What is Negative Harmony?
To explain negative harmony, first we have to look at functionality of our bread and butter major scale.
Taking C major for example; C D E F G A B C.
The scale can here be divided into stable notes and their unstable/active neighbours. The strong stable notes of the C major scale are C E and G and they make up the C major triad. The rest of the notes in the scale, D F A and B are all unstable or active. B wants to resolve upwards to C, A wants to resolve downwards to G, F to E and D is more bidirectional as it can resolve to C or E.
If the uses of Negative harmony are to be understood, this basic functionality of the scale degrees and their relationships is to be acknowledged. The reason we get such a satisfying resolve from a V-I cadence is because two of the notes in G maj; B and D are unstable. Once B resolves to C and D to E, we are back to the completed sounding ‘Home’ chord.
Right but, where does this apply to Negative harmony? I clicked on this for Negative harmony not a grade 1 theory refresher.
Ok so, Negative harmony works as an axis between the Tonic and Dominant scale degrees, in C major this would be C and G, in B♭ major it’s B♭ and F and so on.
Taking C major for example again, if we map the chromatic scale in a circular diagram with C and G immediate opposites, we can add in the additional variables, moving clockwise from C if we ascend a semitone to Db, then moving anticlockwise from G we should be descending to G♭. Graphed correctly, this will result in a complete chromatic scale in order; C, D♭, D, Eb, E, F, G♭, G, A♭, A, B♭, B.
For ease of readability, a ‘mirror’ can be drawn through the centre of the diagram, which allows us to convert the notes to their Negative harmonic equivalents.
To get the negative equivalent of a note, effectively we’re working in the opposing direction from the opposite axial value. I know that’s wordy but, if we’re looking for the Negative harmonic value of E in this key, which is a Major 3rd from the tonic note C, we’re instead going to descend the same distance from the Dominant note G.
So instead of a Major 3rd up from C, it’s a Major 3rd down from G; thus giving us E♭.
Taking another example; A. Instead of ascending a Major 6th from C we’re descending a Major 6th from G; giving us B♭. The same works descending a minor 3rd from C and Ascending a minor 3rd from G.
The Negative Harmonic equivalent from C major as a scale give us the following set of notes:
If we look, closely this set of notes gives us more information on the uses of Negative Harmony.
Negative Harmony in Application
The notes produced by crossing the I-V axis produce the notes of the Parallel minor; C minor. Not only this but the stable notes of the scale; C E and G become the stable notes in C minor albeit inverted to G E♭ C. This can then be observed that the unstable scale degrees of C major also correspond to the unstable/active notes in C minor.
This can then be applied in composition where we exchange a chord from the Parallel minor in place of an otherwise safer sounding chord choice. If you will, Negative harmonic equivalents can almost be seen as a cheat-sheet for chord substitution in this way.
| C major | C minor (i Minor) |
| D minor | B♭ Major (♭VII Major) |
| E minor | A♭ Major (♭Vi Major) |
| F Major | G minor (v minor) |
| G Major | F minor (iv minor) |
| A minor | E♭ Major (♭III Major) |
| B dim | D dim (ii dim) |
Of course, there are many examples that predate the introduction of Negative Harmony into the common musical vernacular (as of the time of writing, Negative harmony is widely talked about yet still does not have a Wikipedia page. The book A Theory of Harmony by Ernst Levy that explores the concept of Negative Harmony was first published in 1985)
In the example below, taken from the chorus of ‘Obviously’ by McFly we can see an example of a negative harmonic equivalent at play in a pop song.
C E
Cos Obviously, shes outta my league
F D
I’m wasting my time cos she’ll never be mine and i no i
F G C E
never will be good enough for her, no no.
F Fm C E
never will be good enough for her.
Since the song is in C major, the notes of the G chord; G B and D, become C A♭ and F, making it an F minor. As active tonalities within the key; A♭ and F both want to resolve to G and E respectively and the harmonic function of iv-I works perfectly as a substitution despite being wildly different to a perfect V-I cadence.
The example of ‘Obviously’ by McFly does us the further favour of outlining the harmonic difference of this variation since the previous 4 bars contain the V-I cadence our ears are expecting to hear.
The Visual Negative
So, what else can Negative Harmony teach us?
I could easily leave this essay here and save the rest for a different day but I’ve started now and I’m on a writing streak. So, if we go back to the earlier image mapping the Negative Harmonic values of a C major scale, we can notice something else about the notes. Not only are they C minor but they start and end on G and descend whereas the Major scale degrees ascend.
The Negative of Ionian is a descending Phrygian scale.
The observation makes sense, since Ionian is built on the pattern
tone, tone, semitone, tone, tone, tone, semitone
Reversing this will give us
semitone, tone, tone, tone, semitone, tone, tone
which is the exact formula for Phrygian. This further shows us the relationship between Ionian and Phrygian as modes; they ascend and descend in exact opposites.
If we were to quickly find the Negative Harmonic values for G major, all we have to do is think of a descending D Phrygian, since D is the 5th scale degree in G major.
Thus giving us D C B♭ A G F E♭.
And using the same chord values as before; G min, A Maj, B♭ Maj, C min, D min, E♭ maj and F Dim.
What about converting a minor scale?
By converting the notes of C minor to their negative harmonic equivalents (this is actually the same axis as the major scale since the I and V are identical) C D E♭ F G A♭ and B♭ becomes G F E D C B and A, which is a descending G mixolydian scale.
This opens a whole new question on the observation of Phrygian and Mixolydian as negative reflections of Major and Minor, and their respective relationship as dominant tonalities.
Negative Harmony, like all music theoretical concepts is a tool for composition derived from a geometric mapping of given notes to achieve a completely new set of notes with similar harmonic functionality. Beyond just being a cheat sheet for employing harmonic complexity and variation, it’s a very widely talked about but still under researched topic that like everything, can teach us so much more than it initially claims.
It is yet another nutshell to be cracked open and explored.
As always, thanks so much for reading. If you have any questions or comments or further observations I’d love to hear them. Feel free to get in touch with me via the contacts page.
Peaceful holidays and a Happy New Year to all.
A Study in Audiosynthesis 