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0:02
Hi everybody; welcome back. I’m still Seth Monahan, a guy who *actually* does music theory for a living, and by some miracle, you made it all the way video 17 in my series on classical harmony and counterpoint. In this video, we start to learn how chord progressions work in the classical style, using a concept known as “harmonic function.” Now, if you spend some time studying the classical style, you’re gonna notice that certain
0:26
chord progressions appear again and again and again, and other ones occur rarely…or maybe not at all. And this is something people have tried to explain for a long time. For three hundred years at least, some of the best minds in music—composers and theorists alike—set out to find that Holy Grail, a single set of laws that would explain everything, that would solve, in a single stroke, the great mystery of harmonic progression. Well...it didn’t work.
0:56
I think it’s safe to say now that there’s just is no one set of laws that accounts for every harmonic progression in this music. But a lot of theories have had partial successes, and together they can help us give a reliable sense of how classical harmony works. And one of the most useful ones to start with, in my opinion, is that of harmonic function. So, traditionally, functional theory divides chords into three families based on how they behave: TONIC, PREDOMINANT, and DOMINANT.
1:30
And the idea is that we typically move from left to right through these functions, ending up where we began. So we might start with one or more chords from the TONIC family, then move to one or more chords from the PREDOMINANT family, which take us (as their name suggests) to one or more chords from the DOMINANT family, and then probably back to TONIC, where we’d start over again. I call this entire motion a “functional cycle.”
1:58
And each of these three functions is associated with one or two Roman numerals: the main exponent of the TONIC function is (big surprise) the Tonic (I) chord; PREDOMINANT function is typically realized by II or IV; and the DOMINANT function is associated with Roman numerals V and vii and this is true in major and minor and you’ll remember that in minor the dominant function chords V and vii are the same as they are in major because of the raised leading tone.
2:24
So let’s apply these functions to the chords of the Big 18, which we learned in the last video. And we can do this with three rules and two exceptions. Rule 1: only tonic gets a tonic function. Hmm. Rule 2: all instances of II and IV are pre-dominants. And rule number 3: the only chords that get a dominant function are the ones containing the leading tone of the key. So there’s three rules and then two exceptions. Exception no. 1: depending on context, VI can either be a tonic or a predominant.
2:58
Alright, and we’ll see both of those instances today. And exception no. 2, a very important one: I6/4 typically has a dominant function, not the tonic function that you might expect. So that’s pretty much all the “theory” I’m gonna give you in this video. But before we go on to the musical examples I want to give you just a few quick disclaimers. Number one: function theory is deceptively simple: you can’t just combine chords randomly
3:28
based on their functions—or especially ignore the handful of special exceptions—and expect to sound anything like Beethoven or Schubert. In fact, lots of functional cycles that are possible in theory actually sound pretty awful by classical standards. Let’s just compare two functional cycles that both seem to follow the rules I’ve given. So here’s first one...and to this, the ghost of Mozart would probably say “sure—whatever…that sounds fine, I know how that goes…”
4:02
But the second one, that sounds like this…well, the ghost of Mozart does tend to overreact a bit, but he would probably describe as “repulsive” or maybe “accursed” or even “infamous.” And he would be super annoyed that we ignored the rule that I6/4 can’t be a tonic chord. That’s something you need to remember from day one. If you go around confusing I6/4 for a tonic chord, Mozart’s ghost is gonna fling unnamable
4:34
substances your way [SPLAT] and denounce you in the town square in front of your friends, and probably, like, vanish in a column of flame. So let’s try to avoid that if we can. Now, I don’t have time right now to explain exactly why the rest of that second progression sounds so unidiomatic. So instead I’ll just say: you have to actually study the classical style—and especially its rules of counterpoint—to learn which progressions got used and which ones didn’t. So, moving on.
5:03
Disclaimer number two: function is not an inherent property of chords; it depends on context. And in later videos, we’ll see that there are plenty of situations where chords don’t carry their typical function; and when this happens, they’re often in some kind of embellishing role, supporting some other function. We’ll see that in the future. And this brings us to point three: there are lots of progressions in this music that function theory just can’t explain.
5:28
And that’s totally fine—we’ll get to them in time. It doesn’t change the fact that function theory still gives us a strong starting place for learning the style. And finally, I should stress that the way I teach harmony in these videos is different from anything you’ll find in mass-market textbooks. My aims are similar, obviously, I want you to be able to understand how this style works— I want you to know what’s typical, what’s unusual, and I want to help you better understand
5:54
and describe what you hear. But the organization of my teaching is different, as is a lot of the terminology. So just be wary of this if you’re, say, a student who’s using one of those mainstream textbooks in class. Just be aware of the possible differences, and you may have to do a little bit of translation from my terms to their terms and so forth. But I’m doing it the way I do it in my classes and I think it works really well. OK—so that’s enough of the theory.
6:18
Let’s look at some music now to hear these harmonic functions in action. And we’ll start with just about the simplest example I could find. Here is the opening of the slow movement from Haydn’s second Op. 64 string quartet. And, as this analysis shows, Haydn moves at the rate of one chord per bar, and these together create a complete functional cycle: Tonic, Predominant, Dominant, Tonic. So here’s your first listen.
6:55
So, right out of the gate, I want you to notice a few things. First, the functions here are color coded, as they are throughout the video, just to make them easy to spot. Second, notice that I’ve marked all non-harmonic tones in red. One reason I’ve done this is simply to clarify what I’ve filtered out in my harmonic analysis. Another one is to help you home in on the important expressive role of a lot of these non-harmonic tones.
7:19
They don’t play much of a role in this one but wait until you see the next excerpt. And the last point I want to make right now is that all of the musical excerpts I’ve chosen in this vide use only chords of the Big 18. (There’s exactly one exception in one of the excerpts, and I’ll let you find that on your own.) So I’m inviting you to think of this entire video as a kind of giant footnote to Video 16, in that it actually shows you how essential the Big-18 chords are to this style.
7:47
Now—that said, I wanna stress, I haven’t loaded the video up with musical examples just to prove, over and over again, that functional cycles exist. I hope you'd trust me on that point. Instead our interest is gonna be focusing on all the different ways that functional cycles get used to build broader musical ideas. So to this end, we’re also gonna wanna focus on how these functions sound and feel. This is a little trickier.
8:12
I suspect that if you’re watching these videos, you probably have some sense of what “tonic” feels like—it’s the point, harmonically, where we feel that we’re relatively stable and at rest. And the feeling of “dominant” comes in large part from the power of the leading tone, which gives dominant-functioned chords that sense that they “point” back toward the tonic; there’s a sort of gravity back home. “Predominant” is maybe the hardest one to describe.
8:39
Very often, it feels like a motion away from tonic—something that contrasts with the tonic—but which doesn’t necessarily pull back to the tonic in the same way that the dominant does. And its most characteristic note might be scale degree ^6, which—at least in the Big 18, at least—only appears in predominants. So let’s talk about scale degrees for a second. Scale degree ^6 is certainly the main predominant signal in this example.
9:04
When we hear it again, I want you to listen specifically to the melody, the top voice here, to hear how its tones tell a story of stability, instability, and resolution. More concretely: our starting point here, is scale degree ^5, which is relatively stable; but it’s displaced by scale degree ^6, that little flag of the predominant, which doesn’t feel particularly unstable, but it does feel like a move away from home.
9:31
And then When ^7 enters—and notice Haydn doesn’t just go up by step; he leaps down by a seventh which gives that seventh a particular kind of energy to it—when ^7 enters, we suddenly have a clear sense of purpose and direction: we know where we’re going, and we know how we’re gonna get there. We’re going home, to scale degree ^1, which is typically the most stable note in the key. So, If you can follow this melody and feel all this as the music unfolds, motion away
9:56
from stability and then back, you’re feeling harmonic function at work.
10:14
On screen now is the solo entrance from Mozart’s famous D-minor piano concerto, and it’s a really interesting counterpoint to the Haydn we just heard. Because here, too, we get a complete functional cycle that unfolds evenly over the course of a single phrase. But virtually everything else has changed: obviously, it’s in minor now rather than major; the harmonies move at a slower rate (now it’s two bars per function); and it’s
10:41
a much more complicated texture, too, with tons of really expressive non-chord tones. Look at all the red notes here. Every one of those is a special note that carries a lot of expressive meaning. It’s also an excerpt that forces us to make some decisions about what the real bass line is. So notice how the left-hand works here. In each case, you've got three quarter notes leading into a half note. With left hand figures like this, we typically want to take the lowest note of each grouping
11:15
as a single “real” bass note—so in other words, D, Bb, A, and D. That’s why I’ve given you only four Roman numerals and not sixteen. And when you listen, I want you to tune in to those changing functions—and also, I have to say, to notice this awesome Bb, it’s a non-chord tone that Mozart approaches by a dissonant leap of an augmented second and then just leaves hanging, unresolved, for over half a bar.
11:42
It’s really kind of the crowning moment of this phrase, which is very dark for Mozart’s language.
12:03
Now, functions don’t always unfold at an even rate like this. But when they do, it’s also common for composers to split them up into a kind of call-and-response pattern, where the opening tonic to predominant is then answered by a dominant-to-tonic motion, like this idea from Beethoven’s “Egmont” overture.
12:32
Or the opening of Haydn’s“Farewell” Symphony....
12:44
Or at the opening of the slow movement of Mozart’s E-flat major wind serenade— which actually uses exactly the same chord progression we just heard in Haydn, but now it’s in major rather than minor.
13:09
So, in every passage we’ve heard so far, there’s been exactly one chord per function. But you very often see a single function represented by several chords in a row. Have a look at the opening of the slow movement from Beethoven’s C-minor violin sonata. The first subphrase unfolds a complete functional cycle. But notice that the dominant here is realized by two chords: V and V4/2. So we use a horizontal line there to show that the Dominant function just continues across that chord change.
13:40
And we see something similar (but on a bigger scale) in the second subphrase: now all three functions are drawn out by several chords. (And notice, because we end on a half-cadence, there is no closing tonic function for this phrase. I’m gonna talk more on that in a little bit.
14:18
And I hope you notice how special Beethoven has made these both of these pre-dominant harmonies. Not only do they each appear on a strong beat; they each are decorated by really poignant non-harmonic tones. The first one—that C above the Bb minor chord—is so gorgeous, and then the same thing later on: and now a double suspension C and E flat held above D flat and F until they finally resolve in the middle of the bar. Pretty fantastic!.
14:50
Now, so far, every functional cycle we’ve seen has spanned a single musical idea—a self-contained phrase or subphrase. But very often, a single phrase will contain several overlapping functional cycles. Here’s a chorale phrase from Bach’s St. Matthew Passion. (And you might remember this from Video 9, where we talked a lot about one of these chords.) Here, in just two bars, we get two complete functional cycles, where the tonic that ends the first one also begins the second one.
15:21
So they go by very quickly.
15:29
And this is another case of a composer putting the pre-dominants on strong beats to give them special expressive power. Look at that last bar. We see a similar overlap of cycles in a passage from Mozart’s A-major piano concerto. Here we’re in F# minor (this is the slow movement) and once again we’ve got two cycles which overlap on a mid-phrase tonic chord. So the ending tonic of one is the starting tonic of the next one. Let's Listen.
16:16
Notice also that this phrase, like one we heard two slides ago, ends on a half-cadence and thus ends without a concluding tonic function. This is really common. But it’s only one of many ways that a functional cycle might be incomplete. Another option is simply to leave out the pre-dominant chord. We see this in the opening of Beethoven’s Fourth Piano Concerto. Now just like in the past two examples, this one features several overlapping functional cycles.
16:42
But the first one just has no pre-dominant: we just go from tonic to dominant and back. And by doing this, Beethoven gets to save that very characteristic pre-dominant sound for the second half of the phrase, where he takes the trouble to make it pop with a sforzando and a syncopation. So listen for that when I play the example. I also want you to notice how weak this closing tonic function is. Notionally, the passage ends with a very short, incomplete third cycle: tonic goes to dominant, and
17:11
ends with a half cadence. But in a way, the tonic only feels like kind of momentary blip within a dominant function that goes throughout the last two bars. Later in the series, I’ll dedicate a whole video to this idea—this notion that certain chords can be so fleeting or superficial that we might “listen through” them in a way to hear deeper harmonic functions underneath. In this case, I’m just inviting you to hear how dominant function kinda seems to extend
17:38
through both of the last bars and tonic just seems like a momentary blip on the radar and then it’s gone.
18:00
Here’s another instance of a phrase that starts with a basic tonic-to-dominant motion; this one moves on—without overlapping—to a complete functional cycle, that includes the pre-dominant. And I want you to notice two things in this one. First: the opening cycle shows us how the vi chord can take on a tonic function just by substituting for the I chord. V7 would normally go to I, but here it resolves to vi, and I put scare-quotes around the tonic
18:30
symbol ("T") because vi doesn’t quite give us the stability of a true tonic but it does give us the sense that the dominant resolves somehow. And the second thing I want you to notice is just how the character of thise phrase changes as it unfolds: it starts with these bold fanfares, and then, in only three bars, stalls out and gets stuck on this dominant that goes on way too long, melting away, through all these trailing chromatic lines, and It just sort of floats down to
18:56
tonic—rather than kind of crashing into tonic triumphantly as you might have expected from the opening of the phrase. This is one of these wonderful Mozartean twists – you never know what’s in store, even if it seems so confident at first, it just kind of fades into a dream by the end.
19:46
Now, I wanna stress here that incomplete cycles are by no means some rare or special phenomenon. They’re just as common—maybe more common—than the complete ones. Check out the phrase that opens the minuet of Beethoven’s first D-major piano sonata. Because it uses a functional design that is extremely common in this repertoire: it starts with multiple overlapping cycles of just tonic and dominant, and then it saves the predominant for the functional cycle that actually brings us to the cadence.
20:14
(In this case, that’s another half cadence.) This kind of pattern—alternating tonics and dominants that finally give way to a predominant before the cadence—this is absolutely everywhere in this style. So take note of it!
20:32
So, our next example is like the last few, in that an incomplete functional cycle overlaps with a complete one. But there’s something new here: this is the first time we’ll hear a functional cycle cross the boundary between phrases. This is probably open to debate, but I’m gonna call this a very short period, beginning with a 3-bar antecedent and a 3-bar consequent. But the second functional cycle begins with the last chord of the first phrase and continues
21:01
with the first chord of the next phrase. So it starts here, goes over the phrase gap and continues here with a predominant. So here we get is a phrase that starts not on tonic, but on the pre-dominant instead.
21:22
Something similar happens in the opening of Mendelssohn’s A-minor string quartet. Here as well, we’ve got two phrases, with the tonic that ends the first phrase connecting, over the phrase gap, to the predominant that starts the next phrase. What’s different here is that each phrase begins with a brief upbeat, such that the first function of each phrase is actually much weaker than the second one, which falls on a strong beat.
21:44
So when you listen, notice what this does to the harmonic pacing: now both phrases begin by emphasizing non-tonic functions, leaving the strong tonic functions just for the ends of phrases, it gives it a very goal directed quality. This is different from most of the examples we’ve heard so far, which typically began with some strong articulation of tonic.
22:26
And it turns out, there are lots of cases in which phrases really do start on some function other than tonic—and this gives a very different sense of harmonic balance, because we’re starting from a position of instability rather than stability. Here’s a pretty simple one, from Chopin’s F# major nocturne. It starts with a simple two-bar idea that leans into the dominant, and only then resolves to tonic. And then he repeats this with a variation. Have a listen.
23:03
And here’s an even more exaggerated case, from Beethoven’s op. 7 piano sonata. On the whole, it’s like a parallel interrupted period, where the first phrase ends on a half cadence and the second one on a PAC. But each of the two phrases begins with a long, sustained, and tension-building dominant. And because the first phrase begins and ends on dominant, the tonic harmonies get kind of swallowed up and don’t offer much in the way of repose.
23:29
So for that, we have to the end of the second phrase, where the cadential progression—which includes a pre-dominant now—finally gives way to a strong, end-weighted tonic.
23:58
And this game that Beethoven’s experimenting in here, making us wait for the tonic chord, this really took off in the later nineteenth century. In more extreme cases, you can find the tonic simply implied without being stated at all. Here’s a very famous case. This is the opening of Schumann’s song cycle “Dichterliebe” or “Poet’s Love.” And it’s partly famous just cause it’s completely awesome, and it's also famous for the fact
24:20
that it begins by vamping pre-dominant–to–dominant without ever getting to tonic.
24:39
And if you know the whole song, you’ll know this is actually all part of a big ruse: because the song’s not even in F# minor; that’s what’s so great about it. It’s actually in the relative key of A major. But it starts off with this wonderful misdirection, which creates a melancholy mood of longing (where is my tonic chord?) that the song never really shakes off. But notice that this is 1840. And of course Schumann’s going to do things with harmony that would
25:04
be almost unthinkable for Mozart fifty years earlier. It’s pretty rare in the classical period to just start a whole piece with a pre-dominant function—or to start a phrase with a predominant that doesn't link back to a tonic that comes before it. But there is one exception: the consequent phrase of a parallel or contrasting period. We see that all the time, actually. So for our last example, let's look at this contrasting period from Mozart’s “Haffner” symphony.
25:29
This is a harmonic formula we hear all the time: antecedent phrase ends on a half-cadence; and then the consequent phrase is built as an incomplete cycle that starts on a pre-dominant and then ends with an authentic cadence on tonic. Very common pattern. Have a listen.
25:55
There’s almost a sense that we arrive on the dominant, we rewind a little bit, go back to the predominant, start over and then make it all the way over to the tonic at the end. So that is your big introduction to functional harmony—with musical examples that use only chords from the Big 18. In the next video, I’m going to show how an understanding of these concepts—of functional harmony and the Big 18—can give you a huge boost of speed in your harmonic analysis. I’ll see you then!
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