20edo: Difference between revisions
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{{ | {{Interwiki | ||
| en = 20edo | |||
| de = | | de = | ||
| es = 20 EDO | | es = 20 EDO | ||
| ja = 20平均律 | | ja = 20平均律 | ||
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{| class="wikitable center-all right-2" | {| class="wikitable center-all right-2" | ||
|- | |- | ||
![[Degree]] | ! [[Degree]] | ||
![[Cents]] | ! [[Cents]] | ||
! Approximate ratios | ! Approximate ratios | ||
! colspan="3" |[[Ups and downs notation]] | ! colspan="3" |[[Ups and downs notation]] | ||
![[2L 7s|Balzano]]<br>Notation | ! [[2L 7s|Balzano]]<br>Notation | ||
![[6L 1s|Archeotonic]]<br>notation | ! [[6L 1s|Archeotonic]]<br>notation | ||
! Nearest<br>harmonic | ! Nearest<br>harmonic | ||
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=== | === Chord names in color notation === | ||
20edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). | 20edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). | ||
* 0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor" | * 0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor" | ||
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* 0-5-12-17 = D ^F A ^C = D^m7 = "D upminor-seven", or D ^F A ^B = D^m6 = "D upminor-six" | * 0-5-12-17 = D ^F A ^C = D^m7 = "D upminor-seven", or D ^F A ^B = D^m6 = "D upminor-six" | ||
For a more complete list, see [[ | For a more complete list, see [[Kite's ups and downs notation #Chords and chord Progressions]]. Because many intervals have several names, many chords do too. | ||
== Notation == | |||
Like [[15edo]], every note has many names. D is also C# and Eb. The major third is also a perfect fourth and a diminished fifth. | |||
=== Stein–Zimmermann–Gould notation === | |||
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows: | |||
{{Sharpness-sharp4-szg}} | |||
=== Kite's ups and downs notation === | |||
20edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat. | |||
{{Sharpness-sharp4a}} | |||
=== Sagittal notation === | |||
This notation is a superset of the notations for edos [[10edo #Sagittal notation|10]] and [[5edo #Sagittal notation|5]]. | |||
==== Evo and Revo flavors ==== | |||
{{Sagittal chart|}} | |||
==== Evo-SZ flavor ==== | |||
{{Sagittal chart|Evo-SZ}} | |||
== Approximation to JI == | |||
=== Interval mappings === | |||
{{Q-odd-limit intervals|20}} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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* [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025) | * [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025) | ||
* ''Nocturne in 20edo'' (2025) | * ''Nocturne in 20edo'' (2025) | ||
** [https://www.youtube.com/shorts/GxElRqwqz-o | ** [https://www.youtube.com/shorts/GxElRqwqz-o Lumatone view] | ||
** [https://www.youtube.com/watch?v=PMgYSG4-XaY Visualizer view] | ** [https://www.youtube.com/watch?v=PMgYSG4-XaY Visualizer view] | ||
* [https://www.youtube.com/shorts/peypGQ_h0ys ''another 20edo groove''] (2026) | * [https://www.youtube.com/shorts/peypGQ_h0ys ''another 20edo groove''] (2026) | ||
; [[E8 Heterotic]] | ; [[E8 Heterotic]] | ||
* [https:// | * [https://www.youtube.com/watch?v=GRW1GFHFIys ''T w e n t y / T w e n t y''] (2019) – synthwave, Blackwood[10] in 20edo tuning | ||
* [https:// | * [https://www.youtube.com/watch?v=zcvsvc6Hl5g "Wood"], from [https://www.youtube.com/playlist?list=PLbe8k6ZUb2FiSx8Jal1N0XjzWJM_cjgsp ''Elements''] (2019–2020) – tetracot in 20edo tuning | ||
* [https:// | * [https://www.youtube.com/watch?v=KnSSdiv_rS0 ''Decade''] (2020) – synthwave | ||
; [[Francium]] | ; [[Francium]] | ||
* [https://www.youtube.com/watch?v=rkgXkQ2D3mw ''Horrible Night Of Horror''] (2023) | * [https://www.youtube.com/watch?v=rkgXkQ2D3mw ''Horrible Night Of Horror''] (2023) | ||
* [https://www.youtube.com/watch?v=26XqPsnx16w ''Madeira Preta''] (2023) – | * [https://www.youtube.com/watch?v=26XqPsnx16w ''Madeira Preta''] (2023) – Blackwood[10] in 20edo tuning | ||
; [[Frostburn]] | |||
* [https://www.youtube.com/watch?v=nlF6al8MEuk ''Galloping Nightmares''] (2024) – synth metal | |||
; [[groundfault]] | |||
* "The Lake Reflects a Black Sky" from ''A New Dusk'' (2024) – [https://groundfco.bandcamp.com/track/the-lake-reflects-a-black-sky-29-31-20edo Bandcamp] | [https://www.youtube.com/watch?v=1bnEO8vGvbo YouTube (0:00–2:38)] – in part, the rest being in 29edo and 31edo | |||
; [[Andrew Heathwaite]] | ; [[Andrew Heathwaite]] | ||
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; [[Aaron Andrew Hunt]] | ; [[Aaron Andrew Hunt]] | ||
* [http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3 | * [http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3 ''Prelude & Fugue a3''] | ||
; [[Mandrake]] | ; [[Mandrake]] | ||
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* ''Canon on Twinkle Twinkle Little Star'' (2023–2024) | * ''Canon on Twinkle Twinkle Little Star'' (2023–2024) | ||
** [https://www.youtube.com/watch?v=6n_a9SfAjsY for organ] · [https://www.youtube.com/watch?v=UuIsIeEc-7w for baroque oboe & viola] | ** [https://www.youtube.com/watch?v=6n_a9SfAjsY for organ] · [https://www.youtube.com/watch?v=UuIsIeEc-7w for baroque oboe & viola] | ||
* [https://www.youtube.com/watch?v=5cIYrrxFN9Q ''Chacony & Fugue, in 20edo for Baroque Consort''] (2026) | |||
; [[Herman Miller]] | ; [[Herman Miller]] | ||
* ''Etude in 20-tone equal tuning'' – [https://web.archive.org/web/20070219044535/http://www.io.com/~hmiller/midi/20tet.mid midi file] [https://web.archive.org/web/20201127014350/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/20-et-Pianoteq-Schantz.mp3 play] | * ''Etude in 20-tone equal tuning'' – [https://web.archive.org/web/20070219044535/http://www.io.com/~hmiller/midi/20tet.mid midi file] [https://web.archive.org/web/20201127014350/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/20-et-Pianoteq-Schantz.mp3 play] | ||
* | * [https://soundcloud.com/morphosyntax-1/spinning-the-web ''Spinning the Web''] (2017) | ||
* | * [https://soundcloud.com/morphosyntax-1/ivari-na-taniravi ''Ivari na taniravi''] (2020) | ||
* | * [https://soundcloud.com/morphosyntax-1/drifting ''Drifting''] (2020) | ||
; [[NullPointerException Music]] | ; [[NullPointerException Music]] | ||
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* [https://soundcloud.com/overtoneshock/gods-favorite-tuning-20-edo ''God's Favorite Tuning''] (2017) – xen-pop | * [https://soundcloud.com/overtoneshock/gods-favorite-tuning-20-edo ''God's Favorite Tuning''] (2017) – xen-pop | ||
* [https://soundcloud.com/overtoneshock/you-lied-and-im-not-mentioning-your-name-20-edo ''You Lied, and I'm not Mentioning your Name''] (2017) – xen-pop | * [https://soundcloud.com/overtoneshock/you-lied-and-im-not-mentioning-your-name-20-edo ''You Lied, and I'm not Mentioning your Name''] (2017) – xen-pop | ||
== Books == | == Books == | ||