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== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2"
|-
! #
! Cents
! Approximate ratios*
! [[Kite's ups and downs notation|Ups and downs notation]]
|-
| 0
| 0.0
| [[1/1]]
| {{UDnote|step=0}}
|-
| 1
| 29.3
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
| {{UDnote|step=1}}
|-
| 2
| 58.5
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
| {{UDnote|step=2}}
|-
| 3
| 87.8
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
| {{UDnote|step=3}}
|-
| 4
| 117.1
| [[14/13]], [[15/14]], [[16/15]]
| {{UDnote|step=4}}
|-
| 5
| 146.3
| [[12/11]], [[13/12]]
| {{UDnote|step=5}}
|-
| 6
| 175.6
| [[10/9]], [[11/10]], [[21/19]]
| {{UDnote|step=6}}
|-
| 7
| 204.9
| [[9/8]]
| {{UDnote|step=7}}
|-
| 8
| 234.1
| [[8/7]], [[15/13]]
| {{UDnote|step=8}}
|-
| 9
| 263.4
| [[7/6]], [[22/19]]
| {{UDnote|step=9}}
|-
| 10
| 292.7
| [[13/11]], [[19/16]], [[32/27]]
| {{UDnote|step=10}}
|-
| 11
| 322.0
| [[6/5]]
| {{UDnote|step=11}}
|-
| 12
| 351.2
| [[11/9]], [[16/13]]
| {{UDnote|step=12}}
|-
| 13
| 380.5
| [[5/4]], [[26/21]]
| {{UDnote|step=13}}
|-
| 14
| 409.8
| [[14/11]], [[19/15]], [[24/19]]
| {{UDnote|step=14}}
|-
| 15
| 439.0
| [[9/7]], [[32/25]]
| {{UDnote|step=15}}
|-
| 16
| 468.3
| [[21/16]], [[13/10]]
| {{UDnote|step=16}}
|-
| 17
| 497.6
| [[4/3]]
| {{UDnote|step=17}}
|-
| 18
| 526.8
| [[15/11]], [[19/14]], [[27/20]]
| {{UDnote|step=18}}
|-
| 19
| 556.1
| [[11/8]], [[18/13]], [[26/19]]
| {{UDnote|step=19}}
|-
| 20
| 585.4
| [[7/5]], [[45/32]]
| {{UDnote|step=20}}
|-
| 21
| 614.6
| [[10/7]], [[64/45]]
| {{UDnote|step=21}}
|-
| 22
| 643.9
| [[13/9]], [[16/11]], [[19/13]]
| {{UDnote|step=22}}
|-
| 23
| 673.2
| [[22/15]], [[28/19]], [[40/27]]
| {{UDnote|step=23}}
|-
| 24
| 702.4
| [[3/2]]
| {{UDnote|step=24}}
|-
| 25
| 731.7
| [[20/13]], [[32/21]]
| {{UDnote|step=25}}
|-
| 26
| 761.0
| [[14/9]], [[25/16]]
| {{UDnote|step=26}}
|-
| 27
| 790.2
| [[11/7]], [[19/12]], [[30/19]]
| {{UDnote|step=27}}
|-
| 28
| 819.5
| [[8/5]], [[21/13]]
| {{UDnote|step=28}}
|-
| 29
| 848.8
| [[13/8]], [[18/11]]
| {{UDnote|step=29}}
|-
| 30
| 878.0
| [[5/3]]
| {{UDnote|step=30}}
|-
| 31
| 907.3
| [[22/13]], [[27/16]], [[32/19]]
| {{UDnote|step=31}}
|-
| 32
| 936.6
| [[12/7]], [[19/11]]
| {{UDnote|step=32}}
|-
| 33
| 965.9
| [[7/4]], [[26/15]]
| {{UDnote|step=33}}
|-
| 34
| 995.1
| [[16/9]]
| {{UDnote|step=34}}
|-
| 35
| 1024.4
| [[9/5]], [[20/11]], [[38/21]]
| {{UDnote|step=35}}
|-
| 36
| 1053.7
| [[11/6]], [[24/13]]
| {{UDnote|step=36}}
|-
| 37
| 1082.9
| [[13/7]], [[15/8]], [[28/15]]
| {{UDnote|step=37}}
|-
| 38
| 1112.2
| [[19/10]], [[21/11]], [[36/19]], [[40/21]]
| {{UDnote|step=38}}
|-
| 39
| 1141.5
| [[27/14]], [[35/18]], [[48/25]], [[64/33]]
| {{UDnote|step=39}}
|-
| 40
| 1170.7
| [[49/25]], [[63/32]], [[96/49]], [[160/81]]
| {{UDnote|step=40}}
|-
| 41
| 1200.0
| [[2/1]]
| {{UDnote|step=41}}
|}
<nowiki>*</nowiki> Based on treating 41edo as a 2.3.5.7.11.13.19-subgroup temperament; other approaches are possible.
=== Proposed interval names and solfèges ===
{{See also| 41edo solfege }}
{{See also| 41edo solfege }}


{| class="wikitable center-1 right-2 center-5 center-6 center-8 center-9"
{| class="wikitable center-all right-2 left-3 left-6 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios*
! colspan="3" | [[Kite's ups and downs notation]]<br>([[Kite's thoughts on enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^d2)
! colspan="3" | [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^d2)
! colspan="3" | [[SKULO interval names|SKULO notation]]<br>(K or S = 1, U = 2)
! colspan="3" | [[SKULO interval names|SKULO notation]] (K or S = 1, U = 2)
! Kite's<br>solfège
! [[41edo solfege|Kite's<br>solfege]]
! Andrew's<br>solfège
! [[41edo solfege|Andrew's<br>solfege]]
|-
|-
| 0
| 0
| 0.0
| 0.0
| [[1/1]]
| perfect unison
| perfect unison
| P1
| P1
Line 63: Line 282:
| 1
| 1
| 29.3
| 29.3
| [[49/48]], [[50/49]], [[64/63]], [[81/80]]
| up-unison
| up-unison
| ^1
| ^1
Line 75: Line 293:
| 2
| 2
| 58.5
| 58.5
| [[25/24]], [[28/27]], [[33/32]], [[36/35]]
| dup-unison, downminor 2nd
| dup-unison, downminor 2nd
| ^^1, vm2
| ^^1, vm2
Line 87: Line 304:
| 3
| 3
| 87.8
| 87.8
| [[19/18]], [[20/19]], [[21/20]], [[22/21]]
| down-aug 1sn, minor 2nd
| down-aug 1sn, minor 2nd
| vA1, m2
| vA1, m2
Line 99: Line 315:
| 4
| 4
| 117.1
| 117.1
| [[14/13]], [[15/14]], [[16/15]]
| augmented 1sn, upminor 2nd
| augmented 1sn, upminor 2nd
| A1, ^m2
| A1, ^m2
Line 111: Line 326:
| 5
| 5
| 146.3
| 146.3
| [[12/11]], [[13/12]]
| mid 2nd
| mid 2nd
| ~2
| ~2
Line 123: Line 337:
| 6
| 6
| 175.6
| 175.6
| [[10/9]], [[11/10]], [[21/19]]
| downmajor 2nd
| downmajor 2nd
| vM2
| vM2
Line 135: Line 348:
| 7
| 7
| 204.9
| 204.9
| [[9/8]]
| major 2nd
| major 2nd
| M2
| M2
Line 147: Line 359:
| 8
| 8
| 234.1
| 234.1
| [[8/7]], [[15/13]]
| upmajor 2nd
| upmajor 2nd
| ^M2
| ^M2
Line 159: Line 370:
| 9
| 9
| 263.4
| 263.4
| [[7/6]], [[22/19]]
| downminor 3rd
| downminor 3rd
| vm3
| vm3
Line 171: Line 381:
| 10
| 10
| 292.7
| 292.7
| [[13/11]], [[19/16]], [[32/27]]
| minor 3rd
| minor 3rd
| m3
| m3
Line 183: Line 392:
| 11
| 11
| 322.0
| 322.0
| [[6/5]]
| upminor 3rd
| upminor 3rd
| ^m3
| ^m3
Line 195: Line 403:
| 12
| 12
| 351.2
| 351.2
| [[11/9]], [[16/13]]
| mid 3rd
| mid 3rd
| ~3
| ~3
Line 207: Line 414:
| 13
| 13
| 380.5
| 380.5
| [[5/4]], [[26/21]]
| downmajor 3rd
| downmajor 3rd
| vM3
| vM3
Line 219: Line 425:
| 14
| 14
| 409.8
| 409.8
| [[14/11]], [[19/15]], [[24/19]]
| major 3rd
| major 3rd
| M3
| M3
Line 231: Line 436:
| 15
| 15
| 439.0
| 439.0
| [[9/7]], [[32/25]]
| upmajor 3rd
| upmajor 3rd
| ^M3
| ^M3
Line 243: Line 447:
| 16
| 16
| 468.3
| 468.3
| [[21/16]], [[13/10]]
| down-4th
| down-4th
| v4
| v4
Line 255: Line 458:
| 17
| 17
| 497.6
| 497.6
| [[4/3]]
| perfect 4th
| perfect 4th
| P4
| P4
Line 267: Line 469:
| 18
| 18
| 526.8
| 526.8
| [[15/11]], [[19/14]], [[27/20]]
| up-4th
| up-4th
| ^4
| ^4
Line 279: Line 480:
| 19
| 19
| 556.1
| 556.1
| [[11/8]], [[18/13]], [[26/19]]
| mid-4th, downdim 5th
| mid-4th, downdim 5th
| ~4, vd5
| ~4, vd5
Line 291: Line 491:
| 20
| 20
| 585.4
| 585.4
| [[7/5]], [[45/32]]
| downaug 4th, dim 5th
| downaug 4th, dim 5th
| vA4, d5
| vA4, d5
Line 303: Line 502:
| 21
| 21
| 614.6
| 614.6
| [[10/7]], [[64/45]]
| aug 4th, updim 5th
| aug 4th, updim 5th
| A4, ^d5
| A4, ^d5
Line 315: Line 513:
| 22
| 22
| 643.9
| 643.9
| [[13/9]], [[16/11]], [[19/13]]
| mid-5th, upaug 4th
| mid-5th, upaug 4th
| ~5, ^A4
| ~5, ^A4
Line 327: Line 524:
| 23
| 23
| 673.2
| 673.2
| [[22/15]], [[28/19]], [[40/27]]
| down-5th
| down-5th
| v5
| v5
Line 339: Line 535:
| 24
| 24
| 702.4
| 702.4
| [[3/2]]
| perfect 5th
| perfect 5th
| P5
| P5
Line 351: Line 546:
| 25
| 25
| 731.7
| 731.7
| [[20/13]], [[32/21]]
| up-5th
| up-5th
| ^5
| ^5
Line 363: Line 557:
| 26
| 26
| 761.0
| 761.0
| [[14/9]], [[25/16]]
| downminor 6th
| downminor 6th
| vm6
| vm6
Line 375: Line 568:
| 27
| 27
| 790.2
| 790.2
| [[11/7]], [[19/12]], [[30/19]]
| minor 6th
| minor 6th
| m6
| m6
Line 387: Line 579:
| 28
| 28
| 819.5
| 819.5
| [[8/5]], [[21/13]]
| upminor 6th
| upminor 6th
| ^m6
| ^m6
Line 399: Line 590:
| 29
| 29
| 848.8
| 848.8
| [[13/8]], [[18/11]]
| mid 6th
| mid 6th
| ~6
| ~6
Line 411: Line 601:
| 30
| 30
| 878.0
| 878.0
| [[5/3]]
| downmajor 6th
| downmajor 6th
| vM6
| vM6
Line 423: Line 612:
| 31
| 31
| 907.3
| 907.3
| [[22/13]], [[27/16]], [[32/19]]
| major 6th
| major 6th
| M6
| M6
Line 435: Line 623:
| 32
| 32
| 936.6
| 936.6
| [[12/7]], [[19/11]]
| upmajor 6th
| upmajor 6th
| ^M6
| ^M6
Line 447: Line 634:
| 33
| 33
| 965.9
| 965.9
| [[7/4]], [[26/15]]
| downminor 7th
| downminor 7th
| vm7
| vm7
Line 459: Line 645:
| 34
| 34
| 995.1
| 995.1
| [[16/9]]
| minor 7th
| minor 7th
| m7
| m7
Line 471: Line 656:
| 35
| 35
| 1024.4
| 1024.4
| [[9/5]], [[20/11]], [[38/21]]
| upminor 7th
| upminor 7th
| ^m7
| ^m7
Line 483: Line 667:
| 36
| 36
| 1053.7
| 1053.7
| [[11/6]], [[24/13]]
| mid 7th
| mid 7th
| ~7
| ~7
Line 495: Line 678:
| 37
| 37
| 1082.9
| 1082.9
| [[13/7]], [[15/8]], [[28/15]]
| downmajor 7th
| downmajor 7th
| vM7
| vM7
Line 507: Line 689:
| 38
| 38
| 1112.2
| 1112.2
| [[19/10]], [[21/11]], [[36/19]], [[40/21]]
| major 7th
| major 7th
| M7
| M7
Line 519: Line 700:
| 39
| 39
| 1141.5
| 1141.5
| [[27/14]], [[35/18]], [[48/25]], [[64/33]]
| upmajor 7th
| upmajor 7th
| ^M7
| ^M7
Line 531: Line 711:
| 40
| 40
| 1170.7
| 1170.7
| [[49/25]], [[63/32]], [[96/49]], [[160/81]]
| dim 8ve
| dim 8ve
| v8
| v8
Line 543: Line 722:
| 41
| 41
| 1200.0
| 1200.0
| [[2/1]]
| perfect 8ve
| perfect 8ve
| P8
| P8
Line 553: Line 731:
| Do
| Do
|}
|}
<nowiki>*</nowiki> Based on treating 41edo as a 2.3.5.7.11.13.19 subgroup temperament; other approaches are possible.


=== Interval quality and chord names in color notation ===
=== Interval quality and chord names in color notation ===
Line 665: Line 842:
* 0-14-28 = D F# A# = Da = D aug
* 0-14-28 = D F# A# = Da = D aug


For a more complete list, see [[41edo Chord Names]] and [[Ups and downs notation #Chords and chord progressions]].
For a more complete list, see [[41edo chord names]] and [[Ups and downs notation #Chords and chord progressions]].


== Notations ==
== Notations ==
Retrieved from "https://en.xen.wiki/w/41edo"