‌‌As we go deeper and deeper into music theory, concepts appear to be intimidating. The subject matter becomes increasingly complex, but this does not mean that it has to be hard to understand. Today I'm going to explain what negative harmony is in the simplest way possible.

Sometimes the creativity flows, but some other times, creating music can be a maze 🙇. Our musical intuition is a great gift and guide but can fall short when translating our ideas into a song. And this is normal. It happens to all of us. Consequently, things as the negative harmony exist.

Have you ever had an idea for a song but thought: "I am not quite there yet"?

For example, wanting the melody to stay similar but sound different.

Well, that has happened to me too. The first idea that comes to my mind in those cases, naturally, is changing the key from major to minor.

From major to minor

Let's go over how to make this change with a quick example.

The main idea is to take a melody and change it from the major key to the minor key (eg. from A to Am).

Let's think about the opening melody of the song Get Lucky by Daft Punk (which I love 🤫).

The melody is in A.

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

A more appealing way of doing this is keeping the key but changing the mode.

💡 If you don't know what the modes are, or just want to refresh your memory, check out this article.

Changing the mode

This time, we will make the inversion using the Aeolian mode (or the minor relative). In this case, it corresponds to F#m, which is the minor relative scale of A major.

As you can see in the score of the original song☝️, the melody goes:

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

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

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

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

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

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 lovely, and it 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, it is a transposition system based on the inversion of a melody or harmony on a symmetry axis.‌‌

Don't worry. Keep reading, and I promise this will be crystal clear by the end of this article.

So, what does it mean to have an inversion on a symmetry axis?

You choose a point as a central axis from which you make a mirror inversion from one side to the other.

Let's go back to Get lucky.

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

A keyboard helps a lot since it helps you visualize the information. You can use a keyboard if you have one, or you can use the one available on our platform.

Now, following the melody, and having the symmetry axis, we got the following:

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

  1. You play a 4th down (to the left) from the axis: E
  2. You play a 3d down from the axis: F#
  3. You play a 2d up (to the right) from the axis: B
  4. You play A
  5. You play a 2d down from the axis: G
  6. You play A
  7. You play a 2d down from the axis: G
  8. You play a 3d down from the axis: F#

What you are going to do now is to invert the melody using your axis. The times you went down, you will go up and the other way around.

In other words:

  1. You play a 4th up (to the right) from the axis: D
  2. You play a 3d up from the axis: C#
  3. You play a 2d down (to the left) from the axis: F#
  4. You play A
  5. You play a 2d up from the axis: B
  6. You play A
  7. You play a 2d up from the axis:  B
  8. You play a 3d up from the axis: C#

You get:

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

You can listen to it here:

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

It is getting interesting. Don't you think?

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

The negative inversion

This time we have to put the symmetry axis between not one but two notes: the 3d minor and the 3d Major of the key. In this case, for A, the 3m and 3M are C and C#.

Each note on the left side will have a corresponding one on the right side at the same distance from the axis and vice versa.

This is what I mean:

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:

Therefore, our negative melody is:

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

Let's listen to it!

For harmony, we need to take a chord progression and make the negative inversion for each note of each chord.

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

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.
I leave you this piano. You can take a screenshot, print it, and use it whenever you need:

Now, let's get our hands dirty! I invite you to make an inversion of this type with one of your favorite songs.

See you next time,