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Discover the theoretical basis for negative harmony.
How can it improve your songwriting?
We provide examples to help you make sense of it all.
The concept of negative harmony draws on the work of Ernst Levy and Steve Coleman to codify a reimagining of harmony across the plane along which tonal harmony is constructed.
The tonic upon which tonal harmony is built gives way to a “generator” tone from which pitch relations emanate in two directions at once.
From the primarily theoretical work of Ernst Levy’s A Theory of Harmony to the more practical improvisational applications of Steve Coleman’s Symmetrical Movement Concept, negative harmony offers an innovative approach for musicians spanning a broad range of genres and skillsets.
Having drawn the spotlight recently thanks to a Jacob Collier video, discussions of negative harmony have picked up some momentum.
In the world of music theory it is a relatively recent innovation, but Ernst Levy’s A Theory of Harmony, which lay the groundwork for negative harmony, was published in 1985, leaving plenty of time for composers, theorists, and improvisers to make use of the concept.
What Is Negative Harmony?
The lion’s share of music theory content related to harmony is based on tonal harmony, in which pitches are categorized and arranged based on their relationship to a central pitch, known as the tonic.
The tonic is the foundation upon which harmonic structures are built. Steve Coleman’s restatement of Ernst Levy’s elegant metaphor situates tonal harmony as earthbound, with a conception of gravity as a force constantly pulling pitches and harmonic structures downwards towards the tonic, whereas negative harmony recognizes a more accurate perception of gravity, as something that pulls towards a center.
In this way, negative harmony is a means of representing the tendency towards a center from both directions, not simply from above.
The word preferred by both Ernst Levy and Steve Coleman to characterize this center and thus replace the “tonic” is “generator.”
The generator tone is essentially the same thing as the tonic, but harmonic structures emanate from it in both directions: the positive (tonal harmony, or “telluric” harmony) and the negative (negative harmony, “absolute” harmony, or as Steve Coleman refers to it, the “Symmetrical Movement Concept”).
How Do We Make Negative Harmony?
Initially, it would seem that negative harmony would turn everything we know about harmony on its head. While it may seem like a major shift in our understanding of harmony, it is less earth-shattering than one might think. Let us begin with triads.
Our most common triads are the major and minor triads, but this distinction is not necessary with this new conception of harmony. This makes sense, as major triads are triads generated from the tonic upwards, whereas minor triads are the same thing generated absolutely, from the generator tone down.
Thus, a C Major triad is generated upwards from C (the tonic), E (the major third above C), and G (the perfect fifth above C). The C minor triad is generated using the same formula, but downwards from G as the generator, E♭ as the major third below G, and C as the perfect fifth below G.
This process of reflecting the C Major triad to generate a C minor triad, or a triad built on the generator tone G, makes these two chords mirror chords, as they are reflected across an axis exactly halfway between C and G, right in between E♭ and E.
This axis, re-conceived as the flat-3/3 axis in any key, is the one Jacob Collier mentions specifically as that which “converts perfect to plagal” in those dominant triads in the telluric conception become pre-dominant triads when flipped across the flat-3/3 axis.
Negative harmony is not restricted to single triads; it can be applied to melodies, key areas, and entire chord progressions. Take, for instance, the key of C Major, made up of the diatonic pitches C, D, E, F, G, A, B, and C.
These pitches, like those of any major scale, are derived using a formula of whole-steps (W’s) and half-steps (h’s) arranged as follows: W, W, h, W, W, W, h. If we were to reflect this formula across the flat-3/3 axis, we would generate the following absolute scale: G, F, E♭, D, C, B♭, A, and G.
The pitches of the key of C, reflected across the flat-3/3 axis into absolute harmony, are thus the same as the parallel minor of the key of C Major, which is C minor.
It is worth noting that the relative minor key area, which contains the same diatonic pitches as the original key, can be derived through a reflection across the axis halfway between 1 and 3, which in the case of the key of C Major spans D to flat-6, A♭.
Reflecting the pitches of C Major across this axis yields the pitches of a minor, the relative minor of the key of C Major, but the root note C becomes E, D is unchanged, E becomes C, F becomes B, G becomes A, A becomes G, B becomes F, and C becomes E.
Returning now to the flat-3/3 axis from Jacob Collier’s example, let’s reflect a common chord progression across the axis into negative harmony. In C Major, the ii – V – I chord progression is D minor – G Major – C Major.
We will hold off on 7th chords for the moment because they complicate things just a bit and require an extra step to work smoothly when reflected into negative harmony.
The D minor chord reflected across the flat-3/3 axis trades its root note, D, for the root F. The minor third below F, D, becomes the third of the chord, and the major third below D, B♭, becomes the fifth. This chord – B♭, D, F – is the same thing as flat-VII written in telluric terms.
The G, B, D of the G Major triad reflected across the E-flat/E axis become C, A-flat, F, which is iv in telluric terms. This is what Jacob Collier refers to in his statement that this reflection “converts perfect to plagal”: the V – I of a perfect cadence is replaced by the iv – i of a plagal cadence in this particular reflection across the flat-3/3 axis.
As previously mentioned, I (Major) becomes i (minor) when reflected across the flat-3/3 axis, thus the ii – V – I chord progression in this instance of negative harmony becomes flat-VII – iv – i.
If instead of a V triad the V chord was a V7 chord, we would be working with a G7 on the telluric side of the axis. Reflecting the G7 across the flat-3/3 axis would present us with more than one possible chord, which complicates things somewhat.
The G would become a C, the B would become an A♭, the D would reflect to an F, and the F would reflect to a D. The two possible chords formed by this reflection would thus be D-7♭5 (a D half-diminished 7th chord) or an F-6 chord (an F minor triad with the 6th added).
This question, which is really a question of which reflected pitch makes the most sense as the root of the chord, should inevitably lead us to choose the latter, F-6, as our preferred construction of this chord, as the 7th on the telluric side of the reflective axis should not end up with an outsized role on the absolute side of the axis. Thus a V triad reflecting to a iv- triad balances most intuitively with a V7 chord reflecting to a iv-6 chord.
If you need a more concrete explanation of why this line of thinking makes the most sense, check out Frédéric Chopin’s Nocturne In A-flat Major (covered in our examples below).
Now that you know the more technical elements of negative harmony, let’s spend some time with the human faces who gave us this idea.
We will begin with Ernst Levy, the originator of the concept, and proceed to Steve Coleman, who really fleshed it all out into practice, and finally to Jacob Collier, who is responsible for re-popularizing negative harmony in recent times.
Ernst Levy was a performer, composer, and theorist born in Basel, Switzerland in 1895. He gave his first public piano performance at the age of six and lived in the United States from 1941 to 1966, during which time he taught at the New England Conservatory, the University of Chicago, Bennington College, the Massachusetts Institute of Technology, and Brooklyn College.
He considered his work as a theorist to pick up where Riemann and Rameau left off, and his book, “A Theory of Harmony,” was published in 1985, four years after his death. In the text, he outlines his theory of “harmonic undertones,” which lay the foundation for negative harmony.
Levy was a well-rounded musician, with an impressive body of compositional work including over a dozen symphonies, a concerto for cello and orchestra, seven piano sonatas, a large collection of chamber music, and art songs in English, French, and German.
His recordings of the last Beethoven sonatas and the Liszt sonata are equally formidable, making him equally regarded as a theorist, composer, and performer.
Steve Coleman grew up in South Side, Chicago, and started playing saxophone at the age of 14. By the time he was 22, he had moved to New York to play in big bands and begin a series of collaborations that would take him all over the world to play and work with other musicians.
His body of recorded work is immense and his original thinking on the subject of harmony and rhythm has no equal among contemporary theorists.
In collaboration with several other young African-American musicians in the 1980s, he launched the M-Base Movement, which stands for “macro-basic array of structured extemporization.”
The movement represents a particular approach to making music and other art forms, as there are poets and dancers associated with the movement as well.
Coleman is particularly interested in tracing his music to its roots in the African Diaspora, which led him to travel to Ghana to encounter the complex polyrhythms of the drumming tradition of the Dagomba people.
He would later travel to Cuba, Senegal, and Southern India to collaborate and record with musicians associated in one way or another with the music of the African Diaspora. In 2014 Coleman was awarded a MacArthur Fellowship for his innovative work in traditional musical forms.
Jacob Collier grew up in a very musical family in North London. His mother, Susan Collier, is a concert violinist, conductor, and professor at the Royal Academy of Music’s Junior Academy.
Her father, Derek Collier, was also a violinist who performed around the world with orchestras and taught at the Royal Academy. To say that Jacob was surrounded by music from an early age would be an understatement.
From childhood, he had singing roles in film and theatrical productions and then began uploading homemade films of multi-tracked vocals to YouTube at the age of seventeen.
These impressive feats of musical ingenuity attracted the attention of Quincy Jones, who flew him out to the Montreaux Jazz Festival, where he would meet Herbie Hancock and later, in 2015, open for Herbie Hancock and Chick Corea.
Collier’s live shows and his high profile collaborations with acts like Dr. Dre, Pentatonix, Snarky Puppy, and even Pharrell Williams and Hans Zimmer, have put him center stage as an arranger and performer, but he continues to gain notoriety as a theorist as well through his video content and appearances on other channels.
One such video uploaded by June Lee features Jacob Collier explaining the theory behind negative harmony, and thus ignited a flurry of activity by fans hoping to learn more about the subject. Hopefully, the sections that follow will help to answer some of the questions born of that interview.
Examples Of Negative Harmony In Use
Depending on one’s purpose, negative harmony can provide anything from a broad new palette of less common chord progressions to some fresh ideas for use in re-harmonizations and arrangements of familiar tunes.
As our first example demonstrates, it can also provide a useful framework for analysis in understanding musical choices that sound good even though they break the rules of diatonic harmony.
Frédéric Chopin – Nocturne In A-flat Major
Frédéric Chopin is among a handful of late romantic composers who made extensive use of the iv-6 chord. One perfect example of this chord in action can be found at the beginning of his Nocturne in A-flat Major; Op. 32 No. 2.
The piece opens with an A♭ Major chord, proceeds to a D♭ minor chord, to which the 6th, B♭, is added, before resolving in a plagal cadence to A♭ Major.
The usage of the iv-6 could be explained in one of two possible ways. Traditionally, it would be presented as a modal interchange.
In other words, the iv-6 chord is not diatonic in a major key area, so the composer who employs a iv-6 chord in a passage constructed in a major key area is essentially taking one step into a different key area to borrow this chord before crossing back over.
This traditional explanation leaves something to be desired, though, because it does not explain why this “borrowed” chord sounds so at home in the progression. Take a moment to listen to the first three chords once more: does the iv-6 chord sound out of place?
The other possible explanation dispenses with the notion of modal interchange to identify the iv-6 chord as the reflection of the V7 chord across the flat-3/3 axis turning perfect to plagal.
It is impossible to say exactly what was going through Chopin’s mind when he wrote the first three measures of this piece, nor can we say with certainty what he, Mendelssohn, or Rachmaninov were thinking any other time they used the iv-6 chord outside of its typical diatonic context.
Regardless of how this chord found its way into their music, the use of negative harmony as a tool for analysis offers us a much more satisfying explanation for why certain non-diatonic chords work so well within an otherwise diatonic passage.
Phil Wilkinson Trio – Giant Steps
Phil Wilkinson’s re-working of Giant Steps makes use of negative harmony to reflect the ii – V – I across the flat-3/3 axis into plagal cadences.
Have a listen to the recording from his first album with the Phil Wilkinson Trio and compare it with the original Giant Steps to get an idea of one practical application of negative harmony for arrangement and reharmonization purposes.
You might have noticed that our examples of negative harmony in use were rather sparse. The unfortunate state of things at the moment is that all of the excitement about negative harmony as a theoretical tool has yielded fairly little actual music.
There are likely to be more YouTube videos online explaining negative harmony than there are actual examples of music applying negative harmony.
That’s where you come in. Whether you came here looking for a new way to fill an empty track or a means of understanding something that doesn’t seem to follow the rules of diatonic music, now is the time to take on the challenge of writing something new with these new skills at your disposal.
Turn what you already know on its head and see what happens, and whatever the result, be sure to share it with us!