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Negative Harmony – An Explanation That Makes Sense
Negative harmony is one of those rare, ultra-heady theoretical concepts that has found favor among even mainstream musicians in recent years.
The unusual spark in interest in such an advanced theoretical concept has traceable roots; in 2017, jazz musician Jacob Collier discussed negative harmony in a widely viewed YouTube video. At the time, many just shrugged the concept off as a product of Collier’s genius.
Also, because of how the video is filmed, it is a little difficult to hear exactly how Collier explained it.
However, that didn’t stop musicians’ desire to pursue a pragmatic understanding of negative harmony.
What makes negative harmony interesting for classical musicians is this; it’s not widely discussed in university music programs.
In advanced theory courses, we frequently learn about set theory, 12-tone technique, and even Schenkerian analysis. This writer cannot remember a single time negative harmony was mentioned during conservatory studies.
However, what also makes negative harmony interesting is that it has true utility; when composers want to substitute one chord for another in their music, it is another tool in the toolbox for generating creative ideas.
Let’s talk exactly about negative harmony.
The Origins of Negative Harmony
Although negative harmony became more popular due to Collier, it was not invented by the YouTube star.
Rather, it was conceived by Ernst Levy, a 20th-century Swiss musicologist and theorist whose teaching career spanned positions at MIT, New England Conservatory, and the University of Chicago.
Levy passed in 1981, and his 1985 text A Theory of Harmony was posthumously published in 1985.
Although it was not a widely read textbook, Levy did postulate several interesting concepts in music, including harmonic “undertones” (the opposite of musical “overtones”).
Additionally, Ernst Levy laid out his theory of negative harmony in this text.
While negative harmony is frequently credited to Ernst Levy, another scholar did write about a similar subject of musical “dualism,” which has several similarities to Levy’s interpretation of negative harmony. Concepts derived from Hugo Riemann have their own term known as “Riemannian Theory.”
Negative Harmony: A Verbal Explanation
Today, we will illustrate negative harmony verbally, then show you exactly how it works visually.
If you are unfamiliar with music theory, this will definitely be a head scratcher; but if you are familiar with basic tonal functions, then you will likely understand how this all works by the end of the article.
Negative harmony exists in a perfect fifth axis based on the tonic and dominant of a scale.
So, if we are in the key of C Major, the axis is exactly between C and G.
What note is exactly between C and G? Well, it’s not a defined note, but rather, a note in between E and E♭.
Now, imagine this: Between E and E♭a mirror exists, and notes reflect off each other in this mirror.
So, the mirror E is E♭. Go a half-step up from E to F, and the note in the “mirror” travels a half-step down to D. Go a half-step up from F to F♯, and the note in the mirror will travel from D to C♯.
This will continue until you have exhausted all the notes in the chromatic scale.
Negative Harmony: A Visual Explanation
Now, we can illustrate this concept using a visual explanation.
Let’s start with the perfect fifth axis for the key of C major. Keep in mind this works in any key, but for the sake of simplicity we are using C Major.
Here is the perfect fifth in C Major.
Now, try to find the exact note between C and G.
To do this, go up one half-step from C and down one half-step from G, then continue to proceed forward this way.
Eventually you will land on E♭ and E. This is where the mirror exists.
Once we have established the mirror, the fun and understanding truly begins.
In the next image, we can see the relationships between the notes in this mirror.
Here it is as follows:
The mirror exists in C Major right between the dominant and tonic, E♭ and E. Every chromatic ascending interval on the right side of the mirror has a corresponding descending chromatic interval on the left side.
This might seem like just a visual game, however this theoretical concept actually has practical applications as well…
Negative Harmony: Examining Pachelbel’s Canon
So why should this concept exist at all? Does it have any practical application whatsoever?
The answer is resoundingly yes, and here’s how:
Negative harmony is a great method for figuring out chord substitutions. Instead of using A minor in the key of C major, for example, you can use the negative harmony equivalent.
Using the chart above, you can discover the negative harmony equivalent of A minor is, strangely enough, E flat major!
Normally, a composer would never substitute A minor with E flat major, as they are not only a tritone apart, but also completely different sonorities – one is major, the other is minor!
But, when using the toolbox of negative harmony, such a decision may not be so strange.
Let’s take an example of a traditional chord progression vs. its negative harmony equivalent, a I-vi-IV-V-I chord progression in C Major.
What you see above is the traditional Pachelbel chord progression transposed into C Major (of course, the original rendition is in D Major).
Here you can see the chord progression labeled very clearly: I – V – vi – iii – IV – I – IV – V
In C Major, this chord progression C, G, a, e, F, C, F, G (where lowercase letters, and previously Roman numerals, represent minor, and uppercase represents major).
Now, using the negative harmony chart we outlined earlier, let’s take Pachelbel’s Canon and turn it into a negative harmony equivalent of itself:
Pretty interesting result!
Because C and G relate to each other in the negative harmony mirroring, the only note that changes in the first chord is the middle E to E♭!
The entire chord progression actually fits nicely into C minor, which is why we have analyzed it as such.
So, the negative harmony equivalent of I-V-vi-iii-IV-I-IV-V?
IS in fact, in minor, i-iv-III-VI-v-i-v-iv!
Negative Harmony – Practical or Academic
As you can see above with Pachelbel’s Canon, writing chord progressions with negative harmony offers an unconventional tool for writing music.
It starts to get even more interesting incorporating 7ths and 9ths into negative harmony related chords; while in the example above major often becomes minor, and minor becomes major, 7th chords can start to take on other kinds of qualities.
For example, in the key of C Major, the negative harmony equivalent of G7, the dominant 7th chord built on the 5th scale degree, becomes D half-diminished 7th.
Strangely, this feels very musical to replace G7 with D half-diminished 7th; both resolve very well into the root position triad.
So, all of this leads to a question about the practical application of negative harmony. Is this exercise practical, or is it completely academic?
Our perspective is that it’s both. For the composer who wants to write a chord progression that is unconventional or different from a previously stated progression, negative harmony is a sounds-good method for choosing new chords.
However, the academic study of negative harmony is fascinating as well. Something that I hope a researcher will eventually do is find instances of negative harmony in traditional classical music.
For example, perhaps there is a piece of Chopin’s, Beethoven’s, or Mozart’s where musically it makes sense to go from I to V7, but instead goes from I to ii half diminished 7th.
It’s amazing that a single concept of high-level musical theory has even made it this far into the collective conscious of musicians’ minds. I guess that’s the power of making music on YouTube.