Negative Harmony

Negative Harmony is a harmonic tool. It was first described by Ernst Levy, who was a Swiss musicologist, composer, pianist and conductor (1895-1981). For the Jazz Musician, this tool is interesting, because it helps creating new sounds.
What is negative harmony? How is it created?

An axis of tonality is defined such that the circle of fifths is divided by that axis into mirroring halves. e.g. in the key of C, the axis would be drawn between C and G; in E-flat, it would be drawn between E-flat and B-flat.

Look at the table for the related negative solution in the key of C:
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As you can see, in the key of C the f becomes d.
This procedure you can use for putting the melody to its negative but also to create the negative chords for a progression.

In the key of C, we create the negative of C:
c becomes g, e becomes eb and g becomes c. The C-Chord in C has a negative Cm-Chord.
In the key of C, we create the negative of G:
g becomes c, b becomes bb and d becomes f. The G-Chord has a negative Fm-Chord.

The Progression G-C in the key of C becomes a negative Fm-Cm Progression.

The discussion also is about having only replaced the harmonic progression to its negative, but not the solution.
In this case, our progression would sound like: Fm - C

If you try to use the Negative Harmony Tool to the first 8 bars of „All the Things“ you will get:

(Axis in Ab:) B6 - Gb6 - Dbm7 - Abm - Ebm - (Change of Axis to C:) Fm6 - Cm

Have fun to check out new sounds!