As we delve deeper into music theory, the concepts can become intimidating but this does not mean that it has to be difficult to understand. Today, I will answer the question of what negative harmony is in the simplest way possible.

Sometimes creativity flows, but other times, creating music can be a maze 🙇. Our musical intuition is a great gift and guide, but it can fall short when translating our ideas into a song. And this is normal; it happens to all of us. Consequently, things like negative harmony comes in handy.

Have you ever had an idea for a song written in your music notation software but thought, "I am not quite there yet"? Wanting the melody to stay similar but sound different. Well, that has happened to me too. The first resource that comes to my mind in those cases is changing the key from major to minor (e.g. from C major to C minor).

💡 If you want to learn more about melodies check out these resources:

💡 If you want

Changing the melody from a Major key to a Minor key

Let's go over how to make a key change from major to minor using a quick example. We'll start with a melody and change it from the major key (A) to the minor key (Am). To illustrate this process, let's consider the opening melody of the song Get Lucky by Daft Punk (which I personally love 🤫).

The original melody is in the key of A major.

Now, we know Am does not have any alterations. So the melody in Am will go like this:

A more appealing approach is to keep the key but change the mode.

💡 If you are unfamiliar with modes or would like to refresh your memory, check out this article.

Changing the mode

This time, we will use the Aeolian mode (also known as the minor relative) for the inversion. In this case, it corresponds to F#m, which is the minor relative scale of A major.

As shown in the score of the original song☝️, the melody goes:

V - VI - II - I - VII - I - VII - VI

For the major mode (with A as the starting point), it would correspond to:

E - F# - B - A - G# - A - G# - F

For the minor mode (with F as the starting point), it would correspond to:

C - D - G# - F# - E - F# - E - D

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Now, let's listen to them played at the same time.



Do you notice that it retains the same identity but has a different color? This type of inversion works beautifully and is simple.

🤯 But what if I told you that there is a more elegant way to do it?

Now, let's get down to business.

What is negative harmony?

In a nutshell, negative harmony is a transposition system based on the inversion of a melody or harmony along a symmetry axis. Don't worry if this sounds confusing at first. By the end of this article, it will be crystal clear.

But what does it mean to have an inversion on a symmetry axis? Essentially, you choose a point to act as the central axis, and then create a mirror image of the melody or harmony on either side of that axis.

Let's now return to the example of "Get Lucky."

Get lucky by Daft Punk

Let's say we chose our symmetry axis to be A.

A keyboard can be very helpful for visualizing information. If you have one, use it, otherwise you can use the touch keyboard available on our platform.

Symetry axis in A

Following the melody and the symmetry axis, we get the following:

Original Melody: E - F# - B - A - G# - A - G# - F

  1. Play a 4th down (to the left) from the axis: E
  2. Play a 3rd down from the axis: F#
  3. Play a 2nd up (to the right) from the axis: B
  4. Play A
  5. Play a 2nd down from the axis: G
  6. Play A
  7. Play a 2nd down from the axis: G
  8. Play a 3rd down from the axis: F#
Symetry axis in A graphic

To invert the melody using your axis, reverse the direction of each interval from the axis. If you previously went down, go up, and vice versa.

Here are the new notes:

  1. 4th down (to the left) from the axis: A
  2. 3rd down from the axis: Bb
  3. 2nd up (to the right) from the axis: Eb
  4. A
  5. 2nd down from the axis: G#
  6. A
  7. 2nd down from the axis: G#
  8. 3rd down from the axis: Bb

The resulting melody is:

D - C# - F# - A - B - A - B - C#

Symetry axis in A graphic #2

You can listen to it here:

Now, let's listen the original melody and the inverted one played together:

It's getting interesting, don't you think?

Now that we understand what the symmetry axis is, we can dive into negative harmony.

Negative inversion

This time, we need to put the symmetry axis between not one, but two notes: the third minor and the third major of the key. In this case, for A, the third minor and the third major are C and C#.

Symmetry axis in C

Each note on the left side will have a corresponding note on the right side at the same distance from the axis, and vice versa. This is what I mean:

Transposition with negative harmony
Symmetry axis in C with colors

Now, we take the melody of the song and change the notes.

In our case, the melody goes:

E - F# - B - A - G# - A - G# - F

According to our symmetry axis:

Symmetry axis inversion

Therefore, our negative melody is:

A - G# - D - E - F# - E - F# - G#

Let's listen to it!

To achieve harmony, we should take a chord progression and create the negative inversion for each note of every chord.


For example, let's think about the chord A Major. According to our symmetry axis:

Symmetry axis chord inversion

What chord is that?

Am (A - C - E).

That's it!

This is an excellent example of negative harmony:

Final tip

🎶 I always have a drawing of a piano at hand, on which I place the notes and the symmetry axis. Using a color code, I visualize which note corresponds to which. Here's a piano for you to use. Feel free to take a screenshot or print it out and use it whenever you need it:

Keyboard drawing

Now, let's get our hands dirty! I invite you to open a new score in Flat and make an inversion of this type with one of your favorite songs.

See you next time,