What's The Actual DEFINITION Of Harmonic Functions?
What do the terms ‘tonic’, ‘dominant’, and ‘subdominant’ mean?
You may have heard these terms thrown around before, and you may have also found yourself wondering not hust what they mean, but also what the point of having terms like this even is.
There’s just 7 chords in a key, do we really need to file them into three categories -- that can’t even be explicitly defined!! -- instead of just giving all seven chords their own function and definition?
Of course we do! This is music theory!
If we aren’t coming up with terms and theories that rival the complexity of theoretical physics then what is the point? Who will ever respect us?
Let me make it clearer. The true value of these terms is in how it feels to say words like ‘subdominant’.
Next time you’re about to say "the four chord", like a common ape, try instead saying “the subdominant chord”, and pay attention to:
the way it makes you feel.
the look of respect from other people
the fact that a lot of people are reading this email as serious and have not caught the joke yet. Lol.
Now, aside from making you feel more smarter, is there any other good reason for using these terms? And how are they even defined?
Surprisingly enough, there are actually more reasons to understand these terms!
And unsurprisingly enough, their definitions are complicated and hard to explain. (Groan) But I make them as simple as possible (*) in the video below:
(*) But not simpler. After all: "Everything should be made as simple as possible, but not simpler" (Einstein)
If you want to learn more about harmonic functions, chord substitutions, and more, check out my Complete Chord Mastery guitar course to start expanding your chord knowledge immediately!
Video Transcription
Hello internet, so nice to see you! Tonic, subdominant, dominant, the three harmonic functions. What are those, okay? So the idea is that you take the chords you can use in a musical piece and not only the chords in a scale, but with practically any chord you can use in a musical piece and you try to classify them in those three areas, tonic, subdominant and dominant, which in theory sound different, okay?
And then all the tonic chord more or less sounds similar, all the subdominant chords more or less sound similar, all the dominant chords more or less sound similar, and inside those areas you can substitute chord for each other.
That will be the basic idea, okay? So how does that work? What does it look like? Well, if we go on the board for a moment, we see that the thing that everybody agrees, at least, is that the first chord of the key, the one, it's always tonic.
The fourth chord of the key, it's always subdominant. And the fifth chord of a key is always dominant. Okay, so if you're in the key of C, for instance, C major, F major, and G major, okay, or G7 sometimes, okay, those would be the chords, okay?
That's the key, see? This is actually taken by definition of the three areas by most people, meaning that if you can substitute a chord for the C, it's tonic. If you can substitute a chord for the F, it's a subdominant.
Again, in the key of C. If you can substitute for a G7, it's a dominant. So that's a possible definition, okay? Which is okay. It's not a great definition because, of course, if you... can substitute a chord with another one, always requires an element of judgment from the listener, for some people it may work, for some people it may not work, so it's not a precise definition, but it works fairly well.
Other people prefer to give a more extensive definition, and the typical definition you find is the definition by enumeration, meaning that you have other chords here, now the second, the third, the sixth, and the seventh, for instance, seventh, seventh is diminished in major, okay, so like in C is a D minor, E minor, A minor, and B diminished triad in this case, and then people just say, what are those?
Well, the second is usually considered as subdominant, okay, the third is usually considered tonic, though some people consider it dominant, and you see that's going to be a problem, okay, and the sixth is typically considered tonic, Though, it could be considered as subdominant, okay.
And the 70s typically consider dominant, it can be substituted for the G7. So, that's the definition you find usually, and it's absolutely true that in some situation the E minor can sound more tonic, and in some situations it can sound a bit more dominant.
Though those are rare, typically the third sounds more tonic, but it's even more true that the sixth chord can sound subdominant occasionally, okay. Meaning that you can substitute it for F rather than for C.
So, but there is a big problem with all these, right. And if, like me, you're a nerd, okay, you spot the problem immediately. The problem is that we are just making a list of things, and we are just making a list of functions, okay.
And we are just saying this is this with no extra justification. This is not a great way to proceed. So, let me, this is not a great way to proceed. The thing, the way to proceed would be to give a definition of what a tonic chord is.
So, what is the actual criterion? What is the actual characteristic a tonic chord should have to be called tonic? And what is the characteristic a subdominant chord should have to be called subdominant?
And what is the characteristic of a dominant chord to be called dominant? So, at this point, I mean, one definition would be, again, it can be substituted for, but this requires an element of judgment.
So, people give you different definitions, okay. And one popular definition is this, tonic chords are at rest. When you play a tonic chord, it feels like the piece is slowing down, it's at rest, it's low tension.
Dominant chord wants to resolve to tonic. Subdominant chord wants to resolve to dominant. Okay, so. So again, on the board, you will have that the typical circle of resolution will be that sub -dominant.
Ooh, you cannot read that. That's too much light here, but I'm going to put it here, okay? Sub -dominants want to resolve to dominant, that want to resolve to tonic. That's a horrible definition, honestly, okay?
That's a horrible definition for a number of reasons, okay? And let me tell you exactly why, because... tonic, sub -dominant, dominant, tonic, okay, C, F, E, F. We can hear that this wants to proceed here, and even better than this wants to proceed here.
But can we? If I didn't tell you, okay, if I didn't tell you that this was the case, would you have heard it this way? Would you have felt the resolution? I mean, 5 to 1, so dominant to tonic, seems to be fairly strong.
But 4 to 5, I mean, some people will hear this as a resolution too, meaning that the F chord, the subdominant chord onto the C chord, the tonic chord, feels like a resolution too, indeed, it is, it's called a plagal canons, it exists in music theory, but you notice it's not at all what you see here.
It's not subdominant, dominant, tonic, subdominant can resolve the tonic, so this definition here, not a great definition, especially when we don't say exactly what we mean by resolving. You see, resolving, it's one of those words that everybody uses in music, but if we are hard -pressed to define it, it's a problem.
Indeed, when you do, when you read the music theory book, they will start using the word resolving, without even telling you what it means, it's just understood that you know what resolving means. And nobody ever explains it to you, except the point is just accept it.
They say it eliminates tension, and in some cases it's evident, like, again, G7 to C, it's evident that the tension gets eliminated, but in other situations it's not. So, again, I don't like this resolution definition.
Even if resolution is a real thing, and even if it can be heard, in some situations it's subtle, or different people have different opinions if the resolution is actually happening or not. So, not a great definition because of that.
We need a more precise definition, so there is a more precise definition, and a more precise definition is... this, okay? So let me delete all these for a moment. The more precise definition would be that a chord would be considered a subdominant, subdominant, if it contains the fourth note of the key and does not contain the seventh note of the key.
In C major, that will mean that the chord containing the note F and does not contain the note B, and let me make this seven better, but if a chord contains note F and it does not contain the note B, it would be considered a subdominant chord.
The two subdominant chords in our scheme, before you can go back in the video and see it, were the minor, and F. Both of them contain the F note, both of them do not contain the 7th note, the B. We also said that the A minor can be considered subdominant.
Occasionally the A minor does not contain the F, does not contain the B, so not great here, but okay, let's keep it for a moment, okay? A chord would be considered dominant if it contains both the 4th and the 7th.
So when a chord contains both those notes, so the F and the B, which are a triton apart, by the way, okay, then it will be considered dominant, okay? That works for the two dominant chord we have there.
It works because G7, G7 contains the B and the F, because G7 is GBDF, and it will work. The seventh chord of the key, like the B diminished triad, contains the seventh and the fourth, because it contains the notes B, D and F.
So, so far it works. Tonic is essentially all the chords, tonic, tonic, okay? All the chords that do not contain the 4th note period, they can contain the 7th, okay? And here, here definition differ a little bit, okay?
But that's a fairly good definition. It has one great advantage. It tells you what is the characteristic of every harmonic function before we go and see it on the chords. So when we go and see them on the chords, okay, when we go and talk about the chords, we can, we have an objective way to tell if you are in or out.
Now, the problem is if this objective way we have here on the whiteboard, that's the problem, if this actually corresponds to what our ear perceives, that would be the problem. But at least we have a definition, okay?
Okay, turns out this definition is not precise enough. Okay, and we have a problem essentially, because when you start listening with your ears, okay, and checking, you will discover that in some chord progression, some chords sound differently, okay, so that would be the problem.
So for instance, you see, let me say, what if I play a chord, again in the key of C, what if I play a chord that contains the note G, D, and F, that will be an incomplete G7 chord, a G7 chord will have G, B, D, and F, okay, so just to give you an idea on how that sounds, let me say, if I play a G7 followed by a C, it's a G7, contains both B and F, it's clearly a dominant, and then I land on a C major,
it doesn't contain either, so it's clearly a tonic chord. But if I play G, D, and F... Okay, I get this. Now, this still kind of sounds dominant -ish, okay? But not as much as this one. Because you don't have the B.
This chord... By this definition, this chord will be a subdominant, contains the 4, but not the 7th. And some people can even hear this as a subdominant, because a subdominant will technically resolve to dominant.
So if you play this first, you will be here, and you play this, and you see it feels like it's moving now. And then from here... But this definition will tell you this chord is subdominant. If I were to take this strictly and seriously, but at the same time...
And it kind of sounds like it's resolving from here to here, it's progressing. But most music theorists will say, no, this is just an incomplete G7 chord. So it would be able to classify that as dominant.
And they will have a point, because this can definitely resolve here with the same kind of feeling of a dominant tonic, okay? So here we have a problem, essentially. But how do we manage this definition?
We could go either way, we need to make a decision, okay? So, makes sense. Some theorists were like, okay, let's just say that if it contains the 7th, it's automatically a subdominant. So let's just say, let's change the definition, and we go like, okay, if it contains the 7th, it's a dominant.
And the tonic has to not contain the 4th and not contain the 7th. But that gives another problem, because for instance, the 3rd chord of the key E minor, okay, the 3rd chord... which is E minor will contain the B note, because it's made by the note E, G and B and so by this definition it would be a dominant chord but if I play an E minor followed by a C it doesn't sound the same as if I play a G7 sorry,
a G7 followed by a C okay I mean here wait I mean this sorry this E minor followed by a C it doesn't feel like a resolution the same way that I don't know this would go to here right so again based on this new definition E minor would be dominant but it's not really also based on this new definition a C major seventh which is clearly a tonic chord, it's a C chord, it's clearly the first chord of the key,
it has to be tonic, it would be C, E, G, B, would be considered a dominant chord, and it's mostly definitely not a dominant chord. So even this new definition doesn't work, and so you may want to amend it again.
So, why am I doing all this? Okay, all this tells you one thing. It tells you that if you just look at a single chord, the note content may or may not actually reliably tell you how this chord sounds in terms of function, okay?
You will have to see how the chord actually resolves, so what are the chords around? But at this point, the snake starts to bite its tail, because we're like, if the harmonic function, if the point of the harmonic function is to tell you where the chord resolves, and to know the harmonic function, you need to look around and see where the chord resolves, well, what is the point of the harmonic function at this point,
okay? Makes sense. Can we just say this chord resolves via or this chord resolves to all those seven, those other chords, and that be done with the harmonic function, because they're not giving us anything new, okay?
So, the reality is this. So, how do we solve all this problem? All these big mess here, how do we solve that, okay? The point is this, is that the harmonic function are a good rule of thumb, okay? They are not a theory that tells you how music works.
It's because when you push this theory, and you actually take the definition seriously, and you go into details and try to see exactly how it works, the theory will break, okay? Because there will be chords that can be both subdominant or tonic depending on how you're using them, okay?
And indeed, some theorists tried to patch that. For instance, now we don't talk much about subdominant anymore. We talk about predominant chord, which is a larger class of chords that all seem to resolve the dominant chord, again, predominant.
It's kind of a cop -out, okay? We could go in depth in that, but it's kind of a cop -out. But the idea is it doesn't need to be a theory where we have to take all the definitions super -seriously, okay?
And to make it work. It's a rule of thumb, okay? It's a useful rule of thumb. It's just a recognition that different chords in the key have different level of tensions. And if we squint a little bit, okay?
We can say that there is a group of chord with low tension, a group which has a tonic chord, a group of chord with high tension, which has a dominant chord, and a group of chord with halfway through tension, which are considered subdominant.
Okay, and that more or less, when you listen to it, you can tell if it's more this or more that. Okay, it's like colors, okay? Lots of people know what green is, lots of people know what blue is, but if you ask people to discriminate exactly what is the exact color that distinguish blue from green, you're gonna have several different answers, because people don't agree, there are colors in between blue and green,
and people don't agree on how to classify it as green or as blue. This is exactly the same. There are plenty of chords in between that could be one thing or the other, and then it depends on the colors around, and the chords around.
Other chords with a virtual, sure, they're definitely tonic, the first chord of the key is always tonic, the fourth chord of the key is always subdominant, the fifth is always dominant. Okay, so it's a good rule of thumb that help us work with music, because when we have a dominant chord and we have a lot of other dominant chords, when we have a chord as dominant function, we can substitute a number of other chords that we all agree have dominant function,
okay, and so we can, we have a tool essentially, like that's a dominant function, we can have all these other options that sound good in that position. When we have a tonic chord, we know what are the other chords that are clearly classified as tonic, and we can substitute them.
If we take this theory, which is again just a rule of thumb, but if we take this theory too seriously and we go and see the definitions, when you push those definitions enough and try to be precise, it breaks, it doesn't work anymore, okay, and that's okay, not all theories have to be precise and perfectly correct until the end, okay, the one of you who know anything about science, for instance, know that classical mechanics,
okay, the physics you study in high school, classical mechanics is not correct, because if you go too fast, if you spit are too high, you have to use relativity instead, Einstein's relativity, and if you have objects too small, okay, or energies too high, you need, sorry, objects too small or energies too low, you need to start using quantum mechanics, okay?
So classical mechanics is just an approximation that seems to work for most of the world around you, but not when pushed to the extreme limits, okay? The theory of harmonic function is exactly the same, it's the classical mechanics of music.
It's a theory that works if you stay in key more or less, and if you play basic chord progression, and as long as you don't push this to the limit, it works. When you push it to the limit, it doesn't work anymore.
It's not the fundamental theory of music, but it is a good rule of thumb. It works, and it has its usefulness when you want to work on substituting chords. That's how it works. Those are the... This is how these things work, okay?
Now, if you want to know... how to do the substitutions, okay? You want to know how these old things work in practice, how the harmonic function can actually work in practice. And especially, one thing that I don't like about this theory, and this should be changed, is that the thing that's subdominant, resolved to dominant, resolved to tonic, it's actually not true.
Okay, you can play any chord in any order, but the order in which you play those chord influence the emotion of the chord progression, okay? So, if you want to know all those, and how to work with these in practice, I recommend you guys take my course, Complete Chord Mastery, okay?
In which I do explain all those things, okay? And I explain the theory of harmonic function as this, as a rule of thumb, okay? And what you can do with that, and what kind of substitution you can do with that, and how you can influence the mood of the chord progression by changing the order of the resolution of those chords, essentially, okay?
So, totally recommended, okay? If you're curious about all that, get the course, because that's probably the easiest way to learn all these. This is not something that cannot be done in a 10 minute or 15 minute YouTube video.
Very good, this is Tommaso Zillio for musictheoryforguitar.com, and until next time, enjoy.