 Let us begin then with the subject of today, which is the fugue. Every educated person should know what a fugue is. Why? Because it's an intellectual model, an intellectual paradigm that surfaces in a number of disciplines. For example, in poetry, oddly, if you've ever peaked at Thomas T.S. Eliot's The Four Quartetes, the structure of a fugue, is referenced there frequently. We could go to literature, a novel written about the same time, Aldous Huxley's Point Counterpoint. It's framed in the shape of a fugue. We could go to geology. Geologists occasionally will say this particular crystal has a fugue-like structure to it, turning to painting. There are painters of the twentieth century, I can name at least three, Franz Kopka, Henri Valenz, and Joseph Albers, who used to be the dean of our own School of Art and Architecture. They all painted fugues. We will be looking at Albers' fugue, which actually happens to be in your textbook when we come to section this week. Be sure to bring your textbooks to section this week, because we will be using them. I'm interested in the fugue also because of this book, Douglas Hofstadter's Girdel Escher Bach. Oh my, it's heavy. I didn't bring in my copy. This is the bass copy that Linda was kind enough to pull over. Mine is a paperback. It's not this heavy. But in a way, this is indicative, because it's heavy reading. Anybody ever peaked at this book and any other? Good. Is it Adam? Yeah, Adam. What course did you read this in? I'm recommended by a friend. I can follow about the first twenty-five or thirty pages or so. Then when it gets to the math, it really gets over my head. But what it is, is an attempt to use the fugue as a way of bringing a common mode of understanding to the visual arts, to mathematics, and to music. The musician that is foregrounded here, of course, is J.S. Bach, the master of the fugue. So we want to know about how fugues operate. So let's take a look at the specifics here. The term fugue actually comes from an old Latin word, fuga, which means flight, or to fly. So in a fugue what you get is one voice going ahead, leading ahead, and another voice following it. Now I just used the term voice there. Fugues can be written for actual voices, sounding voices, or they can be written for instruments such as the violin or the cello, individual lines. They can even be written for instruments that can play several lines or several parts at once. The piano can do that, the organ can do that, even the guitar, and occasionally the violin will be asked to do that. Fugues have been written for as few as two voices. Yes, you could have a two-voice fugue, up to as many as thirty-two voices, and they can be, as mentioned, written for, and they are best, perhaps, performed on these keyboard instruments that have the capacity to play many lines, many parts, many voices at once. The greatest collection of fugues, as you may have bumped into, heard about, or at least heard the term, is this collection of preludes and fugues by J.S. Bach called the Well-Tempered Clavier. First of all, what's a prelude? It's just a warm-up piece. You sort of get relaxed, you get to see your fingers get a feel of the keyboard or of the lute or whatever it might happen, maybe a prelude, a preplay, a warm-up. And then we go on to the meat of the issue, which is the fugue. Now why is this called the Well-Tempered Clavier? Anybody know? Anybody have? That's an odd term. Clavier just means keyboard, the well-tuned keyboard. Thoughts there? Well, what was going on in Bach's day is that they didn't have a keyboard that they didn't have a tuning system in which all of the pitches were exactly a half-step apart. Some were slightly closer together and then others farther apart. And the key of C actually had a slightly different sound than the key of D. And it's only in the eighteenth and nineteenth century that we gradually shifted from an unequal keyboard to an equally-tuned keyboard. So Bach is kind of part of this transition to the equal tuned keyboard. He was getting close to the equal temperament of the modern keyboard. And that's why he called it the well-tuned keyboard. And by tuning it this way it allows you to modulate to all keys. And that's what he did in this collection. He wrote two books, one in about 1722 when he was in Curtin and another about 1742 when he was in Leipzig. And in each of these books we have a total of twenty-four preludes and fugues. One prelude and fugue in C major, one prelude and fugue in C minor, one prelude and fugue in C sharp major, and one prelude and fugue in C sharp minor, and so on. It goes all the way up the keyboard in that fashion. Two books of those. And this is kind of standard fodder for those that want to become professional musicians. Okay. So that's what that is about, the well-tempered clavier. We've been referencing Bach here, and nobody, of course, wrote better fugues than J.S. Bach. Some continued to write fugues. Mozart wrote some fugues. Haydn wrote some fugues. Beethoven wrote some fugues, and so on. And even into the twentieth century we have a few composers. Paul Hinamith used to teach at Yale. Dimitri Shostakovich, they wrote fugues. But generally speaking, the fugue has its heyday in the Baroque period, roughly 1600 to 1750, the heyday of Bach and Handel. How do fugues work? Well, they start out, as mentioned, with one voice leading forward, and then another voice imitates that voice. Exactly. Now if that following voice, here's a question, if that following voice imitated the leader exactly from beginning to end, what would we have? A round. Okay. Good. That's what we would have, a round. Or we could use the fancier music word, a canon. Canon, round, the same thing. One voice imitating the other exactly from beginning to end. But in a fugue what happens is, after the main idea, which we'll be calling the subject, the main idea is stated, then the parts go their independent ways, generating counterpoint. But they're not exact. They're not precise duplications of the rhythms and the pitches of the leaders. So what we could do would be to visualize this in a sort of crude way up here. You have a leader and then a follower. And the follower duplicates the main idea, which we're going to call the subject, for a period of time, but then it kind of breaks off. So voices will come in and duplicate a certain amount of material and then break off and go their own way. So that's a good way of thinking of the beginning of a fugue, which we will call the exposition. I'll come back to that point in a moment. Notice here I put a little, silly little tree up here. We could say that we have the genus polyphony here. We've got monophonic texture, homophonic texture, and polyphonic texture. So within polyphonic texture we have non-imitative texture, and then a stream of imitative polyphony, and then two forms of imitative polyphony, rather strict, exactly strict, imitative polyphony, the canon, and less strict imitative polyphony, the fugue. Okay, questions about that so far? All right, let's go back to the beginning of a fugue. We have this opening melody, the distinctive part of it, which we're going to call the subject. That's just what we call the melody in a fugue, the subject. And the way this works is, in a fugue, each of the voices in turn will come in with that subject. One will start out, then another will come in, then another will come in. After all of the voices are in, we're at the end of what we call the exposition of the fugue. Now, we've had the term exposition before, and where was that? Over there, Elizabeth, I hear you? Yes, sonata form, sonata allegro form. And what do we mean by exposition there? What's the chance where you present all the themes? And we talked about first theme and second theme and closing theme. Here in a fugue we have just one theme, but everybody's going to get a chance to present it. And after everyone has a chance to present it, every voice has a chance to present it, then we're finished with the exposition. All the voices have exposed the theme in their range. After that, we go on to what's called the episode of a fugue. What happens in an episode? Well, usually it modulates key, and the vehicle through which composers frequently modulate is melodic sequence, either up or down. You can kind of move around by using sequence. You can get to different places by using sequence. So it tends to be a contrapuntal because it's using little motives from the theme. It modulates, moves around a lot, goes to different keys, sounds a bit unsettled. If you were to think back on Sonata Allegro form and try to find an analog for Sonata Allegro form in the fugue episode, what would it be? What is the episode of a fugue like in Sonata Allegro form? Roger? Exactly, the development section. So these episodes in a fugue are sort of mini development sections. So visualize, if you will, we start out here with the exposition where all voices present the subject. Then you have this kind of free period in which the motive out of the subject is played with, developed, moved around different pitches. Then the subject will come back in a new key because we've modulated in the episode. Subject in just one voice, new key. Then another episode in which there's modulation, more counterpoint, more movement. Another statement of the subject in a new key. Another episode, another statement of the subject, and on it goes until we run out of energy, usually about after four or five minutes or so, at which point the composure will bring the subject back, maybe in the bass or in the soprano, in a very prominent range in the tonic key. And we have a sense, this is a very solid moment. Yes, this fugue is ending. It may be to throw one or two chords on it to end, but that's it. So it's a complex form, but maybe not quite as complex as sonata allegro form. What's a definition, and if you're taking notes there, what's a definition of a fugue? Well, I wrote a definition of a fugue, and I will read the definition out of the textbook. Students don't like this, I've found, if you read out of a textbook. But I ought to be able to do this since I wrote the textbook. Okay? So I'm going to read a good definition of a fugue here. A definition of a fugue. A composition for two, three, or four parts. Played or sung by voices or instruments, which begins with a presentation of a subject in imitation, in each part, the episode, excuse me, the exposition, continues with modulating passages of free counterpoint, the episodes, and further appearances of the subject, and ends with a strong affirmation of the tonic key. Well, you can't write all that down, but if you want to just put in your notes for definition of fugue, see page 144 of the text. Fortunately, as I say, it's easier to hear and look at fugues than it is to define them. All right. Now, today we're going to do something different. It's the only day in our course where we're actually going to look at music. Okay? We've handed out music for you, an entire piece, an entire fugue by J.S. Bach here. And ideally, I guess we'd be in a seminar format, and we'd all be standing around the piano here. So my first question for you is, for how many voices is this fugue written? Look at just the first page, and look vertically, and see what's the maximum number of pitches you have sounding simultaneously at any one moment. Caroline, is it? Three, okay? Yeah, we have three. If you look through there, sometimes at the very beginning, there's just one voice, and then there are two voices, and then there are three voices, three lines. But it never gets to be more than three lines. So we have our X position here, and it consists of three statements of the subject. We're going to call these three voices, or lines, the alto, the soprano, and the bass, which comes in in bar seven there. So here's the little bit of the beginning of this. So that's our X position, because each of the voices, alto, soprano, and bass, has come in and presented the subject. Then we have bars nine and ten here. What's that? We just go very much that. It's a melodic sequence. And which direction is it going, up or down? Well, that's maybe harder than you think. It's generally going down. Not because the line is going down, but we're starting time on a successively lower pitch. And this sequence takes this. So we've started in this kind of tonality, which is minor, but now by the time we've got ten and eleven particularly, he's modulated. So that's what our little episode was in bars nine and ten there. It allowed us to move from a minor key to a major key. And now the subject comes back in, and as you can see, what voice is it in there? What voice is the subject in in bar eleven? Pretty straightforward. Somebody yell it out? Okay, so here it heads up in the soprano. So there we are, a nice statement of the theme in a major in the soprano. What happened in that little episode? We were here, and now we're here. Modulated again to minor, and there in bar fifteen, where's the subject? Chris? Alto part. Good, thanks. So there it is in the alto part. That's an interesting moment there because we've got a three voice fugue, and how many hands does the performer have? Obviously two. So at some moments these hands are going to have to share a subject, and that's what happens in that voice. When you play this, take a look there at the very last measure of that page. It must be fifteen. It starts out, my left hand is playing here, and then the left hand has to get out and pick up the counterpoint in the bass, and the right hand takes over that subject. But it's the job of the pianist there, or the keyboardist who's ever playing it, to really lean on the inside of your hand there, because when you normally play these instruments there's a tendency, and I'm sure Santana is a far better keyboardist than I will confirm this, there's a tendency to roll the either side. It's easier to play bass than soprano. What's hard to do is to get those inner voices. So the keyboard player has to play, and then really hear that. If you didn't hear it, then that wasn't a good performance. All right. Now that takes us across the page there. We're now back in a minor key. This is bar sixteen and seventeen. And in bar seventeen, eighteen, nineteen, beginning of twenty we have an interesting moment. It's called invertible counterpoint. What do we mean by that? Well, he has a motive. We're going to call that motive A, and he has another motive, motive B. So there's B in the alto, A in the bass, and together they sound sort of like this. Cool. Now, next three bars. What happens? Well, he takes B, and so he takes B, and puts that below A. He's switching the positions here. A is now... Both of these motives are coming up in rising sequence. So let's go back to the beginning of seventeen there, and we'll listen to the switch. Goes by very quickly, right? How long do you think it took Bach to figure that out? I don't know. He's a very good contrapunitalist. Maybe boom, like that. I'd have to sit there, Santana. I'll take you to figure out some invertible counterpoint that you could think of one melody, think of another melody that would be harmony against it, but yet you could flip the two, and it would still sound pretty darn good. It'd take a long time to kind of work that out. So that's what's kind of neat about fugue. There's all these intricacies embedded in them that almost sail by the general listener unless we happen to have the music right in front of us and can dwell on them. All right. So that takes us over now to bar twenty, where we are here back, I guess, in our tonic key of C minor, and the theme is up in the soprano. And one final statement in the soprano. A couple of interesting points there. When we concluded this piece, we had this sound. What's a little bit surprising about that? We're ending a piece. It's called fugue number two in C minor. We are ending here with... Does that sound like a minor chord at the end? No, no. A major chord. All right. So he's changed it. This is a standard gambit from the late sixteenth right through the eighteenth century. Last chord, they didn't like the end pieces in minor. Maybe it was too depressing or whatever. I want to do that. So... with the major third up there above. That's called a Picardy third. Maybe from the old French word picard, which means sort of sharp or pointed. So we have a pointed ending there. We have a major ending. Here's another issue, since we're on the topic of points, and that's called a pedal point. What was J.S. Bach known as in his day? Was he known as a great composer? Who was he known as? Basically, how did he earn his living? He played the organ. He was the great organ virtuoso of his day. And I think at the end of this particular fugue here, it's interesting. He just has that line sit there. Okay. On the organ, that would just be fine and dandy, because you'd put your foot down there on that low C, and that tonic note would continue to hold. But if you were writing this for the clavichord, or the harpsichord, or the piano, what happens to that sound once you hit it? It dies away. I think in the end of this piece here, Bach had the sound of the organ. He didn't read it. He wasn't thinking, gee, if this is really for a harpsichord or something, I'd better write this like this. So we get a nice, strong tonic sound at the end. He may have had the sound of the organ there in his ear. But perhaps the important point here is this idea of a pedal point, because we've actually even talked about that before in the Johannes Brahms' variations on the theme of Haydn that was performed Saturday night. Pedal point is what? Anybody can define pedal point for us? Well, what goes on? It's pretty simple. Roger? Yeah. A bass holds a note and basically you're just kind of running over top of one, possibly two harmonies up above it, but it all sounds consonant. So just be sure of the idea of one note, usually in the bass, just holding, holding, holding for a long period of time. I'm going to turn the volume down. I hear a humming. Okay. Any questions about that fugue by J.S. Bach? Anybody want to ask anything about that? Marcus, that works for you? Hugona? Okay. Thaddeus? No questions? Frederick. Ah, okay, good. Yeah, thanks for bringing that out. There at the end we could even have, you're right, four maybe even five notes played at once. So this idea that once you have three parts, you can only have three parts. Or once you have a five voice fugue, you can have no more than five voices, down at the very end. Why would you imagine a composer would want to do that, Frederick? Well, no, it's not that hard, because once you get used to the idea of a C major triad, a musician would look at that end and say, I've just got a C major triad. I'm going to just bang down on it. So that's not hard technically or intellectually, but why would a composer, you raised a very interesting point here. Why would a composer want to add more notes at the end? I think it's a pretty straightforward idea. Dave? Michael, Michael, yeah. Just make it louder. Make it more sonorous. Big bang ending sort of thing. Yeah? Tell the listener once again that this is something special that we're probably at the end. All right, so let's listen to just a bit of this. We've had one version of this. Let's listen to a contemporary jazz ensemble playing. It starts out with a kind of guitar synthesizer with a piano here, and then we'll see what the other instruments are. Here's a jazz rendition of the same fugue by Bach. What instrument is playing this bass line? Thirteen. Subject in the inner voice. Here's our invertible counterpoint. Switch. Subject soprano. It's modulating from one key to the next here. Here they actually do repeat that tonic note. Boom, boom, boom. And then what they do is go off and improvise on them. But it's interesting the similarity between jazz style and jazz style and Baroque music. Why is that the case? Well, Baroque music has a lot of driving rhythm in it, kind of regular, regular rhythm in it. And jazz has a kind of regular pulsating rhythm in it too. I ask you, what instrument was playing the bass line there? And Daniel, you started going like this. So what were you doing? The double bass. But is it ebode? No, it's a plucked pizzicato double bass. But that's a standard instrument in a jazz quartet, jazz ensemble. But it's a very strong bass, and Baroque music also has a very strong bass. So lots of similarities between contemporary jazz and Baroque music. And sometimes these jazz ensembles like to get to this Baroque music and resurrect them in a modern idiom. All right. So normally a fugue is a freestanding piece. Or you could have an entire movement written as a fugue. Haydn quartets will sometimes do that, a Beethoven piano sonata might do that. But usually they're freestanding pieces. Occasionally you run into a fugue that's embedded inside another movement. You might have a movement in sonata allegro form, and you get to a particular section, let's say the development section, and the composer says, well I want to write a fugue here as my development. When that happens we call it a fugato, a fugato. So a fugato is a fugue placed inside another form. So we're going to listen to an example of this from the Romantic period in which we have the young composer Georges Bizet. He was exactly your age when he wrote this. He was nineteen years old. Georges Bizet wrote this symphony. It's a lovely romantic string sound, sort of break your heart string sound. And then we have a segue. We have kind of a romantic transition here as he changes mood. And then a fugue will break out. And it will start in the bottom voice. So I'll tell you that much. And my question to you or my challenge to you is this. What's the order? Let's say, and I'll tell you this, we've got a four voice fugue that's going to start here. Can you track the order in which the voices enter? You know, you've got the four. You've got the bass tenor soprano or bass tenor alto and soprano or soprano alto tenor bass. They can come in any one of four different, well, probably even more than four permutations, but the order might be alto, bass, soprano, tenor. It might be bass, alto, tenor, soprano or soprano, alto, tenor and bass. We don't know. And that's your challenge here to see if you can track the subject. Here we go. That's all four voices are in there. Could anybody on just one hearing tell me what the order was? Okay, let me show you. Somebody different here. Robert, I haven't called on you this morning. Okay, start with bass. Or maybe even octave lower. Then where did it go? Yeah, it actually went to the alto. Now we're going to get an episode in which he's going to play with just a motive and then the subject will come back. So here are two questions for you. In which voice is the subject coming back? And what's happened to the subject when it comes back? It's changed in one way. Let's stop it there. Any takers on that? If we were doing a quiz on this, we'd give you three or four playings of that. Which voice did it come back in? That is not bad. We would take that because it's kind of high ten. I'm playing a kind of tenor range here. I think it was more cellos and we'd probably, with bassoons, we'd probably call that bass, bass voice. But fair enough, tenor. And what happened to it? So he'd modulated to a different key and then gave you the subject in a minor key. And that's kind of the way these fugues operate. Give you an exposition, episode in which you change key, bring back the subject in a different key. All right. So we've now had a fugue from the nineteenth century, although we would call it a fugato because it's embedded in this lovely, lovely Sonata Allegro movement. Let's turn to a fugue from the twentieth century. And for this we go to Leonard Bernstein. You can see the playlist up on the board. New Haven used to be a favorite try-out city for Broadway musicals. But there was a musical entitled, never went anywhere, entitled We Bombed in New Haven, meaning that the try-out of the particular musical was not a success. And where would they try out in New Haven? What was the great theater for this? The Yale Rep Theater? Any other takers? The Schubert Theater. Yeah, actually in that period the Yale Rep was actually a functioning house of worship. It was a church at that time, what's now the Yale Rep. So it was at the Schubert Theater, which has been here for a long, long time. So Leonard Bernstein came in here with a show in 1952 called Wonderful Town. And he tried it out there. And generally speaking it was a success and he took it down the train tracks there to Broadway. But he took some music out of it, some music that he thought actually was a little bit too complicated for the choreography that he wanted to work into it. Later took that material and worked it into a freestanding piece called Prelude, Fugue, and Jazz Riff. So we're going to look at now just the fugue portion of it, because it's a very interesting kind of fugue. It's a very complex fugue. So we're going to start out here, and I'm going to break this, we'll listen, we'll stop, we'll listen and stop so that we can focus on particular passages. So as we start to listen, see how many voices there are in Leonard Bernstein's fugue. I have a general sense of what the range is, soprano, alto, bass. What else do we need? Oh yeah, what instruments are playing here? That's the exposition and a little bit of a development there. So what instruments? Ducks? Yeah, saxophones. Yeah. Okay, Nieland says saxophones. He's right. Yeah, so saxophones there. So we've gotten roughly how many did you hear? Two, three, four? Yeah, maybe four. Maybe four different saxophones, sort of alto sax, maybe baritone sax in there. And there was one, so we were playing this out, and this is a rather syncopated fugue, so we dop, beep, beep, beep, beep, beep, beep, bop, bop, bop, bop, bop. Let's listen to it again. No, we don't have time to do that, but here's one thing that happened. That kind of sound deep. Then after one episode, one of the saxes brought back that subb. What's it doing there? What is that? What's the relationship there? Yeah, it's just inverting it. It's taking the intervals and flipping them, and that's what composers love to do with fugues. And we'll be talking about interchangeable parts, reciprocal relationships with the mathematical quality of fugues. And so that's what's happening here. We have a moment of melodic inversion. And sometimes in fugues, and Bach did this in the musical offering, he can take his fugue subject and run it backwards, run it backwards from beginning to end. So they like to have these kind of mathematical permutations of these intervals. It's very cerebral stuff, this fugue business. So there we had just a moment of Leonard Bernstein writing a little bit of inversion. Now what we're about to hear next is something of a surprise, because we get a second fugue subject. And it's a different fugue subject. It's not syncopated. It's rather lyrical. Da-dee, da-dee, da-dee, da-dee, da-dee, da-dee, da-dee. Something like that. So it's nice and lyrical. And let's listen to how he now unfolds a second fugue subject. So what we have here is called a double fugue. He's got one exposition with one fugue subject. Now he's going to give us a completely different exposition with yet a second fugue subject. And then number one comes back. Okay. We're going to pause it here because he's now about to do something rather interesting. The Bach used to do as well. And Bernstein was a consummate musician and studied Bach, had Bach coming out of his ear. So he knew about this particular trick. It's called Stretto. You can design a fugue subject, not only that it could go upside down, but in which the intervals, instead of coming in long succession, could be piled right on top of one another. So the way he sets this thing up to begin with is this, this, maybe this, and then this. But in the next section it's going to go this, this, this, and this. The intervals back up on each other because they have been arranged to be consonant at key points. And that's called Stretto. Italian word Stretto kind of tight, tight entries here. So here is a fancy little bit of Counterpoint by Leonard Bernstein that once again goes by very quickly. Here, now he's going to bring back the two subjects together. We have one and two together. Episode, syncopated episode, two. So it's a pretty nifty little fugue there by Leonard Bernstein with lots of intricate counterpoint involved in it. All right. Let's end now with a fugue of J.S. Bach. And for that we're going to turn to an organ fugue that he wrote about 1710. 1710 when he was a young man in Weimar. Here is that fugue subject. Ya-bum-bum-bum-bum-bum-bum-bum-bum-bum-bum-bum-bum-bum. Da-da-da-da-da-da-da-da-da-da-da-da-da-da-da. And on and on and on it goes. What's of interest about this subject? Well, two things. First of all, as I sing this, ya-bum-bum-bum. bit like that. Yum-ba-ba-bom-bom-bom-bom-bom. Arpeggio. Yes, it is, but it's an arpeggio of what? Yum-ba-bom-bom-bom-bom-bom-bom-bom-bom-bom. Just a minor triad. Minor triad. One, five, three, one. If I skip this note here. Yum-ba-bom-bom-bom-bom. As I come to every strong beat in this theme, every strong beat I have a member of the triad, It's the same either G, Bb, or D. So these trias, as we said before, are really the structure, the backbone on which a composer like Bach will place the flesh of a fugue subject. So it's very triadic, and it sounds pretty secure for that. Now, here's another thing that this fugue subject does, and many other fugues subject. It starts with quarter notes. Yum, quarter, quarter, quarter. Then next measure, eight, eight, eight, eight, eight, eight, and then we get in here eight, eight, eight, eight, eight, eight, The beat isn't going any faster. The tempo is saying the same. He's simply writing shorter note values which has a psychological impact, as we said several times, of giving the sense of movement, gathering speed here. It's like a train pulling out of the station. We want to get on this train. This thing is really starting to roll after five measures or so. So, it's a pretty nifty fugue subject here. And we're going to listen to this now. And what I'd like to do is the following. We're going to listen to the entire piece, listen to the entire piece. Think about, as the voices come in, think about where they're coming in. Can you tell me what the trajectory of the voices is in the exposition? And I'm going to turn out the lights here because sometimes it's good just to kind of go off in your own world, close your eyes. But I would like you to do the following thing, kind of lean back, get comfortable, close your eyes. But every time you hear the fugue subject and so on, every time you hear that fugue subject, raise your hand, so that I know you're recognizing that as the subject, because listening to fugues, it's basically one thing, differentiating between a passage in which you've got a statement of the subject and an episode where there ain't no statement of the subject. Okay, so this is a three-minute and twenty-second fugue and we're going to listen to the whole thing. But do raise your hand when you think that fugue subject is in there. Soprano, alto, tenor and now bass. This is in one of those inner voices. It's a little bit disguised, but it's in there. The way up on top in the soprano episode, descending sequence this time, rising sequences here, falling sequences. Okay, so that's a wonderful fugue by J.S. Bach. And we're going to talk more about this in section, this idea, how you can run your fugue parts this way or you could order them this way. You can think of these constructs mathematically or you can think of them musically, but you're all working with the same kind of material. As you go out, one final fugue by Glenn Gould, who is going to teach you how to write a fugue as he sings a fugue to you.