First described by the musicologist Ernst Levy, then popularised by Jacob Collier, negative
harmony is a way of generating notes, chords, and progressions using inversion. It’s based
on the idea that, in any given key center, every note or chord has a “negative” or
“inverted” equivalent that can be found by reflecting the chord across that key centre.
If that sounds confusing, don’t worry: negative harmony is quite intuitive when explained
visually.
However, in order to understand negative harmony, you must first understand that, in relation
to a given key, chords and progressions can be described by a set of qualitative properties,
each one with an opposite. Forc example, major chords sound “happy”, while minor chords
sound “sad”, at least to Western audiences. Other pairs of attributes include “clear”
vs. “muddy”, and “perfect” vs. “plagal” for cadences.
In essence, all of these characteristics are derivatives of the “bright” and “dark”
sides of the circle of fifths. The light side refers to the sequence of notes clockwise
from a given note, while the dark side refers to the notes counterclockwise from this given
note. For example, using c as our chosen note, a chord constructed from the “bright”
side sounds like this [...], while a chord constructed from the “dark” side sounds
like this [...]. In terms of the properties discussed earlier, the light side is “happy”,
“clear”, and is a series of perfect cadences. Oppositely, the dark side is “sad”, “muddy”,
is a series of plagal cadences.
The idea of negative harmony is to switch all of these attributes for a given chord.
Major becomes minor, clear becomes muddy, perfect becomes plagal, bright becomes dark.
Negative harmony can be thought of as a musical “function” that takes a note and a key
center as inputs, and outputs a note. So, how is this function defined? How do we actually
convert notes, chords, and progressions?
Before converting entire chords, we must start with single notes. In a given key, every note
has a “negative equivalent” that can be found by “reflecting” the note across
the key’s axis. Now, this doesn’t make much sense without being explained visually
using a circle of fifths. On the circle, this key’s axis is the space between the tonic
and the dominant of the key. For example, in the key of c, the axis is between c, the
tonic, and g, the dominant, and looks like this. We can then take a note, say d, and
reflect it by finding the note directly across the axis from it. Thus, in the key of c, the
negative version of f is d, and the negative version of d is f. That’s it!
Now, if you’ve studied music, especially counterpoint or composition, this shouldn’t
seem particularly new: composers have been inverting melodies since at least the baroque
era. However, those composers only inverted melodies around a pivot note, usually the
tonic. Ernst Levy’s stroke of genius was not only
pivoting around a key center instead of a note, but by applying this idea to harmony.
Entire chords can be reflected along a key center: just reflect each note in the chord
individually like before.
Just like every note has a negative equivalent in a given key center, so too does every chord.
The negative equivalent of a major chord is a minor chord. Next, the dominant 7th is equivalent
to the half-diminished 7th, the major 7th is equivalent to the minor 6th, and the minor
7th is equivalent to the major 6th. The diminished 7th stays equivalent to itself.
Similarly, entire chord progressions have negative equivalents. Take cadences as an
example: the negative version of a major perfect cadence [...] is a minor plagal cadence [...]. Likewise,
the negative equivalent of a major plagal cadence [...] is a minor perfect cadence [...].
To get a feel for how negative harmony actually sounds, listen to this chord progression,
consisting of a chain of half cadences around the bright, clockwise, side of the circle
of fifths. [...]. Now, listen to the “negative” version. [...]. As you can see, the “negative
version” travelled in the opposite direction, in a series of a plagal half cadences. Thus,
the effect of negative harmony illustrated.
The reason that both of these versions sound equally coherent, musically speaking, is because
the voice leading is equivalent: every note carries the same amount of tension. This is
the fundamental beauty of negative harmony: a musical incarnation of duality, of symmetry,
of dark and light, of two equal and opposite halves, coming together to make
a whole.