Xenharmonic Wiki

16edo: Difference between revisions

← Older edit
VisualWikitext
Overthink (talk | contribs)
autopatrolled
2,974 edits
→Intervals: add simpler ratios
Francium (talk | contribs)
4,840 edits
 
(5 intermediate revisions by 3 users not shown)
Line 40: Line 40:
Inconsistent intervals are in ''italics''.
Inconsistent intervals are in ''italics''.


{| class="wikitable center-all right-2"
{| class="wikitable center-1 right-2"
|-
|-
! rowspan="2" | Degree
! rowspan="2" | #
! rowspan="2" | [[Cent]]s
! rowspan="2" | [[Cent]]s
! colspan="3" | Approximate ratios
! colspan="3" | Approximate ratios
|-
|-
! [[2.3.5.11 subgroup|2.3.5.11]] mavila
! 7-limit
! 13-limit armodue
! 13-limit
! JI approximation*
! No-3 approach*
|-
|-
| 0
| 0
Line 58: Line 58:
| 1
| 1
| 75
| 75
| [[25/24]]
| ''[[15/14]]'', [[21/20]], [[25/24]]
| ''[[15/14]]'', [[21/20]], [[22/21]], [[26/25]]
| [[22/21]], [[26/25]]
| [[28/27]], [[27/26]]
| [[28/27]], [[27/26]]
|-
|-
| 2
| 2
| 150
| 150
| ''[[9/8]]'', [[11/10]], [[12/11]], ''[[16/15]]''
| ''[[9/8]]'', ''[[16/15]]''
| [[13/12]], [[14/13]]
| [[11/10]], [[12/11]], [[13/12]], [[14/13]]
| 12/11, [[35/32]]
| 12/11, [[35/32]]
|-
|-
| 3
| 3
| 225
| 225
| ''[[10/9]]'', [[25/22]]
| [[8/7]], ''[[10/9]]'', [[28/25]]
| [[8/7]], [[15/13]], [[28/25]]
| [[15/13]], [[25/22]]
| 8/7
| 8/7
|-
|-
| 4
| 4
| 300
| 300
| [[6/5]]
| [[6/5]], [[7/6]], [[25/21]]
| [[7/6]], [[13/11]], [[25/21]]
| [[13/11]]
| [[19/16]], [[32/27]]
| [[19/16]], [[32/27]]
|-
|-
| 5
| 5
| 375
| 375
| [[5/4]], [[11/9]]
| [[5/4]], ''[[9/7]]''
| ''[[9/7]]'', [[16/13]], [[26/21]]
| [[11/9]], [[16/13]], [[26/21]]
| 5/4, 16/13, 26/21
| 5/4, 16/13, 26/21
|-
|-
| 6
| 6
| 450
| 450
| [[32/25]]
| [[21/16]], [[32/25]]
| [[14/11]], [[13/10]], [[21/16]]
| [[14/11]], [[13/10]]
| 13/10, [[35/27]]
| 13/10, [[35/27]]
|-
|-
| 7
| 7
| 525
| 525
| [[4/3]], [[11/8]], [[15/11]]
| [[4/3]]
| ''[[18/13]]''
| [[11/8]], ''[[18/13]]'', [[15/11]]
| [[19/14]], [[27/20]], [[35/26]]
| [[19/14]], [[27/20]], [[35/26]]
|-
|-
| 8
| 8
| 600
| 600
| [[25/18]], [[36/25]]
| [[7/5]], [[10/7]], [[25/18]], [[36/25]]
| [[7/5]], [[10/7]]
|
| 7/5, 10/7
| 7/5, 10/7
|-
|-
| 9
| 9
| 675
| 675
| [[3/2]], [[16/11]], [[22/15]]
| [[3/2]]
| ''[[13/9]]''
| [[16/11]], ''[[13/9]]'', [[22/15]]
| [[28/19]], [[40/27]], [[52/35]]
| [[28/19]], [[40/27]], [[52/35]]
|-
|-
| 10
| 10
| 750
| 750
| [[25/16]]
| [[25/16]], [[32/21]]
| [[11/7]], [[20/13]], [[32/21]]
| [[11/7]], [[20/13]]
| 20/13, [[54/35]]
| 20/13, [[54/35]]
|-
|-
| 11
| 11
| 825
| 825
| [[8/5]], [[18/11]]
| [[8/5]], ''[[14/9]]''
| ''[[14/9]]'', [[13/8]], [[21/13]]
| [[18/11]], [[13/8]], [[21/13]]
| 8/5, 13/8, 21/13
| 8/5, 13/8, 21/13
|-
|-
| 12
| 12
| 900
| 900
| [[5/3]]
| [[5/3]], [[12/7]], [[42/25]]
| [[12/7]], [[22/13]], [[42/25]]
| [[22/13]]
| [[27/16]], [[32/19]]
| [[27/16]], [[32/19]]
|-
|-
| 13
| 13
| 975
| 975
| ''[[9/5]]'', [[44/25]]
| [[7/4]], ''[[9/5]]'', [[25/14]]
| [[7/4]], [[26/15]], [[25/14]]
| [[26/15]], [[44/25]]
| 7/4
| 7/4
|-
|-
| 14
| 14
| 1050
| 1050
| ''[[16/9]]'', [[20/11]], [[11/6]], ''[[15/8]]''
| ''[[16/9]]'', ''[[15/8]]''
| [[24/13]], [[13/7]]
| [[20/11]], [[11/6]], [[24/13]], [[13/7]]
| [[11/6]], 64/35
| [[11/6]], 64/35
|-
|-
| 15
| 15
| 1125
| 1125
| [[48/25]]
| ''[[28/15]]'', [[40/21]], [[48/25]]
| ''[[28/15]]'', [[40/21]], [[21/11]], [[25/13]]
| [[21/11]], [[25/13]]
| [[27/14]], [[52/27]]
| [[27/14]], [[52/27]]
|-
|-
Line 149: Line 149:
| 1200
| 1200
| [[2/1]]
| [[2/1]]
| [[2/1]]
| 2/1
| [[2/1]]
| 2/1
|}
|}


Line 921: Line 921:
{{Catrel| 16edo tracks }}
{{Catrel| 16edo tracks }}


=== Modern renderings ===
; Caramella Girls
* [https://www.youtube.com/watch?v=Zl3ha6I9HN0 ''Caramelldansen''] (2003) – arranged for two pianos, rendered by [[Francium]] (2026)
=== 21st century ===
; [[Abnormality]]
; [[Abnormality]]
* [https://www.youtube.com/watch?v=zao6E8GdQh0 ''it's not not opposite day''] (2023)
* [https://www.youtube.com/watch?v=zao6E8GdQh0 ''it's not not opposite day''] (2023)
Line 943: Line 948:
* [https://www.youtube.com/shorts/H-abpioYj5k ''improv in 16edo''] (2022)
* [https://www.youtube.com/shorts/H-abpioYj5k ''improv in 16edo''] (2022)
* [https://www.youtube.com/shorts/IfVvjoRqqNk ''16edo jam''] (2025)
* [https://www.youtube.com/shorts/IfVvjoRqqNk ''16edo jam''] (2025)
* [https://www.youtube.com/shorts/PXiWkZ9wDdU ''16edo waltz''] (2025)
* [https://www.youtube.com/shorts/PXiWkZ9wDdU ''16edo waltz''] (2025) — includes Lumatone view
* [https://www.youtube.com/watch?v=cUgbkkIvy0g ''Waltz in 16edo''] (2025) — this is the full version of the ''16edo waltz'' above
* [https://www.youtube.com/watch?v=cUgbkkIvy0g ''Waltz in 16edo''] (2025) — this is the full version of the ''16edo waltz'' above
* [https://www.youtube.com/shorts/UA97cjUN5eE ''Doubt by Bryan Deister (microtonal 16edo snippet)''] (2025)
* [https://www.youtube.com/shorts/UA97cjUN5eE ''Doubt by Bryan Deister (microtonal 16edo snippet)''] (2025)
Line 1,007: Line 1,012:
* [https://www.youtube.com/watch?v=0t7ZmlmrE0Q ''Shot Fades the Sum Of'']
* [https://www.youtube.com/watch?v=0t7ZmlmrE0Q ''Shot Fades the Sum Of'']
* [https://www.youtube.com/watch?v=2y01AlgOPvk ''When the Saints go Marching'']
* [https://www.youtube.com/watch?v=2y01AlgOPvk ''When the Saints go Marching'']
; Stephen Weigel (on 16edo keyboard) with [[Clarissa]] (vocal)
* [https://www.youtube.com/shorts/ZUBE817kwk8 Microtonal cover of ''All I Want for Christmas is You"'' by Mariah Carey] (2024)


; [[Randy Winchester]]
; [[Randy Winchester]]
Retrieved from "https://en.xen.wiki/w/16edo"