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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
}}
}}
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|20}}
{{ED intro}}
 
== Theory ==
== Theory ==
20edo contains smaller {{EDOs|legend=1| 2, 4, 5, and 10 }} and is part of the 5''n'' family of equal divisions of the octave. It fairly approximates the harmonics 7 (from [[5edo]]), 11, 13 & 15 (from [[10edo]]), 19 & 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15. As 7, 11, & 15 are all flat by approximately 10 cents, their flatness cancels out when combined in composite ratios, making an 11:14:15 chord (0-7-9 steps) and its utonal inversion particularly precise. Using 9/20 as the generator and treating these as the primary major and minor triads produces Balzano nonatonic and undecatonic scales, which is probably the clearest arrangement for the black/white keys on a 20 tone keyboard. Treating the generator as 11\20 creates the same scale, but the primary triads are now 13:16:19 (0-6-11 steps) and its inversion instead. The 11\20 generator is a near-optimal tuning for both [[No-threes_subgroup_temperaments#Mavericks|Mavericks]] temperament (which has a ~[[19/13]] generator) and [[Chromatic pairs#Score|Score]] temperament (which has a ~[[16/11]] generator).
20edo contains smaller edos {{EDOs| 2, 4, 5, and 10 }} and is part of the 5''n'' family of equal divisions of the octave. It fairly approximates the harmonics 7 (from [[5edo]]), 11, 13, 15 (from [[10edo]]), 19, 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20edo does a reasonably convincing approximation of harmonics 4:7:11:13:15.  
 
20edo is around the point where 5edo's 3rd harmonic starts to become notably inaccurate relative to the size of the edo (that is, it is over 25 relative cents off). It thus inherits 5edo's crude [[archy]] temperament, with its particularly accurate approximation of 7/4 at 960 cents. 
 
As 7, 11 and 15 are all flat by approximately 10 cents, their flatness cancels out when combined in composite ratios, making an 11:14:15 chord (0–7–9 steps) and its utonal inversion particularly precise. Using 9/20 as the generator and treating these as the primary major and minor triads produces [[Balzano]] nonatonic and undecatonic scales, which is probably the clearest arrangement for the black/white keys on a 20-tone keyboard.  
 
Treating the generator as 11\20 creates the same scale, but the primary triads are now 13:16:19 (0–6–11 steps) and its inversion instead. The 11\20 generator is a near-optimal tuning for both [[no-threes subgroup temperaments #Mavericks|mavericks]] temperament (which has a ~[[19/13]] generator) and [[no-threes subgroup temperaments #Score|score]] temperament (which has a ~[[16/11]] generator).


Alternately, 20edo can be used as a tuning of the [[blackwood]] temperament, combining minor and major thirds to generate a highly symmetrical decatonic scale where every note is root to a major or minor triad and 7-limit tetrad that are heavily tempered, but in a useful way, as you can easily modulate to anywhere in the small cycle of 5ths, and build extended chords that use every note in the scale without clashing. Either of these works better than trying to force 20 into a diatonic framework.
Alternately, 20edo can be used as a tuning of the [[blackwood]] temperament, combining minor and major thirds to generate a highly symmetrical decatonic scale where every note is root to a major or minor triad and 7-limit tetrad that are heavily tempered, but in a useful way, as you can easily modulate to anywhere in the small cycle of 5ths, and build extended chords that use every note in the scale without clashing. Either of these works better than trying to force 20 into a diatonic framework.


20edo also possesses a [[6L 1s]] scale generated using the narrow major second of 3\20 that is probably best interpreted as the sharp extreme of [[Tetracot_family#Tetracot|tetracot]] temperament and a [[3L 5s]] generated by 7/20 that functions as the flat end of [[squares]].
20edo also possesses a [[6L 1s]] scale generated using the narrow major second of 3\20 that is probably best interpreted as the sharp extreme of [[tetracot]] temperament and a [[3L 5s]] generated by 7/20 that functions as the flat end of [[squares]].  


=== Odd harmomics ===
Thanks to its sevenths, 20edo is an ideal tuning for its size for [[metallic harmony]].
 
=== Odd harmonics ===
{{Harmonics in equal|20}}
{{Harmonics in equal|20}}


== Intervals ==
== Intervals ==
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.
{| 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]] Notation
! [[2L 7s|Balzano]]<br>Notation
! [[6L 1s|Archeotonic]] notation
! [[6L 1s|Archeotonic]]<br>notation
! Nearest Harmonic
! Nearest<br>harmonic
|-
|-
| 0
| 0
Line 52: Line 59:
| 2
| 2
| 120
| 120
| [[15/14]], 14/13
|[[15/14]], 14/13
| dup unison, mid 2nd
| dup unison, mid 2nd
| ^^1, ~2
| ^^1, ~2
Line 92: Line 99:
| 6
| 6
| 360
| 360
| [[16/13]], 5/4
|[[16/13]], 5/4
| mid 3rd
| mid 3rd
| ~3
| ~3
Line 102: Line 109:
| 7
| 7
| 420
| 420
| [[14/11]], [[51/40]]
|[[14/11]], [[51/40]]
| downmajor 3rd
| downmajor 3rd
| vM3
| vM3
Line 122: Line 129:
| 9
| 9
| 540
| 540
| [[15/11]], 11/8
|[[15/11]], 11/8
| up-fourth
| up-fourth
| ^4
| ^4
Line 142: Line 149:
| 11
| 11
| 660
| 660
| [[22/15]], 16/11
|[[22/15]], 16/11
| down-fifth
| down-fifth
| v5
| v5
Line 172: Line 179:
| 14
| 14
| 840
| 840
| [[13/8]], 8/5
|[[13/8]], 8/5
| mid 6th
| mid 6th
| ~6
| ~6
Line 212: Line 219:
| 18
| 18
| 1080
| 1080
| [[28/15]], 15/8, 13/7
|[[28/15]], 15/8, 13/7
| mid 7th
| mid 7th
| ~7
| ~7
Line 241: Line 248:
|}
|}


=== Selected 19-limit just intervals ===
=== Chord names in color notation ===
{| class="wikitable center-all"
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).
|+[[Direct approximation]] (even if [[inconsistent]])
* 0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"
* 0-5-12 = D ^F A = D^m = "D upminor"
* 0-6-12 = D ^^F A = D~ = "D mid"
* 0-7-12 = D vF# A = Dv = "D down" or "D downmajor"
* 0-8-12 = D G A = Dsus4, or D F# A = D = "D" or "D major"
* 0-4-12-16 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six"
* 0-5-12-16 = D ^F A C = D^m,7 = "D upminor add-seven", or D ^F A B = D^m,6 = "D upminor add-six"
* 0-6-12-16 = D ^^F A C = D~,7 = "D mid add-seven", or D ^^F A B = D~,6 = "D mid add-six"
* 0-7-12-16 = D vF# A C = Dv,7 = "D down add-seven", or D vF# A B = Dv,6 = "D down add-six"
* 0-8-12-16 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six"
* 0-7-12-19 = D vF# A vC# = DvM7 = "D downmajor seven"
* 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 [[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 ==
=== Uniform maps ===
{{Uniform map|edo=20}}
 
=== Commas ===
20et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 20 32 46 56 69 74 }}.
 
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
! Interval, complement
! [[Harmonic limit|Prime<br>limit]]
! Error (abs, [[Cent|¢]])
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name(s)
|-
|-
| [[16/13]] '''[[13/8]]'''
| 3
| 0.5276
| [[256/243]]
| {{monzo| 8 -5 }}
| 90.22
| Sawa
| Blackwood comma, Pythagorean limma
|-
|-
| [[15/14]] [[28/15]]
| 5
| 0.5571
| [[16875/16384]]
| {{monzo| -14 3 4 }}
| 51.12
| Laquadyo
| Negri comma
|-
|-
| [[10/9]] [[9/5]]
| 5
| 2.4037
| [[34171875/33554432|(16 digits)]]
| {{monzo| -25 7 6 }}
| 31.57
| Lala-tribiyo
| Ampersand comma
|-
|-
| '''[[19/16]]''' [[32/19]]
| 5
| 2.4869
| [[2048/2025]]
| {{monzo| 11 -4 -2 }}
| 19.55
| Sagugu
| Diaschisma
|-
|-
| [[14/11]] [[11/7]]
| 7
| 2.4920
| [[525/512]]
| {{monzo| -9 1 2 1 }}
| 43.41
| Lazoyoyo
| Avicennma, Avicenna's enharmonic diesis
|-
|-
| [[19/13]] [[26/19]]
| 7
| 3.0146
| [[49/48]]
| {{monzo| -4 -1 0 2 }}
| 35.70
| Zozo
| Semaphoresma, slendro diesis
|-
|-
| [[15/11]] [[22/15]]
| 7
| 3.0492
| [[50/49]]
| {{monzo| 1 0 2 -2 }}
| 34.98
| Biruyo
| Jubilisma, tritonic diesis
|-
|-
| [[15/13]] [[26/15]]
| 7
| 7.7410
| [[686/675]]
| {{monzo| 1 -3 -2 3 }}
| 27.99
| Trizo-agugu
| Senga
|-
|-
| [[16/15]] [[15/8]]
| 7
| 8.2687
| [[64/63]]
| {{monzo| 6 -2 0 -1 }}
| 27.26
| Ru
| Septimal comma, Archytas' comma, Leipziger Komma
|-
|-
| [[14/13]] [[13/7]]
| 7
| 8.2982
| <abbr title="854296875/843308032">(18 digits)</abbr>
| {{monzo| -10 7 8 -7 }}
| 22.41
| Lasepru-aquadbiyo
| [[Blackjackisma]]
|-
|-
| [[8/7]] '''[[7/4]]'''
| 7
| 8.8259
| [[1029/1024]]
| {{monzo| -10 1 0 3 }}
| 8.43
| Latrizo
| Gamelisma
|-
|-
| [[13/11]] [[22/13]]
| 7
| 10.7902
| [[225/224]]
| {{monzo| -5 2 2 -1 }}
| 7.71
| Ruyoyo
| Marvel comma, septimal kleisma
|-
|-
| '''[[11/8]]''' [[16/11]]
| 7
| 11.3179
| [[16875/16807]]
| {{monzo| 0 3 4 -5 }}
| 6.99
| Quinru-aquadyo
| Mirkwai comma
|-
|-
| [[11/9]] [[18/11]]
| 7
| 12.5920
| <abbr title="578509309952/576650390625">(24 digits)</abbr>
| {{monzo| 11 -10 -10 10 }}
| 5.57
| Saquinbizogu
| [[Linus comma]]
|-
|-
| [[11/10]] [[20/11]]
| 7
| 14.9957
| [[2401/2400]]
| {{monzo| -5 -1 -2 4 }}
| 0.72
| Bizozogu
| Breedsma
|-
|-
| '''[[17/16]]''' [[32/17]]
| 11
| 15.0445
| [[121/120]]
| {{monzo| -3 -1 -1 0 2 }}
| 14.37
| Lologu
| Biyatisma
|-
|-
| [[9/7]] [[14/9]]
| 13
| 15.0840
| [[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap comma, biome comma
|-
|-
| [[6/5]] [[5/3]]
| 13
| 15.6412
| [[676/675]]
|-
| {{monzo| 2 -3 -2 0 0 2 }}
| [[7/5]] [[10/7]]
| 2.56
| 17.4878
| Bithogu
|-
| Island comma, parizeksma
| '''[[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
|}
|}
<references />


== Chord names ==
== Instruments ==
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).
* Like other members of the 5EDO family, 20-EDO lends itself well to guitar (and other fretted string instruments), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an "E" chord would be 0-4-4-2-0-0 (low to high), an "A" chord would be 0-0-4-4-2-0, and a "D" chord would be 2-0-0-4-4-2.
* 0-4-12 = D E A = Dsus2 = "D sus 2", or D F A = Dm = "D minor"
* [[Lumatone mapping for 20edo]]
* 0-5-12 = D ^F A = D^m = "D upminor"
* 0-6-12 = D ^^F A = D~ = "D mid"
* 0-7-12 = D vF# A = Dv = "D down" or "D downmajor"
* 0-8-12 = D G A = Dsus4, or D F# A = D = "D" or "D major"
* 0-4-12-16 = D F A C = Dm7 = "D minor seven", or D F A B = Dm6 = "D minor six"
* 0-5-12-16 = D ^F A C = D^m,7 = "D upminor add-seven", or D ^F A B = D^m,6 = "D upminor add-six"
* 0-6-12-16 = D ^^F A C = D~,7 = "D mid add-seven", or D ^^F A B = D~,6 = "D mid add-six"
* 0-7-12-16 = D vF# A C = Dv,7 = "D down add-seven", or D vF# A B = Dv,6 = "D down add-six"
* 0-8-12-16 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D six"
* 0-7-12-19 = D vF# A vC# = DvM7 = "D downmajor seven"
* 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.


== Modes ==
== Modes ==
Line 347: Line 443:
|-
|-
| 3 1 3 1 3 1 3 1 3 1
| 3 1 3 1 3 1 3 1 3 1
| Blackwood Major Decatonic [[5L_5s|(bi-equal decatonic]], according to the [[MOSNamingScheme|MOS naming scheme]])
| Blackwood Major Decatonic [[5L_5s|(pentawood]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
|-
| 1 3 1 3 1 3 1 3 1 3
| 1 3 1 3 1 3 1 3 1 3
| Blackwood Minor Decatonic (also bi-equal decatonic)
| Blackwood Minor Decatonic (also pentawood)
|-
|-
| 2 1 1 2 1 1 2 1 1 2 1 1
| 2 1 1 2 1 1 2 1 1 2 1 1
Line 362: Line 458:
|-
|-
|2 3 2 2 2 3 2 2 2
|2 3 2 2 2 3 2 2 2
| Balzano Nine-tone ([[2L_7s|fair mavila]], [[score9]]) <ref>[https://www.jstor.org/stable/833490?seq=1 Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach]</ref>
| 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
|2 2 2 2 1 2 2 2 2 2 1
Line 368: Line 464:
|-
|-
|2 2 2 3 2 2 2 3 2
|2 2 2 3 2 2 2 3 2
|Balzano Nine-tone inverse (also fair mavila, score9)
|Balzano Nine-tone inverse (also balzano, score9)
|-
|-
|1 2 2 2 2 2 1 2 2 2 2
|1 2 2 2 2 2 1 2 2 2 2
Line 374: Line 470:
|-
|-
| 2 3 2 3 2 3 2 3
| 2 3 2 3 2 3 2 3
| Octatonic ([[4L_4s|diminished]], according to the [[MOSNamingScheme|MOS naming scheme]])
| Octatonic ([[4L_4s|tetrawood]], according to the [[MOSNamingScheme|MOS naming scheme]])
|-
|-
|3 2 3 2 3 2 3 2
|3 2 3 2 3 2 3 2
Line 404: Line 500:
|-
|-
|3 3 3 3 3 3 2
|3 3 3 3 3 3 2
|Major quasi-equal Heptatonic ([[6L_1s|archaeotonic or Grumpy heptatonic]])
|Major quasi-equal Heptatonic ([[6L_1s|archaeotonic]])
|-
|-
|3 2 3 3 3 3 3
|3 2 3 3 3 3 3
Line 432: Line 528:
|5 2 2 5 2 2 2
|5 2 2 5 2 2 2
|[[score7]] ([[2L_5s|mavila, anti-diatonic]])
|[[score7]] ([[2L_5s|mavila, anti-diatonic]])
|}
<references />
== Regular temperament properties ==
=== Uniform maps ===
{{Uniform map|13|19.5|20.5}}
=== Commas ===
20 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 20 32 46 56 69 74 }}.)
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
![[Harmonic limit|Prime<br>Limit]]
![[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
![[Monzo]]
![[Cent]]s
! [[Color name]]
! Name(s)
|-
|3
|[[256/243]]
|{{monzo| 8 -5 }}
|90.22
|Sawa
|[[Limma]], Pythagorean Minor 2nd
|-
|-
|5
|4 1 3 2 2 3 1 4
|[[16875/16384]]
|[[polymicrotonal|8-tone 4&5edo scale]]
|{{monzo| -14 3 4 }}
| 51.12
|Laquadyo
|Negri Comma, Double Augmentation Diesis
|-
| 5
|[[34171875/33554432|(16 digits)]]
|{{monzo| -25 7 6 }}
|31.57
|Lala-tribiyo
|[[Ampersand]], Ampersand's Comma
|-
| 5
| [[2048/2025]]
|
{{monzo| 11 -4 -2 }}
|19.55
|Sagugu
|Diaschisma
|-
|7
|[[525/512]]
|{{monzo| -9 1 2 1 }}
|43.41
|Lazoyoyo
|Avicennma, Avicenna's Enharmonic Diesis
|-
|7
|[[49/48]]
|{{monzo| -4 -1 0 2 }}
|35.70
|Zozo
|Slendro Diesis
|-
|7
|[[50/49]]
|{{monzo| 1 0 2 -2 }}
|34.98
|Biruyo
|Tritonic Diesis, Jubilisma
|-
|7
|[[686/675]]
|{{monzo| 1 -3 -2 3 }}
|27.99
|Trizo-agugu
|Senga
|-
| 7
|[[64/63]]
|{{monzo| 6 -2 0 -1 }}
|27.26
|Ru
|Septimal Comma, Archytas' Comma, Leipziger Komma
|-
|7
|<abbr title="854296875/843308032">(18 digits)</abbr>
| {{monzo| -10 7 8 -7 }}
|22.41
|Lasepru-aquadbiyo
|[[Blackjackisma]]
|-
|7
|[[1029/1024]]
|{{monzo| -10 1 0 3 }}
|8.43
|Latrizo
|Gamelisma
|-
|7
|[[225/224]]
|{{monzo| -5 2 2 -1 }}
|7.71
|Ruyoyo
|Septimal Kleisma, Marvel Comma
|-
|7
|[[16875/16807]]
|{{monzo| 0 3 4 -5 }}
| 6.99
|Quinru-aquadyo
|Mirkwai
|-
|7
| <abbr title="578509309952/576650390625">(24 digits)</abbr>
|{{monzo| 11 -10 -10 10 }}
|5.57
|Saquinbizogu
|[[Linus comma|Linus]]
|-
| 7
|[[2401/2400]]
|{{monzo| -5 -1 -2 4 }}
|0.72
|Bizozogu
|Breedsma
|-
|11
|[[121/120]]
|{{monzo| -3 -1 -1 0 2 }}
| 14.37
| Lologu
|Biyatisma
|-
|13
|[[91/90]]
|{{monzo| -1 -2 -1 1 0 1 }}
| 19.13
|Thozogu
|Superleap
|-
|13
|[[676/675]]
|{{monzo| 2 -3 -2 0 0 2 }}
|2.56
|Bithogu
|Parizeksma
|}
|}
<references />
<references />
== Instruments ==
* Like other members of the 5EDO family, 20-EDO lends itself well to guitar (and other fretted string instruments), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an "E" chord would be 0-4-4-2-0-0 (low to high), an "A" chord would be 0-0-4-4-2-0, and a "D" chord would be 2-0-0-4-4-2.
* [[Lumatone mapping for 20edo]]
== Books ==
{{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}}


== Music ==
== Music ==
{{Catrel| 20edo tracks }}
{{Catrel| 20edo tracks }}
; [[Ambient Esoterica]]
* [https://www.youtube.com/watch?v=xRNZJhFcoL8 ''20EDO Tablet of Union | Enochian Vision Magick''] (2025)


; [[Beheld]]
; [[Beheld]]
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* [https://www.youtube.com/watch?v=duJHUo_ACgk ''Composition for cello and clavier in 20-tone equal temperament''] (2017)
* [https://www.youtube.com/watch?v=duJHUo_ACgk ''Composition for cello and clavier in 20-tone equal temperament''] (2017)
* [https://www.youtube.com/watch?v=u6k4lgCnHqs ''5 compositions for violin and clavier in 20-tone equal temperament''] (2017)
* [https://www.youtube.com/watch?v=u6k4lgCnHqs ''5 compositions for violin and clavier in 20-tone equal temperament''] (2017)
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/-GTh0EyxCd0 ''20edo''] (2023)
* [https://www.youtube.com/shorts/bqYA9flwL_g ''20edo prelude''] (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/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 ==
{{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"