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Negative Harmony

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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:

Negative Harmony Chart C

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 a C-Chord: 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.
For example:the first bars of "All the Things", Ab, could be transformed like this:

Negative Harmony Chart C

The first 8 bars of the composition "All the Things" will become this:

Negative Harmony Chart C

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

Bb6 - Fm6 - C.

Another way of using negative harmony flavoured sounds is to only change special chords in the chart.
For example in the first 8 bars of "All the Things" change only the Dominant-7 Chords and the II-V to their negatives:

| F-7 | Bb-7 | Db-6 | Abmaj7 | Dbmaj7 | F-6 | Cmaj7 | Cmaj7 ||

The most important thing:
Have fun to check out new sounds!