CG-31

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CG-31 is an approximation of negative harmony in 31-edo. It is a transformative technique where music is mirrored across a point between the root note and the fifth in a key. It should be noted that using C as the root is solely an example and this works in all keys.

How it works

When you mirror the music, it affects the direction of the melody and the harmonics of a piece. Major becomes minor, and places where the melody moves up will move down instead. The circle of fifths can be used as a tool when practicing CG-31. The way that is done is by drawing lines on the circle pairing two and two notes up with each other. Example: C major -> C minor

The notes are mirrored across the straight line in the middle, this is for keys where C is the root note.

(C -> G, E -> Eb, G -> C)


Because 31 is an odd number, there is one note that does not get a paired note, that is the note directly across from the space between the root and the fifth in the key. As shown in the picture above, that note is Dx (or Fbb) in the key of C. That makes this different from 12-TET negative harmony, where all the notes can be mirrored. When using the note that doesn’t get mirrored, it will simply stay the same as it was.


Table of standard triads with CG-31

Name of triad Triad after mirroring Notes of triad (C as root note) Notes after mirroring
Major Minor C, E, G G, Eb, C
Minor Major C, Eb, G G, E, C
Subminor Supermajor C, D#, G G, Fb, C
Supermajor Subminor C, Fb, G G, D#, C
Neutral Neutral C, Dx, G G, Dx, C
Augmented Diminished C, E, G# G, Eb, Cb
Diminished Diminished C, Eb, Gb G, E, C#
Harmonic dim Subminor dim C, Eb, F# G, E, Db
Subminor dim Harmonic dim C, D#, F# G, Fb, Db
Septimal Wolf major Septimal Wolf minor C, Fb, Abb G, D#, B#
Septimal Wolf minor Septimal Wolf major C, Eb, Abb G, E, B#
Subfifth minor Subfifth neutral C, Eb, Fx G, E, Dbb
Subfifth neutral Subfifth minor C, Dx, Fx G, Dx, Dbb
DRmaj DRmindim C, E, Fx G, Eb, Dbb
DRmindim DRmaj C, D#, Fx G, Fb, Dbb
Orwell Orwell C, D#, Gbb G, Fb, Cx
Squares Squares C, Fb, Gx G, D#, Cbb

Compared to 12-TET

Negative Harmony (12-TET)

In 12-TET the concept this is based off is negative harmony. It works mostly the same but since 12 is an even number, all notes get paired, and the harmonics get affected differently. In 12-TET an augmented chord would still be an augmented chord when mirrored, whereas it would become diminished in 31-edo. The notes still work out in comparison to negative harmony in 12-TET.


Name

The name CG-31 refers to the creators of the system, Christa N. Hansen and Reinn O. Grieg. The C and G can also refer to the placement of the mirroring line in C major in addition to being an abbreviation of Chromatic Grid. In a different EDO it would be referred to as CG-n, where n is the EDO number.


Audio examples

Here we have notes and audio files of a waltz written by Reinn O. Grieg and the CG-31 version of the same waltz.


"Liten vals" a 31-EDO waltz by Reinn O. Grieg










"Liten vals" by Reinn O. Grieg



link=File:CG-31_version_of_%22Liten_vals%22.png








CG-31 version of "Liten vals" by Reinn O. Grieg


History of 12-TET negative harmony

Ernst Levy (1895 – 1981) wrote about negative harmony in his book “A Theory of Harmony” that was published in 1985. At the time, it did not catch much interest. It was not before some years later, when Jacob Collier talked about negative harmony in an interview that gained popularity. According to an article on Opussiencecollective.com (OSC), people have been using negative harmony intuitively for hundreds of years before Levy’s book was written.


On YouTube, there are many videos about negative harmony and if you want to listen to some examples, you can look up Steve Cruickshank’s negative harmony covers of various songs.

Further reading

External links

Websites

Videos

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