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20edo: Difference between revisions

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{{interwiki
{{Interwiki
| en = 20edo
| de =
| de =
| en = 20edo
| 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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|}
|}


=== Selected 19-limit just intervals ===
=== Chord names in color notation ===
{| class="wikitable center-all"
|+[[Direct approximation]] (even if [[inconsistent]])
|-
! Interval, complement
! Error (abs, [[Cent|¢]])
|-
| [[16/13]] '''[[13/8]]'''
| 0.5276
|-
| [[15/14]] [[28/15]]
| 0.5571
|-
| [[10/9]] [[9/5]]
| 2.4037
|-
| '''[[19/16]]''' [[32/19]]
| 2.4869
|-
| [[14/11]] [[11/7]]
| 2.4920
|-
| [[19/13]] [[26/19]]
| 3.0146
|-
| [[15/11]] [[22/15]]
| 3.0492
|-
| [[15/13]] [[26/15]]
| 7.7410
|-
| [[16/15]] [[15/8]]
| 8.2687
|-
| [[14/13]] [[13/7]]
| 8.2982
|-
| [[8/7]] '''[[7/4]]'''
| 8.8259
|-
| [[13/11]] [[22/13]]
| 10.7902
|-
| '''[[11/8]]''' [[16/11]]
| 11.3179
|-
| [[11/9]] [[18/11]]
| 12.5920
|-
| [[11/10]] [[20/11]]
| 14.9957
|-
| '''[[17/16]]''' [[32/17]]
| 15.0445
|-
| [[9/7]] [[14/9]]
| 15.0840
|-
| [[6/5]] [[5/3]]
| 15.6412
|-
| [[7/5]] [[10/7]]
| 17.4878
|-
| '''[[3/2]]''' [[4/3]]
| 18.0449
|-
| [[13/12]] [[24/13]]
| 18.5726
|-
| [[9/8]] [[16/9]]
| 23.9100
|-
| '''[[5/4]]''' [[8/5]]
| 26.3137
|-
| [[7/6]] [[12/7]]
| 26.8709
|-
| [[12/11]] [[11/6]]
| 29.36294
|}
 
== Notation ==
=== Ups and downs notation ===
Like [[15edo]], every note has many names. D is also C# and Eb. The major 3rd is also a perfect 4th and a dim 5th. 20edo can be notated with [[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}}
 
[[Alternative symbols for ups and downs notation]] uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp4}}
 
=== 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 ====
<imagemap>
File:20-EDO_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 351 0 511 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 351 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:20-EDO_Sagittal.svg]]
</imagemap>
 
==== Evo-SZ flavor ====
<imagemap>
File:20-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 327 0 487 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 327                                                                                                                                                                                                                                                                                                                                                                                                                                                          106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:20-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
 
== Chord names ==
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 [[Ups and downs notation#Chords and Chord Progressions|Ups and downs notation - Chords and Chord Progressions]]. Because many intervals have several names, many chords do too.
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|}}


== Modes ==
==== Evo-SZ flavor ====
20 tone equal modes:
{{Sagittal chart|Evo-SZ}}


{| class="wikitable"
== Approximation to JI ==
|-
=== Interval mappings ===
| 3 1 3 1 3 1 3 1 3 1
{{Q-odd-limit intervals|20}}
| Blackwood Major Decatonic [[5L_5s|(pentawood]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
| 1 3 1 3 1 3 1 3 1 3
| Blackwood Minor Decatonic (also pentawood)
|-
| 2 1 1 2 1 1 2 1 1 2 1 1
|Blackwood Major Pentadecatonic (also tri-equal pentadecatonic)
|-
|1 1 2 1 1 2 1 1 2 1 1 2
|Blackwood Diminished Pentadecatonic (also tri-equal pentadecatonic)
|-
|1 2 1 1 2 1 1 2 1 1 2 1
|Blackwood Minor Pentadecatonic (also tri-equal pentadecatonic)
|-
|2 3 2 2 2 3 2 2 2
| Balzano Nine-tone ([[2L_7s|balzano]], [[score9]]) <ref>[https://www.jstor.org/stable/833490?seq=1 Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach]</ref>
|-
|2 2 2 2 1 2 2 2 2 2 1
|Balzano Eleven-tone, Agmon Diatonic DS4, [[score11]]
|-
|2 2 2 3 2 2 2 3 2
|Balzano Nine-tone inverse (also balzano, score9)
|-
|1 2 2 2 2 2 1 2 2 2 2
|Balzano Eleven-tone inverse (also score11)
|-
| 2 3 2 3 2 3 2 3
| Octatonic ([[4L_4s|tetrawood]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
|3 2 3 2 3 2 3 2
|Diminished
|-
|2 2 1 2 2 1 2 2 1 2 2 1
|Dodecatonic
|-
|2 1 2 2 1 2 2 1 2 2 1 2
|Diminished
|-
|1 2 2 1 2 2 1 2 2 1 2 2
|Diminished
|-
|4 3 1 4 3 4 1
|Twenty-tone "Major"
|-
|4 1 3 4 1 4 3
|Twenty-tone "Minor"
|-
|2 2 1 2 1 2 2 1 2 2 2 1
|Twelve-tone Chromatic
|-
|2 2 2 2 1 2 2 2 2 1 2
|Zweifel Major
|-
| 2 1 2 2 2 2 2 1 2 2 2
| Zweifel Natural Minor
|-
|3 3 3 3 3 3 2
|Major quasi-equal Heptatonic ([[6L_1s|archaeotonic]])
|-
|3 2 3 3 3 3 3
|Minor quasi-equal Heptatonic (also archaeotonic)
|-
|2 2 1 2 1 2 1 2 1 2 1 2 1
|Major quasi-equal Triskaidecatonic (Grumpy triskaidecatonic)
|-
|2 1 2 1 2 1 2 1 2 1 2 1 2
|Minor quasi-equal Triskaidecatonic A
|-
|1 2 1 2 1 2 1 2 1 2 1 2 2
|Minor quasi-equal Triskaidecatonic B
|-
|2 1 2 1 2 1 2 1 2 1 2 2 1
|Minor quasi-equal Triskaidecatonic C
|-
|3 2 2 2 2 3 2 2 2
|Rothenberg Generalized Diatonic (also [[2L 7s|balzano]] or [[score9]])
|-
| 3 4 1 4 3 3 2
|Stearns Major
|-
|7 2 7 2 2
|[[score5]] [[2L_3s|pentic, classic pentatonic]]
|-
|5 2 2 5 2 2 2
|[[score7]] ([[2L_5s|mavila, anti-diatonic]])
|}
<references />


== Regular temperament properties ==
== Regular temperament properties ==
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* [[Lumatone mapping for 20edo]]
* [[Lumatone mapping for 20edo]]


== Books ==
== Modes ==
{{External Image| http://ronsword.com/images/20_tet_Coversm.jpg {{dead link}} }}
20 tone equal modes:
[http://www.ronsword.com/ "Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more] by [[Ron Sword]] {{dead link}}
 
{| class="wikitable"
|-
| 3 1 3 1 3 1 3 1 3 1
| Blackwood Major Decatonic [[5L_5s|(pentawood]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
| 1 3 1 3 1 3 1 3 1 3
| Blackwood Minor Decatonic (also pentawood)
|-
| 2 1 1 2 1 1 2 1 1 2 1 1
|Blackwood Major Pentadecatonic (also tri-equal pentadecatonic)
|-
|1 1 2 1 1 2 1 1 2 1 1 2
|Blackwood Diminished Pentadecatonic (also tri-equal pentadecatonic)
|-
|1 2 1 1 2 1 1 2 1 1 2 1
|Blackwood Minor Pentadecatonic (also tri-equal pentadecatonic)
|-
|2 3 2 2 2 3 2 2 2
| Balzano Nine-tone ([[2L_7s|balzano]], [[score9]]) <ref>[https://www.jstor.org/stable/833490?seq=1 Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach]</ref>
|-
|2 2 2 2 1 2 2 2 2 2 1
|Balzano Eleven-tone, Agmon Diatonic DS4, [[score11]]
|-
|2 2 2 3 2 2 2 3 2
|Balzano Nine-tone inverse (also balzano, score9)
|-
|1 2 2 2 2 2 1 2 2 2 2
|Balzano Eleven-tone inverse (also score11)
|-
| 2 3 2 3 2 3 2 3
| Octatonic ([[4L_4s|tetrawood]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
|3 2 3 2 3 2 3 2
|Diminished
|-
|2 2 1 2 2 1 2 2 1 2 2 1
|Dodecatonic
|-
|2 1 2 2 1 2 2 1 2 2 1 2
|Diminished
|-
|1 2 2 1 2 2 1 2 2 1 2 2
|Diminished
|-
|4 3 1 4 3 4 1
|Twenty-tone "Major"
|-
|4 1 3 4 1 4 3
|Twenty-tone "Minor"
|-
|2 2 1 2 1 2 2 1 2 2 2 1
|Twelve-tone Chromatic
|-
|2 2 2 2 1 2 2 2 2 1 2
|Zweifel Major
|-
| 2 1 2 2 2 2 2 1 2 2 2
| Zweifel Natural Minor
|-
|3 3 3 3 3 3 2
|Major quasi-equal Heptatonic ([[6L_1s|archaeotonic]])
|-
|3 2 3 3 3 3 3
|Minor quasi-equal Heptatonic (also archaeotonic)
|-
|2 2 1 2 1 2 1 2 1 2 1 2 1
|Major quasi-equal Triskaidecatonic (Grumpy triskaidecatonic)
|-
|2 1 2 1 2 1 2 1 2 1 2 1 2
|Minor quasi-equal Triskaidecatonic A
|-
|1 2 1 2 1 2 1 2 1 2 1 2 2
|Minor quasi-equal Triskaidecatonic B
|-
|2 1 2 1 2 1 2 1 2 1 2 2 1
|Minor quasi-equal Triskaidecatonic C
|-
|3 2 2 2 2 3 2 2 2
|Rothenberg Generalized Diatonic (also [[2L 7s|balzano]] or [[score9]])
|-
| 3 4 1 4 3 3 2
|Stearns Major
|-
|7 2 7 2 2
|[[score5]] [[2L_3s|pentic, classic pentatonic]]
|-
|5 2 2 5 2 2 2
|[[score7]] ([[2L_5s|mavila, anti-diatonic]])
|-
|4 1 3 2 2 3 1 4
|[[polymicrotonal|8-tone 4&5edo scale]]
|}
<references />


== Music ==
== Music ==
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; [[Bryan Deister]]
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/-GTh0EyxCd0 ''20edo''] (2023)
* [https://www.youtube.com/shorts/bqYA9flwL_g ''20edo prelude''] (2025)
* [https://www.youtube.com/shorts/bqYA9flwL_g ''20edo prelude''] (2025)
* [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025)
* [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025)
* ''Nocturne in 20edo'' (2025)
** [https://www.youtube.com/shorts/GxElRqwqz-o Lumatone view]
** [https://www.youtube.com/watch?v=PMgYSG4-XaY Visualizer view]
* [https://www.youtube.com/shorts/peypGQ_h0ys ''another 20edo groove''] (2026)


; [[E8 Heterotic]]
; [[E8 Heterotic]]
* [https://youtu.be/GRW1GFHFIys?si=l-I64VcbItcZkvZz ''T w e n t y / T w e n t y''] (2019) – synthwave, blackwood[10] in 20edo tuning
* [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://youtu.be/zcvsvc6Hl5g?si=H7i3kia2XKxUYt_U "Elements - Wood"] from ''Elements'' (2019–2020) – tetracot in 20edo tuning
* [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://youtu.be/KnSSdiv_rS0?si=d1DI3fTnrEIJvsCQ ''Decade''] (2020) – synthwave
* [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) – blackwood[10] in 20edo
* [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 20ET — ''Prelude &amp; Fugue a3'']
* [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/spinning-the-web ''Spinning the Web''] (2017)
* ''[https://soundcloud.com/morphosyntax-1/ivari-na-taniravi Ivari na taniravi]'' (2020)
* [https://soundcloud.com/morphosyntax-1/ivari-na-taniravi ''Ivari na taniravi''] (2020)
* ''[https://soundcloud.com/morphosyntax-1/drifting Drifting]'' (2020)
* [https://soundcloud.com/morphosyntax-1/drifting ''Drifting''] (2020)


; [[NullPointerException Music]]
; [[NullPointerException Music]]
Line 698: Line 619:
* [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


; [[User:Frostburn|Frostburn]]
== Books ==
* [https://youtu.be/nlF6al8MEuk ''Galloping Nightmares''] (2024) - synth metal
{{External Image| http://ronsword.com/images/20_tet_Coversm.jpg {{dead link}} }}
[http://www.ronsword.com/ "Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more] by [[Ron Sword]] {{dead link}}


[[Category:Listen]]
[[Category:Listen]]
[[Category:Twentuning]]
[[Category:Twentuning]]
[[Category:Todo:add rank 2 temperaments table]]
[[Category:Todo:add rank 2 temperaments table]]
Retrieved from "https://en.xen.wiki/w/20edo"