WEBVTT 00:00:00.000 --> 00:00:01.976 align:middle line:90% 00:00:01.976 --> 00:00:02.964 align:middle line:90% [SQUEAKING] 00:00:02.964 --> 00:00:04.446 align:middle line:90% [RUSTLING] 00:00:04.446 --> 00:00:06.916 align:middle line:90% [CLICKING] 00:00:06.916 --> 00:00:26.642 align:middle line:90% 00:00:26.642 --> 00:00:28.100 align:middle line:84% MICHAEL CUTHBERT: Hello, everybody, 00:00:28.100 --> 00:00:32.430 align:middle line:84% and congratulations on getting problem set seven in. 00:00:32.430 --> 00:00:35.180 align:middle line:84% This is Michael Cuthbert, and I'm 00:00:35.180 --> 00:00:40.680 align:middle line:84% going to unlock a new set of features on chords for you 00:00:40.680 --> 00:00:44.060 align:middle line:84% now that you have successfully implemented some of them 00:00:44.060 --> 00:00:44.670 align:middle line:90% yourself. 00:00:44.670 --> 00:00:49.070 align:middle line:84% So I'm going to go ahead and import the chord 00:00:49.070 --> 00:00:50.700 align:middle line:90% module from music21. 00:00:50.700 --> 00:00:52.550 align:middle line:84% And we'll remember that within the chord 00:00:52.550 --> 00:00:56.040 align:middle line:84% module is the capital C Chord class. 00:00:56.040 --> 00:01:01.980 align:middle line:84% So we'll say C major equals chord.Chord. 00:01:01.980 --> 00:01:05.570 align:middle line:90% And we'll say C4, E4, G4. 00:01:05.570 --> 00:01:08.600 align:middle line:84% By the way, when creating a chord, 00:01:08.600 --> 00:01:11.060 align:middle line:84% we can create it a couple different ways. 00:01:11.060 --> 00:01:16.080 align:middle line:84% You can put it as a list of strings. 00:01:16.080 --> 00:01:19.620 align:middle line:84% We can make it a single space separated string. 00:01:19.620 --> 00:01:23.090 align:middle line:84% Or if we really want to do this, if we 00:01:23.090 --> 00:01:25.400 align:middle line:84% want to be painful for ourselves but sometimes 00:01:25.400 --> 00:01:28.580 align:middle line:84% that's how we'll do it, we'll create 00:01:28.580 --> 00:01:38.960 align:middle line:84% c4 equals pitch.Pitch C4, e4 is pitch.Pitch, E4. 00:01:38.960 --> 00:01:41.730 align:middle line:84% The next one, g4 is pitch.Pitch G4. 00:01:41.730 --> 00:01:44.133 align:middle line:84% And then we can make C major equals. 00:01:44.133 --> 00:01:47.090 align:middle line:90% 00:01:47.090 --> 00:01:51.390 align:middle line:84% A list of those already created pitch objects. 00:01:51.390 --> 00:01:54.770 align:middle line:84% And depending on what context you're doing, one of these 00:01:54.770 --> 00:01:57.140 align:middle line:90% will be easier than others. 00:01:57.140 --> 00:01:59.540 align:middle line:84% We could also do it with a list of note objects, 00:01:59.540 --> 00:02:01.290 align:middle line:84% but I'm not going to demonstrate that now. 00:02:01.290 --> 00:02:05.030 align:middle line:84% In any case, we have C major and we have this chord going on 00:02:05.030 --> 00:02:06.780 align:middle line:90% and that's all nice and fun. 00:02:06.780 --> 00:02:07.430 align:middle line:90% OK. 00:02:07.430 --> 00:02:09.090 align:middle line:90% I'm going to do that. 00:02:09.090 --> 00:02:13.490 align:middle line:84% So within this chord, one of the things we can do 00:02:13.490 --> 00:02:15.950 align:middle line:90% is we can get the root of it. 00:02:15.950 --> 00:02:18.230 align:middle line:84% And takes a little bit of time, so I've 00:02:18.230 --> 00:02:19.790 align:middle line:90% made it a function call-- 00:02:19.790 --> 00:02:21.860 align:middle line:90% a method call on that. 00:02:21.860 --> 00:02:23.360 align:middle line:90% So that seems to work. 00:02:23.360 --> 00:02:25.890 align:middle line:90% Get the base of the same chord. 00:02:25.890 --> 00:02:30.650 align:middle line:84% And that's the same thing here because the inversion is-- 00:02:30.650 --> 00:02:31.200 align:middle line:90% oops. 00:02:31.200 --> 00:02:32.910 align:middle line:90% The inversion is zero. 00:02:32.910 --> 00:02:33.410 align:middle line:90% Great. 00:02:33.410 --> 00:02:40.290 align:middle line:84% Now let's do C major 6, not in the chord symbol sense, 00:02:40.290 --> 00:02:44.040 align:middle line:84% but in the Roman numeral figured base 6 as a first inversion. 00:02:44.040 --> 00:02:46.080 align:middle line:90% We'll create chord.Chord. 00:02:46.080 --> 00:02:49.380 align:middle line:84% Think through it before you copy down what I'm going to write. 00:02:49.380 --> 00:02:49.970 align:middle line:90% Great. 00:02:49.970 --> 00:02:52.140 align:middle line:90% E4, C5. 00:02:52.140 --> 00:02:54.530 align:middle line:84% Oh, let's go ahead and put an open position. 00:02:54.530 --> 00:02:58.640 align:middle line:90% C major 6 root. 00:02:58.640 --> 00:03:01.430 align:middle line:90% It's still C bass. 00:03:01.430 --> 00:03:04.920 align:middle line:84% It's still an E, but now-- oh, is now an E, 00:03:04.920 --> 00:03:08.380 align:middle line:90% because the inversion is 1. 00:03:08.380 --> 00:03:08.880 align:middle line:90% Great. 00:03:08.880 --> 00:03:18.330 align:middle line:84% We can set the inversion here and see 00:03:18.330 --> 00:03:23.520 align:middle line:84% that everything has moved up above the G 00:03:23.520 --> 00:03:26.340 align:middle line:90% and moved all the way up. 00:03:26.340 --> 00:03:32.730 align:middle line:84% It's pretty far up there, so maybe we'll do 6.transpose 00:03:32.730 --> 00:03:34.090 align:middle line:90% inPlace. 00:03:34.090 --> 00:03:34.590 align:middle line:90% Oops. 00:03:34.590 --> 00:03:37.260 align:middle line:90% Transpose down. 00:03:37.260 --> 00:03:38.940 align:middle line:90% Let's say down two octaves. 00:03:38.940 --> 00:03:42.780 align:middle line:84% InPlace equals true, and now we're here. 00:03:42.780 --> 00:03:46.117 align:middle line:84% And I'm just realizing that this inversion 00:03:46.117 --> 00:03:48.700 align:middle line:84% thing should have returned a new chord or something like that. 00:03:48.700 --> 00:03:55.800 align:middle line:84% So I'll put in TODO msc, make inversion not return-- 00:03:55.800 --> 00:03:59.880 align:middle line:90% not inPlace. 00:03:59.880 --> 00:04:03.090 align:middle line:84% And just in case you're watching this video later 00:04:03.090 --> 00:04:05.160 align:middle line:84% and your inversion does something else, 00:04:05.160 --> 00:04:06.656 align:middle line:90% I fixed that problem. 00:04:06.656 --> 00:04:07.156 align:middle line:90% OK. 00:04:07.156 --> 00:04:10.380 align:middle line:84% So these are some of the things that we can do here. 00:04:10.380 --> 00:04:14.280 align:middle line:84% Notice, let's go back to create our original first inversion 00:04:14.280 --> 00:04:15.570 align:middle line:90% chord. 00:04:15.570 --> 00:04:16.140 align:middle line:90% Great. 00:04:16.140 --> 00:04:20.320 align:middle line:84% And some of the other things we can do. 00:04:20.320 --> 00:04:22.360 align:middle line:84% Those notes are pretty far apart. 00:04:22.360 --> 00:04:31.830 align:middle line:84% So we can say cmaj6closed equals C major 6 in closedPosition. 00:04:31.830 --> 00:04:35.970 align:middle line:90% 00:04:35.970 --> 00:04:40.560 align:middle line:84% And now we see C major 6 in closedPosition. 00:04:40.560 --> 00:04:45.420 align:middle line:84% Still keeps that E in the bass but figured out 00:04:45.420 --> 00:04:49.950 align:middle line:84% that, hey, that G could move all the way down to octave 4. 00:04:49.950 --> 00:04:56.190 align:middle line:84% Because C4 would be below E4, C5 only gets left there. 00:04:56.190 --> 00:04:57.900 align:middle line:84% So these are some of the things that we 00:04:57.900 --> 00:05:00.870 align:middle line:84% can be doing with the kinds of things 00:05:00.870 --> 00:05:07.320 align:middle line:84% that we're doing with chords in our most recent problem set. 00:05:07.320 --> 00:05:12.720 align:middle line:84% Here's a little interesting thing with roots 00:05:12.720 --> 00:05:14.950 align:middle line:84% that I'd hoped to get to in class, 00:05:14.950 --> 00:05:16.240 align:middle line:90% but now we can talk about. 00:05:16.240 --> 00:05:19.565 align:middle line:84% It's one of these strange moments in music. 00:05:19.565 --> 00:05:24.210 align:middle line:90% 00:05:24.210 --> 00:05:27.270 align:middle line:84% So one of the things that came up in our discussion 00:05:27.270 --> 00:05:30.040 align:middle line:84% was, of course, finding the root. 00:05:30.040 --> 00:05:33.900 align:middle line:84% And when you were working on finding the root on something 00:05:33.900 --> 00:05:39.190 align:middle line:84% like a C major triad, OK, that's pretty easy. 00:05:39.190 --> 00:05:42.120 align:middle line:84% Then you end up with a little bit 00:05:42.120 --> 00:05:46.030 align:middle line:84% harder is C major triad in open position. 00:05:46.030 --> 00:05:50.730 align:middle line:84% And maybe even harder is let's do it in open position 00:05:50.730 --> 00:05:52.000 align:middle line:90% and in inversion. 00:05:52.000 --> 00:05:56.230 align:middle line:84% In all of these, of course, the root is going to be C. 00:05:56.230 --> 00:05:58.980 align:middle line:90% But how did we do this? 00:05:58.980 --> 00:06:03.270 align:middle line:84% I haven't had a chance to go through everybody's assignments 00:06:03.270 --> 00:06:06.240 align:middle line:84% yet, but there's different possibilities, some of which 00:06:06.240 --> 00:06:08.920 align:middle line:84% are more efficient, some of which are less efficient. 00:06:08.920 --> 00:06:12.460 align:middle line:84% But basically, whichever route you chose, 00:06:12.460 --> 00:06:15.960 align:middle line:84% it ends up usually trying to find some way 00:06:15.960 --> 00:06:19.540 align:middle line:90% to permute each of the nodes. 00:06:19.540 --> 00:06:22.720 align:middle line:84% So maybe we rewrite them all to be in the same octave, 00:06:22.720 --> 00:06:24.880 align:middle line:90% so tune, tune, tune. 00:06:24.880 --> 00:06:28.180 align:middle line:84% And then we try various permutations. 00:06:28.180 --> 00:06:29.650 align:middle line:90% Maybe we rotate below. 00:06:29.650 --> 00:06:33.640 align:middle line:84% So we take the top note and move it down. 00:06:33.640 --> 00:06:36.280 align:middle line:90% So down to here. 00:06:36.280 --> 00:06:40.000 align:middle line:90% And we have a template in mind. 00:06:40.000 --> 00:06:45.750 align:middle line:84% And that template says that when you have stacked thirds, 00:06:45.750 --> 00:06:48.340 align:middle line:84% then the lowest note is the root. 00:06:48.340 --> 00:06:50.500 align:middle line:84% So here we don't have stacked thirds. 00:06:50.500 --> 00:06:51.280 align:middle line:90% What do we have? 00:06:51.280 --> 00:06:54.360 align:middle line:84% We have fourths and then a third above it. 00:06:54.360 --> 00:06:58.780 align:middle line:84% We would say 6/4 in figured bass, but think of it this way. 00:06:58.780 --> 00:07:00.370 align:middle line:90% And here, we don't have it. 00:07:00.370 --> 00:07:02.290 align:middle line:84% We have a third and a fourth above it. 00:07:02.290 --> 00:07:03.900 align:middle line:90% We call that 6/3 position. 00:07:03.900 --> 00:07:06.670 align:middle line:84% And we don't have it, so we go one more time. 00:07:06.670 --> 00:07:16.180 align:middle line:84% And here, we have this, which we know is 3/3 or 5/3. 00:07:16.180 --> 00:07:19.000 align:middle line:84% And this is our perfect solution. 00:07:19.000 --> 00:07:20.860 align:middle line:90% And yay, we're super happy. 00:07:20.860 --> 00:07:23.880 align:middle line:84% And the cool thing is that this kind of work 00:07:23.880 --> 00:07:28.480 align:middle line:84% works just as well with seventh chords. 00:07:28.480 --> 00:07:32.370 align:middle line:90% So let's say we're doing-- 00:07:32.370 --> 00:07:34.390 align:middle line:84% here, we're going to use some of the same notes, 00:07:34.390 --> 00:07:39.870 align:middle line:84% but will it be a dominant seventh type 00:07:39.870 --> 00:07:43.000 align:middle line:84% position in F major, something like that. 00:07:43.000 --> 00:07:46.385 align:middle line:84% And we can again start moving things into the same octave. 00:07:46.385 --> 00:07:48.960 align:middle line:90% 00:07:48.960 --> 00:07:52.290 align:middle line:84% I always make little noises when I make chords. 00:07:52.290 --> 00:07:55.660 align:middle line:90% And we can see, nope. 00:07:55.660 --> 00:07:57.040 align:middle line:90% What do we have here? 00:07:57.040 --> 00:08:00.580 align:middle line:84% We have third, third, second, so that doesn't work. 00:08:00.580 --> 00:08:05.420 align:middle line:84% We'll take the top note, bring it down an octave. 00:08:05.420 --> 00:08:08.020 align:middle line:90% Oops. 00:08:08.020 --> 00:08:13.510 align:middle line:84% Just anal enough that I want all my notes to be in blue today. 00:08:13.510 --> 00:08:15.680 align:middle line:84% So we can do something like this. 00:08:15.680 --> 00:08:17.960 align:middle line:90% And voila, we have-- 00:08:17.960 --> 00:08:18.920 align:middle line:90% what do we have? 00:08:18.920 --> 00:08:21.200 align:middle line:90% Third, third, third. 00:08:21.200 --> 00:08:22.790 align:middle line:90% And we're all happy. 00:08:22.790 --> 00:08:26.320 align:middle line:90% And so the root is C again. 00:08:26.320 --> 00:08:33.320 align:middle line:84% But what happens if we have a ninth? 00:08:33.320 --> 00:08:36.950 align:middle line:84% Well, I won't make it a ninth chord. 00:08:36.950 --> 00:08:42.260 align:middle line:84% You can, again, put it into this particular position. 00:08:42.260 --> 00:08:48.700 align:middle line:84% And voila, we have C9, whatever inversion it's in, and so on. 00:08:48.700 --> 00:08:50.860 align:middle line:84% But let's take a second and listen 00:08:50.860 --> 00:08:54.670 align:middle line:84% to a piece of music that's going to challenge some 00:08:54.670 --> 00:08:57.800 align:middle line:84% of our assumptions about what does a root mean, 00:08:57.800 --> 00:09:01.340 align:middle line:84% maybe go beyond what we've seen in our theory classes, 00:09:01.340 --> 00:09:03.910 align:middle line:84% but the type of things we have to consider 00:09:03.910 --> 00:09:08.205 align:middle line:84% as computational music analysts, whatever we are. 00:09:08.205 --> 00:09:11.110 align:middle line:90% 00:09:11.110 --> 00:09:14.990 align:middle line:84% The piece we're going to discuss is by Benjamin Britten. 00:09:14.990 --> 00:09:18.500 align:middle line:84% It's his opera "Peter Grimes" from 1945. 00:09:18.500 --> 00:09:21.610 align:middle line:84% And we're going to be looking at one 00:09:21.610 --> 00:09:25.510 align:middle line:84% of the last scenes of the opera where the main character, Peter 00:09:25.510 --> 00:09:29.420 align:middle line:84% Grimes, has become deranged and lost his mind, 00:09:29.420 --> 00:09:32.440 align:middle line:84% and believes the accusations that 00:09:32.440 --> 00:09:35.530 align:middle line:84% have been made against him, that he has been killing 00:09:35.530 --> 00:09:39.940 align:middle line:84% his assistants, when, really, the most recent one has just 00:09:39.940 --> 00:09:41.840 align:middle line:90% died in a tragic mishap. 00:09:41.840 --> 00:09:45.040 align:middle line:84% And the music that we're going to be listening to, 00:09:45.040 --> 00:09:46.250 align:middle line:90% there's no singing. 00:09:46.250 --> 00:09:48.820 align:middle line:84% It's the music that accompanies him going out 00:09:48.820 --> 00:09:50.360 align:middle line:90% to sea to drown himself. 00:09:50.360 --> 00:09:52.190 align:middle line:90% So it's a very somber moment. 00:09:52.190 --> 00:09:54.950 align:middle line:84% I want you to listen particularly, though, 00:09:54.950 --> 00:09:58.470 align:middle line:84% to the arpeggiated chord played by the harp. 00:09:58.470 --> 00:10:04.970 align:middle line:90% 00:10:04.970 --> 00:10:07.470 align:middle line:84% [BENJAMIN BRITTEN, "PETER GRIMES"] 00:10:07.470 --> 00:11:12.970 align:middle line:90% 00:11:12.970 --> 00:11:17.150 align:middle line:84% Let's look at that chord from the harp in detail. 00:11:17.150 --> 00:11:23.350 align:middle line:84% It starts in the bass clef with F, A, C, 00:11:23.350 --> 00:11:30.100 align:middle line:84% continuing up E, G, B, D, and then coming back down. 00:11:30.100 --> 00:11:33.950 align:middle line:84% And when we put it into treble clef and stack everything up, 00:11:33.950 --> 00:11:37.720 align:middle line:84% we see that F, A, C, E, G, et cetera, 00:11:37.720 --> 00:11:41.170 align:middle line:84% we basically have a whole bunch of stacked thirds 00:11:41.170 --> 00:11:42.410 align:middle line:90% going all the way up. 00:11:42.410 --> 00:11:45.020 align:middle line:90% And so that's an F13 chord. 00:11:45.020 --> 00:11:48.050 align:middle line:84% So we know the root because we see all of the stacked thirds. 00:11:48.050 --> 00:11:50.510 align:middle line:84% But now let's take the root and we'll move it to the top. 00:11:50.510 --> 00:11:55.960 align:middle line:84% So we'll start on A, C, E, G, B, D, F. And hey, 00:11:55.960 --> 00:11:57.830 align:middle line:90% that's also a stacked third. 00:11:57.830 --> 00:12:02.830 align:middle line:84% So our original chord could be an A13 chord in first inversion. 00:12:02.830 --> 00:12:05.090 align:middle line:84% I don't know what the figured bass symbol is for that. 00:12:05.090 --> 00:12:08.270 align:middle line:84% But then we can also take the A and put it to the top 00:12:08.270 --> 00:12:12.620 align:middle line:84% and see that, hey, C, E, G, B, D, F, A, that's 00:12:12.620 --> 00:12:14.100 align:middle line:90% also a stack of thirds. 00:12:14.100 --> 00:12:18.320 align:middle line:84% So this is a C13 chord in second inversion. 00:12:18.320 --> 00:12:21.410 align:middle line:84% OK, let's see what happens in music21 when we 00:12:21.410 --> 00:12:23.280 align:middle line:90% try to do something with this. 00:12:23.280 --> 00:12:27.680 align:middle line:90% So we'll import everything. 00:12:27.680 --> 00:12:30.450 align:middle line:84% First we just need chord in this case. 00:12:30.450 --> 00:12:35.030 align:middle line:90% And let's create an F11 chord. 00:12:35.030 --> 00:12:42.580 align:middle line:84% And so we'll do it the same way as we're doing with the "Peter 00:12:42.580 --> 00:12:43.080 align:middle line:90% Grimes." 00:12:43.080 --> 00:12:50.660 align:middle line:90% So F3, A3, C4, E4, G4, B-flat 4. 00:12:50.660 --> 00:12:54.240 align:middle line:84% We're leaving out that high D for now. 00:12:54.240 --> 00:12:59.010 align:middle line:84% And when we look at F11, its root is the F3. 00:12:59.010 --> 00:13:01.950 align:middle line:84% Its inversion is in root position. 00:13:01.950 --> 00:13:02.450 align:middle line:90% Great. 00:13:02.450 --> 00:13:07.800 align:middle line:84% Let's take that B-flat 4 down to the lowest part. 00:13:07.800 --> 00:13:10.820 align:middle line:90% I'll put it in B-flat 2. 00:13:10.820 --> 00:13:13.400 align:middle line:90% Now something like that. 00:13:13.400 --> 00:13:17.600 align:middle line:84% And when we find the root of this, it's still in F, 00:13:17.600 --> 00:13:21.720 align:middle line:84% and it's in the inversion where the 11th is in the base, 00:13:21.720 --> 00:13:23.520 align:middle line:90% which we all learned in-- 00:13:23.520 --> 00:13:24.410 align:middle line:90% no, it didn't. 00:13:24.410 --> 00:13:26.210 align:middle line:90% Is fifth. 00:13:26.210 --> 00:13:28.580 align:middle line:90% Oops. 00:13:28.580 --> 00:13:30.515 align:middle line:90% Is fifth inversion here. 00:13:30.515 --> 00:13:31.015 align:middle line:90% OK. 00:13:31.015 --> 00:13:32.640 align:middle line:84% So that's going along pretty well. 00:13:32.640 --> 00:13:37.040 align:middle line:84% Now let's create the F13 chord in inversion. 00:13:37.040 --> 00:13:44.640 align:middle line:84% And we'll put same, that B-flat 2, F3, A3, C4, E4, G4, 00:13:44.640 --> 00:13:48.150 align:middle line:84% and we'll add that D5 at the top. 00:13:48.150 --> 00:13:54.260 align:middle line:84% And what used to happen when you called root in this point is it 00:13:54.260 --> 00:13:57.720 align:middle line:84% would crash until you couldn't find the root of this chord. 00:13:57.720 --> 00:14:01.500 align:middle line:84% Eventually, I found that to be kind of annoying, 00:14:01.500 --> 00:14:05.090 align:middle line:84% that you had to code around a special case that you could have 00:14:05.090 --> 00:14:08.580 align:middle line:84% a 13th chord or something would crash. 00:14:08.580 --> 00:14:15.890 align:middle line:84% So I've just decided that the root of a 13th chord is always 00:14:15.890 --> 00:14:18.330 align:middle line:90% whatever note is in the bass. 00:14:18.330 --> 00:14:27.480 align:middle line:84% So in this case, now I put the F in the bass. 00:14:27.480 --> 00:14:28.740 align:middle line:90% Now that's the root. 00:14:28.740 --> 00:14:34.260 align:middle line:84% And the inversion is always in root position, 00:14:34.260 --> 00:14:36.986 align:middle line:90% which is kind of-- 00:14:36.986 --> 00:14:40.280 align:middle line:84% that's also maybe a problematic thing 00:14:40.280 --> 00:14:43.140 align:middle line:84% that you can take the same notes, 00:14:43.140 --> 00:14:45.330 align:middle line:84% rearrange them and put them in a different place, 00:14:45.330 --> 00:14:48.930 align:middle line:84% and the inversion stays the same, but the root changes. 00:14:48.930 --> 00:14:52.790 align:middle line:84% So that's just a little thing on how 13th chords are a little bit 00:14:52.790 --> 00:14:54.780 align:middle line:84% different than every other chord, 00:14:54.780 --> 00:14:59.630 align:middle line:84% and why computational musicology and computational music theory 00:14:59.630 --> 00:15:00.720 align:middle line:90% is so much fun. 00:15:00.720 --> 00:15:03.290 align:middle line:90% Thanks, everybody. 00:15:03.290 --> 00:15:09.000 align:middle line:90%