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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 5 edo), 11, 13 & 15 (from 10 edo), 19 & 27 (from 4 edo), 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 | Properties | Chord Names

## Compositions

## Göbekli Tepe (20 edo guitar solo) by Chris Vaisvil

## Properties

## 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.

## 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 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"

For a more complete list, see Ups and Downs Notation - Chord names in other EDOs. Because many intervals have several names, many chords do too.

## Modes

20 tone equal modes:## Commas

20 EDO tempers out the following commas. (Note: This assumes the val < 20 32 46 56 69 74 |.)Books"Icosaphonic Scales for Guitar" - Theory / Scale book with above modes and more by Ron Sword