20edo: Difference between revisions

{{Japanese Version Page|[[20平均律|日本語]]}}

20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[EDO|edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|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.

== Compositions ==

* [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.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]]

== 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" style="text-align:center;"

! Degree

! Cents

! Approximate Ratios

! colspan="3" | [[Ups and Downs Notation]]

! Nearest Harmonic

| 0

| 1/1

| unison

| P1

| D

| 1

| 1

| 29/28

| upminor 2nd

| ^m2

| D^

| 33

| 2

| 14/13, 15/14

| mid 2nd

| ~2

| D^^, Evv

| 69

| 3

| 10/9

| downmajor 2nd

| vM2

| Ev

| 71

| 4

| 8/7, 15/13

| major 2nd, minor 3rd

| M2, m3

| E, F

| 37

| 5

| 13/11, 19/16

| upminor 3rd

| ^m3

| F^

| 19

| 6

| 16/13, 5/4

| mid 3rd

| ~3

| F^^

| 79

| 7

| [[14/11]], [[51/40]]

| downmajor 3rd

| vM3

| F#v

| 41

| 8

| 25/19, 4/3

| major 3rd, perfect fourth

| M3, P4

| F#, G

| 21

| 9

| 15/11, 11/8

| up-fourth

| ^4

| G^

| 11

| 10

| 7/5

| double-up fourth, double-down fifth

| ^^4, vv5

| G^^, Avv

| 91

| 11

| 22/15, 16/11

| down-fifth

| v5

| Av

| 47

| 12

| 38/25, 3/2

| fifth

| P5, m6

| A

| 97

| 13

| 11/7, 25/16

| upminor 6th

| ^m6

| A^

| 25

| 14

| 13/8, 8/5

| mid 6th

| ~6

| A^^, Bvv

| 13

| 15

| 22/13, 32/19

| downmajor 6th

| vM6

| Bv

| 27

| 16

| 7/4, 26/15

| major 6th, minor 7th

| M6, m7

| B, C

| 7

| 17

| 9/5

| upminor 7th

| ^m7

| C^

| 115

| 18

| 15/8, 13/7

| mid 7th

| ~7

| C^^, Dvv

| 15

| 19

| 56/29

| downmajor 7th

| vM7

| Dv

| 31

| 20

| 2/1

| octave

| P8

| D

| 2

== Chord Names ==

* 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 F#v A = D.v = "D dot 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 F#v A C = D7(v3) = "D seven down-three", or D F#v 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 F#v A C#v = D.vM7 = "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"

== Modes ==

| 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]])

| 1 3 1 3 1 3 1 3 1 3

| Blackwood Minor Decatonic (<span style="">also bi-equal decatonic)</span>

| 2 3 2 2 2 3 2 2 2

| Balzano Nine-tone (<span style="">[[2L_7s|fair mavila]], [[score9]])</span>

| 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 <span style="">fair mavila, score9)</span>

| 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|diminished]], according to the [[MOSNamingScheme|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 ([[6L_1s|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]] [[2L_3s|(classic pentatonic]])

| 5 2 2 5 2 2 2

| [[score7]] ([[2L_5s|mavila, anti-diatonic]])

== Commas ==

20 EDO [[tempering out|tempers out]] the following [[Comma|commas]]. (Note: This assumes the [[val]] &lt; 20 32 46 56 69 74 |.)

{| class="wikitable" style="text-align:center;"

! Rational

! Monzo

! Size (Cents)

! Name 1

! Name 2

! Name 3

| 256/243

| {{Monzo| 8 -5 }}

| [[Limma]]

| Pythagorean Minor 2nd

|

| 16875/16384

| {{Monzo| -14 3 4 }}

| Negri Comma

| Double Augmentation Diesis

|

| 9931568/9752117

| {{Monzo| -25 7 6 }}

| Ampersand's Comma

|

|

| 2048/2025

| {{Monzo| 11 -4 -2 }}

| Diaschisma

|

|

| 525/512

| {{Monzo| -9 1 2 1 }}

| Avicennma

| Avicenna's Enharmonic Diesis

|

| 49/48

| {{Monzo| -4 -1 0 2 }}

| Slendro Diesis

|

|

| 50/49

| {{Monzo| 1 0 2 -2 }}

| Tritonic Diesis

| Jubilisma

|

| 686/675

| {{Monzo| 1 -3 -2 3 }}

| Senga

|

|

| 64/63

| {{Monzo| 6 -2 0 -1 }}

| Septimal Comma

| Archytas' Comma

| Leipziger Komma

| 9859966/9733137

| {{Monzo| -10 7 8 -7 }}

| Blackjackisma

|

|

| 1029/1024

| {{Monzo| -10 1 0 3 }}

| Gamelisma

|

|

| 225/224

| {{Monzo| -5 2 2 -1 }}

| Septimal Kleisma

| Marvel Comma

|

| 16875/16807

| {{Monzo| 0 3 4 -5 }}

| Mirkwai

|

|

| 6772805/6751042

| {{Monzo| 11 -10 -10 10 }}

| Linus

|

|

| 121/120

| {{Monzo| -3 -1 -1 0 2 }}

| Biyatisma

|

|

| 91/90

| {{Monzo| -1 -2 -1 1 0 1 }}

| Superleap

|

|

| 2401/2400

| {{Monzo| -5 -1 2 4 }}

| Breedsma

|

|

| 676/675

| {{Monzo| 2 -3 -2 0 0 2 }}

| Parizeksma

|

|

== Books ==

[http://www.ronsword.com/ "Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more] by [[Ron Sword]]

 

[[Category:20edo]]