For me, as a tonality lover, there was a great feeling of achievement as I began to understand new aspects of such a system. The first time I understood IV-V-I progressions, when the concept of having three minor keys clicked, or when I learnt how to expand my progressions by borrowing chords. But as I discovered other systems for composing – like the greek modes and quartal harmony; or even crazier ones like 12 tone technique – I also started wondering if what I knew about functional tonality was all there was to know. And of course it wouldn’t be music if the answer was positive. 

Bela Bartok (1981-1945) was a hungarian composer, pianist and one of the first ethnomusicologists to record folk music, in his case from Hungary and Romania. These recordings were highly influential, as he began to explore ways to mix these folk melodies and sounds into his compositions. He loved folk music, but also wanted in on all those new musical trends from the early XX century, such as the 12 tone technique or polyharmony.

How to merge the emotional rich melodies of folk (backed by arguably simple harmony), with new exciting systems for composing? 

Then he went on to compose all sorts of pieces, basically becoming one of the most influential composers of his era, constantly proclaiming that his music, as dissonant as it could sound, always remained within a tonality system, in order “to show Schoenberg that one can use all twelve tones and still remain tonal”. Years later, Erno Lendvai published various analyses on Bartok’s music, where he developed the Axis Theory in order to analyse some of the Hungarian composer’s work and unravel this new harmonic world.

And now to the juicy stuff… What is axis theory and how do I use it to become better at my craft?

Simply put, Axis Theory is a system that expands the seven notes associated with a major/minor scale, so all twelve western scale notes can form a chord that can play a function. Whereas in the previous version of the tonal system there were seven degrees – each with its own function – now we can play with all twelve notes, assigning each one a function in the traditional sense: tonic, subdominant and dominant.

To know which chords play which functions, you have to look no further than to the circle of fifths. We will do it starting with C as our tonal center. 

Notice that, from f to e, the functions follow a pattern. F subdominant, c tonic, g dominant, d subdominant, a tonic, e dominant (some people like to consider the III degree as tonic, but for this system to work we will consider the dominant point of view), etc. As you can see, a pattern emerges, which we can then extend to all the other tones until we reach f again. Subdominant, tonic, dominant, and so on. An important aspect to note while figuring out your chords, is that if you build a fully diminished chord from one of the notes, you will get all of its Axis Theory equivalent root notes. For example, build a fully diminished chords from C, and you will get the notes C, Eb, Gb/F# and A. These notes will therefore be tonic. If you do the same for G, you get G, Bb, Db and Fb/E, all forming dominant chords within the Axis system. 

We can the separate this classification into the following different diagrams:

As you can see, all the equivalent function tones lie on one end of these axis’ nodes. C lies on the pole of the primary axis, while F# lies on the counternode of the same primary axis. A is located at the pole of the secondary axis, while Eb/D# is in its counterpole. 

Now that we figured which chords play each function, we can begin applying some of these concepts.
Let’s say you have a progression that goes:

C               / F /                G /              C

This is your old friend, the I – IV – V – I progression. Now let’s spice it up by adding some chords in between

C / Eb7       / Ab / B7 /        E / G7 /             C

As you can see, I added a bunch of “strange chords”. But they are all explained within the axis system. C is the tonic, while Eb is the counterpole of the tonic secondary axis, opposite to A. Ab lies on the counterpole of the subdominant secondary axis, while B lies on the counterpole of the subdominant primary axis. Finally, E lies on the pole of the dominant secondary axis, while G is on the pole of the primary dominant axis. So even with all those weird chords, we still have a Tonic (C, Eb), Subdominant (Ab, B7) and dominant (E, G7) progression, which resolves to tonic C.

Now, if you’re a skeptic like me, you must be wondering why this works. It just seems a little random to assign functions this way. And trust me, I was as curious as you to begin testing the system. 

I began by questioning the dominant axis chords. We have G, Db, E and A#/Bb as possible options. G is pretty straight forward, our classic V dominant chord. Db is actually obtained by doing a tritone substitution (Db7 and G7 share the same tritone notes). E would serve as the dominant chord of the IV submediant tone, A, which can be used to resolve to the I degree as well. And finally, Bb is the tritone substitution chord for E, as well as the backdoor resolution for C, popularly used in jazz. As you can see, all dominant chords have a relationship with C, the root note of our axis. And this proves true for all the other chords in the rest of the axis’. Just try different progressions and you’ll definitely get interesting results.

If this wasn’t enough, you can actually think of these chords as tonal centers for sections, passages or to give birth to a wide variety of themes for audio drama, film or video game music. In his Concert for strings, Percussion and Celesta, Bartok divides his first movement into three sections that use C, then F# and finally C again, as their tonal centers. If you go back to our circle of fifths, you will see that C and F# are both tonic and in the same axis! These could represent your hero and your villain as opposites, or even love and heartbreak. Possibilities are endless.

So with this in mind, just remember that Axis Theory, like all music systems, is just a way to organize sound in a way that makes sense for composers and the public alike. Like modal harmony, or polytonality, it is just a convention and expansion of what can be done with our old friend, the 12 tone organization of pitches, but is by no means a set of rules. Just a different light to shine upon a progression to make it sound different.

Leave a Reply