The following examples have been created using the negative harmony app which is available on Google Play and iTunes.
All examples are colour-coded. The color green has been used to signify when any negative harmony chords and progressions are being demonstrated. Blue is for regular 'positive' harmony examples.
Pay attention to the position of the axis in each example. This will determine how the chord is 'negatized'.
We've already seen how a C major triad inverts downards to an F minor triad:
Now let's look at some other interesting developments.
Minor 7th chords are symmetrical. This means that any Minor 7th chord will transpose over the axis naturally to another Min7 chord.
See how D minor 7 will negatize to itself when the axis is placed on G natural:
See how C Major 7 will negatize to another Maj7 chord regardless of the axis position:
Dominant 7 chords negatize to half-diminished chords (min7 flat 5). The enharmonic E flat is represented here instead with a D#:
Diminished chords are, perhaps unsurprisingly, unaffected with negative harmony. The root can move but the basic structure of the chord, built in minor thirds, remains the same:
Now we'll lok at negative harmony chord progressions. This next example takes a standard I-VI-II-V and negatizes it. This progression is extremely common and is heard in classic songs such as 'Octopus's Garden' by the Beatles and 'Bobby Brown' by Frank Zappa, to name a few. Transposing this progression with negative harmony gives us an interesting minor progression. The axis here is between E natural and E flat but you can move this around to create new chord keys.
This particular negative harmony progression can be heard in modern music. You could call it a negative harmony I-VI-II-V progression or a minor I-III-VII-IV progression. One example can be heard during a section of The Red Hot Chili Peppers' song 'Right On Time' from 17 seconds onwards. Take a listen below.
The Negative Harmony app is available to download on iTunes and Google Play now.
iTunes: Download