The Four Ways to Write Music - Most Composers Only Know Two

In total, there are four ways to write music. Two of them live in the diatonic world you (very likely) already know: the world of keys, scales, and chords. The other two live in the world of interval theory, where notes are measured by the distances between them as opposed to sticking to a scale. Most composers spend their whole creative lives inside only two of the four quadrants and never experience the flexibility that comes with interval magic. This article hands you the complete map.

Two questions build the map

The map comes from two simple questions.

Some music unfolds in time, one note after another. That is horizontal writing: lines, melodies, everything you could sing. Instead, we can also stack notes on top of each other so they play at the same time. Of course, that is vertical writing: chords (or vertical structures in general), harmonies, everything you play as one.

Now things get interesting. Most composers stick to the diatonic system, which includes keys, scales, and related scale tones. That's the part most composers gravitate toward because it's the foundation of our music theory education. 

But that's not the only way to think about music. We can also look at the intervals and measure the distances between them in half-steps or chromatic steps. This lets us move away from scales, keys, and diatonic restrictions.

These two questions give us four possible answers, with two answers for each. That's how we create and move through the four quadrants. Each of those quadrants is a valid way to write music and they lead to different results. Think of them as different colors and possibilities that become much clearer once you understand how the quadrants differ from each other.

(1) Horizontal - Diatonic: Lines On Scales

Since we're going to come full circle, it's best for you to start in the quadrant you know best. Most composers like strong, singable melodies, so let's start here.

The usual way to write a melody in the diatonic system is this: first, choose a key and set the tonal center. Then, you write the line using only the notes of the scale. And here is the thing: This approach works really well all the time. Tens of thousands of composers have written hit songs and classical pieces that we can still hear today because they focused on strong melodies.

Since our Western culture loves strong melodies, we’re all pretty good at spotting strong lines, which makes that quadrant the best place to start any melody. I use it a lot, even when the rest of a piece is all about intervals.

Let's listen to a melody just as it is, with no arrangement or accompaniment.

By the way, if you want your audience to remember what you wrote, make your lines easy to sing. A melody that jumps over big intervals or uses only chromatic steps is hard to remember, so it never gets catchy. Melodies you can sing stay in people's memory!

(2) Horizontal - Intervallic: Lines As Distances

Now take the melody you just wrote and look at it through a different lens. Let's stop thinking of notes as scale degrees and start looking at how many chromatic steps there are between each note. That's the change from thinking in diatonic terms to thinking in intervals. We just moved from the upper right quadrant to the upper left quadrant, which we call string theory. 

A string is just a line or a piece of a line that stands on its own and doesn’t need to follow a scale. The true identity, or DNA, of a string is the sequence of numbers that connects one note to the next. That sequence is the horizontal formula, and it fully describes the line, no matter which note you start on.

Why rename something that already works in one system? The numbers are generous and they open many musical doors that would otherwise be hard to see. In fact, a short formula of three to four distances can quickly grow into a full 32-bar composition using interval-based composition techniques. 

These numbers can take you to places that the diatonic approach never reaches unless you define some exceptions and workarounds. This works as a great addition to what you already know, and you can even combine it with the diatonic knowledge you enjoy hearing. 

(3) Vertical - Intervallic: Main ICs (Interval Combinations)

Here is where the map turns a corner, quite literally. We can take the distances from a line and use them vertically. That way, we can create vertical structures that are completely free.

When intervals sound together instead of one after another, we call the result an interval combination, or IC for short. Every chord you have ever learned lives in this family: major and minor triads, sevenths, ninths, elevenths, all the good stuff.

But the family is bigger than the chord catalog. A tight cluster of two half steps stacked on top of each other is a perfectly good IC, and you will not find it on any of the usual seven-tone scales. You might want to check out the "1+1"-interval game we talked about in other places, as it fits nicely into this context.

Now that we know what an interval combination is, let's discuss the "main ICs" and what they mean. You know we can place any vertical structure in different positions. These correspond to the root position, the first inversion, and the second inversion, just like you learn from a triad. The notes are always the same, but they appear in different octaves, and the numbers from one note to the next vary with each position. 

When you look at the distances between the notes of a major triad and all the positions we can move into, the root position actually has the shortest distance on the outer notes, which is 7 chromatic steps. So for major and minor triads, the main IC is either "4+3" for a major triad or "3+4" for a minor triad.

(4) Vertical - Diatonic: Chords

Now that we know ICs live all by themselves, let's bring them back into the diatonic world. The easiest way to do this is to define the root tone of the scale and place it below the IC in the bass register. That root tone acts as the anchor under an IC, and it is the note that helps the vertical structure settle into the diatonic world. 

Not every IC works well in the diatonic world (think of the "1+1"). But we have many anchor notes we can put under an IC, and the context we create with the anchor helps us understand the vertical structure later. The whole foundation of this is the harmonic series. 

Almost all the music you hear on the radio falls into this quadrant when you look at harmony.

All of those transitions can be reversed, and we can always take the anchor off any vertical structure and treat it as an IC. That takes us back to intervallic thinking, where it can do things that no chord symbol would predict.

If you learn and use this single technique, you can write chord progressions that sound fresh and unexpected, and it will set your writing apart from everyone else's.

Your taste defines the blend

Here is what matters most: the four quadrants don’t compete with each other; instead, they work together. They help you write more interesting music and explore new areas that were previously out of reach.

A singable line from a scale becomes a string of numbers which you can use to explore new musical territories and interval combinations. An anchor tone brings an IC home as a chord structure, and lifting it sends the music back out into the open. Your composition can explore all four quadrants, and you decide how much of each quadrant you want to put into the music. That freedom of movement keeps your music alive and in your hands.

In the end, it’s not about theory or how much theory you put into your music but really a matter of taste, and only you can decide that. Think of the quadrants as tools, and their only job is to help you express your vision and musical artistry.