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→Intervals: sed -E "s#[0-9]+/[0-9]+#\\[\\[&\\]\\]#g" 31EDOintervals.txt > 31EDOintervals.new.txt # required manually splicing later subsection to remove duplicate links
→Intervals: split for a CLEAN interval table
Line 35: Line 35:


== Intervals ==
== Intervals ==
{{See also|Table of 31edo intervals|31edo/Individual degrees|31edo solfege}}
{{See also|Table of 31edo intervals|31edo/Individual degrees}}


{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-1 right-2"
|-
|-
! Degree
! #
! Cents
! Cents
! Approximate ratios<ref group="note">{{sg|limit=23-limit}} Inconsistent intervals are in ''italics''.</ref>
! Approximate ratios<ref group="note">{{sg|limit=23-limit}} Inconsistent intervals are in ''italics''.</ref>
! colspan="3" | [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and vd2)
! [[Kite's ups and downs notation|Ups and downs notation]]
|-
| 0
| 0.0
| [[1/1]]
| {{UDnote|step=0}}
|-
| 1
| 38.7
| [[45/44]], [[49/48]], [[46/45]], [[128/125]], [[36/35]]
| {{UDnote|step=1}}
|-
| 2
| 77.4
| [[25/24]], [[21/20]], [[22/21]], [[23/22]]
| {{UDnote|step=2}}
|-
| 3
| 116.1
| [[15/14]], [[16/15]]
| {{UDnote|step=3}}
|-
| 4
| 154.8
| [[12/11]], [[11/10]], [[35/32]]
| {{UDnote|step=4}}
|-
| 5
| 193.5
| [[9/8]], [[10/9]], [[19/17]], [[28/25]]
| {{UDnote|step=5}}
|-
| 6
| 232.3
| [[8/7]], [[144/125]]
| {{UDnote|step=6}}
|-
| 7
| 271.0
| [[7/6]], [[75/64]]
| {{UDnote|step=7}}
|-
| 8
| 309.7
| [[6/5]], ''[[13/11]]'', [[25/21]]
| {{UDnote|step=8}}
|-
| 9
| 348.4
| [[11/9]], [[27/22]], [[16/13]], [[60/49]], [[49/40]]
| {{UDnote|step=9}}
|-
| 10
| 387.1
| [[5/4]]
| {{UDnote|step=10}}
|-
| 11
| 425.8
| [[9/7]], [[14/11]], [[23/18]], [[32/25]]
| {{UDnote|step=11}}
|-
| 12
| 464.5
| [[21/16]], [[64/49]], [[13/10]], [[17/13]], [[125/96]]
| {{UDnote|step=12}}
|-
| 13
| 503.2
| [[4/3]]
| {{UDnote|step=13}}
|-
| 14
| 541.9
| [[175/128]], [[11/8]], [[15/11]], ''[[18/13]]'', [[26/19]]
| {{UDnote|step=14}}
|-
| 15
| 580.6
| [[7/5]], [[45/32]], [[25/18]]
| {{UDnote|step=15}}
|-
| 16
| 619.4
| [[10/7]], [[64/45]], [[36/25]]
| {{UDnote|step=16}}
|-
| 17
| 658.1
| [[256/175]], ''[[13/9]]'', [[16/11]], [[22/15]], [[19/13]]
| {{UDnote|step=17}}
|-
| 18
| 696.8
| [[3/2]]
| {{UDnote|step=18}}
|-
| 19
| 735.5
| [[32/21]], [[49/32]], [[20/13]], [[26/17]], [[192/125]]
| {{UDnote|step=19}}
|-
| 20
| 774.2
| [[14/9]], [[11/7]], [[25/16]]
| {{UDnote|step=20}}
|-
| 21
| 812.9
| [[8/5]]
| {{UDnote|step=21}}
|-
| 22
| 851.6
| [[18/11]], [[44/27]], [[13/8]], [[49/30]], [[80/49]]
| {{UDnote|step=22}}
|-
| 23
| 890.3
| [[5/3]], [[42/25]]
| {{UDnote|step=23}}
|-
| 24
| 929.0
| [[12/7]], [[128/75]]
| {{UDnote|step=24}}
|-
| 25
| 967.7
| [[7/4]], [[125/72]]
| {{UDnote|step=25}}
|-
| 26
| 1006.5
| [[16/9]], [[9/5]], [[34/19]], [[25/14]]
| {{UDnote|step=26}}
|-
| 27
| 1045.2
| [[11/6]], [[20/11]], [[64/35]]
| {{UDnote|step=27}}
|-
| 28
| 1083.9
| [[28/15]], [[15/8]]
| {{UDnote|step=28}}
|-
| 29
| 1122.6
| [[48/25]], [[40/21]], [[21/11]], [[44/23]]
| {{UDnote|step=29}}
|-
| 30
| 1161.3
| [[88/45]], [[96/49]], [[45/23]], [[125/64]], [[35/18]]
| {{UDnote|step=30}}
|-
| 31
| 1200.0
| [[2/1]]
| {{UDnote|step=31}}
|}
<references group="note" />
 
=== Proposed interval names and solfeges ===
{{See also|31edo solfege}}
 
{| class="wikitable center-all right-2 left-4 left-7 left-10 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]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and vd2)
! colspan="3" | Extended pythagorean notation
! colspan="3" | Extended pythagorean notation
! colspan="3" | [[SKULO interval names|SKULO notation]] (S or {{nowrap|U {{=}} 1}})
! colspan="3" | [[SKULO interval names|SKULO notation]]<br>(S or {{nowrap|U {{=}} 1}})
|-
|-
| 0
| 0
| 0.0
| 0.0
| [[1/1]]
| P1
| P1
| perfect unison
| perfect unison
Line 61: Line 232:
| 1
| 1
| 38.7
| 38.7
| [[45/44]], [[49/48]], [[46/45]], [[128/125]], [[36/35]]
| ^1, d2
| ^1, d2
| up-unison, dim 2nd
| up-unison, dim 2nd
Line 74: Line 244:
| 2
| 2
| 77.4
| 77.4
| [[25/24]], [[21/20]], [[22/21]], [[23/22]]
| A1, vm2
| A1, vm2
| aug 1sn, downminor 2nd
| aug 1sn, downminor 2nd
Line 87: Line 256:
| 3
| 3
| 116.1
| 116.1
| [[15/14]], [[16/15]]
| m2
| m2
| minor 2nd
| minor 2nd
Line 100: Line 268:
| 4
| 4
| 154.8
| 154.8
| [[12/11]], [[11/10]], [[35/32]]
| ~2
| ~2
| mid 2nd
| mid 2nd
Line 113: Line 280:
| 5
| 5
| 193.5
| 193.5
| [[9/8]], [[10/9]], [[19/17]], [[28/25]]
| M2
| M2
| major 2nd
| major 2nd
Line 126: Line 292:
| 6
| 6
| 232.3
| 232.3
| [[8/7]], [[144/125]]
| ^M2
| ^M2
| upmajor 2nd
| upmajor 2nd
Line 139: Line 304:
| 7
| 7
| 271.0
| 271.0
| [[7/6]], [[75/64]]
| vm3
| vm3
| downminor 3rd
| downminor 3rd
Line 152: Line 316:
| 8
| 8
| 309.7
| 309.7
| [[6/5]], ''[[13/11]]'', [[25/21]]
| m3
| m3
| minor 3rd
| minor 3rd
Line 165: Line 328:
| 9
| 9
| 348.4
| 348.4
| [[11/9]], [[27/22]], [[16/13]], [[60/49]], [[49/40]]
| ~3
| ~3
| mid 3rd
| mid 3rd
Line 178: Line 340:
| 10
| 10
| 387.1
| 387.1
| [[5/4]]
| M3
| M3
| major 3rd
| major 3rd
Line 191: Line 352:
| 11
| 11
| 425.8
| 425.8
| [[9/7]], [[14/11]], [[23/18]], [[32/25]]
| ^M3
| ^M3
| upmajor 3rd
| upmajor 3rd
Line 204: Line 364:
| 12
| 12
| 464.5
| 464.5
| [[21/16]], [[64/49]], [[13/10]], [[17/13]], [[125/96]]
| v4
| v4
| down-4th
| down-4th
Line 217: Line 376:
| 13
| 13
| 503.2
| 503.2
| [[4/3]]
| P4
| P4
| perfect 4th
| perfect 4th
Line 230: Line 388:
| 14
| 14
| 541.9
| 541.9
| [[175/128]], [[11/8]], [[15/11]], ''[[18/13]]'', [[26/19]]
| ^4, ~4
| ^4, ~4
| up-4th, mid 4th
| up-4th, mid 4th
Line 243: Line 400:
| 15
| 15
| 580.6
| 580.6
| [[7/5]], [[45/32]], [[25/18]]
| A4, vd5
| A4, vd5
| aug 4th, downdim 5th
| aug 4th, downdim 5th
Line 256: Line 412:
| 16
| 16
| 619.4
| 619.4
| [[10/7]], [[64/45]], [[36/25]]
| ^A4, d5
| ^A4, d5
| upaug 4th, dim 5th
| upaug 4th, dim 5th
Line 269: Line 424:
| 17
| 17
| 658.1
| 658.1
| [[256/175]], ''[[13/9]]'', [[16/11]], [[22/15]], [[19/13]]
| v5, ~5
| v5, ~5
| down-5th, mid 5th
| down-5th, mid 5th
Line 282: Line 436:
| 18
| 18
| 696.8
| 696.8
| [[3/2]]
| P5
| P5
| perfect 5th
| perfect 5th
Line 295: Line 448:
| 19
| 19
| 735.5
| 735.5
| [[32/21]], [[49/32]], [[20/13]], [[26/17]], [[192/125]]
| ^5
| ^5
| up-5th
| up-5th
Line 308: Line 460:
| 20
| 20
| 774.2
| 774.2
| [[14/9]], [[11/7]], [[25/16]]
| vm6
| vm6
| downminor 6th
| downminor 6th
Line 321: Line 472:
| 21
| 21
| 812.9
| 812.9
| [[8/5]]
| m6
| m6
| minor 6th
| minor 6th
Line 334: Line 484:
| 22
| 22
| 851.6
| 851.6
| [[18/11]], [[44/27]], [[13/8]], [[49/30]], [[80/49]]
| ~6
| ~6
| mid 6th
| mid 6th
Line 347: Line 496:
| 23
| 23
| 890.3
| 890.3
| [[5/3]], [[42/25]]
| M6
| M6
| major 6th
| major 6th
Line 360: Line 508:
| 24
| 24
| 929.0
| 929.0
| [[12/7]], [[128/75]]
| ^M6
| ^M6
| upmajor 6th
| upmajor 6th
Line 373: Line 520:
| 25
| 25
| 967.7
| 967.7
| [[7/4]], [[125/72]]
| vm7
| vm7
| downminor 7th
| downminor 7th
Line 386: Line 532:
| 26
| 26
| 1006.5
| 1006.5
| [[16/9]], [[9/5]], [[34/19]], [[25/14]]
| m7
| m7
| minor 7th
| minor 7th
Line 399: Line 544:
| 27
| 27
| 1045.2
| 1045.2
| [[11/6]], [[20/11]], [[64/35]]
| ~7
| ~7
| mid 7th
| mid 7th
Line 412: Line 556:
| 28
| 28
| 1083.9
| 1083.9
| [[28/15]], [[15/8]]
| M7
| M7
| major 7th
| major 7th
Line 425: Line 568:
| 29
| 29
| 1122.6
| 1122.6
| [[48/25]], [[40/21]], [[21/11]], [[44/23]]
| ^M7
| ^M7
| upmajor 7th
| upmajor 7th
Line 438: Line 580:
| 30
| 30
| 1161.3
| 1161.3
| [[88/45]], [[96/49]], [[45/23]], [[125/64]], [[35/18]]
| v8
| v8
| down-8ve
| down-8ve
Line 451: Line 592:
| 31
| 31
| 1200.0
| 1200.0
| [[2/1]]
| P8
| P8
| perfect 8ve
| perfect 8ve
Line 462: Line 602:
| 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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