Music Theory Comprehensive: Part 14: The Fugue and Invention

1. Introduction: Hey, everyone, welcome to music theory, part 14. Um, Holy smokes were pretty deep into this thing. So what we're gonna be covering in this class is what I consider to be kind of the apex of counterpoint on. That is the few. We're gonna look at all of the different elements in the fugue. There's a lot of different pieces of it. We're going to look at how composers have written them primarily focusing on Bach Azaz, the kind of undisputed champion of the fugue. We're gonna look at inventions a little bit, which is kind of like a few what actually really similar to a few? Um, And then we're gonna look at some of the tricks that composers have done in fugues to just keep you on your toes. So there's kind of a formula to a few, but there's also all these other things that can happen in it. It is, in many ways, some of the most complex counterpoint we will see in all of music theory and in other ways . Well, in addition to that, it's some of the most enjoyable music you can tackle. I love listening to these, and I really think that after this class, if nothing else, you'll be able to listen to this music with a whole new appreciation and a full, deeper understanding of what's happening. Not to mention knowing how to write them yourselves and analyze them. So let's dive in and talk about fugues and inventors. - G minor. So are it's just gonna figure out what are our implied cords from this melody. Okay, so G d b there's r B flat. There's arpeggio, right? So you can label this by writing the word counter subject. But also, we could write CS for counter subject, and in some cases, you have more than one counter subject. So you might call this CS one? Um, I don't think we have more than one counter subject, so let's for now, just call it C s. Okay, so here we have answer, encounter, subject. Okay, now is when it gets a little trickier. So let's find more into 17.5 up through 22. What's happening here? Um, we're getting the answer in the base, and we're getting free counterpoint everywhere else for our next trick. That's kind of weird to put it that way. I didn't mean that come out as like it was a magic trick, but it's kind of a metric. Um, I want to talk about strayed. Oh, and strata was a technique that we use. Ah, it's something we can do to this subject. Now, in order to demonstrate this, I'm gonna switch over Teoh. 2. Tools You Will Need: All right, everyone, let's get started with the tools that we will need. Now, if you've taken any of the other theory classes, this hasn't really changed much. Eso you could skip past this if you are already up to speed and you already know what I'm going to say in this section. So, uh, let's be quick about it. First thing I want you to have is some staff paper. I hope this is useful to you. So, um, this is just the five line staff paper. I'm going to give you a pdf. That is some staff paper in the next section. Print that out. Ah, few times. Sprint up 45 copies. Keep it by your computer with a pencil for taking notes. During this class, you're gonna want to take notes on staff paper. It's gonna be a lot easier. Um, you could get some nice staff paper. I highly recommend having nice staff paper. I really enjoy nice staff paper like this. Yeah, this is nice staff paper. Uh, get a pattern. I staff paper if you want, but it could be a little expensive, so if you don't want to do that just to use the pdf that I'm going to give you here. The next thing is that we are going to be using a program throughout this class called Muse Score. We've used this for all of the music theory classes so far, and it's gone really well. Um, the version of new score that I'm gonna be using is muse. Score three 3.0 point five. And this is the desktop version. Now I'm told that they have a tablet version for iPad and maybe some of the other tablets available. And, um, the thing is, the version for desktop, the version that I'm using here is free, Which is why I'm recommending it. Um, anybody can use it. Um, it's a great program for plugging in notes and then hearing them back, and we can hear what they sound like. Um, but it's totally free. It's a free program. The version for the tablets is not free, and I don't know what the differences are. I haven't explored the tablet version too much yet. Um, so you're welcome to use the tablet version if you want, but note that it's not a free program, whereas the desktop laptop version of it is a free program, and that's the one I'm gonna be using in this class. If you have a different notation program like there are some browser based ones like Note, Flight and some other things like that, those all will work great. Ah, and then there's the fancier programs like Finale Sibelius Dori Co. If you have any of those programs, they'll all work fun. You don't have to use Muse score. I like recommending music or because it's a free program. But if you have a different notation program, that's fine. You can use which ever one you like. All it really needs to be able to do is let us plug in notes and hearing back pretty simple . So, um, if you don't have one of those programs getting you score in the next section, we're going to give you the staff paper. Print that out, keep it by your computer, and we'll move on from there. 3. Review: okay up next. Um, a little review. What should you review heading into music theory? 14. Um, well, the things we're going to focus on in this part of the class going to be inventions and fugues. So the two biggest things that come to mind that you're gonna want to be sure you have a really good grass Palm is counterpoint. Um, a lot of counterpoint. As much counterpoint is you can stomach because we're gonna need all of that in order to get through the fugue. The other thing is form. Um, because of fugue is ah, complex counterpoint device. And it's also a form. So it has an exposition as a development has a recap. So there's going to be different form elements to it. But more important than that would be the counterpoint stuff. So I would especially review third and fourth species counterpoint. If you're not up to speed on those and, um be ready, Teoh dive into some serious Bach counterpoint because that's what we're gonna dio Once we crack open the lid on the few, which will be not until the second section. We're going to dio ah, little bit on melodic devices that we find in fugues first, That kind of ease us into the full fugue. But, uh, let's we get in there, um, counterpoints gonna be key because this is really, um, basically another type of counterpoint. It's kind of like baroque counterpoint. In a way, we don't really call it that, but that's kind of what it what it is. So be sure you have that stuff on your belt, and you're really comfortable with that. Cool. Okay, let's move up. 4. The Full MuseScore File: okay. Just like last time in the last. I don't know how many classes we've done together, but ah, for a while I've given you this Master Mu score file. I've heard from you all. Um, some of you find it useful. Some of you don't. So, um, and the thing is, I'm gonna make it anyway, because that's how I make these classes as I make this big music or file. So I'm gonna make this for you and do it right now. So with this, you can open this up and you can use it to follow along. Here's all my classes. In case you ever wondered, um, this is going to We're gonna put this in the sixth lecture. Call it master Mused Score file. Okay, so there it is. It's blank for now. But by the by the time you see this, classes will be full of stuff. The stuff we do in this class together, so you can use this to follow along if you want. I'll post it in the next segment, um, as both a new score file and a pdf file. So if it's useful to you, download it and use it following. If it's not skip it. That's totally okay. Cool. But it's there for you if you want it. All right. So grab that in the next lecture and let's move on. Teoh Baroque era Contra Pontell devices. So put on your seat belts. 5. What Are We Really Talking About Here?: Okay, So what are we talking about here? We're gonna be talking about Baroque era counterpoint techniques, okay? And there are a few of them that really rise to the top in the broke era. Uh, notably fugue, but a few others, the invention and canon, all three of those are become very popular in broke era. And, um, all three of them are were studying on their own. Um So what are they, the invention? Let's talk about that first, because it's the most nebulous. Really, There's not really a clear definition of what an invention is. Bach wrote a lot of them and he called it a two part inventions. He called him three part inventions. And really, what they are is the kind of tangling together of to melodic elements using counterpoint. Some of them are relatively simple. Some of them are very complex. Some of them follow a strict form that's very similar to the forum that we find in a fugue . And some of them are more like a fantasy, more like a prelude. And they don't follow a strict form, so they're very nebulous. And I always think of inventions, and I don't know if this is the right way to think about them or not. But I always think of them as more of like a study. You know, it's kind of, um, a way to focus in on, ah, particular idea and see what you can do with it. So when Bach was writing inventions, he was, you know, he had this melody, and then he just kind of spun it around and to see what he could do with it and to in two lines the two part inventions and again in three lines that three part inventions. So that's my kind of interpretation on what the invention is. Because it's not. It doesn't have a standard definition. Now the fugue is more does have, ah, definitive definition, and what a few gives is. It's a composition in which there are one or two themes, and those themes get repeated or imitated. So repeated with some variation. Um, by successively entering voices and contra punctually developed into a continuous, continuous interweaving of the voice parts. So think of a fugue like this. Um, imagine you have two melodies and those are pulled out in a string. Those melodies are a string and now basically, uh, knit a sweater with those strings. You know what I mean? So, like, you're gonna do something really complicated with these strings, so the the melody lines are going to enter at different points, they're going to change, they're gonna morph, and they're going to get all tangled up together. It's a lot more complicated than that Will go into the details of that for now. But as a very kind of broad understanding, um, that will at least get us started. That definition will get us started. And the cannon you've encountered cannons before. Probably a Canada is, in a way, a more scaled down fugue. Um, Canon is like a few, but with less imitation. So you have something like, um, the easiest example is like the, uh around you may have sunk around before where I say I might sing row, row, row your boat gently down the stream And then you start singing the same melody but you start a couple beats later. So I say Row, row, row your boat Gently down the stream Merrily, merrily, merrily, merrily Life is but a dream and you start singing row, row, row Your boat when I get to the word gently down the stream merrily um, so when I say merrily, merrily, merrily, you start row, row, row your boat on the same pitch. Now that has all kinds of variations to There's 100 different kinds of cannons you can dio , Um, and they can also get really complicated and become a tangled web of melodic ideas. So all of these things have this kind of tangling aspect to him, taking melodies and just tangling them together, using the rules of counterpoint and seeing what we can make out of them. So they're really fun. But that can be really hard to write. So so before we get into the nitty gritty of how these work, we need to start with some more. One more basic idea, and that is the kinds of melodic ideas we need to come up with in order for this to work. There's a couple special techniques we use in the melody in order to create a melody that is very appropriate for this kind of, you know, tangling together so that gets us into a couple of techniques. So let's go to a new video and talk about those things first. 6. The Subject: Okay, So the first thing we need to know is that when we start off any of these techniques fugue , canon, invention, we start with the melodic idea, and that's called this subject. Okay, So burn that word into your brain. For the rest of this class, the subject is the main melodic idea. Now there will be other subjects that get introduced. There's things were going to do with the subject, but the subject is the main thing. Okay, so, um, when we write a subject, we have a handful of techniques that we've used or that were used, especially by Bach. I mean, we're really talking about Bach here because he was the master of all of this. We have a couple of techniques that he used to really craft a subject that worked really well for these. So those techniques would be forts, punning, compound, melody, stepped progression. Those are the three things I want us to look at right now. But before we do that, let's talk. Let's just look at an example. So I have here the 1st 2 measures of the subject of the few can see minor. Okay, this is Buck. Okay, so Let's just listen to this subject really quick. Okay? Relatively simple. Now, what can we tell about it? Just by looking at it, we can see it has a fairly steady pattern of 1016th notes. Um, we see a lot of natural is right. I guess only two. But every time the B happens, it's on a natural, and it always goes back to a C and in this case comes from a C. So what does that tell us? We look at our key signature. That probably tells us we're in a minor key, and that's the leading tone. That would be a good guess. Um, that would put us in the key of C minor, which is reinforced by the key signature. It's also reinforced by the name of the bloody piece. The name of this piece is fugue in C minor. So pretty solid guests that were in C minor, right? You can pretty much bank on box gonna name it, what it's called. So that's the opening subject. Now, what I want you to do now is here. This whole few gets only like, two minutes on. I want you to hear the whole thing and keep this little melody. Just these two little bars. The subject. Keep that in your mind as much as you can and try to follow it. Okay? You're gonna hear it coming and going in different places and different keys. It's gonna be all over the place. Hey, let's hear it one more time by itself. Okay, so now let's listen to a recording of the peace. Keep that little melody in mind. Ah, it's gonna be the first thing you hear. The first thing you hear is gonna be that melody and then it's just gonna spin off. Okay, here we go. Way, way, way, way. 7. Fortspinnung: Okay, So what did we hear in that? We heard this melody, right? This subject and we heard it kind of popping up all over the place. Right. We also heard some other music. Okay, so it's not the case that every element in the fugue is made up of the subject. There's other music in there, too. And we're gonna talk about that soon, but, ah, lot of it is made up of the subject and variations on the subject. So another thing you heard in that was maybe something that was hard to describe. But, um, once I explain it, maybe you'll say, Oh, yeah, um, you heard this subject going, and then you heard something else going and something else going and then and there was never really a big break. It was just kind of unraveling through the whole thing. There was this data that I did it. I did it. And it just kept going and going and going and going until the end. Pretty much, Um, that is a technique called forts. Punning. Okay, Now, forts punning is German word that basically means spinning out. And when we hear forts punning What? We're really hearing is ah, couple different things. Um, it is continuous motion. So just kind of keeping that that pulse going, that 16th note going and in this case, this combination of 16 notes and eighth notes that's done it at that. That much of it done it at that. That that that that that that at it, that we heard that all over the place. So it just kept going and going and going and just spinning and spinning and spinning. That's called Fort Spotting. Another characteristic of fort spotting is sequences you might hear, um, where we get the studded it. That that and then Ah, everything. Ah, whole step lower Data. That data. Donald Duck. Duck, Duck. Right. That was not a whole step, because I'm a terrible singer, but you get the point. All right, move things moving in a sequence. Okay, We've talked about sequences before and how that works, So sequences are gonna come back. Um, here in the fugue section, we also enforce punning, get alighted phrases and alighted phrase would be like this subject gets done where this note is the first note of the next time through it. Not always, but sometimes that can happen. Where? Let's just try it if I take this and so what I'd have to do? It was tricky. I'd have to transpose this. So that e is that the first note was e so I could do it if I put that Oh, and I'd have to erase. Oh, no, that would work. So I'm going to get rid of this 1st 8th note. There's our subject again, as is, and we're gonna transpose it down. Where's my transpose? Transpose it down. Um, by interval. Ah, six. And we'll keep it in key. Okay, so that turned that into an e natural. So now this note is the first note of this phrase, and it's also the last note of the previous phrase. That's an allusion. Okay, so in alighted subject is happening here. Let's just hear what it sounds like. This is gonna some wacky, but let's hear. You know what? I screwed it up. I need to be down one more half step because that was an e flat. That's okay. So let's fix that interval down. Minor second. Okay, so now we've now we're in counting. Amuse score. Problem where it's thinking we switched keys to something really strange for now. We're going from D Sharp to see Double Sharp, but it will sound the same. Let's hear organ, right? And then we'd finish that out, too. So I'm going to get rid of that because that was weird. But that would be an example of an allusion. And that is one of the things we here in Fort Spotting. So Ford spawning really just means spitting out. So it's the melody just unravelling, using one of these techniques or multiple techniques. So, uh, file that away in your vocabulary lists for this class forts punning. 8. Compound Melody: Okay. The next thing I want to talk about is a compound melody. Now this is a melody with a single align that implies more than one thing happening at a time. It's a bit of a magic trick, right? So the idea is you have an instrument that is only playing one note at a time, and it's not that it can't play one note at a time. You conduce you this kind of a compound melody technique with piano with anything. Typically, it's done on an instrument that only plays one note at a time usually, but it can be used for anything. Um, we see it a lot in the cello suites. Eso, the Bach cello suites are these beautiful pieces. You've probably heard them all a 1,000,000 times. Or at least the 1st 1 a 1,000,000 times. You've definitely heard the 1st 1 million times. This is from the 3rd 1 Our sorry, the 2nd 1 And what I want to draw your attention to Is this right here? Okay. So what's happening here on Lee? One note at a time is being played nowhere here. Do you see two notes happening at the same time? um, not that a cello couldn't do that, but in this case, it's not being asked to. What's happening here is that is that this is written to imply two things happening at once , and we show the two things with the different stems. Okay, so there is ah, constant 16th note. Right? And there's also just for right here. Ah, Constant. Eighth note going. And actually, it goes all the way to their This should have a stem going up also. Um, so the way you're supposed to play this is you want to give these a little extra time and really try to make him feel like their eighth notes at the same time, you want to keep the 16th note pulse moving right? So it's it's tricky. There, actually really tricky to play. Um, so this is called a compound melody. Two or more musical lines that are expressed within a single melody. Okay, let's hear this little excerpt. This is just, um, maybe 10 bars or so from the second Tell us more cool. So compound melody Onley. One note happening at a time, but the it's trying to imply that there's two melodies happening at the same time, 9. Step Progressions: now there's another thing happening in the later part of this excerpt, and it's a type of compound melody, but we call it a step progression. What it really is is it's a progression where we have this kind of feeling that things are moving by a step. So in order for this to line up, I need to fix our time signature. I realized I put this in 34 when I should have put it in for four, our vice versa. I put it in 44 when I should have put it in 34 as it's written. So now this makes more sense. So here's the step progression. We have this happening here. Now tell me when I play this. Do you hear almost a second thing happening other than just the notes? Let's play at one time, right? You may have set a sequence, and it's kind of a sequence, but it's actually not an exact sequence. It's close, though. What we're really hearing here is this step progression and where that is is it's a stepwise motion oven implied melody between the downbeat of the measures here. So G f E de c sharp right, Those first notes, just moving by step really make you feel like there's a sequence. It feels like there's another melody in there when there's really not. So that is a step progression. Now all of these techniques forts, punning, compound melodies, step progression we're going to see used quite a bit in the fugue. So with that set, let's move on and let's get into the exposition of the fugue. 10. How To Listen To Fugues: Okay, let's talk. Well, just really quick about how we listen to a few. And we've done a little bit of this so far, but I really want to focus in on this idea of this subject, which is what we're gonna be talking about in this section. So when you listen to a fugue, you can kind of think of it like a little bit of a game case. So the the game is to follow the subject. Okay, That's really what what we do. And there's a lot of enjoyment in just listening to a fugue and trying to find the subject all over the place. And just think how How did he do that? How did he make it happen again? Here. How what did he do? Is that an octave? Is that 1/5? Is it in a major key? Now, what's happening? Um, so I thought you just said is an example of that. I want to walk you through this feud. So this is Bach fugue in G minor. Um, and I'll give you the file for this just in the next lecture. But I'm gonna do this really annoying thing that I hate it when people do. But I'm gonna play this and I'm gonna talk over it because I just kind of want to point out what goes through my head when I'm listening to a fugue like this. OK, so first of all, let me just play for you. The subject. Okay, The first part of the subject, I should say eso Here's the subject. OK, that's the main thing. You know, the thing to kind of latch your ear onto Is this this first kind of two bars? That's the easiest to recognize when we're listening to this piece and you'll notice the subject really kind of conforms. Teoh The ideas that we know about with a good melody sentence structure, there's, ah, there's not always a period, but there's usually a period, but there's an antecedent consequent relationship. We'll talk more about that in a minute. But for now, um, I'm gonna just hit play on this and I'm gonna tell you when I hear the subject popping out , Um, and we'll actually before I do that, let me just point out kind of the second entry of it. So here is the beginning, right? And then right here where I stopped. We get it again. Yeah, um, but it's not the same notes right here. It's G d is the 1st 2 notes, and here it's d A. So it comes in 1/5 higher. Our fifth lower. Sorry if it lower. Um, so the entrance the second time is at 1/5. So you'll see, like, different little playing around with it like that. So, uh, I'm gonna hit play, and I'm gonna talk through it. Here we go. Okay, So we're off to the races and are subject is happening here. We're listening to it, and we're thinking, OK, this is the subject. Okay, We get the subject at 1/5 way. Have two voices going now. Something a little different. There it is again, way have the subject again, this time at the original key. But down and active to now, we have three voices going. Now we get a big low low in the base. Feels like we're doing something else here. Maybe we've lost the subject. Oh, there it is again. There it is. A little forts funding. There it is again in a major key. Now, some more playing. We're in kind of a different section here. There's again, but some things very different. We've switched modes now way we've heard this before. This is using some of those techniques we just talked about. There it is again, back in minor eyes again, firmly back in G minor out. But we end on a G major. Typical. It's called a picker. The third, um, have a look. If that's a really a purity third, it probably is where we do a whole piece and then and ah like in G Minor and Don G major long story about that that we'll talk about another time. But that's kind of how we listen to fugues like this. It's just, Ah, it's kind of a game, and it's really quite enjoyable if you get good at listening for the subject. So keep that in mind as we we keep going. Now, a couple of the things about this the subject. So we have different voices that enter, so a voice is considered kind of a different line that has the subject going in it. Usually in fugues, we get up to, um, four or sometimes five voices you can kind of see like down here we have. This is a voice. This is a voice. Is the voice here? So we really only have three going at once Here the flags in the direction of the flags really kind of tell you, Let's find a spot where we have four voices going three There it really only see three at any given. Ah, here we go. Here's four. So this is a voice in the base. This is a voice and then this is a voice and then this is a voice. So there's four voices happening there, so and it might get up to five voices at some point here. Clearly we have four voices. Um, but that's what voices our voices are different kind. It lines in the future. Ah, the difference between fugues and inventions is that invention tends toe have two voices, sometimes three. Ah, and fugues tend tohave. Ah, four or five inventions like we talked about before are it's kind of ah, blurry term. It's not super defined what an invention is, but I tend to think of inventions as a little bit of a simpler fugue, and it's very common in a fugue and less common. An invention to start with the subject by itself and then the second entry being 1/5 away. That's really common in fugues, less common and inventions inventions. The second entrance is usually ah at the octave or the unison, the same notes. Okay, so let's go in and talk a little bit more about this subject. 11. The Subject: Okay, so let's talk a little bit more about this subject and what we can figure out in the subject of what we look for in a subject. Now, first of all, one of the things that we're talking about here is the exposition. The exposition is the first part of the peace. Okay, so we have a few different sections of a few. The first big chunk is the exposition. It's like the A section kind of you could also think of it like an introductory section, A sections, probably a better way to think of it. But we call it the Exposition. It's the introducing of materials. So that's where we encounter this subject for the first time. Because this subject is usually the first thing we here in peace. There are, of course exceptions to that, but usually in the fugue. Um, the subject is the first thing we hear, and we usually hear it unaccompanied. Okay, so the first thing we get in a fugue in most cases is the subject by itself. So what we look for in a subject is something that has ah, little bit of a unique rhythm. Um, so that we can really kind of latch onto it because remember what we just did. We we were able to hear every time that popped up, right? So we often use little scale runs in the subject. We use rhythm, mimic ideas that will help it really kind of stand out. And we also sometimes use Ah, arpeggios. That's something you find a lot in a few. Subject is just spelling out the triad because one of the things that the fugue er that the subject does is introduce the harmonic language of the peace. So in this subject, in the single line that we get right at the beginning of it, we really kind of needed to establish, um, the key, the mode and to a lesser extent, some inkling towards the harmony in the piece so we might see kind of a one in a five in a subject, we might see something more complicated. This particular one is a bit of a longer subject. The subject could be anywhere from maybe two bars up. Teoh six bars, You know, just kind of what we have here. We really have 4.5 bars. I think we would call this one. Ah, we'll look in detail at this particular subject in just a minute. It's kinda want to get a couple things about this subject out of the way first. Remember what we just talked about with voices? So the subject will be in one voice. And then once we see another subject, enter, um, we can, uh, we know that we were at the end of our subject. So this the second entrance of a subject is called the answer. So we're gonna talk about answers in just a minute because there's a few other. There's a few kinds of answers, but sticking with the subject for now, let's see if we can figure out where are subject ends. Let's just hear it one more time, Okay? We could say the subject ends right here because that's when the answer, which is the next version of the subject, comes in. We could also say the subject ends right here. Actually, we could say the subject is nothing but this. That could be the entire subject. I don't think so. In this case, I think this is part of this subject. I actually think in this case this is kind of a weird one. I think in this case, the subject ends right there on that G. The downbeat are sorry. Uh, beat three of that fifth better. So we have 4.5 measures. I'm gonna try to stop it right on that spot, and you'll see what I mean. I got that D in there, but I think from here to here is when we're really setting up the move to five, we see that a natural there. And that's where this comes in on the fifth away. So I think these extra notes are a transition to help us get there. I could do this a little more clearly. Let's do this. Let's take that much and let's go over to our Master Mu score file. Let's make sure I'm in the right key here or in G minor. Of course. Its name of the peace. Okay, I guess I got to get myself back. Trouble Chlef, and let's get to G minor. Let's pace that in. Okay, So here's our subject. Oh, What did I do here? I'm in 34 I had to get us back to 44 Okay, Now let's face it are subject. All right, let's you have got Let's get rid of that, too. We're going way slower. So let's increase our tempo here, Okay? I think that feels like the end of the subject right there. So that's what we're going to call the subject for now. Okay, now, let's analyze this a little bit. Let's see what's in this subject, because the subject is more than just a melody by itself. There's a little, ah, in order to make a good subject, which you can imagine. This is a box subject, and he kind of knows what he's doing. So there's This isn't just a simple melody. There's gonna be a little bit more in here. So let's go to a new video and let's do a quick little analysis of just the subject first 12. Analyzing The Subject: Okay, let's do some analysis here. No, that's not gonna let me go underneath the staff. Okay, so we're in the key of G minor. We know that because that's the name of the peace. So let's assume that's correct, Which is pretty safe. Assumption case. We're in G minor. So are it's just gonna figure out what are our implied cords from this melody. Okay, so G d b. There's r B flat. There's arpeggio. Right? So that is a super strong one. Okay, let's call this a a passing note down to here. Now we have J B flat again. That looks like one passing note to G. So I'm gonna call that first half of this bar a one. Okay, Now I have this f sharp already enough sharp. Is that right? That is right. All right. Well, what we gonna do with that f sharp? It's a leading tone, right? So that tells us probably we've moved to a five chord. So let's see what we can do with that D f sharp A. That makes a nice little triad, which is five of G. And we're in the major five because we've raised that leading tone. Totally okay. In a minor key. Nothing weird there. Case. We've got 15 there. Here we have G D a D B flat. If we call that a a passing note again way have just a big old one right there. So let's call that a one. How about here? These? They're two of this. This A which makes me think it's not a passing tone. It's also on a stronger beat here, but I've also got this B flat and a d. I think we've gone to a five chord again here. We don't have that f sharp, but we have d A make any sense of that B flat? Probably not. That's probably just going to be a passing toned down to here. It doesn't really make any sense of the seventh or anything like that, but I'm pretty comfortable calling that a five, even though we don't have that third in there, I think this is clearly the the root of the cord that's happening here. This d a really kind of point us to that. So let's call it a five. Now. You may be thinking, why isn't it a minor five? Because if We don't know what the third is. Shouldn't we go with what's in key? Which would be a minor five? That would be a very smart thing for you to think. Um, but I would disagree. I think we're a major five year because we've had a major five already. We don't have an f sharp, but we can assume if we did have one, it would probably be the same as that. So it's probably a major five. Cool. Let's go on. Let's see, we've got here g d g a d a. Now we could start calling this one chord per beat if we think that's what's gonna happen here. So G d g. That feels like one a d a. That feels like five. It's called out of five B flat a g. We call that a passing. We have a one again G two b flat a D D. C that see may or may not be relevant. Um, here we have a d. D that looks like a five chord. This makes it a 57 chord, which it could be, but we don't have the third, so I don't know if we want to really call that of 57 It might be that we really just feels like a five that doesn't heavily feel like a seven, But it is a seven. So let's go with it, I think. Okay, then back to here B flat, A g B flat. That feels like another one. De or sorry, a g f sharp A that feels like ah, five again because of that big f sharp. And then this G is just a single note, but certainly does feel like a one. Okay, so what do we have in our malady here? We have a whole bunch of one in five. It doesn't always have to be that way. It doesn't have to be just one in five, but ah, I think in this case, that's what we have. Let's see if it feels that way, I must lower it down a little bit more. See if you feel like one in five in this, I think it does. Um, you know, one thing we could do is we could add it on her staff and plug in some chords. Let's do it just for fun. Um, okay. I'm gonna add a keyboard and I'll actually really only need one staff to do this. But that's OK. Let's do this. This is something I like to do. Just to test if your analysis feels right, you know? So we're going to say there's are one. I was gonna do this with. Half notes. Still one, five. Uh, let's do this, Uh, d f sharp am trying to use reasonably. Okay. Voice leading care about why sitting too much here, but Well, oops. No. Any quarter notes, though. Do accordance. Uh uh, Okay. This is exceptionally useful when you're trying to figure out the chords implied by a single melody. Right, Because these are only one note at a time. It can be hard to tell exactly what court is being implied by the melody. So we're just gonna add the cords in here, And if we analyzed this correctly, this should sound OK. It's not gonna sound super exciting, but nothing should sound off. Let's hear it. Okay. Something did sound really off, though. It was this b flat that we questioned, right? Because we had what we had here was a b flat and then g a d. And we thought maybe that was a five. But now I think maybe it's a one because that B flat really does stick out. So let's try putting ah, one there. And then I'm gonna do one more thing. Just cause it's going to sound a little bit better if we just take this whole thing down. Inactive. So let's transpose down by interval. Um perfect. Active. Ok, oops, we went up. That's not what I wanted to dio did I not select down? Down. That's what I meant to select. Oh, by interval down. That's what I had to do. Got it? Okay, let's hear now. Okay, Cool. I think we got it. So that means we need to change this 21 Or we could get rid of it. Because if there's nothing here that means this whole bars one. But we'll just leave a one there. Okay, Cool. So now we know what's in our subject. Let's move on and talk about the answer. Real answer, Tonal answer and also counter subject 13. Rea lAnd Tonal Answers: Okay, so the second entry of the subject is called the answer. Okay, so this is our answer here. OK? So it's the first time that the subject comes back and it will be transposed. Something will be different about it. Now there's two ways that this can happen. There's what's called a real answer and what's called a tonal answer. Okay, so let's look at a real answer first, because that's what we have here. I was gonna make you guess, But then I thought, Well, let's I'm just gonna tell you. So a real answer is a direct transposition. Okay? Nothing fancy. So here we have G de b flat. Okay, let's just keep track. Let's just keep track those 1st 3 notes. Okay, So what are intervals here? G up to a d is 1/5 and then down to down. Ah, third. So let's actually keep track of this interval and then g two b flat. So we're basically outlining a triad here. A g minor triad. Easy enough. Let's look here. What do we have here? De is our first note. So were transposed up 1/5. Okay, so G d d. Is up 1/5 through our fifth higher. So if everything is transposed exactly correct, this note needs to be 1/5 higher than this'll note, which it is. It's in a and then this note needs to be 1/5 higher than this note, and I'm saying all of this incorrectly. A forced lower is what we're really looking at here, right? So either 1/5 higher or 1/4 lower, which would result in the same notes. I always have this habit of saying fifth higher when it's actually 1/4 lower. So let's let's be actually correct here. This is our subject. The answer is 1/4 lower. Okay, that's what it's actually doing here. So what we typically see almost all the time is the answer is 1/5 higher or 1/4 lower. Either of those two things, So we have here a real answer. That's what it's called when it's a direct transposition, right? Let's look at this next. No. Now this notice altered, right? So it's an E. Is that 1/4 lower? Consistent with the rest of these from a It is right. So we're still just directly transposing things. We have to add some accidental is to keep it in to keep the transposition accurate. That c sharp transposition of that f sharp. Everything lines up just fine. So that's a really answer. Now, what is the result of the rial answer? The result is that we've really kind of propelled ourselves up into the fifth, right? So we're on a We've kind of I don't know if we want to say modulated at this point. It's little too early to tell, but kind of Thomas sized the five here, and the first voice kind of is gonna have to accommodate that. And we'll look at that more in a minute. So because we've transposed everything up to the fifth, we are we have kind of launched ourselves away from the tonic and into the area of the fifth. Now, what if we didn't want to do that? What if we wanted to stay close to the tonic with the answer? We can do that. And that's what's called a tonal answer. What we do with the tonal answers, we cheat just a little bit. Okay? So, typically, if this is gonna go 15 this is gonna go 51 So this is this could be super confusing. And I remember when I learned this being just like scratching my head about this for a long time. Um so let me try to find a good way to explain it. Um, let's imagine this was not an A but was a g. Okay, now what has happened here? What we did is here we went g to D. And then here we went d to G. We stuck close to the won by cheating us down that one note, right? So instead of doing a perfect fifth here, we did 1/4 so that we would, uh, not get in the way or not move to the dominant area for here. We would stay close to the tonic, so we cheated a little bit by keeping us close to the tonic. And this works really well because very, very often in a few, the first interval is 1/5. You see that all the time and the way you do this little tonal answer cheat is you make the answer 1/4 that makes it feel like this is like, 51 and then we're still in G here, right? G minor. All the way through here with little ones and fives. But we're in the key of G minor. And then if we do this, we're in G minor. Now, if we cheat that one note down a little bit so that we stay close to the tonic, what happens to the rest of this? Well, we still we stick with the transposition of 1/5 but we might cheat on a couple other intervals as well. What we need to do is keep the general shape of the answer similar to the original and the original subject and as many of the intervals as possible. But if we need to nudge in interval a little bit in order to keep us close to the tonic, weaken, do that. Okay, so that's the difference between riel and tonal. Answer. Let me give you the technical definition here. A real answer is an exact transposition of the fugue subject up 1/5 or down 1/4. A tonal answer modifies the initial intervals and scale degrees of the subject slightly so that it does not express the dominant too strongly cool. That's a riel in a tonal answer 14. The Countersubject: Okay, So the next element we need to look at is what is this music right here? In other words, have the subject right? The subject goes to about their little transition thing. And then the answer comes in right? But this first voice keeps going. It hasn't started the subject over because the subject is in a new voice now. So what's happening here? What is that music? That is what we call the counter subject. Now we might call it two different things, but let's call it the counter subject for the moment that I'll explain to the other thing. So this is counterpoint to the subject that's happening during the answer. So I guess I should say counterpoint to the answer. It's actually both, um, because it's a counter subject, right? So we have subject encounter subject. Counter subject is music that's happening as a counterpoint to the subject or to the answer . It's actually both in this case. It's to the answer. So then we have two kinds of counter subjects, sort of. There's the counter subject itself, but the counter subject might not be actually a counter subject. The word counter subject implies that this is kind of like another subject. It's another thing that we're going to hear repeating over and over and over. And that may or may not be true. And I don't actually know if it is in this one or not yet. So let's figure it out. So the question would be, does this music up here again after the next entrance of the subject? Do we have the same music? So let's find out. So here's our answer. Let's find the next entry of our subject, I think is right here. Uh huh. Right. So that's our next entry is right there. So I would expect the counter subject to be happening here. So what I'm looking for is this is that happening here? Um, not really. But that's the same as that. It could be transposed. That's okay, but I don't really hear it here. I see it here again. So I don't get this back in your head, see it here again, but that it goes off somewhere different. So I don't think this is strictly speaking a counter subject, because if it was a counter subject, we would expect to see it again, and it being used like another subject, Really? So instead, we call this the other thing, and the other thing is free counterpoint. So free counterpoint means that while the answer is happening, there's still other music happening in the other voices, which is just one voice at this moment. But it's a counterpoint to the answer or the subject that isn't going to be used again over and over and over, like another subject. But it's just free counterpoint. It's some more notes to fill in the space, so let me define those two things for you One more time. Counter subject means it's counterpoint to the subject or the answer that is going to be reused again and again throughout the piece. Like a second subject, Free counterpoint means it's counter. It's counterpoint to thes subject or the answer that is not going to be reused again. Throughout the piece. It's free. It's somewhat more of a disposable kind of counterpoint, so we determine it, whether this counterpoint is a counter subject or free counterpoint by trying to find it again throughout the piece. It's kind of here, but it's kind of in the wrong spot to really work. Here's our subject again. It's not there. There's something different here. So this is all free counterpoint. Here's our subject again. And do we get it there? Way Do? Uh huh. We could get it there. Um, so maybe I'm wrong. Maybe we just don't get it this second time. Let's find another entrance. There's one, Uh, that's different, but it's really close. Go forward one more. Here we go. Very different here. So we get it sometimes here and not sometimes here. So I'm going to reverse my opinion and say, I do think it's a counter subject cause we do get it again. We do get that music later. It's not every time, but we do. It does get reused. So let's call that a counter subject. Um, we have to look around a little bit more to find it, but it's there. It is reused. So I'm okay with calling that a counter subject. Cool. So those are the two things kind of subjects and free counterpoint 15. Invertable Counterpoint: Okay, let's talk about in vertebral counterpoint. This is another thing that we find in fugues a lot. And in order to explain it, let's zoom way in here. Okay? So I'm looking at the answer and the counter subject, right? In veritable counterpoint means that this subject, or the counter and the counter subject, um, can be well are written in a way that they can flip voices. In other words, the subject might might be in the upper voice and the counter subject in the lower voice and in a later spot, the that might be the opposite. K one might be the higher voice, what might be the lower voice and they flip. So what that means is that when they flip, they have to still maintain they have to not upset the harmony when they flip. So what that really translates to is relying on a lot of of, uh, thirds and sixes. Okay, So, for example, um, well, let me explain that a little bit more, so if let's say there was a seventh, for example. So if we had d here in a sea here. Okay, um, then this would be 1/7 and the harmony would be some kind of seventh chord, right? That's fine. Or assuming it's not a passing note. But let's call it let's assume that it's an important note to the Harmony. So then when it when it flipped, it would be a second right, because if this was a C, then it would flip. We'd have a C on the bottom, a c on the bottom in a D on top. So now we've got a second, which implies a different kind of harmony than 1/7 right. That would be some kind of suspended chord, which is really not used in this style of music, very much so. That would be a bit of a problem. So when we do this in vertical counterpoint, we use a lot of thirds. And six is because they can flip and still imply the same harmony, right? So if we go through this and look at all of our harmonies where we should find ah, lot of thirds and sixes and then passing tones, Okay, um, so let's just take a quick look. So we have d upto f. That's 1/3 de up to E. Ah, that's a second But in this case we can call that a passing tone d two d That's an active, so active, also a okay in this situation de toe f that's 1/3 G t e. That's 1/6 G to D. That's 1/5 which is a kind of a dangerous one, right? Because if you flip that you have 1/4 which changes the harmony. So, um, but in this case, we can call that a passing tones, so it won't affect us very much. D. R. Sarriegi, too. C Sharp is a tri tone in this case, an augmented fourth, so we would probably call that a passing tone, although it's on a strong beat, so that's a tricky one. So that might be an exception, but probably a quick passing tone up. And then we jump up to this. E, which is 1/6 F two D, is 1/6 F two A is 1/3 after D is a six e. T is inductive, so you can see lots of thirds and sixes make for more comfortable in vertebral counterpoint . Now you'll see later in these pieces, things get even more complicated where we have that, uh Let's look here might be a good example at this point, what we have, what's called double counterpoint. And that's when there's essentially three things happening. Um, we have a subject or a counter subject, and then two levels of counterpoint. So double counterpoint, all of which are in vertical. So this all has to be in vertebral so they could be switched around. And later. I don't know if we have it here. Probably here. If we looked close, we might have triple counterpoint where we have a subject. Although I don't really see a subject here we have a subject and then three levels of counterpoint, all of which are in vertebral triple counterpoint. This is where you see this is where stuff just gets crazy and you start to think, How does your brain work to be able to write in this way where there's, like in vertebral triple counterpoint, with subjects and counter subjects both going and all of this happening at the same time? It it boggles the mind. Okay, so those are the elements of our exposition. So let's look through this and kind of analyze it a little bit and just kind of identify the main things. Let's go to a new video and do that 16. Exposition Analysis: Okay, let's do an analysis of the exposition of this fugue using the tools that we know so far. Okay, so when I'm analyzing a few guy may remain a analyze the cords. I I should analyze all of the harmony, but that's not what I'm gonna focus on right now. What I'm gonna focus on right now is the elements of the fugue. Okay, so I'm gonna start with the subject. Okay, so we have a subject. Let's go down here and here. We have the answer. Okay. And what do we have here? We have counter subject. Now, we can label this by writing the word counter subject, but also, we could write CS for counter subject. And in some cases, you have more than one counter subject. So you might call this CS one? Um, I don't think we have more than one counter subject, so let's for now. Just call it C. S. Okay, so here we have answer, encounter, subject. Okay. Now is when it gets a little trickier. So let's find more instances of our subject. Okay? So let's actually play through it, cause it'll be easier to hear it than it is to see it. I'm gonna play through a kind of slow from here. Okay, Here are kind of in some free counterpoint here. Um, although this might be part of the counter subjects. Still, we haven't gotten that far yet, but I can see coming up right here is our subject again. Okay. And let's see, is this a subject or an answer? It's G d B flat, G D B flat. So let's call that a subject, because it's at the initial pitch. And here we don't exactly have the counter subject. So at this point, I'm going to call this free counterpoint now. It could be that this is a second counter subject. What? It's different than our first counter subject. So it's not the counter subject again. We call it free counterpoint. For now, there's another subject. Although here we have d A f. That is our answer. I think this is That's an A. I changed it, remember? So now it seemed to back. So this is our answer because it is fifth away. So what's happening here? Is this free counterpoint or is this our counter subject that's here? Is it same as this? No. Is it seems this. Nope. So this is something yet again different. So we're gonna call this free counterpoint. Uh, okay. Now, I think we've reached the end of the exposition, and we've moved on to the second section, which is called an episode which will get into the next section. That is the main parts of the exposition of the fugue. We have subject counter subject answers free counterpoints on. That's it. And you might have a second counter subject. That's possible too. Okay, uh, I'm gonna give you this file again, I suppose, since I added thes things to it. Um, so this will be the same file, but it's got my notes here. Ah, and then we'll go on and talk about episodes. 17. Episode Defined: OK, moving on to talking about episodes. Now, an episode is kind of the connecting tissue of the fugue. Um, so so far, we have the exposition. And in the exposition, we have subjects. We have answers. We have some counterpoint, maybe some free counterpoint. But eventually we leave the subject an answer. And we have some material That's really, really its main purpose is to get us to the next key area. And usually it does that by sequence. Sometimes it does it just through free counterpoint. Um, so that's kind of the main two things were looking for. And we call that an episode. Um, let me just point out one, right? Right here. Let's just in the same piece. Let's go down to right here. And what we're really looking at is, um, this stuff right here, measure 20 twos through, I think 25 these three bars. Okay, you're gonna hear that. We kind of leave the subject and the answer for a minute, and we have a little sequence, and then we get back to the subject, so it's pretty brief. Um, let's just jump in right around here, - okay ? And then we're right back. into the subject again here, Right? So we would call these three measures and Episode one episode could be short, and it couldn't be long. Um, okay, so let's talk about just a couple other key elements of the episode. The main factor of an episode is that it leaves the subject. We don't have any kind of real trace of the subject in it, necessarily, although it might be based on, like, one little riff in the subject, something that might connect it, but more or less, we've completely left the subject. Um, it's usually a sequence. Sometimes there are two sequences. Um, it might be like I just said it might be based off a melodic or rhythmic idea from the subject or the counter subject, but doesn't have to be, um its main thing is to get us to the next key. Typically, ah, dominant of where we are for major keys or a relative major if we're in a minor key of where we start. So once we get there once we've kind of established a new key with the episode, we typically get the subject again. Um, either by itself or with an answer and then often the cycle starts again. We get another episode leading us to another key, and then we get the subject again. So then this kind of cycle starts toe happen. Um, so we have, after we've established the kind of subject answer ah of the exposition. Then we get this kind of pattern of episode subject, sometimes with the answer sometimes not. And then episode again. Subject Answer. Always leading us to a new key until eventually we get to the end of the piece where we get an episode that leads us back to the May, the original key of the peace. And then we get the subject, um, one last time in the original key and in the end of the piece. So that's mainly what the subject is. Now, I'll show you in a few minutes kind of a chart that we like to make when we look at fugues . Um, there's a way that we outline what's happening where, um and we'll do that for this piece in a minute. But for now, let's dive into this little, um episode and, uh, see if we can find the sequence and exactly what it's doing here. 18. Analyzing The Episode: Okay, so let's just take a look real quick at just this little episode right here, okay? And let's just see what we've got in it. Let's hear just these three bars. Maybe that couple beats of the fourth bar, okay? And then the subject is back. So do we hear sequence here? I sure do remember. A sequence is just a pattern that moves by some kind of regular interval. So here's what I hear. Um, if you just latch onto the right hand stuff here, I hear this right. Those four notes, then we get it again up 1/4 and then we get it again up 1/4 there down to fifth. And then again up 1/4. Right. So we have an ascending fourth here. Reason I'm sending. I'm saying us sending forth is just look at the first note. It doesn't the cords. You could look at this by cords, but if you just look at the notes of it, um, the first note is a and then the first notice D. So we're up 1/4. Ah. Then the first note is a G from D, sore of 1/4 and then the first note is a C. So we're up 1/4 again. So, uh, this little melodic pattern is going up 1/4 every time. Cool. So we have ah, ascending fourth pattern here or descending fifth pattern. We could call it if we wanted to. Um, both are fine. Um, and that's enough. We could analyse the cords and say, Well, one chord. Very important. Is this one? What key are we actually in? When the starts. We should figure that out. So we have d d f so probably a big old D minor. Right? We see these. See, Natural is here. Uh, e natural. That tells us. Yeah, we're probably firmly in d minor, and this cord does feel like tonic. If we go back just a little bit up to here, maybe when we get to hear you, you'll see that feels like, Yeah, So I think we're in d minor here pretty comfortably. So we're five away. We started in G minor, moved up to D. That's okay. Okay. And let's just maybe just look at where we're moving through with the cords De. Let's look at where we lend here G b flat. So probably Ah, G minor here. So have we moved up by 1/4 in the same way the sequence has de up Teoh G? Yeah. We moved up 1/4. So G minor up to C E flat C minor. Probably. Um, we were G Now we're up to see So we moved up 1/4 again. We look here f a e flat. We've got 1/7 creeping in there. But if we look at the f in the A, we have in f a natural. Yeah, a natural. So we have an f major here. Where were we? Here. See? Yes, we're up 1/4 again. Got 1/7 in there. I suppose we had 1/7 before. Also. That's okay. So we're moving up by force is great. Now what happens here? Here are sequence breaks, right? Are sequence stops. We don't have this anymore, and we just have something different. So what's happening here? One quick little bar. A free counterpoint. That's totally okay. That's totally allowed. What he's doing here is really just kind of establishing the new key, which in this case, happens to be the old key. So let's figure out where we are. We're in f are. We were in a sequence, so we're not really anywhere, right? We're in transition mode. That's what a sequence does is it moves us. So we land on f here. Let's see what happens here. We get to be flat A de what? We want to call that. Uh, we could call it a B flat. De, you haven't f anywhere really sharp, Slater. Someone I wanted. So maybe be flat. Isn't the route maybe D is? No, I think b flats the root here. I mean, we have a huge activator, so it's probably a B flat chord. Um, does that finish out our sequence? Even its run f yeah. If we went up 1/4 from F, we end on B flat. So that does finish out our sequence from some kind of B flat. Here. Let's look at every bar from here on out here. We haven't e flat e g. We could consider that d that g again. So strong stuff pointing us to G. Ah, let's see. Can we call e flat the route e g? Yeah. So that would be e flat. Major landing on. See here. No real chord here but this could be some kind of a C seven, maybe D f sharp A. There we go. That's what we were looking for because this D F sharp C is what I should've said. D f sharp c There's a over there that gets us to a D dominant seven chord, which is going to lead us back to G minor. And then we get are subject again. So this sequence actually lead us back to G minor. Normally, we expected a sequence to move us 1/5 away, but it doesn't always have to, and this fugue is a little bit weird. So it moved us to, um, fourth away, right? We started on D minor and we went up 1/4 throughout this whole sequence. The sequence was moving up 1/4 all the way through it, and eventually it dropped us off up 1/4 from it, or down 1/5 um, which put us back into G minor where we started, and that's OK, That's OK. It's not the most typical thing we would expect, but it's not that weird. It's totally okay. All right, so that's what happens in our little episode. We have a sequence. Have a tiny bit of free counterpoint to rip us through a couple chords real quick and get us back to G. Miner lets your great Okay, let's move on and talk about this graph thing and sort of walk through how we analyze this , the kind of big picture elements of a few. 19. Graphing A Fugue: Okay. So earlier we did this. We put this text in here. Subject, answer, counter subject free counterpoint, Things like that. So there's a better way to do this. And especially once we start getting two episodes, Um, sometimes you just kind of want to look at the big picture of a fugue. And often, uh, this is how we do it. So is a little bit different method. And this is analysis and analysis that for the first time, we're going to switch over Teoh Ah, database to dio eso We really kind of want, like, graph paper to do this. So basically what we're gonna look at is we're gonna list them the measures of the different sections. We're gonna say what's happening, and we're gonna say so this is going to be what's happening overall. And then what is the soprano doing alto doing in base doing now? I chose soprano, alto and bass because we really only have three voices happening at a time here. There's three voices happening here. Um, I think this is the first time we get three voices. Here is the first time we get three voices, I think, and we have bass, Alto and soprano. So I when we only have three, you could call the middle voice tenor. Or you could call it alto. It's kind of up to you. I called it alto just cause when it enters its written on the top staff, so it looks more like an alto later, it's going to go down to the bottom staff, like here. So it looks like a tenner, but doesn't really matter. I'm just going to call it the middle voice. You can call it alto or tenor, whichever you prefer. Um, and then Sopranos going to top voice and bass is gonna be the bottom voice, obviously. So let's look at what we got. So our first big chunk of stuff happens from Measure one through here. So 11 through five. Okay, so let's say, But you're one through five. What's happening? We're gonna call that the exposition and the soprano has the subject. Okay, this is so the soprano is doing the subject. Alto and bass are doing nothing. Let's capitalize that. Let's be neat about things. Okay, Easy enough. Uh, so then measures six through. Let's see, when I was there, Next kind of big changes right here. So let's say six through 12.5. Six through 12.5. What's happening here? So we're still in the exposition, so I'm just gonna do this. Exposition is still going. Um, we are The soprano is doing counter subject sums going right, CS for counter subject in the Soprano The base is doing subject the subject that gets us all the way through to here. Okay, now we have measures. 12.5 through 17.5. Oops, 12.5 through 17.5. Still exposition. And we have free counterpoint in the soprano. And now the alto is in. So it's a free counterpoint in the out in the soprano free counterpoint, uh, subject in the base and the the middle voice kind of also doing free counterpoint, right? This isn't Yeah. Yeah, that's not anything related. So let's call that free counterpoint also, and then I just want to get us up to the episode. I'm not going to the whole piece doing this, but in college, you if this was a college course, you would be asked to do the whole piece in this way, but so 17.5 up through 22. What's happening here? Um, we're getting the answer in the base, and we're getting free counterpoint everywhere else. Okay, So still free counterpoint. And the soprano An alto, then 22 through 24. Actually, this to be 21 22 through 24. We have episode. Okay, so exposition is still going there. Episode and we don't really need to write anything here because everybody is partaking in the episode. Okay, So the way we would kind of clean this up if we wanted this to look like how we would expect it. So I'm gonna do this, Get a little fancy on my, uh, excel skills here, even though I'm in Google docks, boat, whatever. Uh, I'm just gonna combine similar stuff. So I'm gonna do this. Combined these into one things they don't stop. This gives us a little bit more accurate picture of what's happening. Okay, then let's put that at the top. Okay? So if I do this like that, then that's maybe change the color of these so that it's a little more obvious. Okay, Now we see a little bit more clear what's happening. People combine those? Yeah, So? Exposition episode subject. Counter subject. Free counterpoint. Nothing free counterpoint so we could see the alto enters around here. Subject goes from here to here. Answer happens there. So if you do this for a whole piece, it actually kind of looks really, really nice. And you can actually really kind of understand and see how a few guys working you can trace the subject and things around really nicely. And you can see where episodes pop up, right? So if we did a whole analysis, you would see, you know, kind of after this something like this where you know, there would be more subjects, encounter subjects moving around, but these episodes would pop in, right? Cool. So maybe I'll give you this file in case you want to play around with it and, um, add more to it. Use it as a template to do your own analysis of other fugues. Author this file into the next lecture, and then we'll keep moving forward 20. Another Episode: okay, Before we leave episodes, I thought maybe let's take a look at one more. Um so if we go forward, actually, not very much farther we get another one right at the bottom of this page. Really? This bar. So bar 29. 30 Bar 31 and 32. A real short one. Does two bars. Uh, what's here? And let's get into it a little bit. Uh, let's go from here. And the subject comes in in the tenor line or the out of line you wanna call it? So let's look at what's happening here. Actually kind of starts here this episode. So let's figure out what key were in first to really understand what's happening here. So let's see if we can find something we're gonna call tonic. Maybe this, uh, let's just see what feels like. This kind of doesn't feel like tonic. Uh, this nose, though I don't know what that bass note this B flat G feels like Tonic. So maybe that's a G. Oh, you know, if this was a G, if we were in G minor here, still, this big D would be essentially a big, long potential 64 because it's ah de in the base. So let's assume we're still in G minor because I think that's really what it's feeling like , especially when we look here and then another d but an octave higher. So what's happening here? So we have C and then B flat A and then changes. So we just looked here. C b flat A. We have a descending second pattern and we have that here, too. Uh huh. So descending second pattern here. And then we have a little bit of free counterpoint here to wrap us up to get us to this B flat B flat major. So, ah, if we were in G minor, we went to the relative major, and that would be perfectly expected for this kind of a thing. So another little episode All we did was do a descending second sequence with some free counterpoint at the end to get us to our relative major. Cool. Let's hear one more time. Go from here. No, 21. Beyond The Basic Fugue: Okay, So what we know about the fugue so far to summarize is that we have kind of this pattern that repeats over and over. We have the exposition and an episode. Um, we have the subject appearing and kind of switching off between voices. We have answers, we have counter subjects and we have free counterpoint. Okay. And then we have an episode, which is usually a sequence that leads us to a new key. And then we do variations of this over and over, right? So So those are kind of our key elements. Now, if we just did that and nothing but that, then, uh, eventually that might get a little stale, although not really, because there's still a lot you can do with that and a lot that composers have done with just that. However, there are some special tricks that composers have used throughout the ages. Ah, to get even more complex and really kind of wild with the fugue things like alterations to the subject, using multiple subjects of making the subjects shorter or longer in different sections, inverting the subject, truncating the subject, truncating the answer. There's a lot of kind of other tricks that we do too. Um, keep people on their toes if you will. So with this section, we're going to go over all of that stuff. Ah, some of the cool things that we're gonna listen to a few fuses. Well ah, that have done some particularly cool things. And hopefully, now that you understand how the few works, you'll be able to listen to some of these issues with kind of a new appreciation for what they're doing. So let's dive in. Ah, right away to one of the more complex things which is the double and triple fugue. Here we go. 22. Double And Triple Fugues: Okay, So first, let's talk about double and triple fugues. Now, don't get thes confused with, ah, double counterpoint or triple counterpoint, which is another way of saying the in vertebral counterpoint that we talked about earlier. This is not in vertical counterpoint. Ah, this is different. This is when you have to, in the case of double fugue to subjects and triple fugue, and you have three subjects. Now, if you have two subjects, for example, that means you need to answers. Um, that makes your episodes more complicated. Uh, everything gets more complicated by a lot when you add two subjects and when you add three , you're just getting crazy, right? This is just nuts. But, um, it's been done. Uh, so when we have a double fugue or a triple fugue, uh, typically, how it works is you get one subject, it's beginning. And then in a later part of the piece, you get another subject, so you don't get them both at the same time. Same thing with triple fugue. Um, so probably one of the most famous ah triple fugues is the ST Anne's fugue. This is Bach, um, bwb 552 in case you are wondering, by the way, what B w V stands for. We've looked at a lot of Bach, and I don't think I pointed that out. Um, I believe the B stands for Bach. I can't remember what the W. V stands for, but it's basically a cataloguing number of Bach works. So this is not a system that Bach put on his works. He didn't call his works Beat of UV 552 This is a scholar, came along later and said, Um, we need to figure out, you know, catalogue all of Bach's works, and they put these numbers on them to help us keep track of the insane amount of works that Bach wrote. So, um, each particular piece of music that he wrote has a unique BW V number. Ah, so this is BWB 552 and they're mostly chronological. So be WV. One would be in a really early, early, early piece of music that he wrote BW V 900 is gonna be a later peace. So this is BW V 552 ST Anne's fugue. So this is a triple fugue. It's for Oregon, so it has three subjects. So in three different sections, you'll hear the three different subjects. Um, and the trick to this is that they each have to kind of have their own feel. They can't. They have to be done so differently that they were not confused for one another. And the the idea is that the listener has to be able to keep track of the three subjects. So rather than do, ah, kind of big analysis of this piece, I thought me we just hear it so I can point out, though, the three subjects you're going to hear the 1st 1 is gonna be in half notes, and we can kind of see it here Half notes and whole notes. It's basically these 1st 2 bars, see, And then we get it again here and then later. Won't you see are running eighth note that will be our second subject. And then once you see 16th notes coming in, um, that will be the entrance of our third subject. Okay, so that can kind of give you, um, something to look out for as we listen to this piece. So let's go to a new video and let's listen to this piece. Uh and, um, yeah, just enjoy it. 23. Listening: Bach, St. Annes Fugue: Okay, here we go. ST Anne's Few a triple fugue for organ Way , way, - three way. 24. Stretto: okay for our next trick. That's kind of weird to put it that way. I didn't mean that come out as like it was a magic trick, but it's kind of a metric. Um, I want to talk about strayed. Oh, and strata was a technique that we use. Ah, it's something we can do to this subject. Now, In order to demonstrate this, I'm going to switch over to a different piece. As if you can see, Major. Um, the future we were using before the one in g minor just didn't have ah example of Streeto in it, which is totally okay. These are not things that happen in every fugue. Um, so this technique happens right here in bars. 13 14 15 16 17. Right in this area. But ah, In order to hear this, we've got to really kind of have in our head the subject. So what started beginning, I'm gonna play up to that spot, and then we'll pause and we'll talk about what this straight o thing is. So really try to latch onto this subject. You'll hear it. Ah, whole bunch. In this first, um, this first page or so of music It's basically actually, let me just play the subject really quick. Thought it's It's that That's the subject. Okay, way. Okay, Let's stop there. Now listen for in the subject. This little thing, right? Dated him. Let's just hear that. Okay, that that quick little 32nd note there. Let's actually just see it. So here's one. Here's one. Here's one. Here's one. Here's one. Here's one. And here's one. Okay, so we have 123 for 567 of them. That happened in these four bars. Now, this is a to measure fugue subjects. So that means that really not more than one should happen. Every two bars, but we have seven and four bars. So what that means is that the subject is stacking up, and that is what Streeto is. We have the subject happening here, and then we have it here. Yeah. Uh huh. We have it here. Um um, we have it. Ah, here again. We have it. Here we have it. Uh, here. Right. So the subject is just getting stacked in second stack and fragmented. We're not getting the whole subject. Every time we're getting these little pieces of it all over the place. That is what Streeto is. So Strettle means that were taking the subject and we're overlapping them and we might not be completing them. You could complete them or you could not complete them when you're doing this straight. Oh, technique. So you've got all these subjects just kind of piled up on top of each other, and some of them finish out and some of them don't. So let's just here just from right here and listen for this the subject entries, right? You hear, like how many there are. And the reason that I pointed out the little 32nd now is just because that's something easy to here to kind of latch onto. But we do get you know, the eighth note leading up to it, right? Let's hear one more time. Just listen for those 32nd notes, and you'll hear how many there are happening at once right there, like just building and building and building and layering on top of each other. That's a technique called Streeto, and this is something that can be used to replace free counterpoint sections, um, to kind of a company. The subject, although not really because it is the subject in a way, but it can extend those free counterpoint sections or really any kind of counterpoint section. 25. Inversion: Okay, let's talk about a couple other things that we sometimes he done to the subject to kind of obscure things a little bit. Right. So the next one I want to talk about his inversion. Now, I think we've seen inversion before. I don't think this is a new term to you. Although I can't remember off top my head where we would have encountered it. Um, well, we know inversion from harmony, right? We know that when accord is using an inversion, it has a different note at the bottom, basically than the route. This is not that this is quite a bit different than that. Um, we may have seen it in other areas where, um we have a melody, but basically where the melody goes up, we're gonna go down. It's like a mirror image, basically. So if you congee minor now, this doesn't have use of an inverted subject that I confined, but let's look at what it would be like if it did so I'm gonna take just the 1st 2 bars of the subject, go over to our master file here, lets you make sure we're in the right key were in 44 and oops. Key of G minor. Oh, yeah, we are Great. Okay, so let's just put it right there. Okay? So there's our subject. Now, let's make an inversion of just this part of the subject. So when we have an inversion an inverted subject, it just means that we can use this the same way we've used the subject. We're going to see inversions with melodic ideas more in the future. Um, but let's just calculate what they would be. The easiest way to do this is to just label are intervals. This is what I like to dio. So get rid of that and get rid of that. So I'm just gonna label each interval between the two notes. So melodic intervals right? Means they don't happen in the same time. So g up to D is a perfect fifth. Okay, easy enough. D down to B flat is a major third. Okay, B flat down to a is a minor second down. This will make sense why we're doing this in a minute. Okay. A down to G is a major second g up to B flat is a monitored. Oops. When you put the second measure over here. It's gonna get all tatted B flat down to a is a minor Second a down to G is a major second G down to F Sharp as a minor second have sharp up to a is a minor third than a down to D is 1/5. Oops is a perfect fifth. Okay, so there's our intervals between notes. Now, what we need to dio is shift the direction. So we're gonna start off on the same note, g, and we're gonna use the same rhythm. So here we go up a perfect fifth g up to D. So now we're gonna go down a perfect fifth. Uh, G it's gonna be down to see, See up to G is the perfect fifth. Now, here we go down a major third. So we're gonna go up a major third. That's going to get us to the natural. If we're being chromatic now, you can do this, Diatonic lee. Meaning we're going to kind of force it to stay in the same key. Or you can do it. Chromatic lee. Meaning it's gonna be literally the same intervals. So if I leave this an e flat than it's gonna be diatonic, right? Because it means we're going to force it into the same key. But if we do a chromatic, it's gonna be e natural. Let's do a chromatic just for fun. Um, okay, so now I have, and that's a dotted new. Okay, now I need an eighth note. That's going to be Ah, minor, second downs. We're gonna go minor. Second up. That's gonna get us to death. Okay, so there's our 1st 1 first bar, So now we have a major second down, so we're gonna go major second up. It's gonna get us to a G and then a minor third ups. We're gonna go minor, third down. It's gonna get us to an E. Now we're gonna go a minor second down originally. So we're gonna go minor second up, going back to an F major second downs. We're gonna go major second up and goes back to a G minor second downs. We're gonna go minor, second up. That's gonna get us to a flat if we're going to stick to Chromatic. And then where were we hear? So minor Third upswing. A minor third down F a flat Yet so be an F natural and then perfect fifth down. So perfect fit up Fact of C and that's 1/4 note. Okay, so that is our inverted melody are inverted subject, I should say so we could use this as a subject if we want to get sneaky. Right? Let's hear the difference between the two. Here we go, right. Kind of weird. Let's do it. Diatonic Lee on. Keep it in the same key. That would mean we groups. You probably want to make this enough sharp. Really? If we wanted to match what we're doing over there, let's see what happens now, right? You have that e flat toe f sharp. Interval there gives it that kind of eastern sound. But that is the inverted subject. You might find this in a fugue. Um, there are a few fugues that we can point to. Orbach used it. A lot of people use it at the time, so keep an eye out for inverted subjects. 26. Augmentation: Okay. Another thing that we see in Bach Ah, fuse is augmentation. Now, I know we've done this before, uh, in a different context. Let's talk about it again. Of course. But, um, you've seen this kind of augmentation before. What we're talking about here is rhythmic augmentation. What this means is that each note value is gonna get bigger consistently. That's the trick to it. So we're going to do something like quarter notes become half notes. Okay, So if if quarter note becomes 1/2 note well, we have to really rewrite the law. Melody, copying and pasting is gonna work here. So let's do this and that. So if we're going to do a strict augmentation of this by doubling it, it would be so. Every rhythmic value gets doubled, pictures stay the same. But that means it's gonna be four bars instead of two in this case. So this one dotted quarter note that's 3/8 notes. So whatever we give, it has to be 6/8 notes, uh, which would be a dotted half note, and then an eighth note becomes 1/4 notes quite well, and then quarter notes. Eighths to come. Quarter notes again should work out to fill exactly twice the amount of measures. Okay, so then we have an augmented subject. Sounds the same, but a lot slower. Right? But keep in mind that this doesn't mean that the counterpoint happening underneath it slows down. There can still be ah, lot of music cruising around in the counterpoint, and the subject just gets augmented. It can be really cool. Ah, really. Quote trick to Dio. 27. Diminution: Okay, So if we can do augmentation, then that means we can do diminution as well, right? Rhythmic diminution, uh, cut everything in half. So let's let's do it real quick. So we're gonna take this original subject segment segment of the subject, and, ah, we're gonna double or halve the values. So we're gonna make eighth notes. So things getting get a little tricky here. Eso If this is three eighth notes, it needs to be 1.5 8 notes, Which means Ah, 1.5 8 notes is three 16th notes. So what it needs to be so we could do a dotted eighth note. And now we're going to get kind of off the grid a little bit here. Oh, no, we're not. You need 1/16 note for that eighth note and then 16th notes for the rest, and then should leave us with anything. So it'll be exactly half the number of bars. This was two bars, one bar. Here. It is a lot, right? Exactly how you would expect it. So diminution. It's an obvious one, but worth pointing out 28. Canon: okay. Another kind of different kind of thing that happens is a cannon. So I think we probably talked about cannons before as a very kind of simple idea, Right? A cannon is when you have some music that starts and then kind of echoes along, let me just show you, um, an example like a cannon would be something like, Let's see, let's add a couple measures here and let's do Let's take our fugue subject just for the heck of it. And let's make a cannon out of it. This this will be a little messy, but so let's take this when we get rid of the intervals. So it's not super ugly, and then I'm just gonna do this a few times. Okay, so then here will start another one, and here we'll start another one. So exactly the same. Just like in in Cannon. Right? So we start here, no transposition, and it just keeps going right. Let's let's just out of curiosity here, what that does This might be a total mess. Actually, this one is going to be exactly the same as the top one. They just line up. So let's do. Can I do that. There you. So now this one is off by two beats and let's move it down. Ah, inactive just to make it distinguishable, which is allowed in the canon. Okay. And then we can delete those two notes that I just added to space it out. Okay, let's try No. Okay, so that sounds terrible. Um, it's not as easy as we think, right? It's It could be a little ugly, but that's what a cannon is. Right? So, um, we can use a cannon, but done not as stupid as that one. Uh, if you So check this out. This is an invention. So it's a little bit different than a few, but not all that much different. Um, and this is a new one. This is, uh, invention number two and seem Leyner. What we have here is ah, the subject used as a canon. Now, how is that different? Here's what makes it different. So here's the subject. Okay, that's the subject. What happens next is the counter subject happens in the right hand up here, right? But and the left hand we get the subject again, which is common invention. But then at the end of it, we get the counter subject. It just continues going. So these continue to go in parallel for a long time. So subject encounter subject are kind of chasing each other, and that's a cannon. Let's hear this first part on and eventually will lead Teoh elements of counterpoint, uh, subject, uh, episodes and things like that with it. But the subject is really kind of presented as a cannon where the subject encounter subject are kind of chasing each other like that, and that's how you can use a cannon and fugues and inventions, and it's something that we see box employees quite a bit. 29. Why Do We Care About Fugues?: Okay, so I just want to reiterate one thing. Why do we care about fugues? We've been talking a lot about fugues, and I think we talked about this the beginning of this class. But why? This is important. But, um, now that we've been through it Ah, I want to talk about it one more time and maybe a different way. First of all, I hope that now that you've kind of got in the weeds with how fugues work and what's going on with them, you'll hear them or you'll hear them as more than just a lot of notes going by really fast , right? It's easy to hear if you could be like, Whoa, there's just notes going and going and going and going, um, but now you'll hear them in a way that will might make you think, Wow, that's really ah, beautiful and complicated and intricate. And there's all these things happening, and maybe you'll understand. Ah, enough to maybe hear them in a different way than you had before, right? Another thing that's important to us when it comes to music theory is all of the This is kind of, um, an example of probably the best example of counterpoint at its finest. Right. This is taking everything we know about counterpoint and just going nuts with it, right? This is the kind of most advanced kind of counterpoint that we have. And we will see an other music going forward that from here on out, um, we start to get a little lax. With the rules of counterpoint, we start to bend the rules a lot more, and we haven't looked at like fugues. From the counterpoint perspective, so much you can get into vocal fugues. Whether is four part counterpoint happening with a few, um, or within a few guy, I should say, and it'll blow your mind how every rule has to comply. We've been primarily looking at keyboard fugues where we don't worry so much about the vertical rules. Although they still do all apply. And in most cases, even in a keyboard fugue, they are still followed. So this the fugue and the writing of the few is really kind of the apex of counterpoint of this style. So I hope that throughout this class you've gotten a new appreciation for a few. Maybe you'll decide to sit down and try to write one on your own. I've written a few of them. They were not particularly brilliant, but it's a really fun exercise. So I highly encourage you come up with a subject, find a counter subject. Ah, use all the elements of the few that we've talked about and write a little fugue. It could be really fun. Um, and challenging. Ah, it's not gonna be the easiest thing you've ever written but can be very rewarding. Okay, let's move on. 30. What Next?: Okay, What comes next? We reach the end of this big section on fugues. So, um, what's gonna be in the next big section? Well, a few big things, A few exciting things. We're gonna talk about mode mixture, which is really going to start to dabble us into chromatic harmony. And that means using chords that are not in the key pulling in cords from other keys, which we've sort of looked at a little bit way back when we're talking about Circle of Fifths. But we're gonna look at it a lot more. And we're gonna look at how composers like Schubert, um, Bach, of course. But even Mozart started to use, uh, mode mixture to give their compositions a break from the normal expected harmonies and start to switch things up. In the process of doing that, we're also gonna learn about a few new courts when you're thinking, Well, that's impossible. I know all the cords. I know my majors. When miners my diminished in my augmented and my sevenths, right and my nights and my 13th this is totally different. There's a whole batch of chords that you know nothing about, um, for example than the a politan cord. You never heard of the Neopolitan cord. You thought Neopolitan was just for ice cream, but it's not. There is a Neopolitan cord there. Also think cords called augmented sixth cords, and those get fun nationalities associated with them. There's the Italian augmented six Chord. There's the German augmented six Chord, and there's the French augmented six court. No one knows where those nationalities come from, but that's just what we call them. So we're gonna get to all of that in this next section. And trust me, if you're into songwriting, the Neopolitan Court, the Neopolitan cord it's gonna be one that you want to know about. I love using that. Even in pop songs. It's such a weird turn, but it's really just kind of a goofy major chord. And so it'll be. You'll really like it. Trust me, it'll be a cool trick. So I hope to see you in that class. That will be what, 15 music theory. 15. Holy smokes. Yeah, Music theory 15. That will be so. I hope to see you in that, uh, stick around. I got a couple more things for you yet in this class, and then we'll move on 31. Thanks and Bye! (For now...): all right. That, of course, brings us to the end of this class. The fugue class. Thanks for sticking around. Thanks for being part of these classes. It's been really fun. It's been a real pleasure to make all of these classes, and that makes it sound like I'm above to stop making these classes, which I'm absolutely not going to do because I love to do. This is a super fun. So, um, but I just like to always take this last video just to say thanks for being a part of this . Thanks for being a part of these classes. I hope you're having fun because I'm fine. I hope it's obvious that I'm having fun. Um, as per usual, you'll find in the next segment the very last segment, Um, a pdf with some discounts and all kinds of cool stuff links to check out some other things and do some fun stuff. You know, the drill. You've been in 14 music theory classes. Now you know how it works. So check that out. A sign it for some other stuff. Um, keeping an awesome peace out 32. SkillshareFinalLecture: Hey, everyone want to learn more about what I'm up to? You can sign up for my email list here, and if you do that, I'll let you know about when new courses are released and when I make additions or changes to courses you're already enrolled in. Also check out some of my courses on this site. I post a lot of stuff there, and I check into it every day. So please come hang out with me and one of those two places or both, and we'll see you there.