WEBVTT 00:01.450 --> 00:04.640 Prof: Let us begin then with the subject of today, 00:04.635 --> 00:05.825 which is the fugue. 00:05.830 --> 00:10.150 Every educated person should know what a fugue is. 00:10.150 --> 00:10.680 Why? 00:10.680 --> 00:15.980 Because it's an intellectual model, an intellectual paradigm 00:15.981 --> 00:20.741 that surfaces in a number of disciplines--for example, 00:20.743 --> 00:22.633 in poetry, oddly. 00:22.630 --> 00:26.900 If you've ever peeked at Thomas--T.S. Eliot's "The 00:26.898 --> 00:30.768 Four Quartets," the structure of the fugue is 00:30.772 --> 00:33.462 referenced there frequently. 00:33.460 --> 00:36.080 We could go to literature--a novel written about the same 00:36.082 --> 00:38.472 time, Aldous Huxley's Point Counter Point. 00:38.470 --> 00:41.960 It's framed in the shape of a fugue. 00:41.960 --> 00:44.340 We could go to geology. 00:44.340 --> 00:47.790 Geologists occasionally will say, "This particular 00:47.789 --> 00:50.919 crystal has a fugue-like structure to it." 00:50.920 --> 00:53.040 Turning to painting, there are painters of the 00:53.038 --> 00:53.978 twentieth century. 00:53.980 --> 00:56.630 I can name at least three, Franz Kupka, 00:56.629 --> 00:58.789 Henry Valensi, and Josef Albers, 00:58.790 --> 01:02.700 who used to be the dean of our own Yale School of Art and 01:02.695 --> 01:04.015 Architecture. 01:04.019 --> 01:08.329 They all painted fugues and we will be looking at Alber's 01:08.326 --> 01:10.496 fugue-- which actually happens to be in 01:10.504 --> 01:12.834 your textbook-- when we come to section this 01:12.831 --> 01:16.181 week, so be sure to bring your textbooks to section this week 01:16.180 --> 01:20.110 'cause we'll-- we will be using them. 01:20.110 --> 01:23.550 I'm interested in the fugue also because of this book, 01:23.552 --> 01:26.542 Douglas Hofstadter's Godel, Escher, Bach. 01:26.540 --> 01:28.390 Oh, my. That's heavy. 01:28.390 --> 01:30.190 My--mine--I didn't bring in my copy. 01:30.188 --> 01:32.638 This is the Bass copy that Lynda was kind enough to pull 01:32.638 --> 01:32.948 over. 01:32.950 --> 01:34.430 Mine is a paperback. 01:34.430 --> 01:36.930 It's not this heavy, but in a way this is 01:36.933 --> 01:39.503 indicative, because it's heavy reading. 01:39.500 --> 01:42.480 Anybody ever peeked at this book and any other--good. 01:42.480 --> 01:43.660 Is it Adam? 01:43.660 --> 01:44.090 Student: Yeah. 01:44.090 --> 01:45.100 Prof: Yeah. 01:45.101 --> 01:47.351 Adam, what course did you read this in? 01:47.349 --> 01:49.559 Student: It was recommended by a friend. 01:49.560 --> 01:50.780 Prof: Recommended by a friend. 01:50.780 --> 01:53.140 I can follow about the first twenty-five or thirty pages or 01:53.135 --> 01:53.335 so. 01:53.340 --> 01:56.940 Then when it gets to the math it really gets over my head, 01:56.940 --> 02:00.810 but what it is is an attempt to use the fugue as a way of 02:00.811 --> 02:04.411 bringing a common mode of understanding to the visual 02:04.408 --> 02:07.128 arts, to mathematics and to music. 02:07.129 --> 02:10.109 The musician that is foregrounded here, 02:10.107 --> 02:14.257 of course, is J.S. Bach, the master of the fugue. 02:14.258 --> 02:16.758 So we want to know about how fugues operate, 02:16.760 --> 02:19.380 so let's take a look at the specifics here. 02:19.378 --> 02:22.328 The term "fugue" actually comes from an old 02:22.325 --> 02:24.145 Latin word, "fuga," 02:24.147 --> 02:27.287 which means "flight" or "to fly," 02:27.293 --> 02:30.683 so in a fugue what you get is one voice going ahead, 02:30.680 --> 02:33.760 leading ahead, and another voice following it. 02:33.758 --> 02:36.008 Now I just used the term "voice" 02:36.009 --> 02:36.449 there. 02:36.449 --> 02:41.399 Fugues can be written for actual voices sounding voices or 02:41.395 --> 02:45.985 they can be written for instruments such as the violin 02:45.992 --> 02:49.032 or the cello--individual lines. 02:49.030 --> 02:52.000 They can even be written for instruments that can play 02:51.995 --> 02:54.285 several lines or several parts at once. 02:54.289 --> 02:55.109 The piano can do that. 02:55.110 --> 02:56.060 The organ can do that. 02:56.060 --> 02:58.540 Even the guitar and occasionally the violin will be 02:58.538 --> 02:59.478 asked to do that. 02:59.479 --> 03:04.919 Fugues have been written for as few as two voices. 03:04.919 --> 03:06.969 Yes, you could have a two-voice fugue-- 03:06.968 --> 03:10.288 up to as many as thirty-two voices-- 03:10.288 --> 03:16.098 and they can be, as mentioned, 03:16.103 --> 03:20.493 written for-- and they are best, 03:20.485 --> 03:24.275 perhaps, performed on-- these keyboard instruments that 03:24.276 --> 03:26.736 have the capacity to play many lines, 03:26.740 --> 03:28.620 many parts, many voices at once. 03:28.620 --> 03:30.770 The greatest collection of fugues, 03:30.770 --> 03:35.030 that you may have bumped into, heard about or at least heard 03:35.032 --> 03:37.352 the term, is this collection of preludes 03:37.348 --> 03:39.908 and fugues by J.S. Bach called "The Well-Tempered 03:39.911 --> 03:40.831 Clavier." 03:40.830 --> 03:42.120 First of all, what's a prelude? 03:42.120 --> 03:47.260 It's just a warm-up piece, > 03:47.259 --> 03:49.339 to just sort of get relaxed. 03:49.340 --> 03:51.550 You get to see your fingers, get a feel of the keyboard or 03:51.548 --> 03:53.028 the-- of the lute or whatever it 03:53.027 --> 03:55.897 might happen to may be-- a prelude, a pre play, 03:55.899 --> 04:00.249 a warm-up, and then we go on to the meat of the issue, 04:00.250 --> 04:02.410 which is the fugue. 04:02.408 --> 04:05.468 Now why is this called "The Well-Tempered 04:05.471 --> 04:06.561 Clavier"? 04:06.560 --> 04:07.580 Anybody know? 04:07.580 --> 04:09.430 Anybody have--that's an odd term. 04:09.430 --> 04:10.490 "Clavier" just means 04:10.488 --> 04:11.768 "keyboard," the well-tuned 04:11.766 --> 04:12.676 "keyboard." 04:12.680 --> 04:14.840 Thoughts there? 04:14.840 --> 04:17.690 Well, what was going on in Bach's day is that they didn't 04:17.690 --> 04:20.340 have a keyboard that-- > 04:20.339 --> 04:23.469 they didn't have a tuning system in which all of the 04:23.466 --> 04:25.976 pitches were exactly a half step apart. 04:25.980 --> 04:27.800 Some were slightly > 04:27.800 --> 04:30.700 closer together, and then others farther apart. 04:30.699 --> 04:32.519 And the key of <> 04:32.519 --> 04:35.199 C actually had a slightly different sound than the key of 04:35.199 --> 04:36.729 D, > 04:36.730 --> 04:40.430 and it's only in the eighteenth and nineteenth century that we 04:40.430 --> 04:43.770 gradually shifted from an unequal keyboard to an equally 04:43.766 --> 04:44.916 tuned keyboard. 04:44.920 --> 04:49.580 So Bach is kind of part of this transition to the equal-tuned 04:49.576 --> 04:50.426 keyboard. 04:50.430 --> 04:54.460 He was getting close to the equal temperament of the modern 04:54.461 --> 04:57.941 keyboard and that's why he called it the well-tuned 04:57.935 --> 05:01.305 keyboard, and it--by tuning it this way, 05:01.310 --> 05:04.510 it allows you to modulate to all keys, 05:04.509 --> 05:06.079 and that's what he did in this collection. 05:06.079 --> 05:09.879 He wrote a--two books, one in seventeen- about 1722, 05:13.536 --> 05:15.546 when he was in Leipzig. 05:15.550 --> 05:19.110 And in each of these books we have a total of twenty-four 05:19.113 --> 05:22.363 preludes and fugues: one, the prelude and fugue in C 05:22.360 --> 05:24.780 major, <> 05:24.778 --> 05:26.788 one prelude and fugue in C minor, < 05:27.453 piano>> 05:27.449 --> 05:29.939 one prelude and fugue in C-sharp major, 05:29.939 --> 05:31.839 > 05:31.839 --> 05:33.939 and one prelude and fugue in C-sharp minor < 05:34.507 piano>> 05:34.509 --> 05:36.779 and so on it goes, all the way up the keyboard in 05:36.781 --> 05:38.441 that fashion--two books of those. 05:38.440 --> 05:41.350 And this is kind of standard fodder for those that want to 05:41.346 --> 05:42.976 become professional musicians. 05:42.980 --> 05:43.550 Okay. 05:43.552 --> 05:49.512 So that's what that is about, "The Well-Tempered 05:49.511 --> 05:51.461 Clavier." 05:51.459 --> 05:54.629 We've been referencing Bach here and nobody, 05:54.627 --> 05:58.307 of course, wrote better fugues than J.S. Bach. 05:58.310 --> 05:59.670 Some continued. 05:59.670 --> 06:02.100 Some continued to write fugues. 06:02.100 --> 06:04.220 Mozart wrote some fugues, Haydn wrote some fugues, 06:04.220 --> 06:06.090 Beethoven wrote some fugues and so on, 06:06.088 --> 06:09.688 and even into the twentieth century we have a few composers: 06:09.690 --> 06:12.010 Paul Hindemith, used to teach at Yale, 06:12.007 --> 06:13.167 Dmitri Shostakovich. 06:13.170 --> 06:16.180 They wrote fugues, but generally speaking the 06:16.180 --> 06:19.330 fugue has its heyday in the Baroque period, 06:19.329 --> 06:22.939 roughly sixteen hundred to seventeen fifty, 06:22.939 --> 06:25.569 the heyday of Bach and Handel. 06:25.569 --> 06:27.419 How do fugues work? 06:27.420 --> 06:31.020 Well, they start out--as mentioned--with one voice 06:31.024 --> 06:35.224 leading forward and then another voice imitates that voice 06:35.216 --> 06:36.096 exactly. 06:36.100 --> 06:38.790 Now if that following voice--here's a question. 06:38.790 --> 06:42.060 If that following voice imitated the leader exactly from 06:42.060 --> 06:44.380 beginning to end, what would we have? 06:44.379 --> 06:47.269 Hm? 06:47.269 --> 06:48.599 Student: A round. 06:48.600 --> 06:50.240 Prof: A round. 06:50.240 --> 06:50.630 Okay. 06:50.632 --> 06:51.182 Good. 06:51.180 --> 06:52.540 That's what we would have, a round. 06:52.540 --> 06:55.380 Or we could call--use the fancier music word, 06:55.379 --> 06:56.799 a "canon." 06:56.800 --> 06:59.590 Canon, round--the same thing, one voice imitating the other 06:59.589 --> 07:01.129 exactly from beginning to end. 07:01.129 --> 07:05.299 But in a fugue what happens is after the main idea-- 07:05.300 --> 07:07.010 which we'll be calling the "subject"-- 07:07.009 --> 07:10.739 the main idea is stated, then the parts go their 07:10.738 --> 07:14.228 independent ways generating counterpoint, 07:14.230 --> 07:18.030 but they're not exact; they're not precise 07:18.031 --> 07:21.891 duplications of the rhythms and the pitches of the leaders. 07:21.889 --> 07:26.049 So what we could do would be to visualize this in a sort of 07:26.045 --> 07:27.475 crude way up here. 07:27.480 --> 07:29.980 We have a leader and then a follower. 07:29.980 --> 07:33.030 And the follower duplicates the main idea, which we're going to 07:33.033 --> 07:34.903 call the subject, for a period of time, 07:34.904 --> 07:36.634 but then it kind of breaks off. 07:36.629 --> 07:40.109 So voices will come in and duplicate a certain amount of 07:40.105 --> 07:43.325 material and then break off and go their own way. 07:43.329 --> 07:46.799 So that's a good way of thinking of the beginning of a 07:46.803 --> 07:50.413 fugue, which we will call the "exposition." 07:50.410 --> 07:52.280 I'll come back to that point in a moment. 07:52.279 --> 07:54.769 Notice here I've put a little--silly little tree up 07:54.771 --> 07:55.121 here. 07:55.120 --> 07:58.390 We could say that we have the genus polyphony here and we've 07:58.389 --> 08:00.879 got monophonic texture, homophonic texture and 08:00.884 --> 08:02.164 polyphonic texture. 08:02.160 --> 08:06.560 So within polyphonic texture we have non-imitative texture and 08:06.562 --> 08:10.682 then a stream of imitative polyphony and then two forms of 08:10.675 --> 08:13.885 imitative polyphony, rather strict--exactly 08:13.887 --> 08:17.407 strict--imitative polyphony, the canon, and less strict 08:17.413 --> 08:19.803 imitative polyphony-- the fugue. 08:19.800 --> 08:20.430 Okay? 08:20.425 --> 08:24.045 Questions about that so far? 08:24.050 --> 08:24.650 All right. 08:24.654 --> 08:27.384 Let's go back to the beginning of the fugue. 08:27.379 --> 08:30.299 We have this opening melody, the distinctive part of it, 08:30.302 --> 08:32.432 which we're going to call the subject. 08:32.428 --> 08:34.618 That's just what we call the melody in a fugue, 08:34.615 --> 08:35.275 the subject. 08:35.279 --> 08:39.729 And the way this works is in a fugue each of the voices in turn 08:39.730 --> 08:42.100 will come in with that subject. 08:42.100 --> 08:44.500 One will start out, then another will come in, 08:44.504 --> 08:46.004 then another will come in. 08:46.000 --> 08:49.870 After all of the voices are in, we're at the end of what we 08:49.871 --> 08:52.211 call the exposition of the fugue. 08:52.210 --> 08:54.600 Now we have had the term "exposition" 08:54.602 --> 08:56.062 before and where was that? 08:56.058 --> 08:57.208 Student: > 08:57.210 --> 08:59.790 Prof: Over there, Elizabeth. 08:59.792 --> 09:00.782 I hear you. 09:00.779 --> 09:01.719 Student: --sonata form? 09:01.720 --> 09:03.420 Prof: Yeah, sonata form, 09:03.423 --> 09:06.213 sonata-allegro form, so we--and what do we mean by 09:06.206 --> 09:08.076 "exposition" there? 09:08.080 --> 09:10.240 Well, it's a chance where you present all of the--all the 09:10.241 --> 09:12.331 themes, and we talked about first theme and then second 09:12.327 --> 09:13.407 theme and closing theme. 09:13.408 --> 09:16.768 Well, here in a fugue we have just one theme but everybody's 09:16.774 --> 09:19.004 going to get a chance to present it, 09:19.000 --> 09:20.800 and after everyone has a chance to present it-- 09:20.798 --> 09:22.408 every voice has a chance to present it-- 09:22.408 --> 09:24.998 then we're finished with the exposition; 09:25.000 --> 09:28.390 all the voices have exposed the theme in their range. 09:28.389 --> 09:32.119 After that we go to what's called the "episode" 09:32.115 --> 09:32.975 of a fugue. 09:32.980 --> 09:34.540 What happens in an episode? 09:34.538 --> 09:38.278 Well, usually it modulates key and the vehicle through 09:38.283 --> 09:41.753 composers frequently modulate is melodic sequence, 09:41.745 --> 09:43.295 either up or down. 09:43.298 --> 09:45.798 You can kind of move around by using sequence. 09:45.798 --> 09:48.198 You can get to different places by using sequence. 09:48.200 --> 09:52.520 So it tends to be contrapuntal because it's using little 09:52.517 --> 09:54.477 motives from the theme. 09:54.480 --> 09:56.140 It modulates, moves around a lot, 09:56.143 --> 09:58.693 goes to different keys, sounds a bit unsettled. 09:58.690 --> 10:03.000 If you were to think back on sonata-allegro form and try to 10:02.996 --> 10:06.706 find an analog for sonata-allegro form in the fugue 10:06.711 --> 10:08.941 episode, what would it be? 10:08.940 --> 10:12.790 What is the episode of the fugue like in sonata-allegro 10:12.789 --> 10:13.289 form? 10:13.289 --> 10:14.059 Roger. 10:14.059 --> 10:14.949 Student: The development? 10:14.950 --> 10:16.960 Prof: Exactly--the development section. 10:16.960 --> 10:20.220 So these episodes in a fugue are sort of mini development 10:20.221 --> 10:22.621 sections, so visualize if you will--we've 10:22.615 --> 10:24.745 started out here with the exposition, 10:24.750 --> 10:27.220 in which all voices present the subject. 10:27.220 --> 10:30.550 Then you have this kind of free period in which the motive out 10:30.549 --> 10:33.499 of the subject is played with, developed, moved around, 10:33.498 --> 10:34.698 different pitches. 10:34.700 --> 10:38.110 Then the subject will come back in a new key because we've 10:38.113 --> 10:41.783 modulated in the episode, subject in just one voice, 10:41.775 --> 10:43.975 new key, then another episode in which 10:43.984 --> 10:46.104 there's modulation, more counterpoint, 10:46.099 --> 10:48.489 more movement; another statement of the 10:48.491 --> 10:51.791 subject in a new key; another episode; 10:51.788 --> 10:54.328 another statement of the subject, and on it goes until-- 10:54.330 --> 10:56.750 oh, we run out of energy usually about-- 10:56.750 --> 11:00.260 after four or five minutes or so, at which point the composer 11:00.264 --> 11:03.914 will bring the subject back-- maybe in the bass or in the 11:03.912 --> 11:07.512 soprano in a very prominent range in the tonic key-- 11:07.509 --> 11:08.579 and we have the sense, "oh, 11:08.580 --> 11:12.620 this is a very solid moment; yes, this fugue is ending." 11:12.620 --> 11:15.770 And maybe they'll throw upon one or--throw one or two chords 11:15.768 --> 11:17.208 on the end but that's it. 11:17.210 --> 11:21.790 So it's a complex form, but maybe not quite as complex 11:21.788 --> 11:23.948 as sonata-allegro form. 11:23.950 --> 11:26.590 What's a definition then? 11:26.590 --> 11:29.750 If you're taking notes there, what's a definition of a fugue? 11:29.750 --> 11:33.020 Well, I wrote a definition of a fugue and I will read the 11:33.020 --> 11:34.950 definition out of the textbook. 11:34.950 --> 11:37.670 Students don't like this, I've found, if you read out of 11:37.667 --> 11:38.307 a textbook. 11:38.308 --> 11:42.048 But I ought to be able to do this since I wrote the textbook. 11:42.053 --> 11:42.493 Okay? 11:42.490 --> 11:45.950 So I'm going to read a good definition of a fugue here. 11:45.950 --> 11:50.420 Definition of the fugue: A composition for two, 11:50.418 --> 11:55.138 three or four parts played or sung by voices or instruments 11:55.139 --> 12:00.019 which begins with a presentation of a subject in imitation in 12:00.019 --> 12:01.159 each part. 12:01.159 --> 12:02.279 The episode--excuse me. 12:02.278 --> 12:05.988 The exposition continues with modulating passages of free 12:05.990 --> 12:08.710 counterpoint-- the episodes--and further 12:08.706 --> 12:12.006 appearances of the subject, and ends with a strong 12:12.013 --> 12:13.903 affirmation of the tonic key. 12:13.899 --> 12:17.659 Well, you can't write all that down, but if you want to just 12:17.657 --> 12:20.327 put in your notes: For definition of fugue, 12:20.331 --> 12:22.181 see page 144 of the text. 12:22.178 --> 12:26.408 Fortunately, as I say, it's easier to hear 12:26.414 --> 12:31.274 and look at fugues than it is to define them. 12:31.269 --> 12:31.839 All right. 12:31.841 --> 12:34.651 Now today we're going to do something different. 12:34.649 --> 12:37.799 It's the only day in our course where we're actually going to 12:37.796 --> 12:38.526 look at music. 12:38.529 --> 12:38.949 Okay? 12:38.950 --> 12:42.190 We've handed out music for you--an entire piece, 12:42.186 --> 12:45.346 an entire fugue by J.S. Bach here, and ideally, 12:45.352 --> 12:49.482 I guess, we'd be in a seminar format and we'd all be standing 12:49.484 --> 12:51.554 around the piano here. 12:51.548 --> 12:57.358 So my first question for you is for how many voices is this 12:57.356 --> 12:58.956 fugue written? 12:58.960 --> 13:05.360 Look at just the first page and look vertically and see what's 13:05.360 --> 13:11.760 the maximum number of pitches you have sounding simultaneously 13:11.760 --> 13:14.070 at any one moment. 13:14.070 --> 13:20.750 Caroline, is it? 13:20.750 --> 13:21.650 Student: Three? 13:21.649 --> 13:22.669 Prof: Three. Okay? 13:22.669 --> 13:23.799 Yeah, we have three. 13:23.798 --> 13:26.168 If you look through, there are--sometimes at the 13:26.172 --> 13:29.152 very beginning there's just one voice and then there are two 13:29.150 --> 13:31.070 voices and then the three voices, 13:31.070 --> 13:32.670 three lines. 13:32.668 --> 13:35.868 But it never gets to be more than three lines. 13:35.870 --> 13:40.520 So we have our exposition here and it consists of three 13:40.524 --> 13:42.944 statements of the subject. 13:42.940 --> 13:46.170 We're going to call these three voices, or lines, 13:46.173 --> 13:48.803 the alto, <> 13:48.798 --> 13:50.838 the soprano, > 13:50.840 --> 13:54.070 and the bass, > 13:54.070 --> 13:56.770 which comes in in bar seven there. 13:56.769 --> 13:58.569 So here's a little bit of the beginning of this. 13:58.570 --> 14:25.120 > 14:25.120 --> 14:25.540 Okay. 14:25.538 --> 14:29.898 So that's our exposition, because each of the voices, 14:29.903 --> 14:34.273 alto, soprano and bass, has come in and presented the 14:34.268 --> 14:35.358 subject. 14:35.360 --> 14:38.110 Now we have bars nine and ten here. 14:38.110 --> 14:45.320 > 14:45.320 --> 14:56.400 What's that if I just go >? 14:56.399 --> 14:57.829 Jerry, what's that? 14:57.830 --> 14:58.070 Student: > 14:58.070 --> 15:01.040 Prof: It's a melodic sequence, and which direction is 15:01.044 --> 15:01.604 it going? 15:01.600 --> 15:02.420 Up or down? 15:02.418 --> 15:06.668 Well, that's maybe harder than you think. 15:06.669 --> 15:15.029 > 15:15.028 --> 15:18.578 Generally going down, not because the line is going 15:18.581 --> 15:22.421 down, but we're starting > 15:22.418 --> 15:27.858 each time on a successively lower pitch, and this sequence 15:27.864 --> 15:31.594 takes us <>. 15:31.590 --> 15:36.870 So we've started in this kind of tonality < 15:38.341 piano>> 15:38.340 --> 15:41.510 which is minor, but now by the time we've 15:41.514 --> 15:45.804 gotten to bar ten and eleven particularly < 15:47.149 piano>> 15:47.149 --> 15:48.969 he's modulated. 15:48.970 --> 15:52.740 So that's what our little episode was in bars nine and ten 15:52.740 --> 15:53.270 there. 15:53.269 --> 15:56.479 It allowed us to move from a minor key to a major key. 15:56.480 --> 15:59.880 And now the subject comes back in and, as you can see, 15:59.875 --> 16:01.665 what voice is it in there? 16:01.668 --> 16:07.108 What voice is the subject in bar eleven? 16:07.110 --> 16:08.190 Pretty straightforward. 16:08.190 --> 16:10.290 Somebody yell it out. 16:10.289 --> 16:10.969 Student: Soprano. 16:10.970 --> 16:11.950 Prof: Soprano. 16:11.951 --> 16:13.821 Okay, so here--heads up on the soprano. 16:13.820 --> 16:21.350 > 16:21.350 --> 16:24.930 So there we are, a nice statement of the theme 16:24.926 --> 16:27.306 in the major in the soprano. 16:27.309 --> 16:34.839 > 16:34.840 --> 16:37.680 What happened in that little episode? 16:37.678 --> 16:40.168 We were here <> 16:40.168 --> 16:42.508 and now we're here, > 16:42.509 --> 16:48.469 modulated again to minor, and there in bar fifteen, 16:48.467 --> 16:51.207 where is the subject? 16:51.210 --> 17:00.770 > 17:00.769 --> 17:02.709 Which bar? 17:02.710 --> 17:04.570 Chris. 17:04.569 --> 17:05.099 Student: Alto? 17:05.098 --> 17:05.918 Prof: Alto part. 17:05.920 --> 17:06.100 Good. 17:06.097 --> 17:06.417 Thanks. 17:06.420 --> 17:07.730 So there it is in the alto part. 17:07.730 --> 17:10.680 That's an interesting moment there because we've got a 17:10.682 --> 17:13.192 three-voice fugue, and how many hands does the 17:13.191 --> 17:14.251 performer have? 17:14.250 --> 17:16.840 Obviously two, so at some moments these hands 17:16.838 --> 17:20.368 are going to have to share a subject, and that's what happens 17:20.369 --> 17:21.429 in that voice. 17:21.430 --> 17:24.710 When you play this--take a look there, the very last measure of 17:24.713 --> 17:25.353 that page. 17:25.348 --> 17:26.048 It must be fifteen. 17:26.045 --> 17:27.065 > 17:27.068 --> 17:32.048 It starts out--my left hand is playing here < 17:33.394 piano>> 17:33.390 --> 17:36.280 and then the left hand has to go down and pick up the 17:36.277 --> 17:39.497 counterpoint in the bass and the right hand takes over that 17:39.498 --> 17:49.408 subject, > 17:49.410 --> 17:53.250 but it's the job of the pianist there who-- 17:53.250 --> 17:54.860 or the keyboardist, whoever is playing it-- 17:54.858 --> 17:58.118 to really lean on the inside of your hand there because when 17:58.122 --> 18:00.392 you'd normally play these instruments, 18:00.390 --> 18:02.510 there's a tendency--and I'm sure Santana, 18:02.509 --> 18:04.209 who is a far better keyboardist than I, 18:04.210 --> 18:07.310 will confirm this--there's a tendency to roll to either side. 18:07.308 --> 18:09.028 It's easier to play bass and soprano. 18:09.028 --> 18:12.608 What's hard to do is to get those inner voices so the 18:12.605 --> 18:16.175 keyboard player has to > 18:16.180 --> 18:26.450 and then <> 18:26.450 --> 18:27.800 so you can really hear that. 18:27.798 --> 18:29.968 If you didn't hear it, then that wasn't a good 18:29.972 --> 18:30.652 performance. 18:30.650 --> 18:31.460 All right. 18:31.464 --> 18:34.814 Now that takes us across the page there. 18:34.808 --> 18:36.268 We're now back in <> 18:36.269 --> 18:37.869 a minor key. 18:37.868 --> 18:40.668 This is bar sixteen and seventeen, and in bars 18:40.673 --> 18:43.543 seventeen, eighteen, nineteen, the beginning of 18:43.541 --> 18:46.161 twenty, we have an interesting moment. 18:46.160 --> 18:48.570 It's called invertible counterpoint. 18:48.569 --> 18:50.009 What do we mean by that? 18:50.009 --> 18:57.569 Well, he has a motive > 18:57.568 --> 19:00.358 and we're going to call that motive A, and he has another 19:00.362 --> 19:01.312 motive, motive B. 19:01.309 --> 19:05.439 > 19:05.440 --> 19:09.650 So there is B in the alto, A in the bass, 19:09.653 --> 19:13.973 and together they sound sort of like this. 19:13.972 --> 19:17.242 > 19:17.240 --> 19:18.550 Okay? Cool. 19:18.549 --> 19:20.819 Now the next three bars. 19:20.819 --> 19:21.729 What happens? 19:21.730 --> 19:27.160 Well, he takes B <> 19:27.160 --> 19:31.420 and so he takes B and puts that below A. 19:31.420 --> 19:33.270 He's switching the positions here. 19:33.269 --> 19:38.179 A is now <>. 19:38.180 --> 19:41.390 Both of these motives are coming up in rising sequence. 19:41.390 --> 19:44.430 So let's go back to the beginning of seventeen there and 19:44.428 --> 19:46.028 we'll listen to the switch. 19:46.029 --> 19:59.229 > 19:59.230 --> 20:00.550 All right. 20:00.548 --> 20:03.308 So that goes by very quickly. 20:03.305 --> 20:03.965 Right? 20:03.970 --> 20:07.010 How long do you think it took Bach to figure that out? 20:07.009 --> 20:07.829 I don't know. 20:07.826 --> 20:09.836 He's a very good contrapuntalist, 20:09.836 --> 20:12.156 maybe "boom," like that. 20:12.160 --> 20:15.130 I'd have to sit there--Santana, how long would it take you to 20:15.128 --> 20:17.748 figure out some invertible counterpoint that you could 20:17.751 --> 20:20.161 think of one melody, think up another melody that 20:20.155 --> 20:23.115 would be a harmony against it, but yet you could flip the two 20:23.116 --> 20:25.446 and it would still sound pretty darn good? 20:25.450 --> 20:27.760 It'd take a long time to kind of work that out. 20:27.759 --> 20:29.879 So that's what's kind of neat about fugue. 20:29.880 --> 20:33.230 There's all these intricacies embedded in them that almost 20:33.227 --> 20:36.517 sail by the general listener unless we happen to have the 20:36.517 --> 20:39.627 music right in front of us and can dwell on them. 20:39.630 --> 20:40.210 All right. 20:40.214 --> 20:43.554 So that takes us over now to bar twenty, where we are here 20:43.554 --> 20:46.194 back, I guess, > 20:46.190 --> 21:10.360 in our tonic key of C minor, and the theme is up in the 21:10.358 --> 21:26.918 soprano <> 21:26.920 --> 21:38.010 and then one final statement in the soprano < 21:40.979 piano>> 21:40.980 --> 21:43.070 --a couple of interesting points there. 21:43.068 --> 21:51.818 When we concluded this piece we had this sound < 21:54.187 piano>>. 21:54.190 --> 21:56.800 What's a little bit surprising about that? 21:56.798 --> 22:03.208 We're ending a piece that's called the Fugue Number Two in C 22:03.210 --> 22:04.080 Minor. 22:04.078 --> 22:09.248 We are ending here with >. 22:09.250 --> 22:10.350 Does that sound like a minor chord again? 22:10.349 --> 22:12.019 No, no. A major chord. 22:12.019 --> 22:13.539 All right. So he's changed it. 22:13.538 --> 22:16.268 This is a standard gamut--gambit from the late 22:16.265 --> 22:20.015 sixteenth right through the eighteenth century-- last chord. 22:20.019 --> 22:21.669 They didn't like to end pieces in minor. 22:21.670 --> 22:22.930 Maybe it was too depressing or whatever. 22:22.930 --> 22:25.470 > 22:25.470 --> 22:30.450 Oh, don't want to do that, so > 22:30.451 --> 22:33.341 > 22:33.338 --> 22:36.128 with the major third up there above. 22:36.130 --> 22:38.800 That's called the Picardy third, maybe from the Old French 22:38.798 --> 22:40.998 word picart, which means sort of sharp or 22:40.998 --> 22:41.558 pointed. 22:41.558 --> 22:43.318 So we have a pointed ending there. 22:43.319 --> 22:44.299 We have a major ending. 22:44.298 --> 22:47.768 Here's another issue when we're--since we're on the topic 22:47.766 --> 22:50.486 of points and that's called a pedal point. 22:50.490 --> 22:54.500 What was J.S. Bach known as in his day? 22:54.500 --> 22:55.850 Was he known as a great composer? 22:55.849 --> 22:58.009 What was he known as? 22:58.009 --> 23:00.049 How did he earn--basically, how did he earn his living? 23:00.049 --> 23:02.589 Student: He played-- Prof: He played 23:02.587 --> 23:04.597 the--you're getting warm. 23:04.596 --> 23:05.156 Yeah? 23:05.160 --> 23:05.690 Student: Is it organ? 23:05.690 --> 23:07.020 Prof: He played the organ. 23:07.019 --> 23:11.129 He was the great organ virtuoso of his day, and I think at the 23:11.130 --> 23:14.770 end of this particular fugue here, it's interesting. 23:14.769 --> 23:16.659 He just has this line sit there. 23:16.660 --> 23:23.130 > 23:23.130 --> 23:23.450 Okay. 23:23.453 --> 23:27.543 On the organ that would just be fine and dandy because you'd put 23:27.542 --> 23:31.112 your foot down there on that low C > 23:31.113 --> 23:33.193 > 23:33.190 --> 23:35.370 and that tonic note would continue to hold, 23:35.368 --> 23:38.268 but if you were writing this for the clavichord or the 23:38.268 --> 23:41.378 harpsichord or the piano, what happens to that sound once 23:41.377 --> 23:41.987 you hit it? 23:41.990 --> 23:43.500 It dies away. 23:43.500 --> 23:46.040 I think in the end of this piece here Bach had the sound of 23:46.039 --> 23:46.609 the organ . 23:46.608 --> 23:48.198 He didn't really--he wasn't thinking "gee, 23:48.200 --> 23:50.420 if this is really for a harpsichord or something, 23:50.420 --> 23:58.400 I'd better write this like this-- < 24:01.014 piano>> 24:01.009 --> 24:03.089 so we get a nice, strong tonic sound at the 24:03.094 --> 24:03.694 end." 24:03.690 --> 24:07.620 He may have had the sound of the organ there in his ear, 24:07.618 --> 24:10.858 but perhaps the important point here is this idea of a pedal 24:10.862 --> 24:14.322 point 'cause we've actually even talked about that before in the 24:14.324 --> 24:17.684 Johannes Brahms Variations on a Theme of Haydn that was 24:17.675 --> 24:19.375 performed Saturday night. 24:19.380 --> 24:20.930 Pedal point is what? 24:20.930 --> 24:25.790 Anybody who can define pedal point for us? 24:25.789 --> 24:27.259 Hm? 24:27.259 --> 24:28.079 Well, what goes on? 24:28.077 --> 24:28.937 It's pretty simple. 24:28.940 --> 24:30.730 Roger. 24:30.730 --> 24:34.040 Student: The bass holds a note > 24:34.038 --> 24:35.038 Prof: Yeah. 24:35.038 --> 24:38.038 The bass holds a note and basically you're just kind of 24:38.035 --> 24:41.085 running over top of one, possibly two harmonies up above 24:41.086 --> 24:43.136 it, but it all sounds consonant. 24:43.140 --> 24:46.650 So just be sure of the idea of one note usually in the bass 24:46.648 --> 24:49.068 just holding, holding, holding for a long 24:49.069 --> 24:50.219 period of time. 24:50.220 --> 24:55.710 24:55.710 --> 24:58.090 Okay. 24:58.088 --> 25:01.328 Any questions about that fugue by J.S. Bach? 25:01.328 --> 25:03.348 Anybody want to ask anything about that? 25:03.349 --> 25:07.639 25:07.640 --> 25:09.550 Marcus, that works for you? 25:09.549 --> 25:12.619 Ugonna, okay? 25:12.619 --> 25:15.039 Thaddeus, no questions? 25:15.039 --> 25:17.759 Frederick. 25:17.759 --> 25:21.039 Student: At the very end that's a total of what? 25:21.039 --> 25:22.729 Four notes being played at once? 25:22.730 --> 25:24.380 Prof: Oh, okay. 25:24.378 --> 25:24.768 Good. 25:24.770 --> 25:25.400 Yeah. 25:25.400 --> 25:26.380 Thanks for bringing that out. 25:26.380 --> 25:29.650 There at the end we could even have-- 25:29.650 --> 25:31.750 you're right--four, maybe even five notes played at 25:31.752 --> 25:33.732 once, so this idea that you--once you 25:33.729 --> 25:36.739 have three parts you can only have three parts or once you 25:36.743 --> 25:39.243 have five-voice fugue, you can have no more than five 25:39.242 --> 25:41.672 voices-- breaks down at the very end. 25:41.670 --> 25:44.660 Why would you imagine a composer would want to do that, 25:44.655 --> 25:45.315 Frederick? 25:45.318 --> 25:46.768 Student: > 25:46.769 --> 25:48.589 pieces at one time. 25:48.588 --> 25:51.838 Prof: Well, no, it's not that hard because 25:51.836 --> 25:53.366 you-- once you get used to the idea 25:53.371 --> 25:55.551 of a C major triad, you--a musician would look at 25:55.547 --> 25:57.857 that end and say, "I've just got a C major 25:57.863 --> 25:58.203 triad. 25:58.200 --> 25:59.470 I'm going to just bang down on it." 25:59.470 --> 26:01.530 So that's not hard technically or intellectually, 26:01.534 --> 26:03.944 but why would a--the--you raised a very interesting point 26:03.942 --> 26:04.332 here. 26:04.328 --> 26:07.028 Why would a composer want to add more notes at the end? 26:07.028 --> 26:08.578 I think it's a pretty straightforward idea. 26:08.579 --> 26:11.999 David? Michael, yeah. 26:12.000 --> 26:12.310 Student: They make it louder. 26:12.308 --> 26:14.098 Prof: Yeah, just make it louder, 26:14.101 --> 26:16.341 make it more sonorous, a big bang ending sort of 26:16.344 --> 26:18.404 thing, yeah, to tell the listener once again 26:18.395 --> 26:21.305 that this is something special and we're probably at the end. 26:21.308 --> 26:21.898 All right. 26:21.904 --> 26:24.234 So let's listen to just a bit of this. 26:24.230 --> 26:25.860 We had one version of this. 26:25.858 --> 26:29.768 Let's listen to a contemporary jazz ensemble playing. 26:29.769 --> 26:34.059 It starts out with a kind of guitar synthesizer with a piano 26:34.061 --> 26:38.211 here and then we'll see what the other instruments are. 26:38.210 --> 26:41.890 Here's a jazz rendition of the same fugue by Bach. 26:41.890 --> 27:14.330 > 27:14.328 --> 27:17.028 What instrument is playing this bass line? 27:17.029 --> 27:30.019 > 27:30.019 --> 27:30.659 Okay. 27:30.656 --> 27:38.176 Here we are in bar thirteen, > 27:38.180 --> 27:42.780 fifteen, subject in the inner voice. 27:42.777 --> 27:46.847 > 27:46.848 --> 27:49.268 Here's our invertible counterpoint, 27:49.266 --> 27:51.466 > 27:51.470 --> 28:00.210 switch, <> 28:00.210 --> 28:08.970 subject soprano, > 28:08.970 --> 28:14.020 now just modulating from one key to the next here. 28:14.019 --> 28:36.999 > 28:37.000 --> 28:40.740 And here they actually do repeat that tonic note, 28:40.740 --> 28:42.610 >. 28:42.608 --> 28:42.728 Okay. 28:42.730 --> 28:43.460 > 28:43.460 --> 28:45.810 And then what they do is go off and improvise on that. 28:45.808 --> 28:50.288 But it's interesting, the similarity between jazz 28:50.291 --> 28:52.721 style and Baroque music. 28:52.720 --> 28:53.980 Why is that the case? 28:53.980 --> 28:56.900 Well, Baroque music has a lot of driving rhythm in it, 28:56.897 --> 29:00.197 kind of regular rhythm in it, and jazz has a kind of regular, 29:00.201 --> 29:01.911 pulsating rhythm in it too. 29:01.910 --> 29:06.410 I asked you what instrument was playing the bass line there and 29:06.411 --> 29:10.841 Daniel, you started going like this so what were you doing? 29:10.838 --> 29:11.418 Student: > 29:11.420 --> 29:14.960 Prof: The double bass of the--but is it bowed? 29:14.959 --> 29:15.299 No. 29:15.298 --> 29:17.628 It's a plucked, a pizzicato double bass, 29:17.628 --> 29:20.618 but that's a standard instrument in a jazz quartet, 29:20.615 --> 29:21.685 jazz ensemble. 29:21.690 --> 29:25.960 But it's a very strong bass and Baroque music also has a very 29:25.957 --> 29:29.017 strong bass, so lots of similarities between 29:29.015 --> 29:31.855 contemporary jazz and baroque music. 29:31.858 --> 29:35.638 And sometimes these jazz ensembles like to get to this 29:35.635 --> 29:39.265 Baroque music and resurrect them in modern idiom. 29:39.269 --> 29:40.029 All right. 29:40.028 --> 29:44.198 So normally a fugue is a freestanding piece or you could 29:44.200 --> 29:47.690 have an entire movement written as a fugue. 29:47.690 --> 29:51.430 Haydn--the last movement of the Haydn quartets will sometimes do 29:51.433 --> 29:53.693 that, a Beethoven piano sonata might 29:53.693 --> 29:55.513 do that, but usually they're 29:55.506 --> 29:56.846 freestanding pieces. 29:56.848 --> 29:59.938 Occasionally, you run into a fugue that's 29:59.942 --> 30:02.652 embedded inside another movement. 30:02.650 --> 30:06.620 You might have a movement in sonata-allegro form and you get 30:06.622 --> 30:09.562 to a particular section, let's say the development 30:09.556 --> 30:12.366 section, and the composer says, "Well, I want to write a 30:12.367 --> 30:14.027 fugue here as my development." 30:14.028 --> 30:19.968 When that happens we call it a fugato, so a fugato is a fugue 30:19.969 --> 30:22.839 placed inside another form. 30:22.838 --> 30:26.128 So we're going to listen to an example of this from the 30:26.133 --> 30:29.673 romantic period in which we have the young composer Georges 30:29.670 --> 30:30.280 Bizet. 30:30.278 --> 30:32.538 He was exactly your age when he wrote this. 30:32.539 --> 30:34.339 He was nineteen years old. 30:34.338 --> 30:36.788 Georges Bizet wrote this symphony. 30:36.788 --> 30:39.118 There's a lovely romantic string sound, 30:39.116 --> 30:43.156 sort of break-your-heart string sound, and then we have a segue. 30:43.160 --> 30:46.730 We have kind of a romantic transition here as he changes 30:46.726 --> 30:50.616 mood and then a fugue will break out and it will start in the 30:50.615 --> 30:53.465 bottom voice so I'll tell you that much. 30:53.470 --> 30:55.970 And my question to you or my challenge to you is this: 30:55.971 --> 30:56.871 What's the order? 30:56.868 --> 30:58.518 Let's say--and I'll tell you this. 30:58.519 --> 31:00.839 We've got a four-voice fugue that's going to start here. 31:00.838 --> 31:04.278 Can you track the order in which the voices enter? 31:04.279 --> 31:05.919 You know we've got the four. 31:05.920 --> 31:07.610 You've got the bass, tenor, soprano, 31:07.612 --> 31:08.872 alto--or bass, tenor, alto, 31:08.869 --> 31:10.419 soprano, or soprano, alto, tenor, 31:10.416 --> 31:10.946 bass. 31:10.950 --> 31:13.140 They can come in any one of four different-- 31:13.140 --> 31:18.060 well, probably more than four permutations but the order might 31:18.061 --> 31:19.831 be alto, bass, soprano, 31:19.828 --> 31:22.418 tenor or it might be bass, alto, tenor, 31:22.423 --> 31:25.343 soprano or soprano, alto, tenor and bass. 31:25.338 --> 31:27.408 We don't know, and that's your challenge here 31:27.411 --> 31:29.201 to see if you can track the subject. 31:29.200 --> 31:31.510 Here we go. 31:31.509 --> 31:55.309 > 31:55.309 --> 31:57.349 Start. 31:57.349 --> 32:31.869 > 32:31.868 --> 32:32.158 Okay. 32:32.163 --> 32:34.873 We're going to stop it there just for a minute. 32:34.866 --> 32:36.626 We're going to pause there. 32:36.630 --> 32:38.410 That's the--all four voices are in there. 32:38.410 --> 32:41.430 Could anybody on just one hearing tell me what the order 32:41.430 --> 32:41.760 was? 32:41.759 --> 32:45.689 32:45.690 --> 32:46.360 Okay. 32:46.356 --> 32:50.756 Let me--somebody different here. 32:50.759 --> 32:52.699 Robert, I haven't called on you this morning. 32:52.700 --> 32:53.510 Student: > 32:53.509 --> 32:54.079 Prof: Okay. 32:54.084 --> 32:55.654 It started with bass > 32:55.650 --> 33:00.230 or maybe even an octave lower. 33:00.231 --> 33:04.511 > 33:04.509 --> 33:07.219 Okay. Then where did he go? 33:07.220 --> 33:08.140 Student: Alto. 33:08.140 --> 33:12.420 Prof: Yeah, it actually went to the alto 33:12.421 --> 33:15.121 > 33:15.119 --> 33:16.769 and there--and then where? 33:16.769 --> 33:23.539 Tenor <> 33:23.538 --> 33:27.058 and then finally--yeah, > 33:27.058 --> 33:29.578 way up high in the first violins. 33:29.583 --> 33:31.873 > 33:31.868 --> 33:35.848 And now we're going to get a--an episode in which he's 33:35.851 --> 33:39.831 going to play with just a motive, and then the subject 33:39.832 --> 33:41.262 will come back. 33:41.259 --> 33:43.039 So here are two questions for you. 33:43.038 --> 33:47.048 In which voice is the subject coming back and what's happened 33:47.046 --> 33:49.446 to the subject when it comes back? 33:49.450 --> 33:50.520 It's changed in one way. 33:50.519 --> 34:03.169 > 34:03.170 --> 34:04.870 Okay. Let's stop it there. 34:04.869 --> 34:06.189 Any takers on that? 34:06.190 --> 34:08.370 And if we were doing a quiz on this, we'd give you three or 34:08.367 --> 34:09.267 four playings of that. 34:09.269 --> 34:12.179 Which voice did it come back in? 34:12.179 --> 34:17.859 > 34:17.860 --> 34:19.210 Thaddeus. 34:19.210 --> 34:20.090 Student: > 34:20.090 --> 34:21.300 Prof: Not bad. 34:21.295 --> 34:24.845 We would take that because it's kind of high--I'm playing it in 34:24.853 --> 34:26.463 kind of tenor range here. 34:26.460 --> 34:29.470 I think it was more cellos and we'd probably-- 34:29.469 --> 34:31.759 with bassoons--and we'd probably call that bass, 34:31.760 --> 34:34.050 a bass part, but fair enough, 34:34.052 --> 34:39.132 tenor, and what happened to it? 34:39.132 --> 34:44.202 > 34:44.199 --> 34:44.759 Roger. 34:44.755 --> 34:45.305 Minor. 34:45.311 --> 34:48.001 > 34:48.000 --> 34:51.540 So he modulated to a different key and then gave you the 34:51.536 --> 34:55.416 subject in a minor key, and that's kind of the way 34:55.422 --> 34:58.812 these fugues operate, give you an exposition episode 34:58.809 --> 35:01.549 in which you change key, bring back the subject in a 35:01.547 --> 35:02.377 different key. 35:02.380 --> 35:02.980 All right. 35:02.983 --> 35:06.313 So we've now had a fugue from the nineteenth century, 35:06.309 --> 35:09.469 although we would call it a fugato because it's embedded in 35:09.472 --> 35:12.392 this lovely, lovely sonata-allegro movement. 35:12.389 --> 35:14.979 Let's turn to a fugue from the twentieth century, 35:14.978 --> 35:18.108 and for this we go to Leonard Bernstein and you can see the 35:18.106 --> 35:19.666 playlist up on the board. 35:19.670 --> 35:24.470 New Haven used to be a favorite try-out city for Broadway 35:24.474 --> 35:25.424 musicals. 35:25.420 --> 35:28.720 Indeed there was a musical entitled--it never went 35:28.719 --> 35:29.459 anywhere. 35:29.460 --> 35:31.760 It was entitled We Bombed in New Haven, 35:31.762 --> 35:34.272 meaning that the try-out > 35:34.268 --> 35:37.658 of the particular musical was not a success, 35:37.655 --> 35:41.115 and where would they try out in New Haven? 35:41.119 --> 35:44.449 What was the great theater for this? 35:44.445 --> 35:44.915 Hm? 35:44.920 --> 35:45.630 Student: The repertory theater? 35:45.630 --> 35:47.160 Prof: The Yale Rep Theatre? 35:47.159 --> 35:48.369 Any other takers? 35:48.369 --> 35:50.549 The Shubert Theater. 35:50.550 --> 35:54.010 Yeah, actually in that period the Yale Rep was actually a 35:54.005 --> 35:55.915 functioning house of worship. 35:55.920 --> 35:58.600 It was a church at that --what's now the Yale Rep. 35:58.599 --> 36:01.709 So is it the Shubert Theater, which has been here for a long, 36:01.708 --> 36:02.328 long time? 36:02.329 --> 36:05.669 So Leonard Bernstein came in here with a show in 1952 called 36:05.670 --> 36:08.560 Wonderful Town and he tried it out there, 36:08.559 --> 36:12.039 and generally speaking it was a success and he took it down the 36:12.038 --> 36:13.888 train tracks there to Broadway. 36:13.889 --> 36:17.089 But he took some music out of it, some music that he thought 36:17.092 --> 36:20.412 actually was a little bit too complicated for the choreography 36:20.405 --> 36:24.085 that he wanted to work into it-- later took that material and 36:24.092 --> 36:27.622 worked it in to a freestanding piece called "Prelude, 36:27.621 --> 36:29.481 Fugue, and Jazz Riff." 36:29.480 --> 36:33.130 So we're going to look at now just the fugue portion of it 36:33.132 --> 36:36.212 because it's a very interesting kind of fugue. 36:36.210 --> 36:37.940 It's a very complex fugue. 36:37.940 --> 36:40.380 So we're going to start out here and I'm going to break 36:40.382 --> 36:40.702 this. 36:40.699 --> 36:43.989 We'll listen, we'll stop, we'll listen and 36:43.987 --> 36:48.077 stop so that we can focus on particular passages. 36:48.079 --> 36:52.029 So as we start to listen, see how many voices there are 36:52.030 --> 36:54.300 in Leonard Bernstein's fugue. 36:54.300 --> 36:56.770 Have a general sense of what the range is: 36:56.773 --> 36:58.103 soprano, alto, bass. 36:58.099 --> 36:59.019 What else do we need? 36:59.018 --> 36:59.388 Oh, yeah. 36:59.391 --> 37:00.841 What instruments are playing here? 37:00.840 --> 37:29.260 > 37:29.260 --> 37:29.630 Okay. 37:29.628 --> 37:33.988 So that's the exposition and a little bit of the development 37:33.987 --> 37:36.127 there so what instruments? 37:36.130 --> 37:39.400 Hm? Ducks? 37:39.400 --> 37:39.980 Student: Saxophones? 37:39.980 --> 37:41.120 Prof: Yeah, saxophones. 37:41.119 --> 37:41.399 Yeah. 37:41.402 --> 37:41.692 Okay. 37:41.686 --> 37:44.066 Kneeland said saxophones and he's right. 37:44.070 --> 37:45.320 Yeah, so saxophones there. 37:45.320 --> 37:48.170 So we've got--and then how--roughly how many did you 37:48.168 --> 37:48.558 hear? 37:48.559 --> 37:51.029 Two, three, four? 37:51.030 --> 37:53.450 Yeah, maybe four, maybe four different 37:53.452 --> 37:57.382 saxophones, sort of alto sax, maybe baritone sax in there. 37:57.380 --> 38:02.310 And there was one--and so we are playing this out and it's a 38:02.307 --> 38:07.067 rather syncopated fugue, sort of >. 38:07.070 --> 38:09.460 Let's listen to it again. 38:09.460 --> 38:11.680 No, we don't have time to do that but here's one thing that 38:11.677 --> 38:13.167 happened, <> 38:13.170 --> 38:15.910 that kind of sound, >. 38:15.909 --> 38:19.479 Then after one episode one of the saxes brought back that 38:19.483 --> 38:19.993 subject. 38:19.994 --> 38:21.914 > 38:21.909 --> 38:24.879 What's it doing there? 38:24.875 --> 38:28.645 > 38:28.650 --> 38:29.940 What is that? 38:29.940 --> 38:31.240 What's the relationship there? 38:31.239 --> 38:32.019 Student: Is it inverting it? 38:32.018 --> 38:34.488 Prof: Yeah, it's just inverting it. 38:34.489 --> 38:36.679 It is taking the intervals and flipping them and that's what 38:36.675 --> 38:38.005 composers love to do with fugues, 38:38.010 --> 38:40.450 and I'll be talking about interchangeable parts, 38:40.449 --> 38:44.599 reciprocal relationships with the mathematical quality of 38:44.601 --> 38:45.271 fugues. 38:45.268 --> 38:47.068 And so that's what's happening here. 38:47.070 --> 38:49.810 We have a moment of melodic inversion. 38:49.809 --> 38:52.209 And sometimes in fugues--and Bach's did this in the musical 38:52.211 --> 38:54.501 offering-- he can take his fugue subject 38:54.498 --> 38:58.018 and run it backwards from beginning to end so they like to 38:58.016 --> 39:02.146 have these kind of mathematical permutations of these intervals. 39:02.150 --> 39:04.630 It's very cerebral stuff, this fugue business. 39:04.630 --> 39:09.900 So there we had just a moment of Leonard Bernstein writing a 39:09.898 --> 39:12.218 little bit of inversion. 39:12.219 --> 39:15.689 Now what we're about to hear next is something of a surprise 39:15.688 --> 39:18.038 because we get a second fugue subject. 39:18.039 --> 39:20.349 And it's a different fugue subject; 39:20.349 --> 39:22.419 it is not syncopated. 39:22.420 --> 39:27.410 It's rather lyrical, > 39:27.409 --> 39:30.939 > 39:30.940 --> 39:32.210 something like that. 39:32.210 --> 39:34.260 So it's nice and lyrical. 39:34.260 --> 39:40.660 And let's listen to how he now unfolds a second fugue subject. 39:40.659 --> 39:43.079 So what we have here is called a double-fugue. 39:43.079 --> 39:45.859 He's got one exposition with one fugue subject. 39:45.860 --> 40:01.110 Now he's going to give us a completely different exposition 40:01.114 --> 40:17.954 with yet a second fugue subject, > 40:17.949 --> 40:19.299 and then number one comes back. 40:19.295 --> 40:20.595 > 40:20.599 --> 40:20.879 Okay. 40:20.880 --> 40:24.030 We're going to pause it here because he's now about to do 40:24.030 --> 40:27.460 something rather interesting that Bach used to do as well. 40:27.460 --> 40:30.810 And Bernstein was a consummate musician, had studied Bach, 40:30.809 --> 40:33.929 had Bach coming out of his ears, so he knew about this 40:33.925 --> 40:35.155 particular trick. 40:35.159 --> 40:36.329 It's called stretto. 40:36.329 --> 40:39.419 You can design a fugue subject, not only that it could go 40:39.420 --> 40:42.080 upside down, but in which the intervals 40:42.081 --> 40:46.031 instead of coming in long succession could be piled right 40:46.027 --> 40:47.787 on top of one another. 40:47.789 --> 40:50.589 So the way he sets this thing up to begin with is this, 40:50.590 --> 40:55.260 this, maybe this and then this, but in the next section it's 40:55.257 --> 40:59.647 going to go this, this, this and this. 40:59.650 --> 41:02.900 The intervals back up on each other because they have been 41:02.900 --> 41:06.040 arranged to be consonant at key points and that's called 41:06.039 --> 41:08.889 stretto, Italian word stretto, 41:08.885 --> 41:10.995 kind of tight-- tight entries here. 41:11.000 --> 41:14.450 So here is fancy little bit of counterpoint by Leonard 41:14.454 --> 41:17.654 Bernstein that once again goes by very quickly. 41:17.650 --> 41:20.960 > 41:20.960 --> 41:22.590 Do you hear it? 41:22.590 --> 41:34.020 > 41:34.018 --> 41:36.878 Now he's going to bring back the two subjects together. 41:36.880 --> 41:42.600 We have one and two together, > 41:42.599 --> 41:46.489 episode, <> 41:46.489 --> 41:50.349 syncopated episode, > 41:50.349 --> 41:53.479 one, <> 41:53.480 --> 41:57.180 two, <> 41:57.179 --> 41:57.909 and so on. 41:57.911 --> 42:00.111 > 42:00.110 --> 42:03.330 So it's a pretty nifty little fugue there by Leonard Bernstein 42:03.331 --> 42:06.131 with lots of intricate counterpoint involved in it. 42:06.130 --> 42:07.120 All right. 42:07.117 --> 42:12.747 Let's end now with a fugue of J.S. Bach and for that we're 42:12.751 --> 42:18.981 going to turn to an organ fugue that he wrote about 1710 when he 42:18.978 --> 42:22.238 was a young man in Weimar. 42:22.239 --> 42:42.289 Here is that fugue subject > 42:42.289 --> 42:43.439 and on and on and on it goes. 42:43.440 --> 42:45.990 What's of interest about this subject? 42:45.989 --> 42:47.159 Well, two things. 42:47.159 --> 42:50.779 First of all, as I sing this 42:50.782 --> 42:53.872 > 42:53.869 --> 42:55.149 what is that? 42:55.150 --> 43:01.320 > 43:01.320 --> 43:04.680 It's an-- Student: Arpeggio. 43:04.679 --> 43:06.399 Prof: Arpeggio. 43:06.400 --> 43:09.150 Yes, it is, but it's an arpeggio of what? 43:09.150 --> 43:11.890 > 43:11.889 --> 43:13.999 > 43:14.000 --> 43:18.380 It's a triad, just a minor triad. 43:18.380 --> 43:19.810 > 43:19.811 --> 43:23.011 One, five, three, one, if I skip this note here. 43:23.014 --> 43:24.654 > 43:24.650 --> 43:27.860 As I come to every strong beat in this theme, 43:27.864 --> 43:31.304 every strong beat, I have a member of the triad, 43:31.298 --> 43:33.928 that same either G, B-flat or D. 43:33.929 --> 43:38.409 So these triads as we said before are really the structure, 43:38.411 --> 43:41.661 the backbone, on which a composer like Bach 43:41.659 --> 43:45.059 will place the flesh of a fugue subject. 43:45.059 --> 43:48.269 So it's very triadic and it sounds pretty secure for that . 43:48.268 --> 43:51.148 Now here's another thing that this fugue subject does and many 43:51.152 --> 43:52.242 other fugue subjects. 43:52.239 --> 43:54.209 It starts with quarter notes, > 43:54.210 --> 43:57.470 quarter, quarter, quarter, then next measure, 43:57.469 --> 43:58.959 eighth, eighth, eighth, eighth, 43:58.961 --> 44:01.061 eighth, eighth, and then we get in here 44:01.063 --> 44:03.743 eighth, eighth, eighth, 44:03.735 --> 44:07.115 >. 44:07.119 --> 44:08.719 It's gathering speed. 44:08.719 --> 44:10.439 Of course, the beat isn't going any faster. 44:10.440 --> 44:11.920 The tempo is staying the same. 44:11.920 --> 44:14.420 He's simply writing shorter note values, 44:14.420 --> 44:16.010 which has the psychological impact, 44:16.010 --> 44:18.910 as we've said several times, of giving the sense of 44:18.905 --> 44:21.385 movement, gathering speed here. 44:21.389 --> 44:23.979 It's like a train pulling out of the station. 44:23.980 --> 44:25.420 We want to get on this train. 44:25.420 --> 44:30.110 This thing is really starting to roll after five measures or 44:30.112 --> 44:30.512 so. 44:30.510 --> 44:34.690 So it's a pretty nifty fugue subject here and we're going to 44:34.693 --> 44:38.173 listen to this now, and what I'd like to do is the 44:38.166 --> 44:39.156 following. 44:39.159 --> 44:41.269 We're going to listen to the entire piece. 44:41.268 --> 44:51.208 Think about--as the voices come in, think about where they're 44:51.210 --> 44:53.200 coming in. 44:53.199 --> 44:57.049 Can you tell me what the trajectory of the voices is in 44:57.047 --> 44:58.257 the exposition? 44:58.260 --> 45:00.690 And I'm going to turn out the lights here because sometimes 45:00.690 --> 45:03.040 it's good just to kind of go off into your own world, 45:03.039 --> 45:05.199 close your eyes, but I would like you to do the 45:05.202 --> 45:06.052 following thing. 45:06.050 --> 45:11.860 Kind of lean back, get comfortable, 45:11.860 --> 45:19.210 close your eyes, but every time you hear the 45:19.208 --> 45:27.238 fugue subject-- <> 45:27.239 --> 45:30.889 and so on--every time you hear that fugue subject raise your 45:30.885 --> 45:34.035 hand so that I know you're recognizing that it's the 45:34.038 --> 45:34.778 subject. 45:34.780 --> 45:37.300 Because listening to fugues, it's basically one thing: 45:37.302 --> 45:39.872 Differentiating between a passage in which you've got a 45:39.873 --> 45:42.683 statement of the subject and an episode where there ain't no 45:42.682 --> 45:44.162 statement of the subject. 45:44.159 --> 45:44.439 Okay. 45:44.443 --> 45:47.753 So this is a three minute and twenty-second fugue and we're 45:47.748 --> 45:49.968 going to listen to the whole thing, 45:49.969 --> 45:53.079 but do raise your hand when you think that fugue subject is in 45:53.081 --> 45:53.491 there. 45:53.489 --> 46:45.239 > 46:45.239 --> 46:49.299 So we've gone soprano, alto, tenor and now bass. 46:49.300 --> 47:05.990 > 47:05.989 --> 47:07.649 Yeah, there it is. 47:07.650 --> 47:10.090 It's in one of those inner voices. 47:10.090 --> 47:12.860 It's a little bit disguised but it's in there. 47:12.860 --> 47:29.230 > 47:29.230 --> 47:36.910 Yep, <> 47:36.909 --> 47:38.239 inner voice. 47:38.239 --> 47:49.949 > 47:49.949 --> 47:52.419 Yep, way down in the bass. 47:52.420 --> 48:03.900 > 48:03.900 --> 48:08.960 A nice, long sequence here > 48:08.960 --> 48:19.150 > 48:19.150 --> 48:23.600 Yep, all the way up on top in the soprano. 48:23.599 --> 48:31.699 > 48:31.699 --> 48:36.649 Another episode, descending sequence this time. 48:36.650 --> 48:44.350 > 48:44.349 --> 48:48.029 Rising sequences here, > 48:48.030 --> 48:54.530 falling sequences <> 48:54.530 --> 48:58.170 in the bass. 48:58.170 --> 49:12.460 > 49:12.460 --> 49:15.230 Okay, so that's a wonderful fugue by J.S. Bach and we 49:15.228 --> 49:18.368 could--we're going to talk more about this in section, 49:18.369 --> 49:21.529 this idea how you can run your fugue parts this way or you 49:21.534 --> 49:23.094 could order them this way. 49:23.090 --> 49:25.860 You can think of these constructs mathematically or you 49:25.856 --> 49:28.876 can think of them musically, but you're all working with the 49:28.878 --> 49:30.208 same kind of material. 49:30.210 --> 49:33.260 As you go out, one final fugue by Glenn Gould 49:33.257 --> 49:37.337 who is going to teach you how to write a fugue as he sings a 49:37.342 --> 49:38.522 fugue to you. 49:38.519 --> 49:56.739 > 49:56.739 --> 50:01.999