WEBVTT 00:00:00.000 --> 00:00:01.491 align:middle line:90% [RUSTLING] 00:00:01.491 --> 00:00:02.485 align:middle line:90% [CLICKING] 00:00:02.485 --> 00:00:03.976 align:middle line:90% [SQUEAKING] 00:00:03.976 --> 00:00:06.958 align:middle line:90% [CLICKING] 00:00:06.958 --> 00:00:27.802 align:middle line:90% 00:00:27.802 --> 00:00:29.760 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Hello, everybody. 00:00:29.760 --> 00:00:32.540 align:middle line:84% We're going to be talking today about something 00:00:32.540 --> 00:00:35.330 align:middle line:84% that sounds really esoteric, really confusing, 00:00:35.330 --> 00:00:38.230 align:middle line:90% vocabulary reduction. 00:00:38.230 --> 00:00:40.440 align:middle line:84% How do we go to vocabulary reduction? 00:00:40.440 --> 00:00:42.450 align:middle line:90% How do we reduce our vocabulary? 00:00:42.450 --> 00:00:45.785 align:middle line:84% Are we talking about see Spot run? 00:00:45.785 --> 00:00:46.950 align:middle line:90% What does this mean? 00:00:46.950 --> 00:00:49.940 align:middle line:84% It really is about something that we 00:00:49.940 --> 00:00:52.910 align:middle line:84% do every time we do analysis whether we 00:00:52.910 --> 00:00:55.100 align:middle line:84% do music analysis or textual analysis 00:00:55.100 --> 00:00:58.670 align:middle line:84% or we're trying to think about what really happened 00:00:58.670 --> 00:01:02.922 align:middle line:84% on that last phone conversation I had with my partner, friend, 00:01:02.922 --> 00:01:03.880 align:middle line:90% or something like that. 00:01:03.880 --> 00:01:06.840 align:middle line:84% We're trying to reduce the number of complexities 00:01:06.840 --> 00:01:10.960 align:middle line:84% down to something smaller and more manageable. 00:01:10.960 --> 00:01:14.910 align:middle line:84% And one of the places where we do vocabulary reduction quite 00:01:14.910 --> 00:01:18.040 align:middle line:84% a bit is in Roman numeral analysis. 00:01:18.040 --> 00:01:21.160 align:middle line:84% We don't label everything a Roman numeral. 00:01:21.160 --> 00:01:23.700 align:middle line:84% We tend to label the things depending 00:01:23.700 --> 00:01:24.880 align:middle line:90% on who your teacher was. 00:01:24.880 --> 00:01:27.000 align:middle line:84% Maybe she or he said we only label 00:01:27.000 --> 00:01:29.460 align:middle line:90% things that are really chords. 00:01:29.460 --> 00:01:32.100 align:middle line:90% What does that mean? 00:01:32.100 --> 00:01:35.470 align:middle line:84% When we're thinking about how we do this as humans, 00:01:35.470 --> 00:01:38.170 align:middle line:84% we don't really have to think too much about how we do this. 00:01:38.170 --> 00:01:40.570 align:middle line:84% We just have to get better at doing this. 00:01:40.570 --> 00:01:42.870 align:middle line:84% But if we're going to train a computer 00:01:42.870 --> 00:01:48.240 align:middle line:84% system to be able to tell us only the things that are really 00:01:48.240 --> 00:01:51.780 align:middle line:84% there to reduce the vocabulary of a score 00:01:51.780 --> 00:01:54.930 align:middle line:84% into something more manageable, then we're 00:01:54.930 --> 00:01:57.520 align:middle line:84% going to have to understand this process quite a bit better. 00:01:57.520 --> 00:01:59.380 align:middle line:84% So that's what we're going to do today. 00:01:59.380 --> 00:02:02.470 align:middle line:84% I'm going to move over to the Jupyter Notebook, 00:02:02.470 --> 00:02:07.140 align:middle line:84% and today I didn't have time to make every single thing 00:02:07.140 --> 00:02:10.300 align:middle line:90% a little bit really polished. 00:02:10.300 --> 00:02:14.860 align:middle line:84% So you'll get a sense of how I program, 00:02:14.860 --> 00:02:19.290 align:middle line:84% how I make up assignments for us, and how some of the wrong 00:02:19.290 --> 00:02:21.240 align:middle line:84% turns that happened along the way. 00:02:21.240 --> 00:02:22.510 align:middle line:90% Maybe it'll be useful. 00:02:22.510 --> 00:02:25.770 align:middle line:90% So let's go over to Jupyter. 00:02:25.770 --> 00:02:27.990 align:middle line:84% We're going to start by importing 00:02:27.990 --> 00:02:32.100 align:middle line:84% from music21 the corpus method, and let's 00:02:32.100 --> 00:02:36.120 align:middle line:84% load up a piece by Clara Schumann, her Piano Trio, 00:02:36.120 --> 00:02:38.800 align:middle line:84% slow movement, one of my favorite pieces. 00:02:38.800 --> 00:02:41.977 align:middle line:84% And we've looked at this once in class before, 00:02:41.977 --> 00:02:43.810 align:middle line:84% and it's going to take a little bit of time. 00:02:43.810 --> 00:02:45.310 align:middle line:84% It's a little bit of a slower thing. 00:02:45.310 --> 00:02:46.670 align:middle line:90% You might need to wait here. 00:02:46.670 --> 00:02:50.190 align:middle line:90% 00:02:50.190 --> 00:02:53.400 align:middle line:84% It's a piano trio, but it begins with just the piano 00:02:53.400 --> 00:02:56.260 align:middle line:90% parts, really lovely section. 00:02:56.260 --> 00:02:59.135 align:middle line:84% Let me find a YouTube video and place that in here. 00:02:59.135 --> 00:03:02.248 align:middle line:90% [MUSIC PLAYING] 00:03:02.248 --> 00:03:03.160 align:middle line:90% 00:03:03.160 --> 00:03:07.390 align:middle line:84% And you can click on that or just Google it, 00:03:07.390 --> 00:03:08.270 align:middle line:90% find it in there. 00:03:08.270 --> 00:03:12.460 align:middle line:84% Anyhow, the next eight measures we looked at once in class, 00:03:12.460 --> 00:03:15.340 align:middle line:84% and we can see it's when the violin and the cello 00:03:15.340 --> 00:03:18.205 align:middle line:84% enter and the piano switches to something else. 00:03:18.205 --> 00:03:19.580 align:middle line:84% The violins play the same melody, 00:03:19.580 --> 00:03:24.490 align:middle line:84% and we looked at it because of those grace notes, which 00:03:24.490 --> 00:03:25.940 align:middle line:90% if we can highlight that there. 00:03:25.940 --> 00:03:30.280 align:middle line:90% There we go, and they-- 00:03:30.280 --> 00:03:33.700 align:middle line:84% yeah, they were a problem for some of our representations 00:03:33.700 --> 00:03:35.110 align:middle line:90% of encodings. 00:03:35.110 --> 00:03:39.200 align:middle line:84% So let's just extract the piano part from here, 00:03:39.200 --> 00:03:41.260 align:middle line:84% and you can see some of the mistakes 00:03:41.260 --> 00:03:45.040 align:middle line:84% that I've made with my own music21 package 00:03:45.040 --> 00:03:46.370 align:middle line:90% that this happens. 00:03:46.370 --> 00:03:49.390 align:middle line:84% I'm like, oh, I want to extract two parts. 00:03:49.390 --> 00:03:52.190 align:middle line:84% Well, first off that should be two to four anyhow. 00:03:52.190 --> 00:03:55.280 align:middle line:84% But in any case, it's given me a list of things. 00:03:55.280 --> 00:03:56.630 align:middle line:90% So I've made two mistakes. 00:03:56.630 --> 00:03:58.340 align:middle line:90% That's not giving me a stream. 00:03:58.340 --> 00:03:59.590 align:middle line:90% It's giving me a list. 00:03:59.590 --> 00:04:01.250 align:middle line:90% I'm going to-- 00:04:01.250 --> 00:04:03.390 align:middle line:90% Now I'm going to do this again. 00:04:03.390 --> 00:04:04.830 align:middle line:84% We're going to import the stream. 00:04:04.830 --> 00:04:09.890 align:middle line:84% We're going to-- to create a new score, not 00:04:09.890 --> 00:04:13.740 align:middle line:90% part, for putting things in. 00:04:13.740 --> 00:04:15.990 align:middle line:90% And we're going to put in-- 00:04:15.990 --> 00:04:19.100 align:middle line:84% gosh, I cannot type piano after all these years-- 00:04:19.100 --> 00:04:23.333 align:middle line:84% we're going to put in part two, which is the piano right hand, 00:04:23.333 --> 00:04:25.250 align:middle line:84% and we're going to also put in part one, which 00:04:25.250 --> 00:04:28.520 align:middle line:90% is the piano left hand. 00:04:28.520 --> 00:04:33.270 align:middle line:84% And in order to make this run faster, 00:04:33.270 --> 00:04:35.610 align:middle line:84% we'll just take the first 16 measures. 00:04:35.610 --> 00:04:38.018 align:middle line:84% I put measure 0 just out of habit in case 00:04:38.018 --> 00:04:39.060 align:middle line:90% there's a pickup measure. 00:04:39.060 --> 00:04:40.760 align:middle line:84% There isn't in this case, so I could 00:04:40.760 --> 00:04:43.550 align:middle line:90% have really started with one. 00:04:43.550 --> 00:04:46.580 align:middle line:84% So now we're going to look at just that little excerpt, just 00:04:46.580 --> 00:04:49.560 align:middle line:84% the piano part, all that to get rid of some empty rests. 00:04:49.560 --> 00:04:54.000 align:middle line:90% But that's OK here. 00:04:54.000 --> 00:04:59.730 align:middle line:84% So we're going to play with just creating the chords of this, 00:04:59.730 --> 00:05:02.160 align:middle line:84% and we'll remember the chordify function, which 00:05:02.160 --> 00:05:05.860 align:middle line:84% is a fun part of music21, and we'll show it. 00:05:05.860 --> 00:05:08.590 align:middle line:84% And because we're taking a treble clef and a bass clef 00:05:08.590 --> 00:05:11.850 align:middle line:84% put together an instrument, this is always a little bit wacky. 00:05:11.850 --> 00:05:16.830 align:middle line:84% You get used to counting obscene numbers of ledger lines 00:05:16.830 --> 00:05:19.600 align:middle line:84% when you are playing with chordify 00:05:19.600 --> 00:05:23.940 align:middle line:84% And there were times in my life when I could actually 00:05:23.940 --> 00:05:27.160 align:middle line:84% eyeball that first note and say, yep, that's G. I got it. 00:05:27.160 --> 00:05:29.320 align:middle line:90% But those times have passed. 00:05:29.320 --> 00:05:31.150 align:middle line:84% So instead we're going to recurse, 00:05:31.150 --> 00:05:37.000 align:middle line:84% go through every single element in every measure and everything, 00:05:37.000 --> 00:05:39.910 align:middle line:84% and get all the chords from that. 00:05:39.910 --> 00:05:41.088 align:middle line:90% C chords is now a part. 00:05:41.088 --> 00:05:43.380 align:middle line:84% And we're going to take every one of those chords which 00:05:43.380 --> 00:05:45.690 align:middle line:84% we call C and put it into closed position 00:05:45.690 --> 00:05:48.120 align:middle line:84% and say that it's going to be an octave four. 00:05:48.120 --> 00:05:51.640 align:middle line:84% And in place equals true, we're going to replace the old chord, 00:05:51.640 --> 00:05:55.660 align:middle line:84% and now we're going to show that the-- are the same thing. 00:05:55.660 --> 00:05:58.800 align:middle line:84% And now things look quite a bit better. 00:05:58.800 --> 00:06:00.840 align:middle line:90% So, yep, there's a-- 00:06:00.840 --> 00:06:05.710 align:middle line:84% think we compare back up if we look at same page. 00:06:05.710 --> 00:06:07.650 align:middle line:90% Yeah, a little bit. 00:06:07.650 --> 00:06:09.760 align:middle line:90% Yep, that's a D down there. 00:06:09.760 --> 00:06:13.060 align:middle line:90% That's a G. So it worked. 00:06:13.060 --> 00:06:15.190 align:middle line:90% Worked pretty well. 00:06:15.190 --> 00:06:19.780 align:middle line:84% We'll zoom back in again so that we can see-- 00:06:19.780 --> 00:06:21.960 align:middle line:90% great. 00:06:21.960 --> 00:06:23.880 align:middle line:84% Now what we're going to do is we want 00:06:23.880 --> 00:06:28.600 align:middle line:84% to label everything that's happening in this. 00:06:28.600 --> 00:06:30.640 align:middle line:84% So first we're going to analyze the key. 00:06:30.640 --> 00:06:31.510 align:middle line:90% What key are we In. 00:06:31.510 --> 00:06:32.500 align:middle line:90% We're in G major. 00:06:32.500 --> 00:06:33.270 align:middle line:90% Yep. 00:06:33.270 --> 00:06:37.090 align:middle line:84% You'll see that this is called The Piano Trio in G Minor. 00:06:37.090 --> 00:06:39.820 align:middle line:90% But this movement is in G major. 00:06:39.820 --> 00:06:40.530 align:middle line:90% Great. 00:06:40.530 --> 00:06:45.280 align:middle line:84% So we're going to iterate over every one of these chords again, 00:06:45.280 --> 00:06:46.860 align:middle line:84% and we're going to create a Roman 00:06:46.860 --> 00:06:49.420 align:middle line:90% numeral for each of the chords. 00:06:49.420 --> 00:06:54.990 align:middle line:84% Actually we're going to import the Roman package from-- 00:06:54.990 --> 00:06:58.470 align:middle line:84% Roman module from music21, and there's this cool thing 00:06:58.470 --> 00:07:02.530 align:middle line:84% that you wish you had in your last time you were programming 00:07:02.530 --> 00:07:05.240 align:middle line:84% your last problem set, Roman numeral from chord. 00:07:05.240 --> 00:07:08.740 align:middle line:84% So we're going to take the chord and say that we want the Roman 00:07:08.740 --> 00:07:09.830 align:middle line:90% numeral in G. 00:07:09.830 --> 00:07:12.760 align:middle line:84% We're actually going to create an object called 00:07:12.760 --> 00:07:17.320 align:middle line:84% G underscore major, which is a variable which is the key of G 00:07:17.320 --> 00:07:19.930 align:middle line:84% object, and the reason for this is otherwise 00:07:19.930 --> 00:07:23.330 align:middle line:84% we would have to create a new key object for every chord 00:07:23.330 --> 00:07:25.430 align:middle line:90% and over time that becomes slow. 00:07:25.430 --> 00:07:28.070 align:middle line:84% So what we'll say is for our original chords, 00:07:28.070 --> 00:07:30.310 align:middle line:84% we'll give them the lyrics which are 00:07:30.310 --> 00:07:32.450 align:middle line:84% equal to the figure of the Roman numeral. 00:07:32.450 --> 00:07:34.780 align:middle line:84% So whatever the Roman numeral is, 00:07:34.780 --> 00:07:36.373 align:middle line:90% we'll assign that to the lyric. 00:07:36.373 --> 00:07:38.540 align:middle line:84% You can see it's not the fastest thing in the world, 00:07:38.540 --> 00:07:40.845 align:middle line:84% but now you can have it and we can look in. 00:07:40.845 --> 00:07:43.570 align:middle line:90% 00:07:43.570 --> 00:07:46.240 align:middle line:84% We can look at those odd chords in a little bit. 00:07:46.240 --> 00:07:47.740 align:middle line:84% You can go ahead and pause the video 00:07:47.740 --> 00:07:49.970 align:middle line:84% if you want to look at them in more detail. 00:07:49.970 --> 00:07:52.390 align:middle line:90% Have a nice laugh. 00:07:52.390 --> 00:07:56.638 align:middle line:84% But I'm just going to just get a quick excerpt, the first four 00:07:56.638 --> 00:07:58.180 align:middle line:84% measures, that first line there, just 00:07:58.180 --> 00:08:02.000 align:middle line:84% so that we can compare without having to move our eyes up 00:08:02.000 --> 00:08:03.420 align:middle line:90% and down a lot. 00:08:03.420 --> 00:08:08.570 align:middle line:84% So now we'll compare this to the original piano 00:08:08.570 --> 00:08:10.850 align:middle line:84% part with the left and the right hand 00:08:10.850 --> 00:08:15.860 align:middle line:84% and just see do these chords look about right. 00:08:15.860 --> 00:08:19.340 align:middle line:84% Yep, you see, there's that weird thing that that second chord 00:08:19.340 --> 00:08:21.180 align:middle line:90% isn't really 6/4 chord. 00:08:21.180 --> 00:08:24.050 align:middle line:84% It's really that that low G is self-sustaining, 00:08:24.050 --> 00:08:28.777 align:middle line:84% and then it's at a four chord or is that 5/4/2 chord? 00:08:28.777 --> 00:08:30.860 align:middle line:84% It's going to be a little bit difficult because we 00:08:30.860 --> 00:08:33.590 align:middle line:84% want to make sure is that an appoggiatura or is that 00:08:33.590 --> 00:08:34.860 align:middle line:90% a chord tone. 00:08:34.860 --> 00:08:36.360 align:middle line:90% It's a little bit difficult. 00:08:36.360 --> 00:08:40.730 align:middle line:84% In fact, this would be the challenge problem 00:08:40.730 --> 00:08:43.669 align:middle line:84% to be able to take something where 00:08:43.669 --> 00:08:46.730 align:middle line:84% we have arpeggios, melodies, and things 00:08:46.730 --> 00:08:51.420 align:middle line:84% and do vocabulary reduction on a piano part like this. 00:08:51.420 --> 00:08:54.930 align:middle line:84% This is still one of the big unsolved problems in the field, 00:08:54.930 --> 00:08:58.040 align:middle line:84% and being able to make progress on how do we 00:08:58.040 --> 00:09:01.790 align:middle line:84% reduce the number of chords of Roman 00:09:01.790 --> 00:09:05.210 align:middle line:84% numerals and analytical things to only the, quote 00:09:05.210 --> 00:09:09.330 align:middle line:84% unquote, real chords on a complex score, 00:09:09.330 --> 00:09:11.520 align:middle line:84% on an orchestral or a piano score. 00:09:11.520 --> 00:09:15.560 align:middle line:84% Still, one thing that you could get A plus plus. 00:09:15.560 --> 00:09:18.290 align:middle line:84% You could get complete published paper out 00:09:18.290 --> 00:09:19.880 align:middle line:90% of being able to do that. 00:09:19.880 --> 00:09:22.340 align:middle line:90% For now, we're going to-- 00:09:22.340 --> 00:09:24.840 align:middle line:84% and there are some great ways to do that. 00:09:24.840 --> 00:09:28.610 align:middle line:84% We'll be looking at a dissertation by a guy 00:09:28.610 --> 00:09:30.470 align:middle line:84% by the name of Christopher William 00:09:30.470 --> 00:09:33.650 align:middle line:84% White at some point for people who are 00:09:33.650 --> 00:09:36.980 align:middle line:90% very interested in such things. 00:09:36.980 --> 00:09:40.730 align:middle line:84% We're going to be applying the concepts of vocabulary reduction 00:09:40.730 --> 00:09:46.430 align:middle line:84% to box four-part chorales because these this is music that 00:09:46.430 --> 00:09:51.300 align:middle line:84% tends to have all of the harmonies changing very often, 00:09:51.300 --> 00:09:54.590 align:middle line:84% and not having a lot of the arpeggiation and things 00:09:54.590 --> 00:09:57.260 align:middle line:90% that we were just seeing. 00:09:57.260 --> 00:09:58.760 align:middle line:84% You're going to be working in groups 00:09:58.760 --> 00:10:00.510 align:middle line:84% and I'll talk about the problem set later, 00:10:00.510 --> 00:10:03.600 align:middle line:84% but I want to say that there's two different approaches 00:10:03.600 --> 00:10:07.260 align:middle line:84% that you could be using and perhaps more 00:10:07.260 --> 00:10:10.440 align:middle line:90% to do this kind of assignment. 00:10:10.440 --> 00:10:12.240 align:middle line:84% What I'll be doing in the rest of the video 00:10:12.240 --> 00:10:15.360 align:middle line:84% is an approach where you start by labeling 00:10:15.360 --> 00:10:18.030 align:middle line:84% every vertical element, and then you 00:10:18.030 --> 00:10:22.140 align:middle line:84% start removing ones that don't seem to actually be chords. 00:10:22.140 --> 00:10:24.160 align:middle line:90% This is a great way of working. 00:10:24.160 --> 00:10:28.800 align:middle line:84% Another way of working that resembles perhaps a little bit 00:10:28.800 --> 00:10:31.530 align:middle line:84% more closely how we as humans work 00:10:31.530 --> 00:10:34.770 align:middle line:84% is to start by identifying non-harmonic tones 00:10:34.770 --> 00:10:37.990 align:middle line:84% and putting them all out in various places 00:10:37.990 --> 00:10:41.010 align:middle line:84% and then removing the vertical chords that are not 00:10:41.010 --> 00:10:49.080 align:middle line:84% real chords perhaps by also using the various Roman numeral 00:10:49.080 --> 00:10:50.400 align:middle line:90% sections. 00:10:50.400 --> 00:10:54.750 align:middle line:84% To give you a sense, I want to show a little bit one 00:10:54.750 --> 00:10:56.620 align:middle line:90% particular Bach chorale. 00:10:56.620 --> 00:10:59.800 align:middle line:84% We'll look at the opening here of a four voice piece, 00:10:59.800 --> 00:11:01.910 align:middle line:84% and you can see moments that, oh, 00:11:01.910 --> 00:11:03.410 align:middle line:90% that looks like a passing tone. 00:11:03.410 --> 00:11:06.910 align:middle line:84% That looks like it's going to be a little bit-- 00:11:06.910 --> 00:11:09.880 align:middle line:90% yeah, just on its way someplace. 00:11:09.880 --> 00:11:13.450 align:middle line:84% Here it looks like a neighbor tone. 00:11:13.450 --> 00:11:15.490 align:middle line:84% This might be a suspension to here, 00:11:15.490 --> 00:11:19.160 align:middle line:84% or this might be a truck suspension and so on. 00:11:19.160 --> 00:11:21.580 align:middle line:84% So we can do it by hand, but then 00:11:21.580 --> 00:11:23.840 align:middle line:84% how do we train the computer to do it? 00:11:23.840 --> 00:11:25.730 align:middle line:84% So that would be one type of question. 00:11:25.730 --> 00:11:27.700 align:middle line:84% And then once you've trained a computer 00:11:27.700 --> 00:11:31.510 align:middle line:84% to identify these tones, you can create a version where 00:11:31.510 --> 00:11:35.110 align:middle line:90% you remove them and chordify. 00:11:35.110 --> 00:11:37.750 align:middle line:84% After this comes an essential step 00:11:37.750 --> 00:11:42.730 align:middle line:84% of identifying where various key changes might be. 00:11:42.730 --> 00:11:45.460 align:middle line:84% So regardless of whether you start 00:11:45.460 --> 00:11:50.510 align:middle line:84% with looking at finding passing tones, neighbor tones, and so on 00:11:50.510 --> 00:11:56.170 align:middle line:84% or start by looking at every particular chord and removing, 00:11:56.170 --> 00:11:58.700 align:middle line:84% the end result ends up being the same, 00:11:58.700 --> 00:12:05.110 align:middle line:84% and your work can be judged by how well each various part had 00:12:05.110 --> 00:12:08.470 align:middle line:84% been identified through your process. 00:12:08.470 --> 00:12:13.450 align:middle line:84% I would suggest if you're working and dividing up 00:12:13.450 --> 00:12:16.520 align:middle line:84% the tasks among people in your group 00:12:16.520 --> 00:12:22.180 align:middle line:84% that you start with the removal of various individual 00:12:22.180 --> 00:12:24.160 align:middle line:90% non-harmonic tones. 00:12:24.160 --> 00:12:26.560 align:middle line:84% If on the other hand your group chooses 00:12:26.560 --> 00:12:30.760 align:middle line:84% to work where everybody is working together 00:12:30.760 --> 00:12:33.730 align:middle line:84% at each stage, then perhaps the technique 00:12:33.730 --> 00:12:35.440 align:middle line:84% I explain in the rest of the video 00:12:35.440 --> 00:12:40.230 align:middle line:84% where you label chords first will yield better results. 00:12:40.230 --> 00:12:47.260 align:middle line:90% 00:12:47.260 --> 00:12:51.100 align:middle line:84% But we can go and do something a little bit easier if we stick 00:12:51.100 --> 00:12:52.760 align:middle line:90% to chorale style compositions. 00:12:52.760 --> 00:12:57.340 align:middle line:84% So we'll go back to our favorite Bach piece, BWV 66.6, which 00:12:57.340 --> 00:13:00.130 align:middle line:84% is going to have its own problems in a little bit, 00:13:00.130 --> 00:13:01.750 align:middle line:90% but we're going to chordify it. 00:13:01.750 --> 00:13:03.750 align:middle line:84% I'm just going to cut and pasting up here 00:13:03.750 --> 00:13:07.350 align:middle line:84% and we're going to again, once we chordify everything, put it 00:13:07.350 --> 00:13:10.120 align:middle line:84% into closed position, put it into octave four, 00:13:10.120 --> 00:13:13.120 align:middle line:84% and, again, replace all the chords in place. 00:13:13.120 --> 00:13:16.570 align:middle line:84% If you haven't seen how this technique works, 00:13:16.570 --> 00:13:21.550 align:middle line:84% look at music21 user's guide, chapter nine and chapter 10. 00:13:21.550 --> 00:13:24.490 align:middle line:84% We do that a lot there, in fact, with this piece. 00:13:24.490 --> 00:13:27.210 align:middle line:84% So you'll see some new techniques 00:13:27.210 --> 00:13:31.200 align:middle line:84% and be able to do it a little bit more slowly. 00:13:31.200 --> 00:13:33.900 align:middle line:84% So this piece has the interesting characteristic 00:13:33.900 --> 00:13:37.300 align:middle line:84% that it ends in a different key than where it began. 00:13:37.300 --> 00:13:40.230 align:middle line:84% So if we look at the key of measure 0 to 2 00:13:40.230 --> 00:13:44.430 align:middle line:84% using Carol Krumhansl's probe tone key analysis 00:13:44.430 --> 00:13:47.200 align:middle line:84% method, which is built into music21, 00:13:47.200 --> 00:13:49.660 align:middle line:90% and we see that it's in A major. 00:13:49.660 --> 00:13:54.490 align:middle line:84% But then if we look at the last seven measures 4-10, 00:13:54.490 --> 00:13:57.360 align:middle line:90% we see it's an F sharp minor. 00:13:57.360 --> 00:14:01.030 align:middle line:84% So we're going to work on each of the two parts separately. 00:14:01.030 --> 00:14:06.220 align:middle line:84% So let's first look at measures 0 to 2 and get this excerpt 00:14:06.220 --> 00:14:08.580 align:middle line:90% as B chords underscore excerpt-- 00:14:08.580 --> 00:14:10.740 align:middle line:84% should probably call the excerpt one, 00:14:10.740 --> 00:14:14.530 align:middle line:84% whatever-- and we can look at those first two measures. 00:14:14.530 --> 00:14:19.800 align:middle line:84% And let's use the same technique that we used with Clara Schumann 00:14:19.800 --> 00:14:25.120 align:middle line:84% to go through each chord and get a Roman numeral from it 00:14:25.120 --> 00:14:27.370 align:middle line:84% and then put the lyrics in so we can see it. 00:14:27.370 --> 00:14:31.570 align:middle line:84% We just have to change G major to A major. 00:14:31.570 --> 00:14:33.880 align:middle line:84% Again, you can just put the string A there, 00:14:33.880 --> 00:14:37.090 align:middle line:90% but I prefer to do this. 00:14:37.090 --> 00:14:43.320 align:middle line:84% So we'll do A major and A major and change C chords 00:14:43.320 --> 00:14:48.510 align:middle line:84% to B chords, excerpt, and of course A maj is not 00:14:48.510 --> 00:14:49.870 align:middle line:90% the same as A major. 00:14:49.870 --> 00:14:52.410 align:middle line:90% So we'll go ahead and fix that. 00:14:52.410 --> 00:14:53.530 align:middle line:90% Put that in. 00:14:53.530 --> 00:14:58.510 align:middle line:84% And now we'll take this excerpt and show it. 00:14:58.510 --> 00:15:01.960 align:middle line:90% 00:15:01.960 --> 00:15:04.510 align:middle line:90% And we can see-- 00:15:04.510 --> 00:15:06.200 align:middle line:90% this is quite a bit simpler. 00:15:06.200 --> 00:15:09.400 align:middle line:90% We have the 1, 5, 6, 6. 00:15:09.400 --> 00:15:11.380 align:middle line:90% Yeah, things like that. 00:15:11.380 --> 00:15:13.000 align:middle line:84% This is actually a really good time 00:15:13.000 --> 00:15:17.038 align:middle line:84% to remember think about references because we haven't 00:15:17.038 --> 00:15:18.080 align:middle line:90% really talked about this. 00:15:18.080 --> 00:15:21.740 align:middle line:84% So this is just the excerpt of just the two measures. 00:15:21.740 --> 00:15:23.930 align:middle line:84% When we go back and look at all of the chords, 00:15:23.930 --> 00:15:30.040 align:middle line:84% one of the things you can see is that the figures do sustain back 00:15:30.040 --> 00:15:31.790 align:middle line:90% to that part. 00:15:31.790 --> 00:15:35.440 align:middle line:84% In other words, the chords in the excerpt 00:15:35.440 --> 00:15:41.320 align:middle line:84% are the exact same objects as the chords in the chord part. 00:15:41.320 --> 00:15:44.780 align:middle line:84% So what you change on one of them will change on the other. 00:15:44.780 --> 00:15:49.750 align:middle line:84% But if we go all the way back to the original Bach part 00:15:49.750 --> 00:15:55.270 align:middle line:84% and we show it, we'll see that, hey, there's no lyrics anywhere, 00:15:55.270 --> 00:15:57.400 align:middle line:84% anything because there were no chords there 00:15:57.400 --> 00:16:01.520 align:middle line:84% and we just can't get back to that. 00:16:01.520 --> 00:16:03.880 align:middle line:84% Anyhow, that was a little bit of a digression 00:16:03.880 --> 00:16:08.770 align:middle line:84% while we look at the Roman numerals here. 00:16:08.770 --> 00:16:12.130 align:middle line:84% These look like the kinds of Roman numerals I was taught. 00:16:12.130 --> 00:16:15.590 align:middle line:84% So there's not too much, too much to do there. 00:16:15.590 --> 00:16:18.800 align:middle line:84% So let's go back to the second block excerpt, 00:16:18.800 --> 00:16:22.370 align:middle line:84% the one that's in F sharp minor and measures 4-10. 00:16:22.370 --> 00:16:26.540 align:middle line:84% So we'll go ahead and get measures 4-10, 00:16:26.540 --> 00:16:32.380 align:middle line:84% and we'll call that block excerpt B chord excerpt 2 00:16:32.380 --> 00:16:34.370 align:middle line:90% and measures 4-10. 00:16:34.370 --> 00:16:36.220 align:middle line:84% When we show this part, you're going 00:16:36.220 --> 00:16:43.120 align:middle line:84% to see that there's one problem with all of our showing things, 00:16:43.120 --> 00:16:46.750 align:middle line:84% and that is to say that the measure numbers are not 00:16:46.750 --> 00:16:49.810 align:middle line:90% going to be kept but whatever. 00:16:49.810 --> 00:16:52.390 align:middle line:84% So we're going to go ahead and create a key of F sharp minor 00:16:52.390 --> 00:16:55.570 align:middle line:84% and pause this for one second in the video 00:16:55.570 --> 00:16:59.990 align:middle line:90% to see that when we make a key-- 00:16:59.990 --> 00:17:04.520 align:middle line:84% a key object really important to make a lowercase f if you want 00:17:04.520 --> 00:17:08.160 align:middle line:84% to show that something's minor, and I call it fis by the way 00:17:08.160 --> 00:17:11.390 align:middle line:84% because you can't obviously put f, number sign, pound sign 00:17:11.390 --> 00:17:13.752 align:middle line:84% to mean a sharp sign as a variable 00:17:13.752 --> 00:17:15.210 align:middle line:84% because it would just be a comment. 00:17:15.210 --> 00:17:17.569 align:middle line:90% So we sometimes use-- 00:17:17.569 --> 00:17:19.410 align:middle line:84% borrow things from other languages, 00:17:19.410 --> 00:17:23.520 align:middle line:84% and so f-i-s, fis, is the German for f sharp. 00:17:23.520 --> 00:17:26.748 align:middle line:90% So getting back here. 00:17:26.748 --> 00:17:28.790 align:middle line:84% Getting back here we're just doing the same thing 00:17:28.790 --> 00:17:32.210 align:middle line:84% that we did before, B chords x sub 2 We're getting each 00:17:32.210 --> 00:17:35.370 align:middle line:84% of the chords, change them to Roman numerals, 00:17:35.370 --> 00:17:38.100 align:middle line:84% taking that Roman numerals figure, and make it into lyrics, 00:17:38.100 --> 00:17:40.260 align:middle line:84% and now we're going to show that section. 00:17:40.260 --> 00:17:43.220 align:middle line:84% And these measure numbers are the thing 00:17:43.220 --> 00:17:45.530 align:middle line:84% I was talking about that I guess we 00:17:45.530 --> 00:17:49.200 align:middle line:84% have to add three to each one of them to get what it is. 00:17:49.200 --> 00:17:52.550 align:middle line:84% Eventually we'll be able to contribute back 00:17:52.550 --> 00:17:55.310 align:middle line:84% to open source projects like MuseScore 00:17:55.310 --> 00:17:57.510 align:middle line:84% and be able to fix this limitation. 00:17:57.510 --> 00:18:00.310 align:middle line:84% I haven't had time to do that yet. 00:18:00.310 --> 00:18:01.830 align:middle line:90% Such a great project. 00:18:01.830 --> 00:18:06.180 align:middle line:84% Anyhow so we can go look through and see that this time there's 00:18:06.180 --> 00:18:08.850 align:middle line:84% a lot more interesting chords and some things 00:18:08.850 --> 00:18:10.680 align:middle line:84% that definitely we want to reduce 00:18:10.680 --> 00:18:14.580 align:middle line:84% the vocabulary of because I don't think all of those chords 00:18:14.580 --> 00:18:15.280 align:middle line:90% actually exist. 00:18:15.280 --> 00:18:18.870 align:middle line:84% Let's just grab that last measure of the second system 00:18:18.870 --> 00:18:28.090 align:middle line:84% here, which is measure 8, and look into that over here. 00:18:28.090 --> 00:18:31.020 align:middle line:84% Yep, so there's an A sharp and then 00:18:31.020 --> 00:18:34.150 align:middle line:90% a B and a C sharp in the bass. 00:18:34.150 --> 00:18:37.000 align:middle line:84% Yep, that's definitely the right measure. 00:18:37.000 --> 00:18:40.290 align:middle line:84% And you can see that that chord, quote unquote, 00:18:40.290 --> 00:18:43.920 align:middle line:84% on the second eighth note is almost certainly not a chord. 00:18:43.920 --> 00:18:47.910 align:middle line:84% That is a leading-- a passing tone, 00:18:47.910 --> 00:18:54.850 align:middle line:84% and so that flat augmented chord on 6/6 or something, 00:18:54.850 --> 00:18:57.630 align:middle line:84% whatever that was, that's something we want to reduce 00:18:57.630 --> 00:18:59.405 align:middle line:90% in the vocabulary. 00:18:59.405 --> 00:19:01.530 align:middle line:90% So how can we do this? 00:19:01.530 --> 00:19:05.080 align:middle line:84% I'm going to give you one quick way that we can do this. 00:19:05.080 --> 00:19:08.400 align:middle line:84% Let's just excerpt measure eight chord-- 00:19:08.400 --> 00:19:13.300 align:middle line:84% 8 and just get that one measure from the-- 00:19:13.300 --> 00:19:15.630 align:middle line:84% this is from the chordified version-- 00:19:15.630 --> 00:19:16.690 align:middle line:90% measure 8. 00:19:16.690 --> 00:19:20.520 align:middle line:84% And we can just show it, make sure we got the right one. 00:19:20.520 --> 00:19:21.785 align:middle line:90% Always do this by the way. 00:19:21.785 --> 00:19:23.160 align:middle line:84% The number of times that somebody 00:19:23.160 --> 00:19:25.960 align:middle line:84% has worked hours and hours and can't figure out the bug, 00:19:25.960 --> 00:19:28.280 align:middle line:84% because it turns out that wasn't the right bug-- 00:19:28.280 --> 00:19:29.530 align:middle line:90% that wasn't the right measure. 00:19:29.530 --> 00:19:32.790 align:middle line:84% So, yeah, I'm going to pause the video for one second 00:19:32.790 --> 00:19:37.200 align:middle line:84% and go through those chords in some detail. 00:19:37.200 --> 00:19:39.340 align:middle line:84% So sorry, I've cut off the soprano, 00:19:39.340 --> 00:19:41.100 align:middle line:84% but it's just a whole bunch of F sharps. 00:19:41.100 --> 00:19:45.250 align:middle line:84% So we can see that the first chord, 1/6, 00:19:45.250 --> 00:19:48.345 align:middle line:90% that's really from the bass. 00:19:48.345 --> 00:19:50.200 align:middle line:84% That's the chord that's happening. 00:19:50.200 --> 00:19:55.305 align:middle line:84% It's either the chord on beat 1 or the chord on beat 2. 00:19:55.305 --> 00:19:57.870 align:middle line:84% The third beat, the bass line looks 00:19:57.870 --> 00:20:00.370 align:middle line:84% like it's doing some kind of a passing tone, 00:20:00.370 --> 00:20:04.430 align:middle line:84% and then it's moving up to that C sharp at the end. 00:20:04.430 --> 00:20:07.780 align:middle line:90% So something is happening and-- 00:20:07.780 --> 00:20:13.330 align:middle line:84% but, well, it's really unclear if anything 00:20:13.330 --> 00:20:16.690 align:middle line:84% except the first beat is something 00:20:16.690 --> 00:20:20.140 align:middle line:84% that we'd want to keep as an actual chord, 00:20:20.140 --> 00:20:22.730 align:middle line:84% especially looking at the alto line 00:20:22.730 --> 00:20:26.930 align:middle line:84% looks like it has both of those Ds might be passing tones 00:20:26.930 --> 00:20:29.360 align:middle line:84% and the tenor also looks like it's passing tone. 00:20:29.360 --> 00:20:31.420 align:middle line:84% So a lot of these chordal motions 00:20:31.420 --> 00:20:36.560 align:middle line:84% are things that are introducing interesting elements, 00:20:36.560 --> 00:20:39.355 align:middle line:84% but are they introducing new chords? 00:20:39.355 --> 00:20:41.890 align:middle line:84% So what we're going to do in the next section 00:20:41.890 --> 00:20:45.770 align:middle line:84% is let's just get a way of saying 00:20:45.770 --> 00:20:51.720 align:middle line:84% which chords do we think have enough stability for us to label 00:20:51.720 --> 00:20:52.220 align:middle line:90% them. 00:20:52.220 --> 00:20:56.270 align:middle line:84% So we're going to look through each chord in measure 8. 00:20:56.270 --> 00:20:59.970 align:middle line:84% In this case I don't need to do recurse because measure 8 only 00:20:59.970 --> 00:21:03.610 align:middle line:84% has chords and time signatures maybe or something like that, 00:21:03.610 --> 00:21:07.870 align:middle line:84% and I'm good at print whether or not the chord is consonant-- 00:21:07.870 --> 00:21:12.070 align:middle line:84% that's a routine, a method that's on every chord object-- 00:21:12.070 --> 00:21:14.020 align:middle line:84% and then print the chord object itself. 00:21:14.020 --> 00:21:18.810 align:middle line:84% We can see that only that first 1/6 chord is actually 00:21:18.810 --> 00:21:20.730 align:middle line:90% a consonant chord. 00:21:20.730 --> 00:21:23.430 align:middle line:84% Everything else is dissonant according 00:21:23.430 --> 00:21:26.790 align:middle line:90% to the rules of tonal harmony. 00:21:26.790 --> 00:21:30.060 align:middle line:84% So what we could do is we could create a new stream 00:21:30.060 --> 00:21:31.810 align:middle line:84% and start putting all of the chords in, 00:21:31.810 --> 00:21:38.745 align:middle line:84% and then let's replace that back into our original, 00:21:38.745 --> 00:21:40.870 align:middle line:84% or we can start copying things and putting them in. 00:21:40.870 --> 00:21:44.680 align:middle line:84% But after thinking aloud at the keyboard for a little bit, 00:21:44.680 --> 00:21:48.690 align:middle line:84% I decided I was going to just go through and let's just remove 00:21:48.690 --> 00:21:51.190 align:middle line:84% all the chords that are not consonant. 00:21:51.190 --> 00:21:59.140 align:middle line:84% So every stream has a nice little remove functionality 00:21:59.140 --> 00:22:00.235 align:middle line:90% from it. 00:22:00.235 --> 00:22:04.390 align:middle line:84% There are some problems by the way just like all Python 00:22:04.390 --> 00:22:06.940 align:middle line:84% and many other languages lists and arrays 00:22:06.940 --> 00:22:09.062 align:middle line:84% and stuff like that that if you remove things 00:22:09.062 --> 00:22:11.270 align:middle line:84% while you're iterating over, there could be problems. 00:22:11.270 --> 00:22:12.260 align:middle line:90% But here it's OK. 00:22:12.260 --> 00:22:15.590 align:middle line:84% So we're going to remove every chord that's not consonant, 00:22:15.590 --> 00:22:19.340 align:middle line:84% and then we're going to get that first chord, the 1/6 chord, 00:22:19.340 --> 00:22:22.070 align:middle line:84% and we'll make the duration of that be a whole note. 00:22:22.070 --> 00:22:24.430 align:middle line:84% So now when we look at measure 8, 00:22:24.430 --> 00:22:28.480 align:middle line:84% we see only that consonant chord. 00:22:28.480 --> 00:22:29.230 align:middle line:90% Ta da. 00:22:29.230 --> 00:22:33.220 align:middle line:84% And that's one of the forms of vocabulary reduction 00:22:33.220 --> 00:22:37.590 align:middle line:84% that's going to be pretty common. 00:22:37.590 --> 00:22:41.650 align:middle line:84% So when we go back and look at the excerpt 00:22:41.650 --> 00:22:46.990 align:middle line:84% here for the first part, we don't have nearly as much 00:22:46.990 --> 00:22:47.870 align:middle line:90% to remove. 00:22:47.870 --> 00:22:50.960 align:middle line:84% So maybe we want to do the same type of thing. 00:22:50.960 --> 00:22:53.170 align:middle line:84% Well, let's just look at that first excerpt 00:22:53.170 --> 00:22:56.210 align:middle line:84% and see what things are consonant, 00:22:56.210 --> 00:22:57.680 align:middle line:90% what things are dissonant. 00:22:57.680 --> 00:23:00.327 align:middle line:90% And here we do need to recurse. 00:23:00.327 --> 00:23:02.160 align:middle line:84% So we're going to look at this first excerpt 00:23:02.160 --> 00:23:05.680 align:middle line:84% and see, wow, almost everything here is constant. 00:23:05.680 --> 00:23:07.090 align:middle line:90% There's that one false. 00:23:07.090 --> 00:23:08.980 align:middle line:90% Which one does it refer to? 00:23:08.980 --> 00:23:10.210 align:middle line:90% What's it refer to? 00:23:10.210 --> 00:23:12.870 align:middle line:84% Oh, let's just replace it and print the figure instead-- 00:23:12.870 --> 00:23:17.790 align:middle line:84% not the figure-- the lyrics instead and see that that one 00:23:17.790 --> 00:23:22.660 align:middle line:84% thing that is not consonant is a 5/7 chord, 00:23:22.660 --> 00:23:24.850 align:middle line:84% something that we might want to keep, 00:23:24.850 --> 00:23:29.020 align:middle line:84% whereas the something else that is constant is a 3/6 chord, 00:23:29.020 --> 00:23:32.770 align:middle line:84% which we might want to remove and say, well, 00:23:32.770 --> 00:23:33.790 align:middle line:90% that's not a real chord. 00:23:33.790 --> 00:23:35.370 align:middle line:84% In this case, it is because we're 00:23:35.370 --> 00:23:38.880 align:middle line:84% about to be modulating into another key. 00:23:38.880 --> 00:23:42.600 align:middle line:84% So we're going to be thinking about how can we 00:23:42.600 --> 00:23:45.660 align:middle line:84% do these things, what are the various criteria that we can 00:23:45.660 --> 00:23:48.950 align:middle line:90% find, and how do we do this? 00:23:48.950 --> 00:24:00.000 align:middle line:90%