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== Intervals ==
== Intervals ==
Inconsistent intervals are in ''italics''.


{| class="wikitable center-all"
{| class="wikitable center-1 right-2"
|+ style="font-size: 105%" | Intervals of 16edo
|-
! rowspan="2" | #
! rowspan="2" | [[Cent]]s
! colspan="3" | Approximate ratios
|-
|-
! Degree
! 7-limit
! [[Cent]]s
! 13-limit
! Approximate ratios*
! No-3 approach*
|-
|-
| 0
| 0
| 0
| 0
| [[1/1]]
| 1/1
| 1/1
| 1/1
|-
|-
| 1
| 1
| 75
| 75
| 28/27, 27/26
| ''[[15/14]]'', [[21/20]], [[25/24]]
| [[22/21]], [[26/25]]
| [[28/27]], [[27/26]]
|-
|-
| 2
| 2
| 150
| 150
| 12/11, 35/32
| ''[[9/8]]'', ''[[16/15]]''
| [[11/10]], [[12/11]], [[13/12]], [[14/13]]
| 12/11, [[35/32]]
|-
|-
| 3
| 3
| 225
| 225
| [[8/7]], ''[[10/9]]'', [[28/25]]
| [[15/13]], [[25/22]]
| 8/7
| 8/7
|-
|-
| 4
| 4
| 300
| 300
| 19/16, 32/27
| [[6/5]], [[7/6]], [[25/21]]
| [[13/11]]
| [[19/16]], [[32/27]]
|-
|-
| 5
| 5
| 375
| 375
| [[5/4]], ''[[9/7]]''
| [[11/9]], [[16/13]], [[26/21]]
| 5/4, 16/13, 26/21
| 5/4, 16/13, 26/21
|-
|-
| 6
| 6
| 450
| 450
| 13/10, 35/27
| [[21/16]], [[32/25]]
| [[14/11]], [[13/10]]
| 13/10, [[35/27]]
|-
|-
| 7
| 7
| 525
| 525
| 19/14, 27/20, 35/26, 256/189
| [[4/3]]
| [[11/8]], ''[[18/13]]'', [[15/11]]
| [[19/14]], [[27/20]], [[35/26]]
|-
|-
| 8
| 8
| 600
| 600
| [[7/5]], [[10/7]], [[25/18]], [[36/25]]
|
| 7/5, 10/7
| 7/5, 10/7
|-
|-
| 9
| 9
| 675
| 675
| 28/19, 40/27, 52/35, 189/128
| [[3/2]]
| [[16/11]], ''[[13/9]]'', [[22/15]]
| [[28/19]], [[40/27]], [[52/35]]
|-
|-
| 10
| 10
| 750
| 750
| 20/13, 54/35
| [[25/16]], [[32/21]]
| [[11/7]], [[20/13]]
| 20/13, [[54/35]]
|-
|-
| 11
| 11
| 825
| 825
| [[8/5]], ''[[14/9]]''
| [[18/11]], [[13/8]], [[21/13]]
| 8/5, 13/8, 21/13
| 8/5, 13/8, 21/13
|-
|-
| 12
| 12
| 900
| 900
| 27/16, 32/19
| [[5/3]], [[12/7]], [[42/25]]
| [[22/13]]
| [[27/16]], [[32/19]]
|-
|-
| 13
| 13
| 975
| 975
| [[7/4]], ''[[9/5]]'', [[25/14]]
| [[26/15]], [[44/25]]
| 7/4
| 7/4
|-
|-
| 14
| 14
| 1050
| 1050
| 11/6, 64/35
| ''[[16/9]]'', ''[[15/8]]''
| [[20/11]], [[11/6]], [[24/13]], [[13/7]]
| [[11/6]], 64/35
|-
|-
| 15
| 15
| 1125
| 1125
| 27/14, 52/27
| ''[[28/15]]'', [[40/21]], [[48/25]]
| [[21/11]], [[25/13]]
| [[27/14]], [[52/27]]
|-
|-
| 16
| 16
| 1200
| 1200
| [[2/1]]
| 2/1
| 2/1
| 2/1
|}
|}


<nowiki />* Based on treating 16edo as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible.
<nowiki />* Based on treating 16edo as a 2.27.5.7.13.19 subgroup temperament; other approaches are possible. Odd 27 is approximated via [[direct approximation]].


== Notation ==
== Notation ==
Line 883: 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)
; {{W|Mariah Carey}}
* [https://www.youtube.com/shorts/ZUBE817kwk8 "All I Want for Christmas is You" from ''Merry Christmas''] (1994) – microtonal cover by [[Stephen Weigel]] (keyboard) and [[Clarissa]] (vocal) (2024)
=== 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)
* [https://www.youtube.com/watch?v=1pa3dztk8o0 ''nightfall''] (2024)
* [https://www.youtube.com/watch?v=1pa3dztk8o0 ''nightfall''] (2024)
; [[Nae Ayy]]
* [https://www.youtube.com/watch?v=H74psBvdeT4 ''Rambling''] (2021)
* [https://www.youtube.com/watch?v=OAhV8ol2Hbw ''a n g e r y''] (2021)
* [https://www.youtube.com/watch?v=-MboZelse90 ''Maundering''] (2021) – remix of ''Rambling''


; [[Beheld]]
; [[Beheld]]
* [https://www.youtube.com/watch?v=kzPeVB2mncc ''Nebulous vibe'']
* [https://www.youtube.com/watch?v=kzPeVB2mncc ''Nebulous vibe''] (2022)


; [[Stevie Boyes]]
; [[Stevie Boyes]]
* [https://youtu.be/jX190TYgQxc ''Tropical Carnival''] (2018)
* [https://youtu.be/jX190TYgQxc ''Tropical Carnival''] (2018)
; [[David Clifton]] (Cameron Watt Music)
* [https://www.youtube.com/watch?v=wSUlNCw9Pds ''Daydream | Meditative Ambient | 16-EDO''] (2025)
* [https://www.youtube.com/watch?v=ftW6VTdNcbg ''An Unsettling Theme | Horror | 16-EDO''] (2025)
* [https://www.youtube.com/watch?v=he47ywCgEFs ''Foreboding | Horror | 16-EDO''] (2025)


; [[City of the Asleep]]
; [[City of the Asleep]]
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* [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) &mdash; 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)


; [[E8 Heterotic]]
; [[E8 Heterotic]]
* [https://youtu.be/a8Jgb_XIj7c "Hexed"]
* [https://www.youtube.com/watch?v=a8Jgb_XIj7c ''Hexed''] (2020)


; [[Fabrizio Fiale]]
; [[Fabrizio Fiale]]
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; [[Aaron Andrew Hunt]]
; [[Aaron Andrew Hunt]]
* [https://soundcloud.com/uz1kt3k/fuga-a3-in-16et ''Fuga a3 in 16ET'']
* [https://soundcloud.com/uz1kt3k/fuga-a3-in-16et ''Fuga a3 in 16ET'']{{dead link}}


; [[Last Sacrament]]
; [[Last Sacrament]]
* [http://lastsacrament.bandcamp.com/album/enantiodromia ''Enantiodromia''] (album) (from 2013)
* [http://lastsacrament.bandcamp.com/album/enantiodromia ''Enantiodromia''] (2013) – 9-piece album
* [https://lastsacrament.bandcamp.com/album/maniacal-meditations-ep ''Maniacal Meditations''] (EP) (2013 EP)
* [https://lastsacrament.bandcamp.com/album/maniacal-meditations-ep ''Maniacal Meditations''] (2013) – 4-piece EP


; [[William Lynch]]
; [[William Lynch]]
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; [[Herman Miller]]
; [[Herman Miller]]
* [http://www.io.com/%7Ehmiller/midi/16tet.mid ''Etude in 16-tone equal tuning'']{{dead link}} [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/16tet.mp3 play]{{dead link}} ([http://soonlabel.com/xenharmonic/archives/2604 organ version]{{dead link}})
* [http://www.io.com/%7Ehmiller/midi/16tet.mid ''Etude in 16-tone equal tuning'']{{dead link}} [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/16tet.mp3 play]{{dead link}} ([http://soonlabel.com/xenharmonic/archives/2604 organ version]{{dead link}})
; [[Nae Ayy]]
* [https://www.youtube.com/watch?v=H74psBvdeT4 ''Rambling'']
* [https://www.youtube.com/watch?v=OAhV8ol2Hbw ''a n g e r y'']
* [https://www.youtube.com/watch?v=-MboZelse90 ''Maundering'']


; [[NullPointerException Music]]
; [[NullPointerException Music]]
* [https://www.youtube.com/watch?v=LXsZIbT6wpM ''Edolian - Seventhic''] (2020)
* [https://www.youtube.com/watch?v=LXsZIbT6wpM "Seventhic"] from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
* [https://www.youtube.com/watch?v=UrQPr7V9feA ''Finality''] (2021)
* [https://www.youtube.com/watch?v=UrQPr7V9feA ''Finality''] (2021)


Line 956: Line 997:


; [[Hans Straub]]
; [[Hans Straub]]
* [https://hansstraub.bandcamp.com/album/nights-in-sixteen ''Nights in Sixteen''] (full album) (2026)
* [https://hansstraub.bandcamp.com/album/nights-in-sixteen ''Nights in Sixteen''] (2026) – 10-piece album


; [[Ron Sword]]
; [[Ron Sword]]
* [https://soundcloud.com/ron-sword/mavila-fog ''The Foggy Road from Pasadena'']{{dead link}}
* [https://soundcloud.com/ron-sword/mavila-fog ''The Foggy Road from Pasadena'']{{dead link}}
; [[System jpg368]] (系统jpg368)
* [https://www.bilibili.com/video/BV1wwnA6wE6Z ''An experimental 16edo music''] (2026)


; [[Chris Vaisvil]]
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/16-ET/20120527-16-malathion.mp3 ''Malathion''] - [http://chrisvaisvil.com/?p=2358 details]
* ''Malathion'' (2012) – [https://www.chrisvaisvil.com/malathion/ blog] | [https://web.archive.org/web/20201127015023/http://micro.soonlabel.com/16-ET/20120527-16-malathion.mp3 play]{{dead link}}
* [http://micro.soonlabel.com/16-ET/20130216_16edo_vesta.mp3 ''Being of Vesta''] - [http://chrisvaisvil.com/?p=3061 details]
* ''Being of Vesta'' (2013) – [https://www.chrisvaisvil.com/being-of-vesta/ blog] | [https://web.archive.org/web/20201127013955/http://micro.soonlabel.com/16-ET/20130216_16edo_vesta.mp3 play]{{dead link}}
* [http://micro.soonlabel.com/simultaneous-tunings/20130607_thin_ice_christiane.mp3 ''Thin Ice''] - [http://chrisvaisvil.com/?p=3354 details]
* ''Thin Ice'' – [https://www.chrisvaisvil.com/thin-ice-for-alto-female-choir-harp-and-percussion-in-adaptive-ji-16-edo-and-8-edo/ blog] | [https://web.archive.org/web/20230531030223/http://micro.soonlabel.com/simultaneous-tunings/20130607_thin_ice_christiane.mp3 play]
 
; [[Anne Veinberg]]
* [https://www.youtube.com/watch?v=fm32IYUtITU ''8 vs 16 vs 32 Notes Per Octave — The 96-Tone Piano in Its Subdivision Glory''] (2026, performed on a digital recreation of [[Julián Carrillo]]'s 96-tone metamorphoser piano, using subsets [[8edo]], 16edo, [[32edo]], and then glissandos in full [[96edo]])
 
; [[Nick Vuci]]
* [https://en.xen.wiki/images/4/44/NickVuci-20220206-16edo-Prelude.mp3 ''Prelude'']
* [https://en.xen.wiki/images/9/9a/NickVuci-20231102-16edo-SofterForJ.mp3 ''Softer for J'']
* [https://en.xen.wiki/images/4/48/NickVuci-20220306-16edo-Invention.mp3 ''2-Part Invention'']
* [https://en.xen.wiki/w/User:Nick_Vuci#Modal_Studies ''Mavila Modal Studies'']
* [https://en.xen.wiki/images/c/c6/NV-20210526-16NEJI128-SerialismDubstepSketch.mp3 ''EDM based on a tone row'']
 
; [[Cameron Watt]]
* [https://www.youtube.com/watch?v=wSUlNCw9Pds ''Daydream''] (2025) – meditative ambient music
* [https://www.youtube.com/watch?v=ftW6VTdNcbg ''An Unsettling Theme''] (2025) – horror music
* [https://www.youtube.com/watch?v=he47ywCgEFs ''Foreboding''] (2025) – horror music


; [[Stephen Weigel]]
; [[Stephen Weigel]]
* [https://www.youtube.com/watch?v=0t7ZmlmrE0Q ''Shot Fades the Sum Of'']
* [https://www.youtube.com/watch?v=0t7ZmlmrE0Q ''Shot Fades the Sum Of''] (2019)
* [https://www.youtube.com/watch?v=2y01AlgOPvk ''When the Saints go Marching'']
* [https://www.youtube.com/watch?v=2y01AlgOPvk ''When the Saints go Marching''] (2019)


; [[Randy Winchester]]
; [[Randy Winchester]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/05%20-%205.%2016%20octave.mp3 Comets Over Flatland 5]{{dead link}}
* [https://web.archive.org/web/20201127013947/http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/05%20-%205.%2016%20octave.mp3 ''Comets Over Flatland 5'']


; [[Woyten]]
; [[Woyten]]
Line 978: Line 1,037:


; [[Xotla]]
; [[Xotla]]
* "Robotic Dialogue" from ''Microtones & Garden Gnomes'' (2017) [https://xotla.bandcamp.com/track/robotic-dialogue-16edo Bandcamp] | [https://youtu.be/sFxny2JNGpo?si=8MKPuIMCR_Xx1DTi YouTube]
* "Robotic Dialogue" from ''Microtones & Garden Gnomes'' (2017) – [https://xotla.bandcamp.com/track/robotic-dialogue-16edo Bandcamp] | [https://www.youtube.com/watch?v=sFxny2JNGpo YouTube]
* "Cognitive Climate" from Science Fraction (2022) [https://open.spotify.com/track/52v382I0OUotQjHo0pPoXs Spotify] | [https://xotla.bandcamp.com/track/cognitive-climate-16edo Bandcamp] | [https://youtu.be/dNBDG4wymN8?si=XGbpNkRp3qUo0Xgb YouTube]
* "Cognitive Climate" from Science Fraction (2022) – [https://open.spotify.com/track/52v382I0OUotQjHo0pPoXs Spotify] | [https://xotla.bandcamp.com/track/cognitive-climate-16edo Bandcamp] | [https://www.youtube.com/watch?v=dNBDG4wymN8 YouTube]
 
; [[User:Nick_Vuci|Nick Vuci]]
* [https://en.xen.wiki/images/4/44/NickVuci-20220206-16edo-Prelude.mp3 ''Prelude'']
* [https://en.xen.wiki/images/9/9a/NickVuci-20231102-16edo-SofterForJ.mp3 ''Softer for J'']
* [https://en.xen.wiki/images/4/48/NickVuci-20220306-16edo-Invention.mp3 ''2-Part Invention'']
* [https://en.xen.wiki/w/User:Nick_Vuci#Modal_Studies ''Mavila Modal Studies'']
* [https://en.xen.wiki/images/c/c6/NV-20210526-16NEJI128-SerialismDubstepSketch.mp3 ''EDM based on a tone row'']


; [[Zewen Senpai]]
; [[Zewen Senpai]]
* [https://www.youtube.com/watch?v=QOzBGd64Pi4 ''Simple Ambient Study No. 1'']
* [https://www.youtube.com/watch?v=QOzBGd64Pi4 ''Simple Ambient Study No. 1''] (2023)


== See also ==
== See also ==
Retrieved from "https://en.xen.wiki/w/16edo"