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== Intervals ==
== Intervals ==
{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-1 right-2"
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios<ref group="note">{{sg|limit=19-limit}} For lower limits see [[Table of 72edo intervals]].</ref>
! Approximate ratios<ref group="note">As a 19-limit temperament, inconsistent intervals in ''italic''. For a table of intervals by prime limit, see [[Table of 72edo intervals]].</ref>
! colspan="3" | [[Ups and downs notation]]
! [[Kite's ups and downs notation|Ups and downs notation]]
|-
| 0
| 0.0
| [[1/1]]
| {{UDnote|step=0}}
|-
| 1
| 16.7
| [[81/80]], [[91/90]], [[99/98]], [[100/99]], [[105/104]]
| {{UDnote|step=1}}
|-
| 2
| 33.3
| [[45/44]], [[49/48]], [[50/49]], [[55/54]], [[64/63]]
| {{UDnote|step=2}}
|-
| 3
| 50.0
| [[33/32]], [[36/35]], [[40/39]]
| {{UDnote|step=3}}
|-
| 4
| 66.7
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| {{UDnote|step=4}}
|-
| 5
| 83.3
| [[20/19]], [[21/20]], [[22/21]]
| {{UDnote|step=5}}
|-
| 6
| 100.0
| [[17/16]], [[18/17]], [[19/18]]
| {{UDnote|step=6}}
|-
| 7
| 116.7
| [[15/14]], [[16/15]]
| {{UDnote|step=7}}
|-
| 8
| 133.3
| [[13/12]], [[14/13]], [[27/25]]
| {{UDnote|step=8}}
|-
| 9
| 150.0
| [[12/11]]
| {{UDnote|step=9}}
|-
| 10
| 166.7
| [[11/10]]
| {{UDnote|step=10}}
|-
| 11
| 183.3
| [[10/9]]
| {{UDnote|step=11}}
|-
| 12
| 200.0
| [[9/8]], [[19/17]]
| {{UDnote|step=12}}
|-
| 13
| 216.7
| [[17/15]], [[25/22]]
| {{UDnote|step=13}}
|-
| 14
| 233.3
| [[8/7]]
| {{UDnote|step=14}}
|-
| 15
| 250.0
| [[15/13]], [[22/19]]
| {{UDnote|step=15}}
|-
| 16
| 266.7
| [[7/6]]
| {{UDnote|step=16}}
|-
| 17
| 283.3
| [[13/11]], [[20/17]]
| {{UDnote|step=17}}
|-
| 18
| 300.0
| [[19/16]], [[25/21]], [[32/27]]
| {{UDnote|step=18}}
|-
| 19
| 316.7
| [[6/5]]
| {{UDnote|step=19}}
|-
| 20
| 333.3
| [[17/14]], [[39/32]], [[40/33]]
| {{UDnote|step=20}}
|-
| 21
| 350.0
| [[11/9]], [[27/22]]
| {{UDnote|step=21}}
|-
| 22
| 366.7
| [[16/13]], [[21/17]], [[26/21]]
| {{UDnote|step=22}}
|-
| 23
| 383.3
| [[5/4]]
| {{UDnote|step=23}}
|-
| 24
| 400.0
| [[24/19]]
| {{UDnote|step=24}}
|-
| 25
| 416.7
| [[14/11]], [[19/15]]
| {{UDnote|step=25}}
|-
| 26
| 433.3
| [[9/7]]
| {{UDnote|step=26}}
|-
| 27
| 450.0
| [[13/10]], [[22/17]]
| {{UDnote|step=27}}
|-
| 28
| 466.7
| [[17/13]], [[21/16]]
| {{UDnote|step=28}}
|-
| 29
| 483.3
| [[33/25]]
| {{UDnote|step=29}}
|-
| 30
| 500.0
| [[4/3]]
| {{UDnote|step=30}}
|-
| 31
| 516.7
| [[27/20]]
| {{UDnote|step=31}}
|-
| 32
| 533.3
| [[15/11]], [[19/14]], ''[[26/19]]''
| {{UDnote|step=32}}
|-
| 33
| 550.0
| [[11/8]]
| {{UDnote|step=33}}
|-
| 34
| 566.7
| [[18/13]], [[25/18]]
| {{UDnote|step=34}}
|-
| 35
| 583.3
| [[7/5]]
| {{UDnote|step=35}}
|-
| 36
| 600.0
| [[17/12]], [[24/17]]
| {{UDnote|step=36}}
|-
| 37
| 616.7
| [[10/7]]
| {{UDnote|step=37}}
|-
| 38
| 633.3
| [[13/9]], [[36/25]]
| {{UDnote|step=38}}
|-
| 39
| 650.0
| [[16/11]]
| {{UDnote|step=39}}
|-
| 40
| 666.7
| ''[[19/13]]'', [[22/15]], [[28/19]]
| {{UDnote|step=40}}
|-
| 41
| 683.3
| [[40/27]]
| {{UDnote|step=41}}
|-
| 42
| 700.0
| [[3/2]]
| {{UDnote|step=42}}
|-
| 43
| 716.7
| [[50/33]]
| {{UDnote|step=43}}
|-
| 44
| 733.3
| [[26/17]], [[32/21]]
| {{UDnote|step=44}}
|-
| 45
| 750.0
| [[17/11]], [[20/13]]
| {{UDnote|step=45}}
|-
| 46
| 766.7
| [[14/9]]
| {{UDnote|step=46}}
|-
| 47
| 783.3
| [[11/7]], [[30/19]]
| {{UDnote|step=47}}
|-
| 48
| 800.0
| [[19/12]]
| {{UDnote|step=48}}
|-
| 49
| 816.7
| [[8/5]]
| {{UDnote|step=49}}
|-
| 50
| 833.3
| [[13/8]], [[21/13]], [[34/21]]
| {{UDnote|step=50}}
|-
| 51
| 850.0
| [[18/11]], [[44/27]]
| {{UDnote|step=51}}
|-
| 52
| 866.7
| [[28/17]], [[33/20]], [[64/39]]
| {{UDnote|step=52}}
|-
| 53
| 883.3
| [[5/3]]
| {{UDnote|step=53}}
|-
| 54
| 900.0
| [[27/16]], [[32/19]], [[42/25]]
| {{UDnote|step=54}}
|-
| 55
| 916.7
| [[17/10]], [[22/13]]
| {{UDnote|step=55}}
|-
| 56
| 933.3
| [[12/7]]
| {{UDnote|step=56}}
|-
| 57
| 950.0
| [[19/11]], [[26/15]]
| {{UDnote|step=57}}
|-
| 58
| 966.7
| [[7/4]]
| {{UDnote|step=58}}
|-
| 59
| 983.3
| [[30/17]], [[44/25]]
| {{UDnote|step=59}}
|-
| 60
| 1000.0
| [[16/9]], [[34/19]]
| {{UDnote|step=60}}
|-
| 61
| 1016.7
| [[9/5]]
| {{UDnote|step=61}}
|-
| 62
| 1033.3
| [[20/11]]
| {{UDnote|step=62}}
|-
| 63
| 1050.0
| [[11/6]]
| {{UDnote|step=63}}
|-
| 64
| 1066.7
| [[13/7]], [[24/13]], [[50/27]]
| {{UDnote|step=64}}
|-
| 65
| 1083.3
| [[15/8]], [[28/15]]
| {{UDnote|step=65}}
|-
| 66
| 1100.0
| [[17/9]], [[32/17]], [[36/19]]
| {{UDnote|step=66}}
|-
| 67
| 1116.7
| [[19/10]], [[21/11]], [[40/21]]
| {{UDnote|step=67}}
|-
| 68
| 1133.3
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| {{UDnote|step=68}}
|-
| 69
| 1150.0
| [[35/18]], [[39/20]], [[64/33]]
| {{UDnote|step=69}}
|-
| 70
| 1166.7
| [[49/25]], [[55/28]], [[63/32]], [[88/45]], [[96/49]]
| {{UDnote|step=70}}
|-
| 71
| 1183.3
| [[99/50]], [[160/81]], [[180/91]], [[196/99]], [[208/105]]
| {{UDnote|step=71}}
|-
| 72
| 1200.0
| [[2/1]]
| {{UDnote|step=72}}
|}
<references group="note" />
 
=== Proposed interval names and solfèges ===
{| class="wikitable center-all right-2 left-4 left-7 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
! #
! Cents
! colspan="3" | [[Kite's ups and downs notation|Ups and downs notation]]
! colspan="3" | [[SKULO interval names|SKULO interval names and notation]]
! colspan="3" | [[SKULO interval names|SKULO interval names and notation]]
! (K, S, U)  
! (K, S, U)  
Line 43: Line 418:
| 0
| 0
| 0.0
| 0.0
| [[1/1]]
| P1
| P1
| perfect unison
| perfect unison
Line 54: Line 428:
| 1
| 1
| 16.7
| 16.7
| [[81/80]], [[91/90]], [[99/98]], [[100/99]], [[105/104]]
| ^1
| ^1
| up unison
| up unison
Line 65: Line 438:
| 2
| 2
| 33.3
| 33.3
| [[45/44]], [[49/48]], [[50/49]], [[55/54]], [[64/63]]
| ^^
| ^^
| dup unison
| dup unison
Line 76: Line 448:
| 3
| 3
| 50.0
| 50.0
| [[33/32]], [[36/35]], [[40/39]]
| ^<sup>3</sup>1, v<sup>3</sup>m2
| ^<sup>3</sup>1, v<sup>3</sup>m2
| trup unison, trudminor 2nd
| trup unison, trudminor 2nd
Line 87: Line 458:
| 4
| 4
| 66.7
| 66.7
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| vvm2
| vvm2
| dudminor 2nd
| dudminor 2nd
Line 98: Line 468:
| 5
| 5
| 83.3
| 83.3
| [[20/19]], [[21/20]], [[22/21]]
| vm2
| vm2
| downminor 2nd
| downminor 2nd
Line 109: Line 478:
| 6
| 6
| 100.0
| 100.0
| [[17/16]], [[18/17]], [[19/18]]
| m2
| m2
| minor 2nd
| minor 2nd
Line 120: Line 488:
| 7
| 7
| 116.7
| 116.7
| [[15/14]], [[16/15]]
| ^m2
| ^m2
| upminor 2nd
| upminor 2nd
Line 131: Line 498:
| 8
| 8
| 133.3
| 133.3
| [[13/12]], [[14/13]], [[27/25]]
| ^^m2, v~2
| ^^m2, v~2
| dupminor 2nd, downmid 2nd
| dupminor 2nd, downmid 2nd
Line 142: Line 508:
| 9
| 9
| 150.0
| 150.0
| [[12/11]]
| ~2
| ~2
| mid 2nd
| mid 2nd
Line 153: Line 518:
| 10
| 10
| 166.7
| 166.7
| [[11/10]]
| ^~2, vvM2
| ^~2, vvM2
| upmid 2nd, dudmajor 2nd
| upmid 2nd, dudmajor 2nd
Line 164: Line 528:
| 11
| 11
| 183.3
| 183.3
| [[10/9]]
| vM2
| vM2
| downmajor 2nd
| downmajor 2nd
Line 175: Line 538:
| 12
| 12
| 200.0
| 200.0
| [[9/8]], [[19/17]]
| M2
| M2
| major 2nd
| major 2nd
Line 186: Line 548:
| 13
| 13
| 216.7
| 216.7
| [[17/15]], [[25/22]]
| ^M2
| ^M2
| upmajor 2nd
| upmajor 2nd
Line 197: Line 558:
| 14
| 14
| 233.3
| 233.3
| [[8/7]]
| ^^M2
| ^^M2
| dupmajor 2nd
| dupmajor 2nd
Line 208: Line 568:
| 15
| 15
| 250.0
| 250.0
| [[15/13]], [[22/19]]
| ^<sup>3</sup>M2, <br>v<sup>3</sup>m3
| ^<sup>3</sup>M2, <br>v<sup>3</sup>m3
| trupmajor 2nd,<br>trudminor 3rd
| trupmajor 2nd,<br>trudminor 3rd
Line 219: Line 578:
| 16
| 16
| 266.7
| 266.7
| [[7/6]]
| vvm3
| vvm3
| dudminor 3rd
| dudminor 3rd
Line 230: Line 588:
| 17
| 17
| 283.3
| 283.3
| [[13/11]], [[20/17]]
| vm3
| vm3
| downminor 3rd
| downminor 3rd
Line 241: Line 598:
| 18
| 18
| 300.0
| 300.0
| [[19/16]], [[25/21]], [[32/27]]
| m3
| m3
| minor 3rd
| minor 3rd
Line 252: Line 608:
| 19
| 19
| 316.7
| 316.7
| [[6/5]]
| ^m3
| ^m3
| upminor 3rd
| upminor 3rd
Line 263: Line 618:
| 20
| 20
| 333.3
| 333.3
| [[17/14]], [[39/32]], [[40/33]]
| ^^m3, v~3
| ^^m3, v~3
| dupminor 3rd, downmid 3rd
| dupminor 3rd, downmid 3rd
Line 274: Line 628:
| 21
| 21
| 350.0
| 350.0
| [[11/9]], [[27/22]]
| ~3
| ~3
| mid 3rd
| mid 3rd
Line 285: Line 638:
| 22
| 22
| 366.7
| 366.7
| [[16/13]], [[21/17]], [[26/21]]
| ^~3, vvM3
| ^~3, vvM3
| upmid 3rd, dudmajor 3rd
| upmid 3rd, dudmajor 3rd
Line 296: Line 648:
| 23
| 23
| 383.3
| 383.3
| [[5/4]]
| vM3
| vM3
| downmajor 3rd
| downmajor 3rd
Line 307: Line 658:
| 24
| 24
| 400.0
| 400.0
| [[24/19]]
| M3
| M3
| major 3rd
| major 3rd
Line 318: Line 668:
| 25
| 25
| 416.7
| 416.7
| [[14/11]], [[19/15]]
| ^M3
| ^M3
| upmajor 3rd
| upmajor 3rd
Line 329: Line 678:
| 26
| 26
| 433.3
| 433.3
| [[9/7]]
| ^^M3
| ^^M3
| dupmajor 3rd
| dupmajor 3rd
Line 340: Line 688:
| 27
| 27
| 450.0
| 450.0
| [[13/10]], [[22/17]]
| ^<sup>3</sup>M3, v<sup>3</sup>4
| ^<sup>3</sup>M3, v<sup>3</sup>4
| trupmajor 3rd, trud 4th
| trupmajor 3rd, trud 4th
Line 351: Line 698:
| 28
| 28
| 466.7
| 466.7
| [[17/13]], [[21/16]]
| vv4
| vv4
| dud 4th
| dud 4th
Line 362: Line 708:
| 29
| 29
| 483.3
| 483.3
| [[33/25]]
| v4
| v4
| down 4th
| down 4th
Line 373: Line 718:
| 30
| 30
| 500.0
| 500.0
| [[4/3]]
| P4
| P4
| perfect 4th
| perfect 4th
Line 384: Line 728:
| 31
| 31
| 516.7
| 516.7
| [[27/20]]
| ^4
| ^4
| up 4th
| up 4th
Line 395: Line 738:
| 32
| 32
| 533.3
| 533.3
| [[15/11]], [[19/14]], ''[[26/19]]''
| ^^4, v~4
| ^^4, v~4
| dup 4th, downmid 4th
| dup 4th, downmid 4th
Line 406: Line 748:
| 33
| 33
| 550.0
| 550.0
| [[11/8]]
| ~4
| ~4
| mid 4th
| mid 4th
Line 417: Line 758:
| 34
| 34
| 566.7
| 566.7
| [[18/13]], [[25/18]]
| ^~4, vvA4
| ^~4, vvA4
| upmid 4th, dudaug 4th
| upmid 4th, dudaug 4th
Line 428: Line 768:
| 35
| 35
| 583.3
| 583.3
| [[7/5]]
| vA4, vd5
| vA4, vd5
| downaug 4th, <br>downdim 5th
| downaug 4th, <br>downdim 5th
Line 439: Line 778:
| 36
| 36
| 600.0
| 600.0
| [[17/12]], [[24/17]]
| A4, d5
| A4, d5
| aug 4th, dim 5th
| aug 4th, dim 5th
Line 450: Line 788:
| 37
| 37
| 616.7
| 616.7
| [[10/7]]
| ^A4, ^d5
| ^A4, ^d5
| upaug 4th, updim 5th
| upaug 4th, updim 5th
Line 461: Line 798:
| 38
| 38
| 633.3
| 633.3
| [[13/9]], [[36/25]]
| v~5, ^^d5
| v~5, ^^d5
| downmid 5th, <br>dupdim 5th
| downmid 5th, <br>dupdim 5th
Line 472: Line 808:
| 39
| 39
| 650.0
| 650.0
| [[16/11]]
| ~5
| ~5
| mid 5th
| mid 5th
Line 483: Line 818:
| 40
| 40
| 666.7
| 666.7
| ''[[19/13]]'', [[22/15]], [[28/19]]
| vv5, ^~5
| vv5, ^~5
| dud 5th, upmid 5th
| dud 5th, upmid 5th
Line 494: Line 828:
| 41
| 41
| 683.3
| 683.3
| [[40/27]]
| v5
| v5
| down 5th
| down 5th
Line 505: Line 838:
| 42
| 42
| 700.0
| 700.0
| [[3/2]]
| P5
| P5
| perfect 5th
| perfect 5th
Line 516: Line 848:
| 43
| 43
| 716.7
| 716.7
| [[50/33]]
| ^5
| ^5
| up 5th
| up 5th
Line 527: Line 858:
| 44
| 44
| 733.3
| 733.3
| [[26/17]], [[32/21]]
| ^^5
| ^^5
| dup 5th
| dup 5th
Line 538: Line 868:
| 45
| 45
| 750.0
| 750.0
| [[17/11]], [[20/13]]
| ^<sup>3</sup>5, v<sup>3</sup>m6
| ^<sup>3</sup>5, v<sup>3</sup>m6
| trup 5th, trudminor 6th
| trup 5th, trudminor 6th
Line 549: Line 878:
| 46
| 46
| 766.7
| 766.7
| [[14/9]]
| vvm6
| vvm6
| dudminor 6th
| dudminor 6th
Line 560: Line 888:
| 47
| 47
| 783.3
| 783.3
| [[11/7]], [[30/19]]
| vm6
| vm6
| downminor 6th
| downminor 6th
Line 571: Line 898:
| 48
| 48
| 800.0
| 800.0
| [[19/12]]
| m6
| m6
| minor 6th
| minor 6th
Line 582: Line 908:
| 49
| 49
| 816.7
| 816.7
| [[8/5]]
| ^m6
| ^m6
| upminor 6th
| upminor 6th
Line 593: Line 918:
| 50
| 50
| 833.3
| 833.3
| [[13/8]], [[21/13]], [[34/21]]
| ^^m6, v~6
| ^^m6, v~6
| dupminor 6th, downmid 6th
| dupminor 6th, downmid 6th
Line 604: Line 928:
| 51
| 51
| 850.0
| 850.0
| [[18/11]], [[44/27]]
| ~6
| ~6
| mid 6th
| mid 6th
Line 615: Line 938:
| 52
| 52
| 866.7
| 866.7
| [[28/17]], [[33/20]], [[64/39]]
| ^~6, vvM6
| ^~6, vvM6
| upmid 6th, dudmajor 6th
| upmid 6th, dudmajor 6th
Line 626: Line 948:
| 53
| 53
| 883.3
| 883.3
| [[5/3]]
| vM6
| vM6
| downmajor 6th
| downmajor 6th
Line 637: Line 958:
| 54
| 54
| 900.0
| 900.0
| [[27/16]], [[32/19]], [[42/25]]
| M6
| M6
| major 6th
| major 6th
Line 648: Line 968:
| 55
| 55
| 916.7
| 916.7
| [[17/10]], [[22/13]]
| ^M6
| ^M6
| upmajor 6th
| upmajor 6th
Line 659: Line 978:
| 56
| 56
| 933.3
| 933.3
| [[12/7]]
| ^^M6
| ^^M6
| dupmajor 6th
| dupmajor 6th
Line 670: Line 988:
| 57
| 57
| 950.0
| 950.0
| [[19/11]], [[26/15]]
| ^<sup>3</sup>M6, <br>v<sup>3</sup>m7
| ^<sup>3</sup>M6, <br>v<sup>3</sup>m7
| trupmajor 6th,<br>trudminor 7th
| trupmajor 6th,<br>trudminor 7th
Line 681: Line 998:
| 58
| 58
| 966.7
| 966.7
| [[7/4]]
| vvm7
| vvm7
| dudminor 7th
| dudminor 7th
Line 692: Line 1,008:
| 59
| 59
| 983.3
| 983.3
| [[30/17]], [[44/25]]
| vm7
| vm7
| downminor 7th
| downminor 7th
Line 703: Line 1,018:
| 60
| 60
| 1000.0
| 1000.0
| [[16/9]], [[34/19]]
| m7
| m7
| minor 7th
| minor 7th
Line 714: Line 1,028:
| 61
| 61
| 1016.7
| 1016.7
| [[9/5]]
| ^m7
| ^m7
| upminor 7th
| upminor 7th
Line 725: Line 1,038:
| 62
| 62
| 1033.3
| 1033.3
| [[20/11]]
| ^^m7, v~7
| ^^m7, v~7
| dupminor 7th, downmid 7th
| dupminor 7th, downmid 7th
Line 736: Line 1,048:
| 63
| 63
| 1050.0
| 1050.0
| [[11/6]]
| ~7
| ~7
| mid 7th
| mid 7th
Line 747: Line 1,058:
| 64
| 64
| 1066.7
| 1066.7
| [[13/7]], [[24/13]], [[50/27]]
| ^~7, vvM7
| ^~7, vvM7
| upmid 7th, dudmajor 7th
| upmid 7th, dudmajor 7th
Line 758: Line 1,068:
| 65
| 65
| 1083.3
| 1083.3
| [[15/8]], [[28/15]]
| vM7
| vM7
| downmajor 7th
| downmajor 7th
Line 769: Line 1,078:
| 66
| 66
| 1100.0
| 1100.0
| [[17/9]], [[32/17]], [[36/19]]
| M7
| M7
| major 7th
| major 7th
Line 780: Line 1,088:
| 67
| 67
| 1116.7
| 1116.7
| [[19/10]], [[21/11]], [[40/21]]
| ^M7
| ^M7
| upmajor 7th
| upmajor 7th
Line 791: Line 1,098:
| 68
| 68
| 1133.3
| 1133.3
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| ^^M7
| ^^M7
| dupmajor 7th
| dupmajor 7th
Line 802: Line 1,108:
| 69
| 69
| 1150.0
| 1150.0
| [[35/18]], [[39/20]], [[64/33]]
| ^<sup>3</sup>M7, v<sup>3</sup>8
| ^<sup>3</sup>M7, v<sup>3</sup>8
| trupmajor 7th, trud octave
| trupmajor 7th, trud octave
Line 813: Line 1,118:
| 70
| 70
| 1166.7
| 1166.7
| [[49/25]], [[55/28]], [[63/32]], [[88/45]], [[96/49]]
| vv8
| vv8
| dud octave
| dud octave
Line 824: Line 1,128:
| 71
| 71
| 1183.3
| 1183.3
| [[99/50]], [[160/81]], [[180/91]], [[196/99]], [[208/105]]
| v8
| v8
| down octave
| down octave
Line 835: Line 1,138:
| 72
| 72
| 1200.0
| 1200.0
| [[2/1]]
| P8
| P8
| perfect octave
| perfect octave
Line 844: Line 1,146:
| D
| D
|}
|}
<references group="note" />


=== Interval quality and chord names in color notation ===
=== Interval quality and chord names in color notation ===
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