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What Is Negative Harmony?

Negative Harmony can be one of the most difficult musical theories to come to terms with. In a sense, it is based on simple principles, and it is just a reversed mirror image of something. 

That is quite a simple concept to understand if you are looking at something physical. But it takes on a whole new level of understanding in music. Because then you have to transpose notes into other notes and then place them in reverse order. It is called inverting notes around an axis.


A Tool for Composition

Music theory is full of different concepts that are tools for the composer. Negative Harmony is just another one. But what is negative harmony in practical terms?

The difference with this theory is that it involves what you could call geometric mapping. Taking one set of notes and creating a different set of notes with a similar harmonic function.

A Theory of Harmony

This was a book written by Ernst Levy who was a composer and a theorist from Switzerland. The book had little impact when it was first published as recently as 1985. 

It gained its momentum when British award-winning vocalist/multi-instrumentalist Jacob Collier started to make it popular. American saxophonist Steve Colman soon followed suit, and now it has gained reasonable recognition.

What Does Negative Harmony Do?

What Does Negative Harmony Do

It is used to create some unique melodies and chord progressions. For some composers, that will be a new box of tricks to play with. However, it is quite complex and involves making some calculations. 

Don’t run away screaming at the thought just yet

A popular quote states that Music Theory is only “mathematics in sound.” It may or not be true, but Negative Harmony might be the closest you ever come to it being true.

Furthermore, it is certainly worth your time to be familiar with it and even use it. It will open up your ideas in different directions. It’s all about how to use harmonies differently. But, before we start, let’s just remind ourselves about harmony.

Do we understand what harmony is?

It is a simple concept and one around which the whole of our listening experience depends. Simply put, it is when there is more than one pitch, or note, being played at the same time. 

That could be just two notes which some will call a “Dyad,” or maybe you know it as an “interval.” If there are three or more notes played together, then we call that a chord.

Look at Chords in a Different Way

That’s exactly what I hope you will do after reading this. A chord is not just a set of notes. Chords are notes that are in harmony with the root note, and of course, all the variations that exist within it. The notes in any chord relate and respond to each other to create a sound.

All the great composers have understood and embraced this, from Bach to Mozart, through to Beethoven and Mahler. At a different and more basic level with Lennon and McCartney, Paul Simon, Rick Wakeman, Dave Gilmour, and Mark Knopfler. And, of course, plenty of others. All of them love constructing their chords to enhance their music.

Harmony is Vertical

The melody and the rhythm of a song could be described as horizontal. That is how it is portrayed to use. It visually travels across the page horizontally from left to right. 

Harmony lines are not like that. The notes sit vertically on top of each other on the page in the sections. To read them, you look up and down, not across. A basic and, some might say, naive explanation. Others have also used it, and it is how I also see it. Okay, it is time to dip our toes into the world of theoretical music.

What is Negative Harmony? 

Everything has an opposite. So says the Law of Polarity. There can be no inside without an outside. No front without a back or a left without a right. 

The Law goes further by telling us that it isn’t only opposite; it is equal and opposite. If it is four feet from the floor to the table, it is also four feet from the table to the floor. If it is fifty miles from Amsterdam to Rotterdam, then it is fifty miles from Rotterdam to Amsterdam.

As I said earlier, Negative Harmony was a concept written about by Ernst Levy in his book “A Theory of Harmony.” He explores the idea of the Law of Polarity within music.

Working Around an Axis

The idea of negative harmony is centralized on the inversion of notes and chords around an axis. Levy says that music has a tonal center. We might call it a key.

The principle is that every note and every chord has an opposite or a “negative” note and chord. These “negatives” are obtained by inversion of the regular chords. The inversion is made around the root note, or keynote, and the fifth above it.

How Do We Invert Notes?

How Do We Invert Notes

You may well have heard of inverted chords or notes before. In standard practice, the lower note of a chord becomes the higher note.

For example, in a C major chord triad, the notes are C, E, and G. In a first inversion, it would place C as the higher note and would read E, G, and C. In Negative Harmony, however, inversions are different. You could say that they are calculated.

Rotation Around an Axis Point

In Negative Harmony, to invert means to rotate around a specific axis point. And that rotation is calculated with consideration of the distance. You take the distance, or interval, between your original note and the axis point. You then move the same distance but in the opposite direction.

Let’s use C as an example again. From C to G is, as we know, a perfect fifth. It has a distance of seven semitones or half steps “up.” So to achieve our opposite or “Negative,” we commence at C. But instead, we go “down” the perfect fifth, or in other words, the seven semitones. This will give us a note of ‘F.’

Therefore, the Negative Harmony inversion of a C to G is F to C. This is because they have the same distance or number of semitones between them.

A Negative Harmony of Personal interest?

Take a C and go up a Major 3rd. That is four semitones giving you an E. The negative harmony will therefore be four semitones down or Ab. C and Ab. Personal Interest? 

I have written a whole album, not yet released, using that Negative Harmony concept. A recurring theme that appears in every track. When we know how to make the inversions, we need to know what axis around which we rotate them. 

Working out the Axis of Inversion

This can be somewhat confusing but bear with me on this part. As we have just seen, the axis of the inversion is a distance between the keynote. In our example C, and the perfect fifth, a G. In the key of G, it would be G, to D, and in Eb, it’s Eb, to Bb, etc.

The rotation is not performed around a specific interval but at a specific point. That point is the middle or halfway point between the key or root note and the perfect fifth. This is where it can be confusing.

In-between Notes

The interval for a perfect fifth from the root note is seven semitones. To find the exact middle point, you divide it by two, giving you 3.5 semitones. Therefore, the middle point is three and a half semitones below the high note or above the lower note.

That is known as an “in-between note” because it doesn’t exist. No note is three and a half semitones between the root and the fifth. In our C example, the halfway point, three and a half semitones, will be a note between E and Eb. There isn’t one.

To complete the inversion…

You take a note that is either above or below the “halfway” note. And then do the same in your negative harmony note. In C, you could choose a semitone below the midpoint, i.e., to Eb, rather than E. 

When calculating the negative harmony note, you apply the same formula. That is to choose a note above or below one of the midpoint notes. Then do the same, above or below, to the other midpoint note.

The Key Center

The Key Center

If you take a melody written in C, then every note has to be inverted around the middle of the axis. That will be the Eb or E point. That is the center of the axis created by the keynote or C, and the perfect 5th, which is G. We call that the key center.

To use another brief example, if the first note of the melody was C, then that is lower than Eb by three semitones. To make the inversion for negative harmony, we need to move three semitones in the opposite direction. That is up to three semitones which take us to G.

Once you have got to grips with this formula and set of practices, it becomes a little easier. It takes practice, and when you need to invert a whole melody, then it becomes time-consuming. All I can say is that as you practice, you get better and much quicker at it.

Like a Reversed Mirror

Think of it as looking in a mirror and reversing the image. Whatever key you are in, find your Perfect 5th, seven semitones up. Then find your axis point. Your axis point is your mirror.

Each note to invert, all of them, moves the same distance in the opposite direction from your axis point. If a note goes up to five semitones, then the negative harmony comes down to five semitones.

Negative Chords

Of course, when dealing with chords, it becomes a little more difficult. You are not dealing with a single note but multiples of them. Each note has to be inverted around the axis. One way that can speed up the process is by using the Circle of Fifths. By using this piece of music theory, you can work out the negative inversions of complete chords

If you are not familiar with the Circle of Fifths, it would be a great advantage to use it. And not only for Negative Harmony. If it is something you would like to study, two options to help are Other Harmony: Beyond Tonal and Atonal and The Circle of Fifths for Piano.

Likewise, if you would like some further reading on Levy’s analysis of harmony, the book we mentioned is A Theory of Harmony.

Interested in Learning More about Music?

Our experts can lend a hand. Have a look at our detailed articles on What is Strophic Form In MusicRelative vs Parallel MinorThe Mixolydian ModeThe Aeolian ModeThe Bass ClefThe Minor ScalesThe Scale Degree Names Explained, and Easy Steps to Learning Basic Songwriting for more useful information.

You may also benefit from an instrument upgrade. Check out our in-depth reviews of the Best Cremona Violins, the Best Electric Violins, the Best Electric Cellos, the Best Portable Keyboard Pianos, the Best Digital Pianos for Under $500, the Best Yamaha Saxophones, and the Best Selmer Saxophones you can buy in 2023.

What Is Negative Harmony – Final Thoughts

It is complex and feels like mathematics in music more than anything else. But then, a lot of music theory can feel like that at first. Practice will help you to become familiar with it. And it’s something that can enhance your writing.

Until next time, let the music play.

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About Corey Hoffman

Corey is a multi-instrumentalist who has played in numerous bands over the years, some good, some not so good. He has also written countless songs and recorded five albums in professional studios across America. Today he is a hobby musician but still loves the guitar after over 15 years of playing.

He considers his writing as a way to share what he has learned over the decades with younger generations ad always can't wait to get his hands on the latest gear.

He lives just outside New York with his wife Barbara and their two German Shepherds, Ziggy and Iggy.

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