20edo: Difference between revisions

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__FORCETOC__
__FORCETOC__
-----
== Compositions ==
* [https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo Underwater Spontaniety] (lo-fi ambient) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [https://soundcloud.com/overtoneshock/gods-favorite-tuning-20-edo God's Favorite Tuning] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [https://soundcloud.com/overtoneshock/you-lied-and-im-not-mentioning-your-name-20-edo?in=overtoneshock/sets/xenharmonic-microtonal You Lied, and I'm not Mentioning your Name] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [http://www.io.com/%7Ehmiller/midi/20tet.mid Etude in 20-tone equal tuning] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/20-et-Pianoteq-Schantz.mp3 play] by [[Herman Miller]]
* [http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3 20ET — Prelude & Fugue a3] by [[Aaron Hunt]]
* [http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=933696 We Call It Sharing Breath] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wecallitsharingbreathin20tet.mp3 play] by [[Andrew Heathwaite]]
* [http://chrisvaisvil.com/the-walrus-and-the-carpenter-from-bethan-reads-in-20edo/ The Walrus and the Carpenter] by[[Chris Vaisvil]] and Bethan Mathis
* [http://chrisvaisvil.com/clean-20-edo-electric-guitar-improvisation/ 20 edo Electric Guitar Improvisation] by[[Chris Vaisvil]]
* [http://chrisvaisvil.com/gobekli-tepe-20-edo-guitar-solo/ Göbekli Tepe (20 edo guitar solo)] by [[Chris Vaisvil]]
* [http://chrisvaisvil.com/a-paradigm-shift-20-edo/ A Paradigm Shift (20 edo)] by [[Chris Vaisvil]]
* [https://www.youtube.com/watch?v=8PCe5u4QsRg Composition for unconventional tempered clavier] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]
* [https://www.youtube.com/watch?v=zQDNqnYqCHg 5 compositions for violin and clavier in 20-EDO] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]
* [https://www.youtube.com/watch?v=duJHUo_ACgk Composition for cello and clavier in 20-tone equal temperament] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]
* [https://www.youtube.com/watch?v=u6k4lgCnHqs 5 compositions for violin and clavier in 20-tone equal temperament] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]
== Intervals ==
== Intervals ==


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{| class="wikitable" style="text-align:center;"
{| class="wikitable" style="text-align:center;"
|-
|-
! Degree
! [[Degree]]
! Cents
! [[Cents]]
! Approximate Ratios
! Approximate Ratios
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and Downs Notation]]
Line 50: Line 31:
| style="text-align:right;" | 60
| style="text-align:right;" | 60
| 29/28
| 29/28
| upminor 2nd
| up unison, upminor 2nd
| ^m2
| ^1, ^m2
| D^
| ^D, ^Eb
| 33
| 33
|-
|-
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| style="text-align:right;" | 120
| style="text-align:right;" | 120
| 14/13, 15/14
| 14/13, 15/14
| mid 2nd
| double-up unison, mid 2nd
| ~2
| ^^1, ~2
| D^^, Evv
| ^^D, vvE
| 69
| 69
|-
|-
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| downmajor 2nd
| downmajor 2nd
| vM2
| vM2
| Ev
| vE
| 71
| 71
|-
|-
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| upminor 3rd
| upminor 3rd
| ^m3
| ^m3
| F^
| ^F
| 19
| 19
|-
|-
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| mid 3rd
| mid 3rd
| ~3
| ~3
| F^^
| ^^F, vvF#
| 79
| 79
|-
|-
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| downmajor 3rd
| downmajor 3rd
| vM3
| vM3
| F#v
| vF#
| 41
| 41
|-
|-
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| up-fourth
| up-fourth
| ^4
| ^4
| G^
| ^G
| 11
| 11
|-
|-
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| double-up fourth, double-down fifth
| double-up fourth, double-down fifth
| ^^4, vv5
| ^^4, vv5
| G^^, Avv
| ^^G, vvA
| 91
| 91
|-
|-
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| down-fifth
| down-fifth
| v5
| v5
| Av
| vA
| 47
| 47
|-
|-
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| style="text-align:right;" | 780
| style="text-align:right;" | 780
| 11/7, 25/16
| 11/7, 25/16
| upminor 6th
| upfifth, upminor 6th
| ^m6
| ^5, ^m6
| A^
| ^A, ^Bb
| 25
| 25
|-
|-
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| mid 6th
| mid 6th
| ~6
| ~6
| A^^, Bvv
| ^^A, vvB
| 13
| 13
|-
|-
Line 164: Line 145:
| downmajor 6th
| downmajor 6th
| vM6
| vM6
| Bv
| vB
| 27
| 27
|-
|-
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| upminor 7th
| upminor 7th
| ^m7
| ^m7
| C^
| ^C
| 115
| 115
|-
|-
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| mid 7th
| mid 7th
| ~7
| ~7
| C^^, Dvv
| ^^C, vvD
| 15
| 15
|-
|-
Line 196: Line 177:
| downmajor 7th
| downmajor 7th
| vM7
| vM7
| Dv
| vD
| 31
| 31
|-
|-
Line 211: Line 192:
20edo chord names using ups and downs:
20edo chord names using ups and downs:
* 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"
* 0-5-12 = D F^ A = D.^m = "D upminor"
* 0-5-12 = D ^F A = D^m = "D upminor"
* 0-6-12 = D F^^ A = D.~ = "D mid"
* 0-6-12 = D ^^F A = D~ = "D mid"
* 0-7-12 = D F#v A = D.v = "D dot down" or "D downmajor"
* 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"
* 0-8-12 = 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"
* 0-4-12-16 = 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 = Dm7(^3) = "D minor seven up-three", or D F^ A B = Dm6(^3) = "D minor six up-three"
* 0-5-12-16 = D ^F A C = Dm7(^3) = "D minor seven up-three", or D ^F A B = Dm6(^3) = "D minor six up-three"
* 0-6-12-16 = D F^^ A C = D7(~3) = "D seven mid-three", or D F^ A B = D6(~3) = "D six mid-three"
* 0-6-12-16 = D ^^F A C = D7(~3) = "D seven mid-three", or D ^F A B = D6(~3) = "D six mid-three"
* 0-7-12-16 = D F#v A C = D7(v3) = "D seven down-three", or D F#v A B = D6(v3) = "D six down-three"
* 0-7-12-16 = D vF# A C = D7(v3) = "D seven down-three", or D vF# A B = D6(v3) = "D six down-three"
* 0-8-12-16 = D F# A C = D7 = "D seven", or D F# A B = D6 = "D 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 F#v A C#v = D.vM7 = "D downmajor seven"
* 0-7-12-19 = D vF# A vC# = DvM7 = "D downmajor seven"
* 0-5-12-17 = D F^ A C^ = D.^m7 = "D dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-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#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]]. Because many intervals have several names, many chords do too.
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 ==
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{| class="wikitable" style="text-align:center;"
{| class="wikitable" style="text-align:center;"
|-
|-
! Rational
! [[Ratio]]
! Monzo
! [[Monzo]]
! Size (Cents)
! [[Cents]]
! [[Color notation/Temperament Names|Color Name]]
! Name 1
! Name 1
! Name 2
! Name 2
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| {{Monzo| 8 -5 }}
| {{Monzo| 8 -5 }}
| style="text-align:right;" | 90.22
| style="text-align:right;" | 90.22
|Sawa
| [[Limma]]
| [[Limma]]
| Pythagorean Minor 2nd
| Pythagorean Minor 2nd
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| {{Monzo| -14 3 4 }}
| {{Monzo| -14 3 4 }}
| style="text-align:right;" | 51.12
| style="text-align:right;" | 51.12
|Laquadyo
| Negri Comma
| Negri Comma
| Double Augmentation Diesis
| Double Augmentation Diesis
|
|
|-
|-
| 9931568/9752117
|34171875/33554432
| {{Monzo| -25 7 6 }}
| {{Monzo| -25 7 6 }}
| style="text-align:right;" | 31.57
| style="text-align:right;" | 31.57
|Lala-tribiyo
| Ampersand's Comma
| Ampersand's Comma
|
|
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| {{Monzo| 11 -4 -2 }}
| {{Monzo| 11 -4 -2 }}
| style="text-align:right;" | 19.55
| style="text-align:right;" | 19.55
|Sagugu
| Diaschisma
| Diaschisma
|
|
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| {{Monzo| -9 1 2 1 }}
| {{Monzo| -9 1 2 1 }}
| style="text-align:right;" | 43.41
| style="text-align:right;" | 43.41
|Lazoyoyo
| Avicennma
| Avicennma
| Avicenna's Enharmonic Diesis
| Avicenna's Enharmonic Diesis
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| {{Monzo| -4 -1 0 2 }}
| {{Monzo| -4 -1 0 2 }}
| style="text-align:right;" | 35.70
| style="text-align:right;" | 35.70
|Zozo
| Slendro Diesis
| Slendro Diesis
|
|
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| {{Monzo| 1 0 2 -2 }}
| {{Monzo| 1 0 2 -2 }}
| style="text-align:right;" | 34.98
| style="text-align:right;" | 34.98
|Biruyo
| Tritonic Diesis
| Tritonic Diesis
| Jubilisma
| Jubilisma
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| {{Monzo| 1 -3 -2 3 }}
| {{Monzo| 1 -3 -2 3 }}
| style="text-align:right;" | 27.99
| style="text-align:right;" | 27.99
|Trizo-agugu
| Senga
| Senga
|
|
Line 359: Line 349:
| {{Monzo| 6 -2 0 -1 }}
| {{Monzo| 6 -2 0 -1 }}
| style="text-align:right;" | 27.26
| style="text-align:right;" | 27.26
|Ru
| Septimal Comma
| Septimal Comma
| Archytas' Comma
| Archytas' Comma
| Leipziger Komma
| Leipziger Komma
|-
|-
| 9859966/9733137
| 854296875/843308032
| {{Monzo| -10 7 8 -7 }}
| {{Monzo| -10 7 8 -7 }}
| style="text-align:right;" | 22.41
| style="text-align:right;" | 22.41
|Lasepru-aquadbiyo
| Blackjackisma
| Blackjackisma
|
|
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| {{Monzo| -10 1 0 3 }}
| {{Monzo| -10 1 0 3 }}
| style="text-align:right;" | 8.43
| style="text-align:right;" | 8.43
|Latrizo
| Gamelisma
| Gamelisma
|
|
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| {{Monzo| -5 2 2 -1 }}
| {{Monzo| -5 2 2 -1 }}
| style="text-align:right;" | 7.71
| style="text-align:right;" | 7.71
|Ruyoyo
| Septimal Kleisma
| Septimal Kleisma
| Marvel Comma
| Marvel Comma
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| {{Monzo| 0 3 4 -5 }}
| {{Monzo| 0 3 4 -5 }}
| style="text-align:right;" | 6.99
| style="text-align:right;" | 6.99
|Quinru-aquadyo
| Mirkwai
| Mirkwai
|
|
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| {{Monzo| 11 -10 -10 10 }}
| {{Monzo| 11 -10 -10 10 }}
| style="text-align:right;" | 5.57
| style="text-align:right;" | 5.57
|Saquinbizogu
| Linus
| Linus
|
|
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| {{Monzo| -3 -1 -1 0 2 }}
| {{Monzo| -3 -1 -1 0 2 }}
| style="text-align:right;" | 14.37
| style="text-align:right;" | 14.37
|Lologu
| Biyatisma
| Biyatisma
|
|
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| {{Monzo| -1 -2 -1 1 0 1 }}
| {{Monzo| -1 -2 -1 1 0 1 }}
| style="text-align:right;" | 19.13
| style="text-align:right;" | 19.13
|Thozogu
| Superleap
| Superleap
|
|
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|-
|-
| 2401/2400
| 2401/2400
| {{Monzo| -5 -1 2 4 }}
| {{Monzo| -5 -1 -2 4 }}
| style="text-align:right;" | 0.72
| style="text-align:right;" | 0.72
|Bizozogu
| Breedsma
| Breedsma
|
|
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| {{Monzo| 2 -3 -2 0 0 2 }}
| {{Monzo| 2 -3 -2 0 0 2 }}
| style="text-align:right;" | 2.56
| style="text-align:right;" | 2.56
|Bithogu
| Parizeksma
| Parizeksma
|
|
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{{External Image| http://ronsword.com/images/20_tet_Coversm.jpg {{dead link}} }}
{{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}}
[http://www.ronsword.com/ "Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more] by [[Ron Sword]] {{dead link}}
== Music ==
* [https://soundcloud.com/overtoneshock/underwater-spontaniety-20-edo Underwater Spontaniety] (lo-fi ambient) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [https://soundcloud.com/overtoneshock/gods-favorite-tuning-20-edo God's Favorite Tuning] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [https://soundcloud.com/overtoneshock/you-lied-and-im-not-mentioning-your-name-20-edo?in=overtoneshock/sets/xenharmonic-microtonal You Lied, and I'm not Mentioning your Name] (xen-pop) by [https://soundcloud.com/overtoneshock Stephen Weigel]
* [http://www.io.com/%7Ehmiller/midi/20tet.mid Etude in 20-tone equal tuning] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/20-et-Pianoteq-Schantz.mp3 play] by [[Herman Miller]]
* [http://aaronandrewhunt.zentral.zone/mp3/20ETPreludeFugue.mp3 20ET — Prelude & Fugue a3] by [[Aaron Hunt]]
* [http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=933696 We Call It Sharing Breath] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wecallitsharingbreathin20tet.mp3 play] by [[Andrew Heathwaite]]
* [http://chrisvaisvil.com/the-walrus-and-the-carpenter-from-bethan-reads-in-20edo/ The Walrus and the Carpenter] by[[Chris Vaisvil]] and Bethan Mathis
* [http://chrisvaisvil.com/clean-20-edo-electric-guitar-improvisation/ 20 edo Electric Guitar Improvisation] by[[Chris Vaisvil]]
* [http://chrisvaisvil.com/gobekli-tepe-20-edo-guitar-solo/ Göbekli Tepe (20 edo guitar solo)] by [[Chris Vaisvil]]
* [http://chrisvaisvil.com/a-paradigm-shift-20-edo/ A Paradigm Shift (20 edo)] by [[Chris Vaisvil]]
* [https://www.youtube.com/watch?v=8PCe5u4QsRg Composition for unconventional tempered clavier] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]
* [https://www.youtube.com/watch?v=zQDNqnYqCHg 5 compositions for violin and clavier in 20-EDO] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]
* [https://www.youtube.com/watch?v=duJHUo_ACgk Composition for cello and clavier in 20-tone equal temperament] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]
* [https://www.youtube.com/watch?v=u6k4lgCnHqs 5 compositions for violin and clavier in 20-tone equal temperament] by [http://chernobrivets.ru/en/ Pyotr Chernobrivets]


[[Category:20edo]]
[[Category:20edo]]

Revision as of 03:38, 14 December 2019

20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 cents each. It contains smaller edos 2, 4, 5, and 10 and is part of the 5n Family of equal divisions of the octave. 20 edo 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.


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.

Degree Cents Approximate Ratios Ups and Downs Notation Nearest Harmonic
0 0 1/1 unison P1 D 1
1 60 29/28 up unison, upminor 2nd ^1, ^m2 ^D, ^Eb 33
2 120 14/13, 15/14 double-up unison, mid 2nd ^^1, ~2 ^^D, vvE 69
3 180 10/9 downmajor 2nd vM2 vE 71
4 240 8/7, 15/13 major 2nd, minor 3rd M2, m3 E, F 37
5 300 13/11, 19/16 upminor 3rd ^m3 ^F 19
6 360 16/13, 5/4 mid 3rd ~3 ^^F, vvF# 79
7 420 14/11, 51/40 downmajor 3rd vM3 vF# 41
8 480 25/19, 4/3 major 3rd, perfect fourth M3, P4 F#, G 21
9 540 15/11, 11/8 up-fourth ^4 ^G 11
10 600 7/5 double-up fourth, double-down fifth ^^4, vv5 ^^G, vvA 91
11 660 22/15, 16/11 down-fifth v5 vA 47
12 720 38/25, 3/2 fifth P5, m6 A 97
13 780 11/7, 25/16 upfifth, upminor 6th ^5, ^m6 ^A, ^Bb 25
14 840 13/8, 8/5 mid 6th ~6 ^^A, vvB 13
15 900 22/13, 32/19 downmajor 6th vM6 vB 27
16 960 7/4, 26/15 major 6th, minor 7th M6, m7 B, C 7
17 1020 9/5 upminor 7th ^m7 ^C 115
18 1080 15/8, 13/7 mid 7th ~7 ^^C, vvD 15
19 1140 56/29 downmajor 7th vM7 vD 31
20 1200 2/1 octave P8 D 2

Chord Names

20edo chord names using ups and downs:

  • 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 = Dm7(^3) = "D minor seven up-three", or D ^F A B = Dm6(^3) = "D minor six up-three"
  • 0-6-12-16 = D ^^F A C = D7(~3) = "D seven mid-three", or D ^F A B = D6(~3) = "D six mid-three"
  • 0-7-12-16 = D vF# A C = D7(v3) = "D seven down-three", or D vF# A B = D6(v3) = "D six down-three"
  • 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. Because many intervals have several names, many chords do too.

Modes

20 tone equal modes:

3 1 3 1 3 1 3 1 3 1 Blackwood Major Decatonic (bi-equal decatonic, according to the MOS naming scheme)
1 3 1 3 1 3 1 3 1 3 Blackwood Minor Decatonic (also bi-equal decatonic)
2 3 2 2 2 3 2 2 2 Balzano Nine-tone (fair mavila, score9)
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 fair mavila, 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 (diminished, according to the MOS naming scheme)
3 2 3 2 3 2 3 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 (Grumpy heptatonic)
3 2 3 3 3 3 3 Minor quasi-equal Heptatonic (also Grumpy heptatonic)
3 2 2 2 2 3 2 2 2 Rothenberg Generalized Diatonic (also score9)
3 4 1 4 3 3 2 Stearns Major
7 2 7 2 2 score5 (classic pentatonic)
5 2 2 5 2 2 2 score7 (mavila, anti-diatonic)

Commas

20 EDO tempers out the following commas. (Note: This assumes the val < 20 32 46 56 69 74 |.)

Ratio Monzo Cents Color Name Name 1 Name 2 Name 3
256/243 [8 -5⟩ 90.22 Sawa Limma Pythagorean Minor 2nd
16875/16384 [-14 3 4⟩ 51.12 Laquadyo Negri Comma Double Augmentation Diesis
34171875/33554432 [-25 7 6⟩ 31.57 Lala-tribiyo Ampersand's Comma
2048/2025 [11 -4 -2⟩ 19.55 Sagugu Diaschisma
525/512 [-9 1 2 1⟩ 43.41 Lazoyoyo Avicennma Avicenna's Enharmonic Diesis
49/48 [-4 -1 0 2⟩ 35.70 Zozo Slendro Diesis
50/49 [1 0 2 -2⟩ 34.98 Biruyo Tritonic Diesis Jubilisma
686/675 [1 -3 -2 3⟩ 27.99 Trizo-agugu Senga
64/63 [6 -2 0 -1⟩ 27.26 Ru Septimal Comma Archytas' Comma Leipziger Komma
854296875/843308032 [-10 7 8 -7⟩ 22.41 Lasepru-aquadbiyo Blackjackisma
1029/1024 [-10 1 0 3⟩ 8.43 Latrizo Gamelisma
225/224 [-5 2 2 -1⟩ 7.71 Ruyoyo Septimal Kleisma Marvel Comma
16875/16807 [0 3 4 -5⟩ 6.99 Quinru-aquadyo Mirkwai
6772805/6751042 [11 -10 -10 10⟩ 5.57 Saquinbizogu Linus
121/120 [-3 -1 -1 0 2⟩ 14.37 Lologu Biyatisma
91/90 [-1 -2 -1 1 0 1⟩ 19.13 Thozogu Superleap
2401/2400 [-5 -1 -2 4⟩ 0.72 Bizozogu Breedsma
676/675 [2 -3 -2 0 0 2⟩ 2.56 Bithogu Parizeksma

Books

External image: http://ronsword.com/images/20_tet_Coversm.jpg [dead link]

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"Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more by Ron Sword [dead link]

Music

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