]], [[14/9]]
|-
| 26
| 800.0
|
| ''[[11/7]]''
| [[8/5]], ''[[11/7]]''
| [[8/5]]
|-
| 27
| 830.8
| [[44/27]]
| ''[[8/5]]''
|
|
|-
| 28
| 861.5
| [[18/11]]
| ''[[5/3]]''
|
|
|-
| 29
| 892.3
|
|
| [[5/3]]
| [[5/3]]
|-
| 30
| 923.1
| ''[[27/16]]''
|
|
| [[12/7]]
|-
| 31
| 953.8
|
| [[7/4]], ''[[12/7]]''
| [[7/4]], ''[[12/7]]''
| [[140/81]]
|-
| 32
| 984.6
| [[16/9]]
|
|
| ''[[7/4]]''
|-
| 33
| 1015.4
|
| ''[[20/11]]''
| [[9/5]]
| [[9/5]]
|-
| 34
| 1046.2
| [[11/6]]
| ''[[9/5]]''
| [[20/11]], ''[[28/15]]''
| [[20/11]]
|-
| 35
| 1076.9
|
| [[15/8]], [[28/15]]
|
| [[28/15]]
|-
| 36
| 1107.7
|
| [[21/11]], ''[[35/18]]'', [[40/21]]
| ''[[15/8]]'', [[21/11]], ''[[48/25]]''
| ''[[15/8]]'', [[40/21]], ''[[48/25]]''
|-
| 37
| 1138.5
| [[64/33]], ''[[243/128]]''
|
| [[35/18]], ''[[40/21]]''
| [[27/14]], ''[[96/49]]''
|-
| 38
| 1169.2
|
| ''[[27/14]]'', [[49/25]], [[63/32]]
| ''[[27/14]]'', [[63/32]], [[160/81]]
| ''[[35/18]]'', [[49/25]], [[160/81]]
|-
| 39
| 1200.0
| [[2/1]]
|
|
|
|}
 
=== Proposed interval names and solfèges ===
{| class="wikitable mw-collapsible mw-collapsed center-1 right-2 center-3 center-5"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
! #
! Cents
! colspan="3" | [[Ups and downs notation]]
|-
| 0
| 0.0
| P1
| P1
| perfect unison
| perfect unison
Line 44: Line 504:
| 1
| 1
| 30.8
| 30.8
| [[55/54]], [[81/80]]
| ''[[28/27]]'', [[64/63]]
| ''[[36/35]]'', [[50/49]], ''[[56/55]]''
| ^1, <br>vm2
| ^1, <br>vm2
| up unison, <br>downminor 2nd
| up unison, <br>downminor 2nd
Line 53: Line 510:
| 2
| 2
| 61.5
| 61.5
| [[33/32]]
| ''[[21/20]]'', [[36/35]]
| [[28/27]], ''[[49/48]]''
| m2
| m2
| minor 2nd
| minor 2nd
Line 62: Line 516:
| 3
| 3
| 92.3
| 92.3
| ''[[16/15]]'', ''[[25/24]]''
| ''[[50/49]]''
| [[21/20]]
| ^m2
| ^m2
| upminor 2nd
| upminor 2nd
Line 71: Line 522:
| 4
| 4
| 123.1
| 123.1
|
|
| [[15/14]]
| ^^m2
| ^^m2
| dupminor 2nd
| dupminor 2nd
Line 80: Line 528:
| 5
| 5
| 153.8
| 153.8
| [[11/10]], [[12/11]]
| ''[[15/14]]''
|
| vvM2
| vvM2
| dudmajor 2nd
| dudmajor 2nd
Line 89: Line 534:
| 6
| 6
| 184.6
| 184.6
| [[10/9]]
|
|
| vM2
| vM2
| downmajor 2nd
| downmajor 2nd
Line 98: Line 540:
| 7
| 7
| 215.4
| 215.4
| [[9/8]]
|
| ''[[8/7]]''
| M2
| M2
| major 2nd
| major 2nd
Line 107: Line 546:
| 8
| 8
| 246.2
| 246.2
|
| [[8/7]], ''[[7/6]]''
| [[81/70]]
| ^M2, <br>vm3
| ^M2, <br>vm3
| upmajor 2nd, <br>downminor 3rd
| upmajor 2nd, <br>downminor 3rd
Line 116: Line 552:
| 9
| 9
| 276.9
| 276.9
|
| ''[[81/70]]''
| [[7/6]]
| m3
| m3
| minor 3rd
| minor 3rd
Line 125: Line 558:
| 10
| 10
| 307.7
| 307.7
| [[6/5]]
|
|
| ^m3
| ^m3
| upminor 3rd
| upminor 3rd
Line 134: Line 564:
| 11
| 11
| 338.5
| 338.5
| [[11/9]]
|
|
| ^^m3
| ^^m3
| dupminor 3rd
| dupminor 3rd
Line 143: Line 570:
| 12
| 12
| 369.2
| 369.2
| [[27/22]]
|
|
| vvM3
| vvM3
| dudmajor 3rd
| dudmajor 3rd
Line 152: Line 576:
| 13
| 13
| 400.0
| 400.0
| [[5/4]]
| ''[[14/11]]''
|
| vM3
| vM3
| downmajor 3rd
| downmajor 3rd
Line 161: Line 582:
| 14
| 14
| 430.8
| 430.8
|
| ''[[35/27]]''
| [[9/7]], [[14/11]]
| M3
| M3
| major 3rd
| major 3rd
Line 170: Line 588:
| 15
| 15
| 461.5
| 461.5
|
| ''[[9/7]]''
| [[35/27]]
| v4
| v4
| down 4th
| down 4th
Line 179: Line 594:
| 16
| 16
| 492.3
| 492.3
| [[4/3]]
|
|
| P4
| P4
| perfect 4th
| perfect 4th
Line 188: Line 600:
| 17
| 17
| 523.1
| 523.1
| [[27/20]]
|
|
| ^4
| ^4
| up 4th
| up 4th
Line 197: Line 606:
| 18
| 18
| 553.8
| 553.8
| [[11/8]]
| ''[[7/5]]''
|
| ^^4
| ^^4
| dup 4th
| dup 4th
Line 206: Line 612:
| 19
| 19
| 584.6
| 584.6
|
|
| [[7/5]]
| vvA4, <br>^d5
| vvA4, <br>^d5
| dudaug 4th, <br>updim 5th
| dudaug 4th, <br>updim 5th
Line 215: Line 618:
| 20
| 20
| 615.4
| 615.4
|
|
| [[10/7]]
| vA4, <br>^^d5
| vA4, <br>^^d5
| downaug 4th, <br>dupdim 5th
| downaug 4th, <br>dupdim 5th
Line 224: Line 624:
| 21
| 21
| 646.2
| 646.2
| [[16/11]]
| ''[[10/7]]''
|
| vv5
| vv5
| dud 5th
| dud 5th
Line 233: Line 630:
| 22
| 22
| 676.9
| 676.9
| [[40/27]]
|
|
| v5
| v5
| down 5th
| down 5th
Line 242: Line 636:
| 23
| 23
| 707.7
| 707.7
| [[3/2]]
|
|
| P5
| P5
| perfect 5th
| perfect 5th
Line 251: Line 642:
| 24
| 24
| 738.5
| 738.5
|
| ''[[14/9]]''
| [[54/35]]
| ^5
| ^5
| up 5th
| up 5th
Line 260: Line 648:
| 25
| 25
| 769.2
| 769.2
|
| ''[[54/35]]''
| [[11/7]], [[14/9]]
| m6
| m6
| minor 6th
| minor 6th
Line 269: Line 654:
| 26
| 26
| 800.0
| 800.0
| [[8/5]]
| ''[[11/7]]''
|
| ^m6
| ^m6
| upminor 6th
| upminor 6th
Line 278: Line 660:
| 27
| 27
| 830.8
| 830.8
| [[44/27]]
|
|
| ^^m6
| ^^m6
| dupminor 6th
| dupminor 6th
Line 287: Line 666:
| 28
| 28
| 861.5
| 861.5
| [[18/11]]
|
|
| vvM6
| vvM6
| dudmajor 6th
| dudmajor 6th
Line 296: Line 672:
| 29
| 29
| 892.3
| 892.3
| [[5/3]]
|
|
| vM6
| vM6
| downmajor 6th
| downmajor 6th
Line 305: Line 678:
| 30
| 30
| 923.1
| 923.1
|
| ''[[140/81]]''
| [[12/7]]
| M6
| M6
| major 6th
| major 6th
Line 314: Line 684:
| 31
| 31
| 953.8
| 953.8
|
| [[7/4]], ''[[12/7]]''
| [[140/81]]
| ^M6, <br>vm7
| ^M6, <br>vm7
| upmajor 6th, <br>downminor 7th
| upmajor 6th, <br>downminor 7th
Line 323: Line 690:
| 32
| 32
| 984.6
| 984.6
| [[16/9]]
|
| ''[[7/4]]''
| m7
| m7
| minor 7th
| minor 7th
Line 332: Line 696:
| 33
| 33
| 1015.4
| 1015.4
| [[9/5]]
|
|
| ^m7
| ^m7
| upminor 7th
| upminor 7th
Line 341: Line 702:
| 34
| 34
| 1046.2
| 1046.2
| [[11/6]], [[20/11]]
| ''[[28/15]]''
|
| ^^m7
| ^^m7
| dupminor 7th
| dupminor 7th
Line 350: Line 708:
| 35
| 35
| 1076.9
| 1076.9
|
|
| [[28/15]]
| vvM7
| vvM7
| dudmajor 7th
| dudmajor 7th
Line 359: Line 714:
| 36
| 36
| 1107.7
| 1107.7
| ''[[15/8]]'', ''[[48/25]]''
| ''[[49/25]]''
| [[40/21]]
| vM7
| vM7
| downmajor 7th
| downmajor 7th
Line 368: Line 720:
| 37
| 37
| 1138.5
| 1138.5
| [[64/33]]
| [[35/18]], ''[[40/21]]''
| [[27/14]], ''[[96/49]]''
| M7
| M7
| major 7th
| major 7th
Line 377: Line 726:
| 38
| 38
| 1169.2
| 1169.2
| [[108/55]], [[160/81]]
| [[63/32]], ''[[27/14]]''
| ''[[35/18]]'', [[49/25]]
| ^M7, <br>v8
| ^M7, <br>v8
| upmajor 7th, <br>down 8ve
| upmajor 7th, <br>down 8ve
Line 386: Line 732:
| 39
| 39
| 1200.0
| 1200.0
| colspan=3 | [[2/1]]
| P8
| P8
| perfect 8ve
| perfect 8ve
Line 392: Line 737:
|}
|}


Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Kite's ups and downs notation #Chords and chord progressions]].


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