The Harmonic Upside Down - Negative Harmony
Updated: Nov 18, 2019
Swiss born classical composer Ernst Levy died in 1981 leaving behind not only a legacy of compositional work, but also an influential body of academic writing from his time as a musicologist at some of the United States' leading music institutions. Published in 1985, A Theory of Harmony was a collection of his academic writings in which there was an entry about a concept he called "Negative Harmony". The concept piqued academic interests upon publication, but naturally as the years rolled by, Negative Harmony faded to the background of music academia as interests shifted and people looked to new concepts and ideas.
Enter Jacob Collier! I won't go into too much detail about him suffice to say this young man from London is one of the most fascinating and awe inspiring musical prodigies of our time. A once-in-a-generation human who simply processes music on levels most people can't comprehend. He has mastery of a multitude of instruments, including his own voice (singing), alongside phenomenal composition, arrangement and production skills. He's still very young, only in his mid 20s, but is already sending shockwaves through the Jazz world, rubbing shoulders with the likes of Herbie Hancock and Quincy Jones (when he's not giving music masterclasses at Berkeley and MIT)!
A few years ago, during an interview Collier mentioned Levy's concept of Negative Harmony as one of the many tools in his arsenal of composition techniques. Naturally, if Jacob Collier says he's using a particular method or technique, the Jazz and academic-music communities turn their attention to it. In the months following this interview, the Internet was awash with discussions and explanations of this concept. Some claimed it to be the new gospel, some struggled to accurately grasp it, while others dismissed it as overcomplicating a simple idea.
I too delved into it and felt that whilst Levy's (and by extension, Collier's) explanations were of course technically accurate, there are arguably less abstract ways to think about the principle; ways that make Negative Harmony an easily accessible tool with which to add a little spice to one's compositions.
So, What is Negative Harmony?
Negative Harmony is a theoretical concept that suggests every scale has a Negative mirror image (or Upside Down scale) from which chords and melodic notes can be substituted to equal harmonic/melodic significance.
These mirrored scales (and the chords constructed within these scales) are believed to carry similar harmonic and melodic weight, gravity, tension, resolve, etc... I.e. Negative notes and/or chords can be substituted with conventional notes and/or chords in your key-signature to add alternative tonal expression to a passage of music (without overly compromising harmony with dissonance).
Understanding Negative Harmony - Step 1: (Sort of) Opposites Attract
Consider all twelve notes of the musical scale laid out in a circle, with the tonic and dominant (sort of) opposite each other and linked together (as per the diagram on the right).
Now consider an axis of symmetry perpendicular to the line between the tonic and dominant.
The notes on either side of this axis are now the reflective, mirrored notes from which we can form new, Negative harmonies.
Replace every note in the scale with its opposite (around the axis of symmetry) to achieve your Negative harmonic scale.
E.g. in the key of C we have:
Original: C D E F G A B
Negative: G F D♯ D C A♯ G♯
Note: the Negative scale is played in the descending order of C B♭ A♭ G F E♭ D (I've switched the sharps to their equivalent flats as that makes more sense in the context of this descending scale).
If this still feels rather abstract or difficult to wrap your brain around don't worry, there is another way to figure out your Negative scale.
Negative Harmony: It's Just an Upside Down Scale
Scales are made up of predetermined numerical intervals. Sticking with the key of C major, the notes in the scale are C D E F G A B C (no ♯'s or ♭'s). Let's look at these on a keyboard:
To figure out any major scale, we simply count the number of notes between each note of this scale (all the white notes) and apply those same numerical intervals to our chosen key. For example, the space between C and D is a whole-step or Tone. The space between E and F is a half-step or Semitone (no black note in between). Counting the Tones (T) and Semitones (S) we can determine the numerical intervals of C major to be:
Tone / Tone / Semitone / Tone / Tone / Tone / Semitone
TTSTTTS is the fundamental building block of all major scales. Pick any note and ascend in this numerical fashion; you will play that note's major scale.
Now let's journey to the Upside Down!
To figure out the Negative Harmony scale for C major, we simply take the same numerical intervals TTSTTTS and turn it Upside Down; working negatively, down the keyboard, but with the same numerical intervals.
This gives us the Negative Harmonic Scale for C. This is a hack of sorts that I find easier to remember than the basketball-like diagram from earlier.
Note: whilst this hack gives us the notes we are going to experiment with, it doesn't address the next (very important) point, which is the substitution of notes.
Understanding Negative Harmony: Substitution
The following process of note-substitution is where Negative Harmony firmly comes into its own.
Let's cast our minds back to the basketball-like diagram from earlier. Each note was linked to its opposite counterpart across the Axis of Symmetry.
Now that we're familiar with the notes of our Negative Harmony scale, let's substitute them for their opposite counterparts and start piecing together some new, alternate chords.
The example given (on the right) shows the notes of a G7 chord circled in red with their opposite counterparts notes circled in purple.
G7 notes: G B D F
G7 Negative counterparts: C G♯ F D
Playing the Negative counterparts in the order of C G♯F D is a bit of an impractical, two-octave stretch, but if we rearrange the order of notes to a more user-friendly F G♯C D we find ourselves with an F minor 6 chord.
The revelation here (and this is where Negative Harmony starts to get very juicy) is that this principle applies to any and every chord in the scale and we can simply pick and choose when to use it and when to leave things in the original major scale.
Sticking with the G7 example; let's imagine we're composing in (C major) and using a G7 in a traditional (tension inducing) sense. G is the Dominant of C and carries a lot of harmonic weight. It induces a sense of tension that leads the listener to (subconsciously) want and/or expect harmonic resolve (a return to the Tonic of C or at least its relative A-minor). The 7th is often added to the G in this scenario to further increase and exaggerate the tension in the chord.
Using the principles of Negative Harmony, we can substitute the G7 for an Fm6 instead. The Fm6 momentarily breaks from the key signature of C major as it contains an A♭ (not found in C major), however there is still a pleasing (non-dissonant), almost curious or suspicious-sounding relationship between C major and A♭ (when used correctly) that the Negative Harmony principle exploits.
Furthermore, whilst not inherently the same, the tension of G7 is reasonably comparable to that of Fm6. I.e. the chord should still provide adequate tension for your composition, but do so with a very different tonal colour that momentarily modulates us out of the key of C major into one of E♭ Major (or C Aeolian).
Less is More (and Melodic Substitutions)
From experience, I've found that applying Negative Harmony just once or twice within a song that otherwise entirely adheres to its key signature can not only be ear-catching but more importantly increase the emotional significance of a passage of music.
The same is true of substituting Negative notes melodically. As soon as you break out of a key signature, you introduce new notes that can (for the duration of the key-breaking chord) be played with little to no dissonance. For example, if we're replacing a G7 with an Fm6 (as discussed above), there's no reason why our melody can't also include an A♭ or possibly other substituted notes from the Negative Harmony scale. This will further enhance and emphasise the emotional significance of the Negatively Substituted section.
C Major Chord Charge - Negative Substitutions
To sum up and for quick reference, let's look at the major and minor triad chords in the key of C and how they convert under Negative Harmony (inverting the substituted notes is required to form a logical and useable chord). Notice how the Majors all become Minors (and vice-versa).
(Note: I think it's safe to say that we can somewhat ignore the B Half-Diminished chord at the top end of the scale (hence I've left it out)! Let's be honest, top of the scale half-diminished chords almost never get used in isolation and are typically used as part of wider (sometimes key-breaking) chordal structures. Furthermore, with Negative Harmony, half-diminished chords convert into half-diminished chords, which really isn't noteworthy as; due to the structural nature of diminished chords, there are in fact only three diminished chords, with all others being inversions of the first three. Either way, the last chord in the scale isn't a major contributor or point of interest when discussing Negative Harmony)
Is that it?!
Well... yes! That's essentially Negative Harmony in a nutshell; some alternative (yet still harmonically key-friendly) notes and chords that you can swap out with the original key, at any given time for added colour and spice; a quick and interesting way to modulate key-signatures, adding more expression and freeing you from the trappings and confines of your key signature, without ever getting into overly dissonant territories.
To save you the hassle of working out lists of alternate chords for whatever key you're working in, I've put together a PDF that charts the triads, 6th and 7th chords of every major scale along with their respective Negative Harmony substitutes. You're welcome :)
In truth, using the kinds of chords the Negative Harmony principle gives you is nothing new. People have been doing it intuitively for hundreds of years and they're especially commonplace today in Jazz, RnB, Soul and Funk. You'll also find them in Pop and Rock, for example Layla by Derek & The Dominos.
This song has two distinctly different passages. The first half of the song is what everybody knows (the one with the riff)! The second half has a slower, more melancholy, piano-led passage (in the key of C♯ Major). At 3:27 on the video we can hear that where one might typically play a G♯7, the pianist plays an F♯m6 (this is Negative Harmony as discussed above, only in the key of C♯ as opposed to C).
OK, the F♯m6 in the case of Layla is actually underpinned by a B bass note, which technically makes it B7add2, but the emotional affect is the same and for the sake of this discussion, let's call it an F♯m6 with a B bass note (as that's what Bobby Whitlock is playing on the piano).
Now, when Eric Clapton and Jim Gordon composed this passage of music, I'm pretty confident that they weren't thinking about Negative Harmony! Levy's theory hadn't yet been published after all. This is what I mean when I say people have been intuitively using these sorts of harmonic variations and tonal palettes for a long time.
So Why all the Fuss?
It's fair to say that Negative Harmony already existed and Levy just distilled it into a tangible, academic principle and working practice. If that's the case, why has there been so much intrigue and discussion about it in the last few years?
I guess it's a case of the more you know; the more you know! I've played the piano for twenty years and have been composing my own tunes and chord sequences for almost as long. It took me a great deal of playing, practice, experimentation, listening and studying before Negative Harmony-esque chords and melodic phrases became part of my subconscious and intuitive arsenal of harmonic options.
I don't begrudge or resent the time spent acquiring this knowledge and experience, but if you'd have shown the Negative Harmony principle to me when I was 14 or 15, I'd have been able to fast forward and leap ahead in my development, making significant progress with regards composition; ultimately making me a better practitioner at a younger age.
I hope therefore that this article has helped demystify what might appear on the outset to be a rather complicated and confusing topic, but one that's actually just a framework for something most composers eventually come to use without necessarily even realising it. There's a high chance you're already using aspects of Negative Harmony without consciously knowing, and perhaps, like me, understanding Negative Harmony (in a more academic sense) will reinforce your intuition with solid, theoretical knowledge resulting in a quicker and broader creative process when composing/arranging.
Happy composing and see you in the Upside Down!
Note: This article is a summary (of sorts) of my knowledge of Negative Harmony. I've gleamed this understanding from various YouTube videos by the likes of Rick Beato and Adam Neely, along with reading a long and winding thread on Reddit. There are however several other ways to think of and understand Negative Harmony. One quite popular method is the Helix approach (although I found this less intuitive than the Basketball method demonstrated above). If you want to learn more about the different ways in which people understand and utilise Negative Harmony, simply get Googling... There's a mountain of information out there.