In music, you’ll often hear people talk about how specific notes or chords “function” in a certain song. How these notes and chords function is linked with the harmonies they create.
This article is all about harmonic function in music – what is it, how does it work, and how can we analyze it? To learn all this, first we have to start with a recap of what harmony is.
What is Harmony in Music?
Harmony, in its most basic sense, is what happens when more than one note is played at a time.
This can be in the form of intervals – two notes at a time – or chords, which are three or more notes played simultaneously.
We can think of harmony as the “vertical” part of a piece of music, whereas melody and rhythm deal with the “horizontal” aspect of music.
Most music you listen to is called tonal music.
This means it has a main note and chord that is considered the central focus of the music – what is called the tonic.
This is usually found out by looking at the key signature of a piece, and a song with a tonic of C Maj is said to be “in the key of C Maj”.
What is Harmonic Function?
The term Harmonic Function (also called Diatonic Function) is used to describe how a specific note or chord relates to the tonal center of a piece of music.
The term “function” means how something is used to perform a specific task or get something to work.
Therefore, the concept of harmonic function takes a chord or a note and describes how it works in a melody or in a chord progression.
Is a specific chord close to the tonic, or far away?
Is it moving from the tonic to somewhere else or leading back to it?
Is it related or unrelated to the tonic?
These are questions that deal with harmonic function.
A chord’s harmonic function can be figured out by the notes that make up the chord, what chords usually tend to precede or follow it, or where it is typically placed in a chord progression.
The Two Types of Harmonic Function
There are two main theories of Harmonic Function and how it works.
- the German Theory
- the Viennese Theory
The German Theory was created by Hugo Riemann in his book Harmony Simplified in 1893, and the Viennese Theory was developed about a half century later by Simon Sechter, Arnold Schoenberg, and Heinrich Schenker.
Both are still in use today, and most musicians you would talk to use a combination of the two theories in their own understanding of Harmonic Functions.
Let’s take a look at both.
German Functional Theory
The German Theory of Harmonic Function states that a note or chord can have one of three functions in a piece of music.
- Tonic function
- Dominant function
- Subdominant function
There are three chords in any key that can be used to fulfil any of these three functions.
Each function has a primary chord associated with it, and then there are two other relative chords – one a 3rd above and the other a 3rd below – that can also function as such.
But, before we talk about these functions we’ll cover how we name them.
We name chords by the note of the tonic scale they are based on.
So, if a song is in C Maj, we take a C Maj scale – C, D, E, F, G, A, B, C – and assign a number to each note, called a scale degree.
Learn more about scale degrees here.
So, in the key of C, a D min chord is built from the note D, which is note #2, so we call it a ii chord, and same for the others.
The tonic, as we first mentioned above, is the main chord of a song – it is the chord built upon the note that the song is in.
If a song is in E Maj, then the note E and the E Maj chord are the tonic.
The tonic has a feeling of stability and rest, because it is usually the place where a song begins and ends.
The primary chord that has a tonic function is the I chord (the chord built from the first note of the scale that the song uses).
The two other chords that could potentially function as tonic chords are the III chord (in the key of C Maj this would be an E min chord) and the VI chord (A minor) which is the relative minor key.
The dominant chord has the second most important function – it is used to move back to the tonic from somewhere else.
It is usually associated with instability and motion.
A lot of pieces of music end with the motion of a dominant chord to a tonic chord.
The chord that primarily functions as a dominant chord is the V chord – G Maj if taken from the C scale above.
The other two chords that could have a dominant function are the VII chord (B diminished) and the III chord (E min).
You may have noticed the III chord is listed in both the tonic and dominant lists, and it can function as either, depending on how it is used in the music.
A subdominant note or chord functions as an in-between middle ground.
It’s not as stable as the tonic, but neither is it really unstable or keen to resolve to a different chord, like a dominant chord is.
The subdominant function primarily belongs to the IV chord (F Maj above), but also the II (D minor) and the VI (A minor) can also be used.
So, A minor can be a tonic chord or a subdominant chord, again based on where and how it is used in the music.
Here is the same scale as above, but underneath each note is the function that chord can provide (some of them have two) – T for tonic, D for dominant and S for subdominant.
Here are some examples of music that shows these functions.
First is a piece by Mozart, “Sonata in G Major”.
The first four bars of the piece move from the tonic (G Major) to the dominant (D Major) and back to G Maj.
Notice how the D Maj chord in bars 2-3 feels like it’s unstable and wants to return back to the tonic in bar 4.
The same progression is played at the beginning of “Hey Jude” by The Beatles.
Starting on the tonic (F Major) and then going to the dominant (C Major) and then finally resolving back to the tonic when he sings “make it better”.
This next piece – Bach’s Prelude and Fugue No. 1 – goes from tonic ⇨ subdominant ⇨ dominant ⇨ tonic, which uses all three of the functions as they are meant to be played.
The tonic (C Major) in bar 1 steps up to the D minor subdominant in bar 2, followed by G Major ⇨ C Major in bars 3-4 as a dominant-tonic cadence.
The Viennese Theory
The Viennese Theory of Harmonic Function is fairly similar to the German Theory.
For example, they both label their scale degrees I – VII, and the Viennese method still uses the labels tonic, subdominant, and dominant.
However, these are only reserved for one specific chord each – the tonic is solely the I chord, the subdominant solely the IV chord, and the dominant solely the V chord.
The other chords are labelled:
- II chord – supertonic
- III chord – mediant
- VI chord – submediant
- VII chord – subtonic/leading tone
The focus of the Viennese Theory is the scale degrees.
Whereas the German Theory is labelled “Function Theory”, the Viennese Theory is labelled “Degree Theory”.
According to those who created this Theory, each specific scale degree has its own function and they all relate to the tonic in a different way.
Harmonic progressions are more important to the Viennese Theory than chord quality (whether a chord is major or minor) – for example, a D Maj – G7 – C Maj (II – V – I) has the same function as a D min – G7 – C (ii – V – I), even though technically a D Maj is not found in the tonic key of C Maj.
In the German “Function Theory”, the primary harmonic model follows the path tonic ⇨ subdominant ⇨ dominant ⇨ tonic (or I ⇨ IV ⇨ V ⇨I in scale degrees).
However, in the Viennese “Degree Theory”, the primary harmonic progression follows the Circle of Fifths, which can go tonic ⇨ subdominant ⇨ leading tone ⇨ mediant ⇨ submediant ⇨ supertonic ⇨ dominant ⇨ tonic, or I ⇨ IV ⇨ VII ⇨ III ⇨ VI ⇨ II ⇨ V ⇨ I.
These kinds of progressions are found a lot in Jazz and Blues music.
Here is an example of the song “All the Things you Are” which has this full progression in Ab Maj.
Starting on bar 4, the progression passes through each scale degree through the Circle of Fifths.
Nowadays, most musicians and composers would know both Theories of Harmonic Function – in fact, they are both seen as two sides of the same coin, and are almost interchangeable.
In the Degree Theory harmonic progression, iii ⇨ vi ⇨ ii ⇨ V ⇨ I, the first two chords (iii and vi) can function as the tonic, the ii would be the subdominant, the V would be the dominant and the I would be back to the tonic.
In this way, the same progression can be analyzed the same by both theories.
To Recap: Harmonic Function
In mathematics, a function is how you describe the role that a particular variable plays in the creation of a larger mathematical unit.
The same is true for the concept of Harmonic Function – it helps us understand how a chord is used in a chord progression, or how a note works in particular melody.
Music starts, ends, and travels to and from the tonic, and every piece of music is unique in how it does this, but knowing which chords function in which way allows musicians and composers to analyze others’ music and create their own.
We hope you were able to learn at least the basics of Harmonic Function today, and let us know if you have any comments or questions below!