WEBVTT 00:00:00.000 --> 00:00:02.495 align:middle line:90% [SQUEAKING] 00:00:02.495 --> 00:00:04.491 align:middle line:90% [RUSTLING] 00:00:04.491 --> 00:00:10.490 align:middle line:90% [CLICKING] 00:00:10.490 --> 00:00:13.950 align:middle line:84% MICHAEL CUTHBERT: I want to wrap up a tiny bit of problem set 7. 00:00:13.950 --> 00:00:18.110 align:middle line:84% But before we do, I want us to jump ahead to the second part 00:00:18.110 --> 00:00:20.620 align:middle line:84% where I say algorithmic composition for a Markov data 00:00:20.620 --> 00:00:21.120 align:middle line:90% set. 00:00:21.120 --> 00:00:23.390 align:middle line:90% If you could get your-- 00:00:23.390 --> 00:00:26.700 align:middle line:84% what do you call it-- your Jupyter Notebooks going. 00:00:26.700 --> 00:00:29.792 align:middle line:84% And now, we're getting to the point in the semester 00:00:29.792 --> 00:00:32.000 align:middle line:84% where I'm just going to say you can import everything 00:00:32.000 --> 00:00:35.510 align:middle line:84% from music21, but I will give you a few restrictions from time 00:00:35.510 --> 00:00:36.060 align:middle line:90% to time. 00:00:36.060 --> 00:00:39.480 align:middle line:84% So I don't really care what you're doing. 00:00:39.480 --> 00:00:43.070 align:middle line:84% And in the past, I've tried to have everyone 00:00:43.070 --> 00:00:46.100 align:middle line:90% download a pre-prepared set. 00:00:46.100 --> 00:00:47.520 align:middle line:90% And it's always had problems. 00:00:47.520 --> 00:00:49.580 align:middle line:84% So we're just going to do something 00:00:49.580 --> 00:00:53.540 align:middle line:84% that takes about 3 or 4 minutes of your processor time 00:00:53.540 --> 00:00:55.560 align:middle line:90% and get that started now. 00:00:55.560 --> 00:00:57.840 align:middle line:84% So this will probably take a second or two. 00:00:57.840 --> 00:01:02.810 align:middle line:84% You're learning a new term, corpus.search Jig. 00:01:02.810 --> 00:01:06.540 align:middle line:84% I can't remember if it's important if this is capital 00:01:06.540 --> 00:01:07.040 align:middle line:90% or not. 00:01:07.040 --> 00:01:08.480 align:middle line:90% But let's say I put it on. 00:01:08.480 --> 00:01:12.118 align:middle line:84% And this will go through music-- so music21 comes with about-- 00:01:12.118 --> 00:01:13.660 align:middle line:84% I can't remember what the number is-- 00:01:13.660 --> 00:01:16.503 align:middle line:84% something like 14,000 pieces when you do it, 00:01:16.503 --> 00:01:17.420 align:middle line:90% just so you can do it. 00:01:17.420 --> 00:01:21.170 align:middle line:84% And this will get everything that calls itself jig. 00:01:21.170 --> 00:01:23.080 align:middle line:84% I don't know if there's any word that 00:01:23.080 --> 00:01:26.780 align:middle line:84% begins with jig that is not a jig, 00:01:26.780 --> 00:01:30.020 align:middle line:84% but this might be garbage in, garbage out. 00:01:30.020 --> 00:01:32.360 align:middle line:90% I'm getting 327. 00:01:32.360 --> 00:01:33.860 align:middle line:84% Depending on what version you're on, 00:01:33.860 --> 00:01:35.920 align:middle line:84% you might be slightly higher or slightly lower. 00:01:35.920 --> 00:01:38.150 align:middle line:84% It won't influence that too much. 00:01:38.150 --> 00:01:38.890 align:middle line:90% Great. 00:01:38.890 --> 00:01:43.600 align:middle line:84% So give me a quick-- actually, the easiest thing so I can tell 00:01:43.600 --> 00:01:46.700 align:middle line:84% is, yeah, up or a snap of a finger when you've got it. 00:01:46.700 --> 00:01:48.250 align:middle line:90% And then I can hear. 00:01:48.250 --> 00:01:48.820 align:middle line:90% [SNAPPING] 00:01:48.820 --> 00:01:49.435 align:middle line:90% OK, good. 00:01:49.435 --> 00:01:51.560 align:middle line:84% All of our computers are slightly different speeds. 00:01:51.560 --> 00:01:55.803 align:middle line:84% But I think you can also start typing the next expressions 00:01:55.803 --> 00:01:56.720 align:middle line:90% while you're doing it. 00:01:56.720 --> 00:01:59.640 align:middle line:84% So Jigs is something called a metadata bundle. 00:01:59.640 --> 00:02:03.540 align:middle line:84% That means it's a collection of everything whose metadata, 00:02:03.540 --> 00:02:07.405 align:middle line:84% whose titles, authors, something match a particular search term. 00:02:07.405 --> 00:02:08.280 align:middle line:90% You can look through. 00:02:08.280 --> 00:02:12.560 align:middle line:84% You can find things by key, by starting meter, 00:02:12.560 --> 00:02:13.620 align:middle line:90% and things like that. 00:02:13.620 --> 00:02:16.400 align:middle line:84% But often searching by title or composer 00:02:16.400 --> 00:02:17.640 align:middle line:90% is one of the first things. 00:02:17.640 --> 00:02:21.410 align:middle line:84% And what you can do is if we look 00:02:21.410 --> 00:02:24.230 align:middle line:84% at this as a very short introduction to this, 00:02:24.230 --> 00:02:27.210 align:middle line:90% jigs is 327 things. 00:02:27.210 --> 00:02:30.560 align:middle line:84% We can look at the first one with jigs(0). 00:02:30.560 --> 00:02:35.420 align:middle line:84% And we can get that it comes from some particular piece, song 00:02:35.420 --> 00:02:42.650 align:middle line:84% 47, in a collection of Irish tunes called airdsAirs_book1. 00:02:42.650 --> 00:02:44.400 align:middle line:90% So it's not a piece. 00:02:44.400 --> 00:02:46.760 align:middle line:84% In order to get that, we can say-- 00:02:46.760 --> 00:02:48.690 align:middle line:90% I'm going to go j1. 00:02:48.690 --> 00:02:52.100 align:middle line:84% I'm going to equals jigs(1), because jigs(0) 00:02:52.100 --> 00:02:55.775 align:middle line:90% has some funny things on it. 00:02:55.775 --> 00:03:00.110 align:middle line:84% And jigs(1).parse, calling it as a method, 00:03:00.110 --> 00:03:02.800 align:middle line:84% and that will actually load it, because, otherwise, 00:03:02.800 --> 00:03:06.980 align:middle line:84% loading 327 pieces would take a little too long. 00:03:06.980 --> 00:03:10.100 align:middle line:84% And then I can do show, hopefully. 00:03:10.100 --> 00:03:13.300 align:middle line:90% 00:03:13.300 --> 00:03:14.840 align:middle line:90% "A Spanish Jigg"! 00:03:14.840 --> 00:03:18.820 align:middle line:84% Everyone get "A Spanish Jigg" on theirs? 00:03:18.820 --> 00:03:19.863 align:middle line:90% OK, good. 00:03:19.863 --> 00:03:21.280 align:middle line:84% So what we're going to do is we're 00:03:21.280 --> 00:03:25.190 align:middle line:84% going to just get every jig that is in G major. 00:03:25.190 --> 00:03:27.130 align:middle line:84% So I'm going to call it-- because I 00:03:27.130 --> 00:03:31.580 align:middle line:90% have my verbose variable names. 00:03:31.580 --> 00:03:34.220 align:middle line:84% I'm going to call it jigs_in_g with underscores. 00:03:34.220 --> 00:03:37.000 align:middle line:84% You might just call it jg, whatever you want. 00:03:37.000 --> 00:03:40.330 align:middle line:90% And I'll just say for. 00:03:40.330 --> 00:03:44.710 align:middle line:90% I'll say j_meta in jigs. 00:03:44.710 --> 00:03:46.730 align:middle line:90% So I remember this a thing. 00:03:46.730 --> 00:03:48.370 align:middle line:90% I'll say j. 00:03:48.370 --> 00:03:48.950 align:middle line:90% Sorry. 00:03:48.950 --> 00:03:49.660 align:middle line:90% I'll go slower. 00:03:49.660 --> 00:03:51.020 align:middle line:90% I'll make this bigger. 00:03:51.020 --> 00:03:53.516 align:middle line:84% Slower and bigger are always important. 00:03:53.516 --> 00:03:56.160 align:middle line:90% 00:03:56.160 --> 00:04:01.210 align:middle line:84% I have a whole big screen if I'm not using it, 00:04:01.210 --> 00:04:02.910 align:middle line:90% so a little bit better. 00:04:02.910 --> 00:04:07.110 align:middle line:84% So I'll parse each one, the metadata. 00:04:07.110 --> 00:04:12.240 align:middle line:84% So we'll say j-- is that one parsed? 00:04:12.240 --> 00:04:16.709 align:middle line:84% And now, I'll do-- just kidding, jk for jigs key 00:04:16.709 --> 00:04:21.125 align:middle line:90% equals j.analyze the key. 00:04:21.125 --> 00:04:24.600 align:middle line:90% 00:04:24.600 --> 00:04:27.540 align:middle line:84% And here, just for now, so we can all get caught up, 00:04:27.540 --> 00:04:28.820 align:middle line:90% I'm going to print them all. 00:04:28.820 --> 00:04:34.840 align:middle line:90% 00:04:34.840 --> 00:04:39.450 align:middle line:90% I'm just letting everybody. 00:04:39.450 --> 00:04:42.810 align:middle line:84% And then I'm going to be grabbing in a second every piece 00:04:42.810 --> 00:04:47.910 align:middle line:90% that is in G major. 00:04:47.910 --> 00:04:48.660 align:middle line:90% Why? 00:04:48.660 --> 00:04:51.220 align:middle line:84% Because it looks like there's a lot of jigs in G major. 00:04:51.220 --> 00:04:53.420 align:middle line:84% So it seems like a good thing to grab. 00:04:53.420 --> 00:04:59.500 align:middle line:90% 00:04:59.500 --> 00:05:06.326 align:middle line:84% Do we feel-- we'll just keep snapping when you're caught up. 00:05:06.326 --> 00:05:07.600 align:middle line:90% [SNAPPING] 00:05:07.600 --> 00:05:08.620 align:middle line:90% OK, good, good. 00:05:08.620 --> 00:05:12.960 align:middle line:84% We'll eventually synchronize on a rhythm for the things. 00:05:12.960 --> 00:05:13.460 align:middle line:90% Good. 00:05:13.460 --> 00:05:17.810 align:middle line:90% Now, I'll say tonic_name. 00:05:17.810 --> 00:05:19.130 align:middle line:90% I'll just be verbose again. 00:05:19.130 --> 00:05:20.390 align:middle line:90% I keep jumping back and forth. 00:05:20.390 --> 00:05:26.920 align:middle line:84% Is that keys .tonic, which returns a pitch object. 00:05:26.920 --> 00:05:30.370 align:middle line:90% And a pitch object has a .name. 00:05:30.370 --> 00:05:32.920 align:middle line:90% 00:05:32.920 --> 00:05:36.300 align:middle line:84% And what we'll do is we'll get all the ones in G major or in G 00:05:36.300 --> 00:05:36.800 align:middle line:90% minor. 00:05:36.800 --> 00:05:40.660 align:middle line:84% But no, actually, maybe we should do-- 00:05:40.660 --> 00:05:42.430 align:middle line:90% nah, we'll just do it all in-- 00:05:42.430 --> 00:05:46.330 align:middle line:90% if tonic_name equals G-- 00:05:46.330 --> 00:05:49.090 align:middle line:84% I don't think there's a lot in G minor-- 00:05:49.090 --> 00:05:50.750 align:middle line:90% jigs_in_g.append(j). 00:05:50.750 --> 00:05:59.340 align:middle line:90% 00:05:59.340 --> 00:06:03.580 align:middle line:84% And that's where we're going to put this aside for a bit. 00:06:03.580 --> 00:06:05.520 align:middle line:84% But you can do the snap when you're 00:06:05.520 --> 00:06:08.440 align:middle line:84% done, because this will take a while to do. 00:06:08.440 --> 00:06:11.040 align:middle line:84% And then I'll move on to the next thing. 00:06:11.040 --> 00:06:12.580 align:middle line:90% Don't snap when it's done. 00:06:12.580 --> 00:06:14.642 align:middle line:84% Snap when you're done programming this, 00:06:14.642 --> 00:06:15.850 align:middle line:90% so that we have it for later. 00:06:15.850 --> 00:06:16.350 align:middle line:90% Good. 00:06:16.350 --> 00:06:19.530 align:middle line:90% 00:06:19.530 --> 00:06:23.050 align:middle line:84% Now, by the way, mine's running a lot faster than yours, 00:06:23.050 --> 00:06:25.360 align:middle line:84% not because MIT has bought me a fancy computer, 00:06:25.360 --> 00:06:28.330 align:middle line:84% but because when you parse something once in music21, 00:06:28.330 --> 00:06:31.810 align:middle line:84% it stores it as a cache somewhere on your hard drive. 00:06:31.810 --> 00:06:33.580 align:middle line:84% And so it goes faster the second time. 00:06:33.580 --> 00:06:37.320 align:middle line:84% So if you're feeling like, ah, I need to upgrade my computer, 00:06:37.320 --> 00:06:39.270 align:middle line:84% because mine was so much slower than his. 00:06:39.270 --> 00:06:42.690 align:middle line:90% No, it's just I may have-- 00:06:42.690 --> 00:06:44.110 align:middle line:84% like they do on the cooking shows, 00:06:44.110 --> 00:06:46.860 align:middle line:84% I might have already baked this once this morning, just 00:06:46.860 --> 00:06:47.800 align:middle line:90% to make sure it works. 00:06:47.800 --> 00:06:49.500 align:middle line:90% OK, good. 00:06:49.500 --> 00:06:53.340 align:middle line:90% Put that aside for a little bit. 00:06:53.340 --> 00:06:55.020 align:middle line:90% I want to open up-- 00:06:55.020 --> 00:06:58.950 align:middle line:84% actually, well, I don't need to put that aside too much-- 00:06:58.950 --> 00:07:02.050 align:middle line:90% your problem set 7. 00:07:02.050 --> 00:07:03.160 align:middle line:90% Where did that go? 00:07:03.160 --> 00:07:04.100 align:middle line:90% Here it is. 00:07:04.100 --> 00:07:07.680 align:middle line:90% 00:07:07.680 --> 00:07:09.440 align:middle line:90% Sorry about that, y'all. 00:07:09.440 --> 00:07:11.140 align:middle line:84% I'm usually a little bit more organized. 00:07:11.140 --> 00:07:11.640 align:middle line:90% Great. 00:07:11.640 --> 00:07:17.310 align:middle line:90% 00:07:17.310 --> 00:07:21.210 align:middle line:84% Problem set 7-- oh, here we go, 7 and 8. 00:07:21.210 --> 00:07:24.515 align:middle line:84% So I want to just talk through some of the things 00:07:24.515 --> 00:07:25.890 align:middle line:84% that you've just been working on. 00:07:25.890 --> 00:07:29.610 align:middle line:84% A couple people have requested and been granted extra time 00:07:29.610 --> 00:07:32.400 align:middle line:84% for the last couple questions, so I'm not 00:07:32.400 --> 00:07:33.790 align:middle line:90% going to go through them. 00:07:33.790 --> 00:07:36.390 align:middle line:84% And besides, we all have different answers 00:07:36.390 --> 00:07:39.120 align:middle line:90% on the open-ended ones. 00:07:39.120 --> 00:07:41.940 align:middle line:84% Actually, actually, yeah, no, we'll do this. 00:07:41.940 --> 00:07:44.430 align:middle line:84% So the major_scales one, how hard did we 00:07:44.430 --> 00:07:47.400 align:middle line:90% find this particular one? 00:07:47.400 --> 00:07:50.066 align:middle line:84% Easy, hard, a little bit-- what was the-- what 00:07:50.066 --> 00:07:53.830 align:middle line:84% do you think a test case that I'm going to run on 00:07:53.830 --> 00:07:56.620 align:middle line:90% that you can already tell me? 00:07:56.620 --> 00:07:57.310 align:middle line:90% Yeah. 00:07:57.310 --> 00:07:59.727 align:middle line:84% AUDIENCE: You're going to do something [? pathological, ?] 00:07:59.727 --> 00:08:00.817 align:middle line:90% like E-flat, flat 54. 00:08:00.817 --> 00:08:02.150 align:middle line:90% MICHAEL CUTHBERT: E-flat, flat-- 00:08:02.150 --> 00:08:02.540 align:middle line:90% what's that? 00:08:02.540 --> 00:08:03.340 align:middle line:84% AUDIENCE: You're going to do something [? pathological. ?] 00:08:03.340 --> 00:08:04.340 align:middle line:90% MICHAEL CUTHBERT: Major. 00:08:04.340 --> 00:08:07.960 align:middle line:84% Yeah, I'm going to probably start with E-sharp major, 00:08:07.960 --> 00:08:10.390 align:middle line:90% or even-- 00:08:10.390 --> 00:08:12.700 align:middle line:84% yeah, so certain things like that to make sure. 00:08:12.700 --> 00:08:15.373 align:middle line:84% Or even a normal thing, like F-sharp major, 00:08:15.373 --> 00:08:16.790 align:middle line:84% what am I going to be looking for? 00:08:16.790 --> 00:08:20.382 align:middle line:84% What's the leading tone in F-sharp major? 00:08:20.382 --> 00:08:22.150 align:middle line:90% [INTERPOSING VOICES] 00:08:22.150 --> 00:08:25.480 align:middle line:84% MICHAEL CUTHBERT: E-sharp, F natural, E double sharp. 00:08:25.480 --> 00:08:28.030 align:middle line:90% Who goes for E-sharp? 00:08:28.030 --> 00:08:30.280 align:middle line:90% F natural? 00:08:30.280 --> 00:08:30.920 align:middle line:90% E double sharp? 00:08:30.920 --> 00:08:32.740 align:middle line:84% Yeah, I'm going to be looking for E-sharp, 00:08:32.740 --> 00:08:36.940 align:middle line:84% because a major scale, one of the things about it is it uses 00:08:36.940 --> 00:08:45.070 align:middle line:84% every one of the lines and spaces once and only once, 00:08:45.070 --> 00:08:45.820 align:middle line:90% regard-- 00:08:45.820 --> 00:08:49.310 align:middle line:84% using some sort of sharp or flat. 00:08:49.310 --> 00:08:51.620 align:middle line:90% Great. 00:08:51.620 --> 00:08:55.620 align:middle line:84% Now, let's talk a little bit about the second question. 00:08:55.620 --> 00:08:59.390 align:middle line:84% Any questions that you had on the routes? 00:08:59.390 --> 00:09:01.790 align:middle line:84% Depending on how much you chose to do this 00:09:01.790 --> 00:09:06.360 align:middle line:84% by hand, which when we didn't combine the two problem sets, 00:09:06.360 --> 00:09:11.090 align:middle line:84% I'd like to use this one as something to do by hand. 00:09:11.090 --> 00:09:12.890 align:middle line:90% It gets quite a bit harder. 00:09:12.890 --> 00:09:14.780 align:middle line:84% What are some of the techniques that anybody 00:09:14.780 --> 00:09:17.140 align:middle line:90% remembers using on this? 00:09:17.140 --> 00:09:17.640 align:middle line:90% Yeah. 00:09:17.640 --> 00:09:20.900 align:middle line:84% AUDIENCE: You want everything to be between 0 and 11. 00:09:20.900 --> 00:09:23.660 align:middle line:84% MICHAEL CUTHBERT: Ah, convert everything to 0 and 11. 00:09:23.660 --> 00:09:25.347 align:middle line:84% AUDIENCE: Well, for now, I guess. 00:09:25.347 --> 00:09:26.430 align:middle line:90% MICHAEL CUTHBERT: For now. 00:09:26.430 --> 00:09:26.930 align:middle line:90% Great. 00:09:26.930 --> 00:09:30.810 align:middle line:84% And then-- so we have the pitch class space. 00:09:30.810 --> 00:09:32.695 align:middle line:84% Maybe I should-- do I have a side? 00:09:32.695 --> 00:09:35.720 align:middle line:90% 00:09:35.720 --> 00:09:37.940 align:middle line:90% Yeah, there we go. 00:09:37.940 --> 00:09:39.440 align:middle line:90% Oops. 00:09:39.440 --> 00:09:43.177 align:middle line:84% So 0, 1-- is this what you're thinking of? 00:09:43.177 --> 00:09:43.760 align:middle line:90% AUDIENCE: Yep. 00:09:43.760 --> 00:09:44.593 align:middle line:90% MICHAEL CUTHBERT: 2. 00:09:44.593 --> 00:09:45.260 align:middle line:90% Great. 00:09:45.260 --> 00:09:46.680 align:middle line:90% So that can be one part of it. 00:09:46.680 --> 00:09:48.312 align:middle line:84% And then what do yo-- what do we do-- 00:09:48.312 --> 00:09:49.520 align:middle line:90% how are we going to use this? 00:09:49.520 --> 00:09:50.103 align:middle line:90% Somebody else. 00:09:50.103 --> 00:09:50.876 align:middle line:90% Yeah, go ahead. 00:09:50.876 --> 00:09:52.376 align:middle line:84% AUDIENCE: [INAUDIBLE] I had an idea, 00:09:52.376 --> 00:09:55.090 align:middle line:84% but I also added like a set( ), so just repeated notes. 00:09:55.090 --> 00:09:57.340 align:middle line:84% MICHAEL CUTHBERT: So if there's repeated notes-- yeah, 00:09:57.340 --> 00:09:59.720 align:middle line:84% so we're going to use the set( ) operation-- 00:09:59.720 --> 00:10:03.850 align:middle line:84% good-- to remove things that are in there multiple times. 00:10:03.850 --> 00:10:06.730 align:middle line:90% What's the-- yeah, so for root-- 00:10:06.730 --> 00:10:08.380 align:middle line:84% for the root of the chord, does it 00:10:08.380 --> 00:10:12.140 align:middle line:84% matter what octave something's in? 00:10:12.140 --> 00:10:12.845 align:middle line:90% AUDIENCE: No. 00:10:12.845 --> 00:10:13.720 align:middle line:90% MICHAEL CUTHBERT: No. 00:10:13.720 --> 00:10:17.440 align:middle line:84% So root is a kind of equivalence class that implies 00:10:17.440 --> 00:10:19.430 align:middle line:90% octave equivalence, right? 00:10:19.430 --> 00:10:20.560 align:middle line:90% Great. 00:10:20.560 --> 00:10:22.610 align:middle line:84% So we're going to be using a set. 00:10:22.610 --> 00:10:26.710 align:middle line:84% We're going to be discarding octaves. 00:10:26.710 --> 00:10:28.450 align:middle line:90% No octaves. 00:10:28.450 --> 00:10:29.410 align:middle line:90% Great. 00:10:29.410 --> 00:10:31.785 align:middle line:84% What are other things that you did in this? 00:10:31.785 --> 00:10:34.450 align:middle line:90% 00:10:34.450 --> 00:10:35.720 align:middle line:90% I just want to spin it around. 00:10:35.720 --> 00:10:36.320 align:middle line:90% Yes. 00:10:36.320 --> 00:10:36.820 align:middle line:90% Go ahead. 00:10:36.820 --> 00:10:39.400 align:middle line:84% AUDIENCE: Oh, mine is similar, but I used the diatonic note 00:10:39.400 --> 00:10:40.400 align:middle line:90% numbers instead. 00:10:40.400 --> 00:10:44.200 align:middle line:84% MICHAEL CUTHBERT: So you used diatonic numbers instead. 00:10:44.200 --> 00:10:51.580 align:middle line:84% Diatonic note numbers, so that you have something like-- 00:10:51.580 --> 00:10:55.050 align:middle line:84% and I can't believe there's a brain cell in my head 00:10:55.050 --> 00:10:56.350 align:middle line:90% that remembers this. 00:10:56.350 --> 00:11:01.060 align:middle line:84% So you had something like 31, 32, 33, 34. 00:11:01.060 --> 00:11:01.560 align:middle line:90% Great. 00:11:01.560 --> 00:11:05.680 align:middle line:84% The number C4 as 29 is pretty arbitrary. 00:11:05.680 --> 00:11:08.260 align:middle line:84% I just like-- if you go to the Media Lab, 00:11:08.260 --> 00:11:10.050 align:middle line:84% they have a Bösendorfer Imperial Grand, 00:11:10.050 --> 00:11:12.760 align:middle line:84% one that has the extra keys down here. 00:11:12.760 --> 00:11:16.080 align:middle line:84% And the lowest note on that one, I assigned to 1, 00:11:16.080 --> 00:11:18.490 align:middle line:90% and just went up from there. 00:11:18.490 --> 00:11:21.670 align:middle line:90% So C4 ends up being 29. 00:11:21.670 --> 00:11:22.200 align:middle line:90% Good. 00:11:22.200 --> 00:11:24.790 align:middle line:84% And so we can use that for certain parts. 00:11:24.790 --> 00:11:28.140 align:middle line:84% Who used diatonic note numbers or something 00:11:28.140 --> 00:11:29.790 align:middle line:90% like that in their example-- 00:11:29.790 --> 00:11:31.530 align:middle line:90% in your answer? 00:11:31.530 --> 00:11:32.970 align:middle line:90% 1, 2, 3, 4. 00:11:32.970 --> 00:11:36.340 align:middle line:84% Who used something like pitch classes? 00:11:36.340 --> 00:11:37.020 align:middle line:90% That's good. 00:11:37.020 --> 00:11:37.650 align:middle line:90% Good. 00:11:37.650 --> 00:11:39.630 align:middle line:90% Who used both? 00:11:39.630 --> 00:11:41.730 align:middle line:90% Anybody? 00:11:41.730 --> 00:11:45.420 align:middle line:84% My implementation ends up using both of them. 00:11:45.420 --> 00:11:46.880 align:middle line:84% So I'm going to say both of these 00:11:46.880 --> 00:11:49.460 align:middle line:90% can be a right way to work. 00:11:49.460 --> 00:11:50.990 align:middle line:90% Good. 00:11:50.990 --> 00:11:52.490 align:middle line:84% Now, what are some other techniques 00:11:52.490 --> 00:11:55.880 align:middle line:90% that we did on rootness? 00:11:55.880 --> 00:11:56.450 align:middle line:90% Yeah. 00:11:56.450 --> 00:11:57.950 align:middle line:84% AUDIENCE: Should I check for fifths? 00:11:57.950 --> 00:11:59.810 align:middle line:84% MICHAEL CUTHBERT: Check for fifths-- good. 00:11:59.810 --> 00:12:04.395 align:middle line:90% Check for fifths. 00:12:04.395 --> 00:12:10.250 align:middle line:90% 00:12:10.250 --> 00:12:12.808 align:middle line:84% What's the best-- which one of these, do you think, 00:12:12.808 --> 00:12:14.350 align:middle line:84% works better for checking for fifths? 00:12:14.350 --> 00:12:20.441 align:middle line:90% 00:12:20.441 --> 00:12:22.850 align:middle line:90% Do you want to take a guess? 00:12:22.850 --> 00:12:25.400 align:middle line:84% AUDIENCE: I wouldn't want to say either, just because they're 00:12:25.400 --> 00:12:26.670 align:middle line:90% both, like, number-based. 00:12:26.670 --> 00:12:29.120 align:middle line:84% So you could have some sort of augmented thing, 00:12:29.120 --> 00:12:31.162 align:middle line:84% and it'd still return the same difference. 00:12:31.162 --> 00:12:32.120 align:middle line:90% MICHAEL CUTHBERT: Yeah. 00:12:32.120 --> 00:12:35.030 align:middle line:84% So it has a lot to do with whether we care about spelling 00:12:35.030 --> 00:12:36.180 align:middle line:90% equivalents or not. 00:12:36.180 --> 00:12:42.425 align:middle line:84% So we can always have a doubly augmented fourth. 00:12:42.425 --> 00:12:45.190 align:middle line:84% It sounds the same as a perfect fifth, 00:12:45.190 --> 00:12:48.570 align:middle line:84% but it repulses me because it is a dissonance, right? 00:12:48.570 --> 00:12:52.140 align:middle line:84% Actually, I'm not repulsed by dissonance, but it is. 00:12:52.140 --> 00:12:54.720 align:middle line:84% And what do we have the problem if we're only looking 00:12:54.720 --> 00:12:56.970 align:middle line:90% at diatonic note numbers? 00:12:56.970 --> 00:12:59.925 align:middle line:90% Give me a fifth that might-- 00:12:59.925 --> 00:13:01.800 align:middle line:84% actually, you're supposed to-- well, change-- 00:13:01.800 --> 00:13:04.415 align:middle line:84% does it change the root, which fifth you find? 00:13:04.415 --> 00:13:06.823 align:middle line:90% 00:13:06.823 --> 00:13:07.865 align:middle line:90% AUDIENCE: No, not really. 00:13:07.865 --> 00:13:08.170 align:middle line:90% MICHAEL CUTHBERT: Good. 00:13:08.170 --> 00:13:09.490 align:middle line:90% So we checked for fifths. 00:13:09.490 --> 00:13:12.600 align:middle line:84% Anybody check for any other intervals? 00:13:12.600 --> 00:13:13.200 align:middle line:90% Yeah. 00:13:13.200 --> 00:13:15.930 align:middle line:84% AUDIENCE: I did the dumb thing and checked for two thirds. 00:13:15.930 --> 00:13:20.020 align:middle line:84% MICHAEL CUTHBERT: Check for two thirds in a row, two thirds. 00:13:20.020 --> 00:13:26.040 align:middle line:84% So if you have one third, and you have two thirds, 00:13:26.040 --> 00:13:27.970 align:middle line:90% then you might have something. 00:13:27.970 --> 00:13:28.810 align:middle line:90% Yeah, you're right. 00:13:28.810 --> 00:13:30.902 align:middle line:84% That was a very dumb thing to say 00:13:30.902 --> 00:13:32.610 align:middle line:84% that it was a dumb thing, because I think 00:13:32.610 --> 00:13:34.300 align:middle line:90% it's a great way of doing it. 00:13:34.300 --> 00:13:40.170 align:middle line:84% So if you can have two thirds, then presumably the bottom 1 00:13:40.170 --> 00:13:42.140 align:middle line:90% is a root. 00:13:42.140 --> 00:13:44.872 align:middle line:90% Where's the problem come? 00:13:44.872 --> 00:13:46.250 align:middle line:90% Yeah. 00:13:46.250 --> 00:13:48.020 align:middle line:84% AUDIENCE: A major triad and a minor triad, 00:13:48.020 --> 00:13:50.490 align:middle line:84% or a major third, minor third, minor third, major third. 00:13:50.490 --> 00:13:51.657 align:middle line:90% MICHAEL CUTHBERT: OK, great. 00:13:51.657 --> 00:13:57.410 align:middle line:84% So minor third versus major third. 00:13:57.410 --> 00:13:58.970 align:middle line:84% I want you to think in your head, 00:13:58.970 --> 00:14:03.600 align:middle line:84% and then tell your neighbor yes or no on the count of 3, 00:14:03.600 --> 00:14:04.310 align:middle line:90% on whether-- 00:14:04.310 --> 00:14:07.230 align:middle line:84% does a major third or minor third, 00:14:07.230 --> 00:14:09.393 align:middle line:90% does this affect the root? 00:14:09.393 --> 00:14:13.250 align:middle line:90% 00:14:13.250 --> 00:14:15.550 align:middle line:90% 1, 2, 3. 00:14:15.550 --> 00:14:16.092 align:middle line:90% AUDIENCE: No. 00:14:16.092 --> 00:14:16.967 align:middle line:90% MICHAEL CUTHBERT: No. 00:14:16.967 --> 00:14:17.490 align:middle line:90% OK. 00:14:17.490 --> 00:14:21.300 align:middle line:84% So we might-- so we're not going to do that for right now. 00:14:21.300 --> 00:14:23.940 align:middle line:84% But I'm going to put this in the save for later pile, 00:14:23.940 --> 00:14:26.180 align:middle line:84% because a root is only one of the things 00:14:26.180 --> 00:14:27.530 align:middle line:90% we're going to want to do. 00:14:27.530 --> 00:14:28.500 align:middle line:90% Save for later. 00:14:28.500 --> 00:14:30.200 align:middle line:84% But no, so it's not going to do-- 00:14:30.200 --> 00:14:34.220 align:middle line:84% what's an issue that we might still have? 00:14:34.220 --> 00:14:36.685 align:middle line:84% But that's going to be important with this. 00:14:36.685 --> 00:14:40.950 align:middle line:90% 00:14:40.950 --> 00:14:43.830 align:middle line:90% So you've gotten rid of octaves. 00:14:43.830 --> 00:14:45.720 align:middle line:84% So let's say we're going to write everything 00:14:45.720 --> 00:14:47.610 align:middle line:90% in the same octave number. 00:14:47.610 --> 00:14:51.180 align:middle line:84% For a second-- can I blank this for a second? 00:14:51.180 --> 00:15:03.677 align:middle line:90% 00:15:03.677 --> 00:15:05.510 align:middle line:84% You still have it over there if you need it. 00:15:05.510 --> 00:15:08.880 align:middle line:90% 00:15:08.880 --> 00:15:13.170 align:middle line:84% So if we're saying everything is in octave 4, 00:15:13.170 --> 00:15:24.468 align:middle line:84% and I'm going to rewrite that F, A, C, the F major triad, F, A, 00:15:24.468 --> 00:15:28.560 align:middle line:90% C. Is that going to work? 00:15:28.560 --> 00:15:31.560 align:middle line:90% Third, third. 00:15:31.560 --> 00:15:33.330 align:middle line:90% Yeah. 00:15:33.330 --> 00:15:37.860 align:middle line:84% AUDIENCE: Do you mean like if we use the pitch class, 00:15:37.860 --> 00:15:42.367 align:middle line:90% then this upper C will be 0? 00:15:42.367 --> 00:15:43.700 align:middle line:90% So you won't be able to find it. 00:15:43.700 --> 00:15:44.425 align:middle line:90% Just [INAUDIBLE]. 00:15:44.425 --> 00:15:45.800 align:middle line:84% MICHAEL CUTHBERT: So it will be-- 00:15:45.800 --> 00:15:47.870 align:middle line:90% yeah, where will it be? 00:15:47.870 --> 00:15:49.740 align:middle line:84% Let's say we put everything in octave 4. 00:15:49.740 --> 00:15:50.900 align:middle line:84% AUDIENCE: It'll look like the one below it. 00:15:50.900 --> 00:15:52.400 align:middle line:84% MICHAEL CUTHBERT: It'll be below it. 00:15:52.400 --> 00:15:56.390 align:middle line:90% 00:15:56.390 --> 00:15:59.752 align:middle line:90% So what is this now? 00:15:59.752 --> 00:16:00.960 align:middle line:90% AUDIENCE: It's still a major. 00:16:00.960 --> 00:16:02.570 align:middle line:84% MICHAEL CUTHBERT: Still a major triad. 00:16:02.570 --> 00:16:05.735 align:middle line:84% What would we call this, by the way? 00:16:05.735 --> 00:16:06.860 align:middle line:90% AUDIENCE: Second inversion. 00:16:06.860 --> 00:16:07.560 align:middle line:84% MICHAEL CUTHBERT: First inversion? 00:16:07.560 --> 00:16:09.060 align:middle line:84% Second inversion, second inversion-- 00:16:09.060 --> 00:16:11.420 align:middle line:90% 64. 00:16:11.420 --> 00:16:14.930 align:middle line:84% Numbering instead of-- I've just switched 00:16:14.930 --> 00:16:17.660 align:middle line:84% between two different systems that are kind 00:16:17.660 --> 00:16:19.440 align:middle line:90% of equivalences of each other. 00:16:19.440 --> 00:16:25.640 align:middle line:84% I switched from calling this 33 system, which we use sometimes, 00:16:25.640 --> 00:16:31.760 align:middle line:84% to the calling this 53 system, which we use more often, where 00:16:31.760 --> 00:16:35.280 align:middle line:84% one system where you measure everything from the note below, 00:16:35.280 --> 00:16:39.670 align:middle line:84% and one thing where you measure everything from the base. 00:16:39.670 --> 00:16:45.100 align:middle line:84% Boy, isn't this terrible in music that we do this? 00:16:45.100 --> 00:16:50.440 align:middle line:84% Do you remember the first time that somebody said to you 00:16:50.440 --> 00:16:53.320 align:middle line:84% something like, oh, I was in F major, 00:16:53.320 --> 00:16:57.230 align:middle line:84% and I was on scale degree 2 on a 57 chord. 00:16:57.230 --> 00:17:00.070 align:middle line:84% And you actually mentally heard in your head, 00:17:00.070 --> 00:17:05.079 align:middle line:84% I was on scale degree 2 in a Roman numeral V, superscript 7 00:17:05.079 --> 00:17:06.310 align:middle line:90% thing. 00:17:06.310 --> 00:17:08.770 align:middle line:84% Somebody figure out what part of our brain 00:17:08.770 --> 00:17:11.690 align:middle line:84% is doing this kind of translation on the fly, 00:17:11.690 --> 00:17:14.500 align:middle line:84% that the exact same numbers are being 00:17:14.500 --> 00:17:16.690 align:middle line:84% translated in different ways in our memory. 00:17:16.690 --> 00:17:19.720 align:middle line:84% So this is not one that we talk about very much, 00:17:19.720 --> 00:17:21.589 align:middle line:90% this particular translation. 00:17:21.589 --> 00:17:25.310 align:middle line:84% But we do it quite a bit, and I just did it maybe too fast. 00:17:25.310 --> 00:17:28.870 align:middle line:84% So yeah, 6, 4, or the other way you could do it is 00:17:28.870 --> 00:17:34.090 align:middle line:84% say it's a third stacked on top of a fourth. 00:17:34.090 --> 00:17:37.060 align:middle line:90% 3 plus 4 in music equals? 00:17:37.060 --> 00:17:37.560 align:middle line:90% AUDIENCE: 6. 00:17:37.560 --> 00:17:38.480 align:middle line:90% MICHAEL CUTHBERT: 6. 00:17:38.480 --> 00:17:38.980 align:middle line:90% Yep. 00:17:38.980 --> 00:17:42.260 align:middle line:90% 00:17:42.260 --> 00:17:44.577 align:middle line:84% This is also something we have to worry about. 00:17:44.577 --> 00:17:46.410 align:middle line:84% That was a parentheses within a parentheses. 00:17:46.410 --> 00:17:47.827 align:middle line:84% How do we get around this problem? 00:17:47.827 --> 00:17:53.360 align:middle line:90% 00:17:53.360 --> 00:17:54.333 align:middle line:90% Yeah. 00:17:54.333 --> 00:17:56.250 align:middle line:84% AUDIENCE: I basically added 12 to the lowest-- 00:17:56.250 --> 00:17:57.833 align:middle line:84% I sorted it and added 12 to the lowest 00:17:57.833 --> 00:18:00.025 align:middle line:90% note twice and then checked. 00:18:00.025 --> 00:18:00.900 align:middle line:90% MICHAEL CUTHBERT: OK. 00:18:00.900 --> 00:18:05.750 align:middle line:84% So you sort, and then if this doesn't match 33, 00:18:05.750 --> 00:18:07.682 align:middle line:90% then what did you do? 00:18:07.682 --> 00:18:09.740 align:middle line:84% AUDIENCE: I bumped the lowest note up an octave. 00:18:09.740 --> 00:18:12.198 align:middle line:84% MICHAEL CUTHBERT: You bumped the lowest note up the octave. 00:18:12.198 --> 00:18:16.550 align:middle line:90% 00:18:16.550 --> 00:18:18.600 align:middle line:90% Will that always be enough? 00:18:18.600 --> 00:18:19.460 align:middle line:90% AUDIENCE: No. 00:18:19.460 --> 00:18:21.918 align:middle line:84% MICHAEL CUTHBERT: So what do you have to decide to do next? 00:18:21.918 --> 00:18:24.710 align:middle line:90% So let's-- sometimes you have-- 00:18:24.710 --> 00:18:25.472 align:middle line:90% yeah, go ahead. 00:18:25.472 --> 00:18:26.930 align:middle line:84% AUDIENCE: I took the initial chord, 00:18:26.930 --> 00:18:29.423 align:middle line:84% and I duplicated it, the whole chord, an octave above. 00:18:29.423 --> 00:18:31.340 align:middle line:84% So I guaranteed that I will see a pattern that 00:18:31.340 --> 00:18:34.040 align:middle line:84% will be either major, minor, augmented, or diminished. 00:18:34.040 --> 00:18:34.915 align:middle line:90% MICHAEL CUTHBERT: OK. 00:18:34.915 --> 00:18:36.530 align:middle line:84% So you take whatever notes you see. 00:18:36.530 --> 00:18:38.420 align:middle line:84% Now I'm going to put it in first inversion, 00:18:38.420 --> 00:18:42.430 align:middle line:84% except there are chords beside C major, Michael. 00:18:42.430 --> 00:18:48.820 align:middle line:84% So we'll put it in first inversion, A, C, F. 00:18:48.820 --> 00:18:51.640 align:middle line:90% Call that a 63 chord. 00:18:51.640 --> 00:18:55.763 align:middle line:84% And if you just keep duplicating things up-- 00:18:55.763 --> 00:18:58.930 align:middle line:90% 00:18:58.930 --> 00:19:03.790 align:middle line:84% is that right-- you will eventually at some point have 00:19:03.790 --> 00:19:06.020 align:middle line:90% this 3-- 00:19:06.020 --> 00:19:06.550 align:middle line:90% ah! 00:19:06.550 --> 00:19:09.500 align:middle line:90% 53 stack, the stack of thirds. 00:19:09.500 --> 00:19:14.680 align:middle line:84% There will be a 53 embedded in there. 00:19:14.680 --> 00:19:17.920 align:middle line:90% Does that-- great hair, or jut-- 00:19:17.920 --> 00:19:20.560 align:middle line:90% good, super. 00:19:20.560 --> 00:19:24.310 align:middle line:84% These are all techniques that work really well here. 00:19:24.310 --> 00:19:29.230 align:middle line:84% What are the techniques that will work if you have sevenths, 00:19:29.230 --> 00:19:31.420 align:middle line:84% or if you might be given something 00:19:31.420 --> 00:19:33.090 align:middle line:90% that is not a triad at all? 00:19:33.090 --> 00:19:36.600 align:middle line:90% 00:19:36.600 --> 00:19:39.450 align:middle line:84% How would you do this with sevenths again? 00:19:39.450 --> 00:19:42.420 align:middle line:84% Did anybody do that as their extension? 00:19:42.420 --> 00:19:43.290 align:middle line:90% You did? 00:19:43.290 --> 00:19:44.040 align:middle line:90% Yeah. 00:19:44.040 --> 00:19:44.820 align:middle line:90% What did you-- 00:19:44.820 --> 00:19:47.890 align:middle line:84% AUDIENCE: The way I did it is I worked off of what-- 00:19:47.890 --> 00:19:52.440 align:middle line:84% I guess, first, I had a function that kind of reduced the input 00:19:52.440 --> 00:19:55.740 align:middle line:84% to see whether or not it could kind of work as a triad 00:19:55.740 --> 00:19:56.800 align:middle line:90% or as a semi chord. 00:19:56.800 --> 00:19:57.450 align:middle line:84% MICHAEL CUTHBERT: So first you had-- 00:19:57.450 --> 00:19:58.770 align:middle line:84% I'm just repeating for the microphone. 00:19:58.770 --> 00:20:00.570 align:middle line:84% First, you had a function that reduced it 00:20:00.570 --> 00:20:02.400 align:middle line:84% as a triad or a seventh to see if it 00:20:02.400 --> 00:20:04.620 align:middle line:90% worked with the previous thing. 00:20:04.620 --> 00:20:05.250 align:middle line:90% And then? 00:20:05.250 --> 00:20:08.460 align:middle line:90% AUDIENCE: And then I kind of-- 00:20:08.460 --> 00:20:10.300 align:middle line:84% I guess I combined both functions. 00:20:10.300 --> 00:20:12.330 align:middle line:84% And so, first, I had to iterate through a list 00:20:12.330 --> 00:20:16.300 align:middle line:90% of potential interval distances. 00:20:16.300 --> 00:20:22.680 align:middle line:84% And then just for each potential candidate I have a root, 00:20:22.680 --> 00:20:25.508 align:middle line:84% and then iterate through each potential candidate and see-- 00:20:25.508 --> 00:20:27.300 align:middle line:84% check whether or not the interval distances 00:20:27.300 --> 00:20:30.817 align:middle line:84% are the same after adjusting for if it was a bigger [INAUDIBLE]. 00:20:30.817 --> 00:20:33.400 align:middle line:84% MICHAEL CUTHBERT: So you checked each one for-- each candidate 00:20:33.400 --> 00:20:36.340 align:middle line:84% as a root, and then you checked to see if the interval distances 00:20:36.340 --> 00:20:37.940 align:middle line:90% matched something. 00:20:37.940 --> 00:20:39.158 align:middle line:90% Great, super. 00:20:39.158 --> 00:20:40.700 align:middle line:84% There was a second hand for doing it. 00:20:40.700 --> 00:20:41.390 align:middle line:90% How-- yeah. 00:20:41.390 --> 00:20:42.400 align:middle line:84% AUDIENCE: I basically did the same thing. 00:20:42.400 --> 00:20:43.360 align:middle line:84% MICHAEL CUTHBERT: Pretty similar? 00:20:43.360 --> 00:20:43.600 align:middle line:90% AUDIENCE: Yeah. 00:20:43.600 --> 00:20:45.642 align:middle line:84% MICHAEL CUTHBERT: So increase the-- great, super. 00:20:45.642 --> 00:20:48.880 align:middle line:84% This, by the way, is not one of the great unsolved problems 00:20:48.880 --> 00:20:51.700 align:middle line:84% in algorithms, but I do not know if it 00:20:51.700 --> 00:20:56.170 align:middle line:84% has been proven what the most algorithmically efficient way 00:20:56.170 --> 00:21:02.080 align:middle line:84% of finding a root in anything, especially when we have chords 00:21:02.080 --> 00:21:03.100 align:middle line:90% like-- 00:21:03.100 --> 00:21:05.653 align:middle line:84% here's one of our favorites in C major. 00:21:05.653 --> 00:21:12.130 align:middle line:90% 00:21:12.130 --> 00:21:15.792 align:middle line:84% What do we want to call that chord? 00:21:15.792 --> 00:21:17.590 align:middle line:90% AUDIENCE: Diminished seventh. 00:21:17.590 --> 00:21:19.465 align:middle line:84% MICHAEL CUTHBERT: Not close, but-- 00:21:19.465 --> 00:21:20.590 align:middle line:90% AUDIENCE: Dominant seventh. 00:21:20.590 --> 00:21:23.060 align:middle line:84% MICHAEL CUTHBERT: Dominant seventh chord. 00:21:23.060 --> 00:21:24.770 align:middle line:90% It should be four pitches. 00:21:24.770 --> 00:21:25.760 align:middle line:90% Which one's missing? 00:21:25.760 --> 00:21:26.260 align:middle line:90% AUDIENCE: D. 00:21:26.260 --> 00:21:28.450 align:middle line:84% MICHAEL CUTHBERT: D, which is the what of the chord? 00:21:28.450 --> 00:21:29.178 align:middle line:90% AUDIENCE: Second. 00:21:29.178 --> 00:21:29.845 align:middle line:90% AUDIENCE: Fifth. 00:21:29.845 --> 00:21:30.680 align:middle line:84% MICHAEL CUTHBERT: Fifth of the chord, 00:21:30.680 --> 00:21:32.222 align:middle line:84% yeah, the fifth of the chord missing, 00:21:32.222 --> 00:21:36.640 align:middle line:84% most common note in the chord to leave out, unless you're Chopin. 00:21:36.640 --> 00:21:39.250 align:middle line:84% And then he likes to leave out that one-- 00:21:39.250 --> 00:21:41.910 align:middle line:90% leave out the third. 00:21:41.910 --> 00:21:44.110 align:middle line:84% Usually, you can't leave out the bass. 00:21:44.110 --> 00:21:46.090 align:middle line:90% Otherwise, you don't have a 5. 00:21:46.090 --> 00:21:47.890 align:middle line:84% Although, there's a music theorist, 00:21:47.890 --> 00:21:50.470 align:middle line:84% Hugo Riemann, who would disagree with you on that. 00:21:50.470 --> 00:21:52.510 align:middle line:84% And of course, you can't leave out the seventh. 00:21:52.510 --> 00:21:54.520 align:middle line:90% Otherwise, you don't have that. 00:21:54.520 --> 00:21:55.300 align:middle line:90% But yeah. 00:21:55.300 --> 00:21:58.800 align:middle line:84% So how to deal with this and how to do 00:21:58.800 --> 00:22:02.080 align:middle line:84% these things is still something that we're working on 00:22:02.080 --> 00:22:05.910 align:middle line:84% And I was giving a presentation a few months ago 00:22:05.910 --> 00:22:07.837 align:middle line:90% on how things were calculated. 00:22:07.837 --> 00:22:09.420 align:middle line:84% And in the middle of the presentation, 00:22:09.420 --> 00:22:11.753 align:middle line:84% I go, oh, my gosh, that's not algorithmically efficient. 00:22:11.753 --> 00:22:13.500 align:middle line:84% And so somewhere in the music21 thing, 00:22:13.500 --> 00:22:17.142 align:middle line:84% I quickly said, to do: remember how to make this faster. 00:22:17.142 --> 00:22:18.850 align:middle line:84% And I've forgotten how to make it faster. 00:22:18.850 --> 00:22:22.710 align:middle line:84% So maybe we'll go back into that. 00:22:22.710 --> 00:22:24.420 align:middle line:90% Great. 00:22:24.420 --> 00:22:26.920 align:middle line:90% Then the last topic-- 00:22:26.920 --> 00:22:28.605 align:middle line:90% sorry, let's put that back. 00:22:28.605 --> 00:22:37.700 align:middle line:90% 00:22:37.700 --> 00:22:44.510 align:middle line:84% So Roman numerals, what are some of the differences 00:22:44.510 --> 00:22:51.480 align:middle line:84% between the Roman numerals and just finding the root? 00:22:51.480 --> 00:22:52.490 align:middle line:90% Yeah, go ahead. 00:22:52.490 --> 00:22:54.410 align:middle line:84% AUDIENCE: So I took the tonic that was 00:22:54.410 --> 00:22:56.760 align:middle line:90% given in native scale of it. 00:22:56.760 --> 00:23:01.790 align:middle line:84% And once I had the scale, I found the root of the chord, 00:23:01.790 --> 00:23:04.110 align:middle line:84% and then saw what position it was in the scale. 00:23:04.110 --> 00:23:05.110 align:middle line:90% MICHAEL CUTHBERT: Great. 00:23:05.110 --> 00:23:08.097 align:middle line:84% So you created a scale based on-- what was given? 00:23:08.097 --> 00:23:08.930 align:middle line:90% AUDIENCE: The tonic. 00:23:08.930 --> 00:23:09.705 align:middle line:90% MICHAEL CUTHBERT: The tonic-- 00:23:09.705 --> 00:23:10.872 align:middle line:90% yeah, I only gave the tonic. 00:23:10.872 --> 00:23:12.800 align:middle line:84% I didn't give the key because we're still-- 00:23:12.800 --> 00:23:15.300 align:middle line:84% created a major scale based on the tonic. 00:23:15.300 --> 00:23:17.880 align:middle line:84% And you saw which position it was in. 00:23:17.880 --> 00:23:20.520 align:middle line:84% That's really a great, great way of doing it. 00:23:20.520 --> 00:23:23.240 align:middle line:84% What if I didn't give it in this, but what 00:23:23.240 --> 00:23:24.990 align:middle line:90% if it wasn't in the scale? 00:23:24.990 --> 00:23:26.650 align:middle line:90% How would you do that? 00:23:26.650 --> 00:23:31.180 align:middle line:90% 00:23:31.180 --> 00:23:34.220 align:middle line:84% Anyone know if things like flat 3 or flat 7? 00:23:34.220 --> 00:23:34.760 align:middle line:90% Yeah. 00:23:34.760 --> 00:23:35.870 align:middle line:90% AUDIENCE: Just match the step. 00:23:35.870 --> 00:23:37.453 align:middle line:84% MICHAEL CUTHBERT: Just match the step, 00:23:37.453 --> 00:23:40.080 align:middle line:84% and then figure out the subtraction of the difference. 00:23:40.080 --> 00:23:40.580 align:middle line:90% So great. 00:23:40.580 --> 00:23:42.940 align:middle line:84% So we can find a position in the scale. 00:23:42.940 --> 00:23:47.200 align:middle line:84% If you were wondering why question 1 was 00:23:47.200 --> 00:23:51.220 align:middle line:84% on major scales, that's exactly one of the approaches 00:23:51.220 --> 00:23:52.550 align:middle line:90% I thought you could do. 00:23:52.550 --> 00:23:58.300 align:middle line:84% Anybody else have a different methodology for this? 00:23:58.300 --> 00:23:58.910 align:middle line:90% Yeah. 00:23:58.910 --> 00:23:59.810 align:middle line:84% AUDIENCE: If it wasn't in the scale, 00:23:59.810 --> 00:24:01.520 align:middle line:84% I just returned an error, saying it was invalid. 00:24:01.520 --> 00:24:01.900 align:middle line:90% MICHAEL CUTHBERT: Yep. 00:24:01.900 --> 00:24:03.680 align:middle line:84% And it's invalid in this assignment. 00:24:03.680 --> 00:24:04.640 align:middle line:90% Was it not? 00:24:04.640 --> 00:24:06.670 align:middle line:90% Yep. 00:24:06.670 --> 00:24:09.520 align:middle line:90% Good. 00:24:09.520 --> 00:24:13.780 align:middle line:84% Any other things to take all your information? 00:24:13.780 --> 00:24:15.370 align:middle line:90% Now, it was Jake, right? 00:24:15.370 --> 00:24:18.580 align:middle line:84% Who brought in major third, minor third? 00:24:18.580 --> 00:24:20.660 align:middle line:84% Yep, now I think it's time to get that in. 00:24:20.660 --> 00:24:23.020 align:middle line:84% What do you-- how do you convert that? 00:24:23.020 --> 00:24:28.630 align:middle line:84% What does this information tell us about the Roman numeral? 00:24:28.630 --> 00:24:29.130 align:middle line:90% Yeah. 00:24:29.130 --> 00:24:30.030 align:middle line:90% AUDIENCE: Uppercase, lowercase. 00:24:30.030 --> 00:24:31.150 align:middle line:84% MICHAEL CUTHBERT: Uppercase, lowercase. 00:24:31.150 --> 00:24:31.650 align:middle line:90% Good. 00:24:31.650 --> 00:24:35.140 align:middle line:84% Or there's one other thing to put on. 00:24:35.140 --> 00:24:39.940 align:middle line:84% What's the Roman numeral that often takes a special symbol? 00:24:39.940 --> 00:24:40.920 align:middle line:90% [INTERPOSING VOICES] 00:24:40.920 --> 00:24:41.310 align:middle line:90% AUDIENCE: --7. 00:24:41.310 --> 00:24:42.610 align:middle line:90% MICHAEL CUTHBERT: Diminished 7. 00:24:42.610 --> 00:24:44.730 align:middle line:84% Yeah, so the seventh scale degree, 00:24:44.730 --> 00:24:47.830 align:middle line:90% quite often the 5 with the O-- 00:24:47.830 --> 00:24:50.760 align:middle line:84% 7 with an O after it, the diminished 7. 00:24:50.760 --> 00:24:51.260 align:middle line:90% Good. 00:24:51.260 --> 00:24:54.580 align:middle line:90% 00:24:54.580 --> 00:24:58.500 align:middle line:84% And then inversions, those become kind of the problem 00:24:58.500 --> 00:25:00.360 align:middle line:90% there. 00:25:00.360 --> 00:25:06.540 align:middle line:84% So I want to give a 2-minute peek on the code that you've now 00:25:06.540 --> 00:25:07.780 align:middle line:90% unlocked. 00:25:07.780 --> 00:25:08.340 align:middle line:90% Sorry. 00:25:08.340 --> 00:25:11.250 align:middle line:84% There is a way to make this bigger. 00:25:11.250 --> 00:25:12.000 align:middle line:90% Nope. 00:25:12.000 --> 00:25:12.755 align:middle line:90% There we go. 00:25:12.755 --> 00:25:17.430 align:middle line:90% 00:25:17.430 --> 00:25:24.120 align:middle line:84% And just to give a little bit of a peek at music21's-- 00:25:24.120 --> 00:25:25.900 align:middle line:90% there we go. 00:25:25.900 --> 00:25:26.830 align:middle line:90% Sorry. 00:25:26.830 --> 00:25:27.830 align:middle line:90% A tiny bit too big. 00:25:27.830 --> 00:25:31.780 align:middle line:84% Tell me-- yeah, that should be the right size. 00:25:31.780 --> 00:25:35.680 align:middle line:90% Sorry a lot of docs over time-- 00:25:35.680 --> 00:25:36.340 align:middle line:90% things. 00:25:36.340 --> 00:25:42.310 align:middle line:84% romanNumeralFromChord-- so this is something-- so given a chord 00:25:42.310 --> 00:25:47.320 align:middle line:84% object and a key object, and then possibly 00:25:47.320 --> 00:25:50.330 align:middle line:84% a preference for do we prefer secondary dominants? 00:25:50.330 --> 00:25:51.890 align:middle line:90% Can you have in major-- 00:25:51.890 --> 00:25:55.730 align:middle line:84% can you have a major chord on two, 00:25:55.730 --> 00:26:00.700 align:middle line:84% or is that the dominant of the dominant, 5 of 5? 00:26:00.700 --> 00:26:05.360 align:middle line:84% And try to give an appropriate name. 00:26:05.360 --> 00:26:09.170 align:middle line:84% So I don't know why my first one is so complicated. 00:26:09.170 --> 00:26:11.938 align:middle line:84% I guess back then it was just like, hey, I can do this. 00:26:11.938 --> 00:26:13.730 align:middle line:84% Let's see if we can come up with something. 00:26:13.730 --> 00:26:19.210 align:middle line:84% So if you have a chord, E, C, G, B flat, and then 00:26:19.210 --> 00:26:23.500 align:middle line:84% a few extra octave things, just to throw off. 00:26:23.500 --> 00:26:27.340 align:middle line:84% In F major, that should be a V65. 00:26:27.340 --> 00:26:31.630 align:middle line:84% Who remembers their inversions of seventh chords? 00:26:31.630 --> 00:26:35.640 align:middle line:90% So root position, 5, 7, then-- 00:26:35.640 --> 00:26:37.084 align:middle line:90% first inversion, V-- 00:26:37.084 --> 00:26:37.626 align:middle line:90% AUDIENCE: 65. 00:26:37.626 --> 00:26:38.501 align:middle line:90% MICHAEL CUTHBERT: 65. 00:26:38.501 --> 00:26:39.540 align:middle line:90% Second inversion? 00:26:39.540 --> 00:26:40.890 align:middle line:90% AUDIENCE: 43. 00:26:40.890 --> 00:26:42.040 align:middle line:90% MICHAEL CUTHBERT: V43. 00:26:42.040 --> 00:26:43.230 align:middle line:90% And third inversion? 00:26:43.230 --> 00:26:43.943 align:middle line:90% AUDIENCE: V42. 00:26:43.943 --> 00:26:44.860 align:middle line:90% MICHAEL CUTHBERT: V42. 00:26:44.860 --> 00:26:47.400 align:middle line:84% Some people also teach the tradition 2. 00:26:47.400 --> 00:26:51.670 align:middle line:84% And some people-- so 42 is the most commonly used one. 00:26:51.670 --> 00:26:55.240 align:middle line:84% I've seen some people have the less-- the even more compact 2, 00:26:55.240 --> 00:26:59.010 align:middle line:84% and some people the more verbose 6/4/2. 00:26:59.010 --> 00:27:00.580 align:middle line:90% Any baseball fans? 00:27:00.580 --> 00:27:04.218 align:middle line:84% I always think of double plays as-- 00:27:04.218 --> 00:27:05.260 align:middle line:90% I mean, second inversion. 00:27:05.260 --> 00:27:08.820 align:middle line:84% That was-- because they always-- never mind. 00:27:08.820 --> 00:27:11.680 align:middle line:90% So you can have certain things. 00:27:11.680 --> 00:27:13.860 align:middle line:84% And then one of the big issues is 00:27:13.860 --> 00:27:19.500 align:middle line:84% that people call Roman numerals VI and VII in minor, 00:27:19.500 --> 00:27:21.880 align:middle line:84% according to different naming traditions. 00:27:21.880 --> 00:27:27.580 align:middle line:84% So some people say that the harmonic minor scale always 00:27:27.580 --> 00:27:30.770 align:middle line:84% dictates what the letter name is. 00:27:30.770 --> 00:27:37.270 align:middle line:84% And some people say that if you say it's diminished, 00:27:37.270 --> 00:27:39.842 align:middle line:84% like diminished 7, you already know it's been raised, 00:27:39.842 --> 00:27:40.800 align:middle line:90% and you say it's major. 00:27:40.800 --> 00:27:42.640 align:middle line:84% You know it's been lowered, and you 00:27:42.640 --> 00:27:44.870 align:middle line:84% don't need a sharp or a flat in front of it. 00:27:44.870 --> 00:27:47.182 align:middle line:84% So there's a whole bunch of different conventions. 00:27:47.182 --> 00:27:48.640 align:middle line:84% And unfortunately, that's something 00:27:48.640 --> 00:27:50.320 align:middle line:90% we haven't standardized. 00:27:50.320 --> 00:27:53.390 align:middle line:84% For anyone who's had two different music theory teachers, 00:27:53.390 --> 00:27:56.000 align:middle line:84% you might have already encountered that. 00:27:56.000 --> 00:28:00.550 align:middle line:84% So let's get down to the code to show some of the things 00:28:00.550 --> 00:28:01.520 align:middle line:90% that I found. 00:28:01.520 --> 00:28:03.340 align:middle line:84% And maybe you'll come up with a better one. 00:28:03.340 --> 00:28:07.000 align:middle line:84% Who has taken 302 or a class that has encountered 00:28:07.000 --> 00:28:08.150 align:middle line:90% augmented sixth chords? 00:28:08.150 --> 00:28:08.650 align:middle line:90% Yeah. 00:28:08.650 --> 00:28:13.123 align:middle line:84% So you know these country codes, Italian, French, Swiss, 00:28:13.123 --> 00:28:15.165 align:middle line:84% some people call it, some people English, German. 00:28:15.165 --> 00:28:18.370 align:middle line:84% You don't need to worry about that for this class 00:28:18.370 --> 00:28:19.670 align:middle line:90% since we didn't have it. 00:28:19.670 --> 00:28:24.990 align:middle line:84% But one of the other things that comes up a lot 00:28:24.990 --> 00:28:31.170 align:middle line:84% is that you need to be able to change certain things that 00:28:31.170 --> 00:28:31.780 align:middle line:90% might come up. 00:28:31.780 --> 00:28:39.220 align:middle line:84% So that's a 57 chord is 753 or 7531, if you want to call it, 00:28:39.220 --> 00:28:41.766 align:middle line:90% but we only call it 7. 00:28:41.766 --> 00:28:47.170 align:middle line:84% 65, seventh chord first inversion is 6/5/3, 00:28:47.170 --> 00:28:48.430 align:middle line:90% but we call it 65. 00:28:48.430 --> 00:28:51.310 align:middle line:84% So you just need a bunch of substitution things. 00:28:51.310 --> 00:28:53.580 align:middle line:84% And these aren't all of them, because we just 00:28:53.580 --> 00:28:57.870 align:middle line:84% grabbed them from a lot of places to make sure ninth works. 00:28:57.870 --> 00:29:00.130 align:middle line:84% That's always a nice thing to do. 00:29:00.130 --> 00:29:04.080 align:middle line:84% So what we find is the first thing you want to know 00:29:04.080 --> 00:29:07.900 align:middle line:84% is, what's the root of the chord? 00:29:07.900 --> 00:29:09.870 align:middle line:84% And finding the root, as I said, is already 00:29:09.870 --> 00:29:11.140 align:middle line:90% an interesting algorithm. 00:29:11.140 --> 00:29:14.310 align:middle line:84% And then figure out how many semitones is there 00:29:14.310 --> 00:29:17.650 align:middle line:84% between that root and whatever is the third, 00:29:17.650 --> 00:29:21.025 align:middle line:84% and find out if it's on the basis of major or minor, 00:29:21.025 --> 00:29:22.400 align:middle line:84% because that's going to determine 00:29:22.400 --> 00:29:24.030 align:middle line:90% uppercase or lowercase. 00:29:24.030 --> 00:29:30.110 align:middle line:84% We'll skip anything that says, if there isn't a key. 00:29:30.110 --> 00:29:31.200 align:middle line:90% Put that in. 00:29:31.200 --> 00:29:35.120 align:middle line:84% Then created this conceptual device called 00:29:35.120 --> 00:29:41.130 align:middle line:84% a figure tuple, which is the notion of something like, 00:29:41.130 --> 00:29:44.060 align:middle line:90% if you had a chord with-- 00:29:44.060 --> 00:29:46.250 align:middle line:90% oh, I don't know-- 00:29:46.250 --> 00:29:47.760 align:middle line:90% you might-- sorry. 00:29:47.760 --> 00:29:49.840 align:middle line:90% That is not a French vocal clef. 00:29:49.840 --> 00:29:53.030 align:middle line:90% 00:29:53.030 --> 00:30:02.630 align:middle line:84% You might have-- call that flat 5, flat 3. 00:30:02.630 --> 00:30:07.220 align:middle line:84% In some ways, this, one of these figures, 00:30:07.220 --> 00:30:10.850 align:middle line:84% call this a figure tuple, which tells you-- 00:30:10.850 --> 00:30:12.170 align:middle line:90% oop! 00:30:12.170 --> 00:30:13.130 align:middle line:90% Trip hazard. 00:30:13.130 --> 00:30:16.880 align:middle line:90% What's the thing over the base? 00:30:16.880 --> 00:30:18.870 align:middle line:84% It's just sometimes easier to keep 00:30:18.870 --> 00:30:21.990 align:middle line:84% track of how many semitones is it altered 00:30:21.990 --> 00:30:24.270 align:middle line:90% and what do we call it? 00:30:24.270 --> 00:30:28.090 align:middle line:84% So you might think that negative 1 always means flat, 00:30:28.090 --> 00:30:30.450 align:middle line:84% but there are some cases where that's implied 00:30:30.450 --> 00:30:33.840 align:middle line:90% by other parts of the thing. 00:30:33.840 --> 00:30:38.791 align:middle line:84% Then correct the flat VI to VI in minor, 00:30:38.791 --> 00:30:40.083 align:middle line:90% depending on people's spelling. 00:30:40.083 --> 00:30:42.780 align:middle line:90% 00:30:42.780 --> 00:30:44.670 align:middle line:84% Then we end up trying to figure out 00:30:44.670 --> 00:30:49.170 align:middle line:84% all these things on how we can figure-- how we can transpose 00:30:49.170 --> 00:30:54.150 align:middle line:84% the tonic so that we can deal with those things that 00:30:54.150 --> 00:30:55.330 align:middle line:90% are outside the scale. 00:30:55.330 --> 00:30:58.770 align:middle line:84% So like what we said, if you have a root that is not 00:30:58.770 --> 00:31:01.380 align:middle line:84% part of the scale, then we just really quickly 00:31:01.380 --> 00:31:05.040 align:middle line:84% construct a whole other scale down a semitone 00:31:05.040 --> 00:31:06.430 align:middle line:90% or up a semitone. 00:31:06.430 --> 00:31:08.940 align:middle line:84% And so we can do all the other calculations, 00:31:08.940 --> 00:31:11.846 align:middle line:84% and then just throw flats on everything afterwards. 00:31:11.846 --> 00:31:14.670 align:middle line:90% 00:31:14.670 --> 00:31:17.450 align:middle line:90% Probably guess what this does-- 00:31:17.450 --> 00:31:21.050 align:middle line:84% capitalize if it's major, lowercase if it's minor. 00:31:21.050 --> 00:31:23.880 align:middle line:84% And then a lot of these things are slow. 00:31:23.880 --> 00:31:26.160 align:middle line:84% So a lot of-- if we've already seen this before, 00:31:26.160 --> 00:31:29.240 align:middle line:90% get it from the cache. 00:31:29.240 --> 00:31:38.310 align:middle line:84% And then something to turn 1 to i, 2 to ii, 3 to whatever-- 00:31:38.310 --> 00:31:42.890 align:middle line:84% convert the number from 1 to 3,999 to a Roman numeral. 00:31:42.890 --> 00:31:48.050 align:middle line:84% I don't know why I stopped at 3,999. 00:31:48.050 --> 00:31:49.320 align:middle line:90% It's because I'm a historian. 00:31:49.320 --> 00:31:52.920 align:middle line:84% And the numbers above 3,999 were never standardized, 00:31:52.920 --> 00:31:55.250 align:middle line:84% no matter what your teachers tell you. 00:31:55.250 --> 00:32:01.220 align:middle line:84% Then we try to figure out what kind figure 00:32:01.220 --> 00:32:03.650 align:middle line:90% it's going to be to try to get-- 00:32:03.650 --> 00:32:05.520 align:middle line:84% what kind of inversion it's going to be. 00:32:05.520 --> 00:32:07.230 align:middle line:90% So what's the string for that? 00:32:07.230 --> 00:32:10.640 align:middle line:84% And that's where a lot of these-- 00:32:10.640 --> 00:32:11.330 align:middle line:90% what is it? 00:32:11.330 --> 00:32:16.740 align:middle line:90% 643 becomes 64 and so on. 00:32:16.740 --> 00:32:21.850 align:middle line:90% 00:32:21.850 --> 00:32:24.620 align:middle line:84% Then there's-- then we'll try to think about-- 00:32:24.620 --> 00:32:27.500 align:middle line:90% so we take-- what's the prefix? 00:32:27.500 --> 00:32:30.050 align:middle line:90% Is it flat too, whatever? 00:32:30.050 --> 00:32:32.600 align:middle line:90% Add to that the Roman letter. 00:32:32.600 --> 00:32:34.990 align:middle line:84% Is it I, II, III, IV, V, VI, VII? 00:32:34.990 --> 00:32:36.790 align:middle line:90% And then the inversion. 00:32:36.790 --> 00:32:40.900 align:middle line:84% And then everything after that is every special case 00:32:40.900 --> 00:32:45.130 align:middle line:84% that we've encountered over time that turns out 00:32:45.130 --> 00:32:52.240 align:middle line:84% to be an inconsistency in the standard of Roman numerals. 00:32:52.240 --> 00:32:54.490 align:middle line:84% This is not a history class, but there's 00:32:54.490 --> 00:32:58.100 align:middle line:84% a really fascinating thing about Roman numerals analysis. 00:32:58.100 --> 00:33:00.490 align:middle line:84% And that is it is a mashing together 00:33:00.490 --> 00:33:05.440 align:middle line:84% two different, incompatible analysis 00:33:05.440 --> 00:33:08.780 align:middle line:84% types that over time got put together into one, 00:33:08.780 --> 00:33:13.270 align:middle line:84% but so that things like the uppercase and lowercase 00:33:13.270 --> 00:33:17.400 align:middle line:84% duplicating the function of putting a flat 3 on something. 00:33:17.400 --> 00:33:20.130 align:middle line:84% And so what happens if you're in C major, 00:33:20.130 --> 00:33:24.655 align:middle line:84% and then you see lowercase v flat 3? 00:33:24.655 --> 00:33:28.190 align:middle line:90% 00:33:28.190 --> 00:33:31.290 align:middle line:84% So let's say you're in C major and you see lowercase v flat 3. 00:33:31.290 --> 00:33:32.810 align:middle line:84% What do you think that should be? 00:33:32.810 --> 00:33:36.450 align:middle line:90% G as the base, as the root. 00:33:36.450 --> 00:33:37.340 align:middle line:90% Yep. 00:33:37.340 --> 00:33:38.120 align:middle line:90% AUDIENCE: B-flat. 00:33:38.120 --> 00:33:40.550 align:middle line:84% MICHAEL CUTHBERT: B-flat and D. What happens 00:33:40.550 --> 00:33:43.806 align:middle line:90% if I leave off the flat 3? 00:33:43.806 --> 00:33:45.202 align:middle line:90% AUDIENCE: The same. 00:33:45.202 --> 00:33:46.160 align:middle line:90% MICHAEL CUTHBERT: Same. 00:33:46.160 --> 00:33:48.390 align:middle line:90% So is this a cautionary? 00:33:48.390 --> 00:33:50.870 align:middle line:84% You can add it, or you can put it out. 00:33:50.870 --> 00:33:52.650 align:middle line:90% But then there are other cases-- 00:33:52.650 --> 00:34:03.505 align:middle line:84% what if I'm in C major and I put I7 versus I flat 7? 00:34:03.505 --> 00:34:07.910 align:middle line:90% 00:34:07.910 --> 00:34:13.630 align:middle line:84% But the same thing with V7 doesn't need the flat. 00:34:13.630 --> 00:34:16.719 align:middle line:90% V flat 7, same thing? 00:34:16.719 --> 00:34:19.690 align:middle line:84% So there are all these inconsistencies 00:34:19.690 --> 00:34:22.429 align:middle line:84% in the world of Roman numeral analysis. 00:34:22.429 --> 00:34:25.060 align:middle line:84% And it really begins to get exposed 00:34:25.060 --> 00:34:28.330 align:middle line:84% when you start doing things that we're going 00:34:28.330 --> 00:34:29.643 align:middle line:90% to be looking into right now. 00:34:29.643 --> 00:34:31.810 align:middle line:84% So we're going to get to the algorithmic composition 00:34:31.810 --> 00:34:32.750 align:middle line:90% in just a bit. 00:34:32.750 --> 00:34:35.610 align:middle line:84% But what I'd like you to do for a second is-- 00:34:35.610 --> 00:34:36.110 align:middle line:90% oops. 00:34:36.110 --> 00:34:39.130 align:middle line:90% Which one's here? 00:34:39.130 --> 00:34:43.580 align:middle line:84% We'll go back into our favorite Bach piece, because corpus-- 00:34:43.580 --> 00:34:44.080 align:middle line:90% sorry. 00:34:44.080 --> 00:34:48.520 align:middle line:84% Switching gears, laptops open again. 00:34:48.520 --> 00:34:52.750 align:middle line:84% We did this once already, bwv66.6. 00:34:52.750 --> 00:34:56.965 align:middle line:90% And we'll remember chordify. 00:34:56.965 --> 00:35:00.130 align:middle line:90% 00:35:00.130 --> 00:35:07.090 align:middle line:84% And we'll say chord_bach today, chord_bach=bach.chordify(). 00:35:07.090 --> 00:35:12.730 align:middle line:84% And I remember this one as basically an F-sharp minor. 00:35:12.730 --> 00:35:19.350 align:middle line:84% # So we'll say, fm=key.Key('f#'), F-sharp. 00:35:19.350 --> 00:35:23.040 align:middle line:90% 00:35:23.040 --> 00:35:27.660 align:middle line:84% And what we'll do on this is just for-- 00:35:27.660 --> 00:35:32.482 align:middle line:84% so actually, snap this up when you've got this. 00:35:32.482 --> 00:35:34.440 align:middle line:84% And also, by the way, if I'm typoing, this one, 00:35:34.440 --> 00:35:35.607 align:middle line:90% I don't have a template for. 00:35:35.607 --> 00:35:38.770 align:middle line:84% So if I typo, definitely correct me on this. 00:35:38.770 --> 00:35:43.650 align:middle line:84% So for chord in ch, I often say, I 00:35:43.650 --> 00:35:45.510 align:middle line:84% don't write the word chord because I 00:35:45.510 --> 00:35:48.120 align:middle line:84% don't want to lose access to my chord module-- 00:35:48.120 --> 00:35:52.620 align:middle line:84% chord_bach chord.Chord for each chord. 00:35:52.620 --> 00:36:04.410 align:middle line:84% We'll say rn=roman.romanNumeralFromChord 00:36:04.410 --> 00:36:07.090 align:middle line:84% ch-- and we're in the key of F minor. 00:36:07.090 --> 00:36:09.880 align:middle line:84% So you could just write the string fm there, 00:36:09.880 --> 00:36:11.950 align:middle line:90% but it'll be a lot slower. 00:36:11.950 --> 00:36:15.040 align:middle line:90% And then we'll just say ch-- 00:36:15.040 --> 00:36:17.270 align:middle line:84% so actually, give a second on that. 00:36:17.270 --> 00:36:21.220 align:middle line:84% So you're going to iterate for the recurse. 00:36:21.220 --> 00:36:23.810 align:middle line:84% The square brackets mean all the chords in chord_bach. 00:36:23.810 --> 00:36:26.650 align:middle line:90% Get the chord out. 00:36:26.650 --> 00:36:28.880 align:middle line:84% Analyze the Roman numeral from chord. 00:36:28.880 --> 00:36:32.030 align:middle line:84% If I were a really, really mean prof, 00:36:32.030 --> 00:36:34.550 align:middle line:84% I would say your next assignment is to reimplement that. 00:36:34.550 --> 00:36:37.880 align:middle line:84% But you can see the gray hairs here. 00:36:37.880 --> 00:36:39.410 align:middle line:90% That's exactly from that-- 00:36:39.410 --> 00:36:41.480 align:middle line:90% from implementing that one. 00:36:41.480 --> 00:36:45.830 align:middle line:84% That and chordify are the two reasons I'm getting old. 00:36:45.830 --> 00:36:50.410 align:middle line:84% And now what we're going to do is we'll say the chord's lyric-- 00:36:50.410 --> 00:36:53.080 align:middle line:90% we did this once, right? 00:36:53.080 --> 00:36:54.440 align:middle line:90% ch.lyric=rn.figure. 00:36:54.440 --> 00:37:00.040 align:middle line:90% 00:37:00.040 --> 00:37:02.870 align:middle line:84% I think we did this, but we did it rather fast. 00:37:02.870 --> 00:37:04.425 align:middle line:90% So I want to make sure that. 00:37:04.425 --> 00:37:08.010 align:middle line:90% 00:37:08.010 --> 00:37:08.510 align:middle line:90% Oops. 00:37:08.510 --> 00:37:12.450 align:middle line:84% That's not going to do anything, right? 00:37:12.450 --> 00:37:14.140 align:middle line:90% Because I put it onto the thing. 00:37:14.140 --> 00:37:16.240 align:middle line:90% I want chord_bach.show. 00:37:16.240 --> 00:37:17.306 align:middle line:90% My apologies. 00:37:17.306 --> 00:37:20.460 align:middle line:90% 00:37:20.460 --> 00:37:22.260 align:middle line:84% And you're going to realize there's 00:37:22.260 --> 00:37:24.420 align:middle line:84% one thing I didn't do that's going 00:37:24.420 --> 00:37:25.870 align:middle line:90% to make it look really funny. 00:37:25.870 --> 00:37:30.430 align:middle line:84% I forgot to put all of the chords in closed position, 00:37:30.430 --> 00:37:32.405 align:middle line:84% but at least it works pretty well. 00:37:32.405 --> 00:37:35.340 align:middle line:90% 00:37:35.340 --> 00:37:39.515 align:middle line:84% So I'm going to scroll to the end, so around here. 00:37:39.515 --> 00:37:43.080 align:middle line:90% 00:37:43.080 --> 00:37:46.950 align:middle line:84% If you didn't get it all, don't worry. 00:37:46.950 --> 00:37:51.070 align:middle line:84% Some of y'all are to be thanked in the class, 00:37:51.070 --> 00:37:54.780 align:middle line:84% especially John and Adam, for when I forget to put a notebook 00:37:54.780 --> 00:37:55.530 align:middle line:90% up. 00:37:55.530 --> 00:37:56.290 align:middle line:90% They remind me. 00:37:56.290 --> 00:37:58.040 align:middle line:84% And now all the previous notebooks are up. 00:37:58.040 --> 00:38:01.053 align:middle line:84% So if you miss anything, they'll be going up later. 00:38:01.053 --> 00:38:02.970 align:middle line:84% But you can see that there's some places where 00:38:02.970 --> 00:38:06.270 align:middle line:84% you see chords that look like chords that you've 00:38:06.270 --> 00:38:11.330 align:middle line:90% seen in your life, iv, V6, i. 00:38:11.330 --> 00:38:14.450 align:middle line:84% And then there are places, again, 00:38:14.450 --> 00:38:16.380 align:middle line:90% V. That looks pretty good. 00:38:16.380 --> 00:38:16.880 align:middle line:90% Sorry. 00:38:16.880 --> 00:38:20.270 align:middle line:84% That autosave thing knocks it down. 00:38:20.270 --> 00:38:25.010 align:middle line:90% And then chords 763. 00:38:25.010 --> 00:38:28.670 align:middle line:90% That's rather unusual. 00:38:28.670 --> 00:38:33.690 align:middle line:84% Flat VI augmented in 64 position. 00:38:33.690 --> 00:38:36.770 align:middle line:84% Y'all remember how to resolve that chord, right? 00:38:36.770 --> 00:38:37.520 align:middle line:90% No, no. 00:38:37.520 --> 00:38:39.270 align:middle line:84% I've never heard of that chord in my life. 00:38:39.270 --> 00:38:44.940 align:middle line:84% So this is a pretty dumb way of working with things. 00:38:44.940 --> 00:38:47.300 align:middle line:84% In fact, I'm just going to go straight from this 00:38:47.300 --> 00:38:50.040 align:middle line:90% to the last part here. 00:38:50.040 --> 00:38:53.540 align:middle line:84% Then if you get to the top, you see 00:38:53.540 --> 00:38:56.310 align:middle line:84% a lot of figures that look pretty normal. 00:38:56.310 --> 00:38:58.640 align:middle line:90% No-- nothing after the III. 00:38:58.640 --> 00:39:01.620 align:middle line:90% You see 6, nothing, 6, whatever. 00:39:01.620 --> 00:39:03.583 align:middle line:90% These look a lot better, 7. 00:39:03.583 --> 00:39:05.250 align:middle line:84% Those are numbers you're used to seeing, 00:39:05.250 --> 00:39:07.520 align:middle line:84% the Arabic numerals you're used to seeing. 00:39:07.520 --> 00:39:10.040 align:middle line:90% But the Romans are way off. 00:39:10.040 --> 00:39:14.200 align:middle line:90% Why are these Romans so weird? 00:39:14.200 --> 00:39:15.670 align:middle line:90% Because we're wearing togas. 00:39:15.670 --> 00:39:16.320 align:middle line:90% No, no. 00:39:16.320 --> 00:39:17.820 align:middle line:84% Why are the Roman numerals so weird? 00:39:17.820 --> 00:39:22.390 align:middle line:90% 00:39:22.390 --> 00:39:25.570 align:middle line:90% I don't remember this piece. 00:39:25.570 --> 00:39:26.800 align:middle line:90% Go ahead. 00:39:26.800 --> 00:39:28.780 align:middle line:90% AUDIENCE: It starts in A. 00:39:28.780 --> 00:39:32.200 align:middle line:84% MICHAEL CUTHBERT: It starts in A. Yeah, if we go back, and-- 00:39:32.200 --> 00:39:36.190 align:middle line:84% we don't have to-- we remember how it goes a bit, right? 00:39:36.190 --> 00:39:39.220 align:middle line:90% It starts in A major. 00:39:39.220 --> 00:39:42.460 align:middle line:84% So one of the things you can start thinking about 00:39:42.460 --> 00:39:46.310 align:middle line:84% on your computer system is if you see a lot of III, 00:39:46.310 --> 00:39:50.500 align:middle line:84% flat 6, flat 6, III or flat VII 3, 3 flat VII, 00:39:50.500 --> 00:39:53.600 align:middle line:84% and you're dealing with a classical piece of music, 00:39:53.600 --> 00:39:56.210 align:middle line:84% what have you probably gotten wrong? 00:39:56.210 --> 00:39:56.960 align:middle line:90% AUDIENCE: The key. 00:39:56.960 --> 00:39:58.043 align:middle line:90% MICHAEL CUTHBERT: The key. 00:39:58.043 --> 00:40:01.070 align:middle line:84% Specifically, you've put it in blank instead of blank. 00:40:01.070 --> 00:40:03.910 align:middle line:90% You've put it in-- 00:40:03.910 --> 00:40:04.648 align:middle line:90% what kind of? 00:40:04.648 --> 00:40:05.690 align:middle line:90% AUDIENCE: Relative minor. 00:40:05.690 --> 00:40:07.920 align:middle line:84% MICHAEL CUTHBERT: Relative minor instead of the relative major. 00:40:07.920 --> 00:40:08.420 align:middle line:90% Good. 00:40:08.420 --> 00:40:11.690 align:middle line:84% What if you accidentally analyze the piece in major 00:40:11.690 --> 00:40:12.630 align:middle line:90% instead of minor? 00:40:12.630 --> 00:40:16.995 align:middle line:84% What would you be seeing a lot of instead for 1 to 5? 00:40:16.995 --> 00:40:20.962 align:middle line:90% 00:40:20.962 --> 00:40:21.528 align:middle line:90% Yeah. 00:40:21.528 --> 00:40:22.320 align:middle line:90% AUDIENCE: Oh, yeah. 00:40:22.320 --> 00:40:23.130 align:middle line:90% You'll see 6 minor. 00:40:23.130 --> 00:40:25.710 align:middle line:90% You'll see 2 minor and 3 major. 00:40:25.710 --> 00:40:26.960 align:middle line:90% MICHAEL CUTHBERT: 6 minor, 2-- 00:40:26.960 --> 00:40:29.370 align:middle line:90% yeah, 6, 2's, and 3's-- 00:40:29.370 --> 00:40:31.760 align:middle line:84% so that might tell you something about, 00:40:31.760 --> 00:40:35.040 align:middle line:84% hey, you're in a different position. 00:40:35.040 --> 00:40:35.540 align:middle line:90% Great. 00:40:35.540 --> 00:40:43.380 align:middle line:84% So strange Roman numerals probably means failure of key. 00:40:43.380 --> 00:40:50.545 align:middle line:84% Strange figures-- what do these strange figures probably mean? 00:40:50.545 --> 00:40:55.500 align:middle line:90% 00:40:55.500 --> 00:40:56.000 align:middle line:90% Yeah, Adam. 00:40:56.000 --> 00:40:57.840 align:middle line:84% AUDIENCE: It isn't a very compatible chord. 00:40:57.840 --> 00:41:00.150 align:middle line:84% MICHAEL CUTHBERT: Isn't a very compatible chord, 00:41:00.150 --> 00:41:04.267 align:middle line:84% or it's a chord that has embedded possibly what in it? 00:41:04.267 --> 00:41:05.350 align:middle line:90% AUDIENCE: Non-chord tones. 00:41:05.350 --> 00:41:07.990 align:middle line:84% MICHAEL CUTHBERT: Non-chord tones, good. 00:41:07.990 --> 00:41:10.940 align:middle line:84% Everybody's favorite non-chord tones. 00:41:10.940 --> 00:41:14.906 align:middle line:84% We'll go-- Hannah, favorite non-chord tone? 00:41:14.906 --> 00:41:16.430 align:middle line:84% It doesn't have to be your favorite. 00:41:16.430 --> 00:41:17.508 align:middle line:90% Just name one. 00:41:17.508 --> 00:41:18.800 align:middle line:90% AUDIENCE: I'm not going to lie. 00:41:18.800 --> 00:41:19.870 align:middle line:90% I don't remember what it is. 00:41:19.870 --> 00:41:20.650 align:middle line:84% MICHAEL CUTHBERT: Don't remember any. 00:41:20.650 --> 00:41:21.380 align:middle line:90% Great, great. 00:41:21.380 --> 00:41:23.380 align:middle line:84% So that's great, because you'll be listening up, 00:41:23.380 --> 00:41:25.297 align:middle line:84% because we're going to be doing some of these. 00:41:25.297 --> 00:41:28.365 align:middle line:90% 00:41:28.365 --> 00:41:29.520 align:middle line:90% AUDIENCE: Diminished fifth. 00:41:29.520 --> 00:41:32.020 align:middle line:84% MICHAEL CUTHBERT: Diminished fifth-- ah, so diminished fifth 00:41:32.020 --> 00:41:36.590 align:middle line:84% is a chord tone when you say it that way. 00:41:36.590 --> 00:41:42.910 align:middle line:84% But it's not-- or non-harmonic tone 00:41:42.910 --> 00:41:45.730 align:middle line:84% is maybe the term that you've heard in other things. 00:41:45.730 --> 00:41:48.440 align:middle line:84% When you say it that way, it might be part of a chord, 00:41:48.440 --> 00:41:51.775 align:middle line:84% but it might-- it has to have a function in order to do it. 00:41:51.775 --> 00:41:52.900 align:middle line:90% So a function-- yeah, John? 00:41:52.900 --> 00:41:53.590 align:middle line:90% AUDIENCE: Anticipation. 00:41:53.590 --> 00:41:54.550 align:middle line:90% MICHAEL CUTHBERT: An-- 00:41:54.550 --> 00:41:55.730 align:middle line:90% --ticipation. 00:41:55.730 --> 00:41:59.210 align:middle line:84% Yeah, where you get to the chord-- 00:41:59.210 --> 00:42:01.400 align:middle line:84% maybe you get to the tonic a little bit too early. 00:42:01.400 --> 00:42:01.630 align:middle line:90% Good. 00:42:01.630 --> 00:42:03.047 align:middle line:84% Anticipation is a really good one. 00:42:03.047 --> 00:42:05.520 align:middle line:90% Anyone else have a favorite one? 00:42:05.520 --> 00:42:06.150 align:middle line:90% Yeah. 00:42:06.150 --> 00:42:07.230 align:middle line:90% AUDIENCE: Suspension. 00:42:07.230 --> 00:42:10.710 align:middle line:84% MICHAEL CUTHBERT: Suspension Yeah, we hold the chord-- 00:42:10.710 --> 00:42:12.910 align:middle line:90% the tone "too long." 00:42:12.910 --> 00:42:13.717 align:middle line:90% I mean, it's great. 00:42:13.717 --> 00:42:15.550 align:middle line:84% Don't-- you know, obviously, it's wonderful, 00:42:15.550 --> 00:42:17.290 align:middle line:84% but too long for the harmonic analysis. 00:42:17.290 --> 00:42:21.720 align:middle line:84% So let's say-- computationally, if your job is 00:42:21.720 --> 00:42:24.670 align:middle line:84% to get rid of non-chord tones, what are you going to do? 00:42:24.670 --> 00:42:28.290 align:middle line:84% How do you get rid of anticipation? 00:42:28.290 --> 00:42:30.912 align:middle line:84% AUDIENCE: You just have the rest of the chord following. 00:42:30.912 --> 00:42:31.870 align:middle line:90% MICHAEL CUTHBERT: Yeah. 00:42:31.870 --> 00:42:33.850 align:middle line:84% You just have the rest of the chord following. 00:42:33.850 --> 00:42:34.350 align:middle line:90% Great. 00:42:34.350 --> 00:42:36.242 align:middle line:84% How do you get rid of suspension? 00:42:36.242 --> 00:42:37.450 align:middle line:90% AUDIENCE: You cut it shorter. 00:42:37.450 --> 00:42:38.992 align:middle line:84% MICHAEL CUTHBERT: You cut it shorter. 00:42:38.992 --> 00:42:39.960 align:middle line:90% Great, great. 00:42:39.960 --> 00:42:42.400 align:middle line:84% So what's another non-chord tone? 00:42:42.400 --> 00:42:44.040 align:middle line:90% Nobody's done the one that you-- 00:42:44.040 --> 00:42:45.940 align:middle line:84% the first one that most of us learn. 00:42:45.940 --> 00:42:47.205 align:middle line:90% These are more-- yeah. 00:42:47.205 --> 00:42:48.270 align:middle line:90% AUDIENCE: Stepwise. 00:42:48.270 --> 00:42:50.478 align:middle line:84% MICHAEL CUTHBERT: Stepwise, yeah, between two things. 00:42:50.478 --> 00:42:51.842 align:middle line:90% What do we call that? 00:42:51.842 --> 00:42:52.800 align:middle line:90% AUDIENCE: Passing tone. 00:42:52.800 --> 00:42:55.840 align:middle line:84% MICHAEL CUTHBERT: Passing tone, yes, the passing tone. 00:42:55.840 --> 00:42:57.060 align:middle line:90% So great. 00:42:57.060 --> 00:43:01.240 align:middle line:84% Well, how do you usually get rid of a passing tone? 00:43:01.240 --> 00:43:04.250 align:middle line:84% Just cut it out and make the previous note longer, right? 00:43:04.250 --> 00:43:07.890 align:middle line:84% How do you identify a passing tone? 00:43:07.890 --> 00:43:11.590 align:middle line:90% 00:43:11.590 --> 00:43:13.220 align:middle line:84% It just looks like it, doesn't it? 00:43:13.220 --> 00:43:16.220 align:middle line:84% It's so easy on our neural processors or our eyes. 00:43:16.220 --> 00:43:17.740 align:middle line:90% It just sounds like it. 00:43:17.740 --> 00:43:19.140 align:middle line:90% What kinds of things-- 00:43:19.140 --> 00:43:22.090 align:middle line:90% 00:43:22.090 --> 00:43:25.510 align:middle line:84% what criteria do we need to know that something is a passing 00:43:25.510 --> 00:43:26.010 align:middle line:90% tone? 00:43:26.010 --> 00:43:43.330 align:middle line:90% 00:43:43.330 --> 00:43:44.670 align:middle line:90% Those are the worst stems ever. 00:43:44.670 --> 00:43:51.190 align:middle line:90% 00:43:51.190 --> 00:43:53.380 align:middle line:84% Actually, the clef doesn't matter, does it? 00:43:53.380 --> 00:43:55.030 align:middle line:90% No, it's still a passing tone. 00:43:55.030 --> 00:43:57.340 align:middle line:90% Which one's the passing tone? 00:43:57.340 --> 00:43:59.110 align:middle line:90% Who votes for C? 00:43:59.110 --> 00:44:00.400 align:middle line:90% Who votes for D? 00:44:00.400 --> 00:44:01.640 align:middle line:90% Who votes for E? 00:44:01.640 --> 00:44:02.140 align:middle line:90% OK, good. 00:44:02.140 --> 00:44:03.687 align:middle line:84% Lots of Ds, especially on the side 00:44:03.687 --> 00:44:05.520 align:middle line:84% of the room that I have privileged by making 00:44:05.520 --> 00:44:07.360 align:middle line:90% it much easier to see. 00:44:07.360 --> 00:44:08.140 align:middle line:90% Sorry about that. 00:44:08.140 --> 00:44:10.410 align:middle line:84% I'm not going to stay here very long, so just squint 00:44:10.410 --> 00:44:14.580 align:middle line:84% for a little bit and feel free to shout out what I'm doing 00:44:14.580 --> 00:44:16.420 align:middle line:90% for free closed captioning. 00:44:16.420 --> 00:44:19.170 align:middle line:90% Great. 00:44:19.170 --> 00:44:22.140 align:middle line:84% So what kinds of things would you be putting if statements 00:44:22.140 --> 00:44:25.372 align:middle line:84% on if you were like, "I'll just throw it in a neural net 00:44:25.372 --> 00:44:26.080 align:middle line:90% and it'll learn"? 00:44:26.080 --> 00:44:28.930 align:middle line:84% But no, if you had to program it, 00:44:28.930 --> 00:44:33.270 align:middle line:90% what would you be looking for? 00:44:33.270 --> 00:44:33.790 align:middle line:90% Yeah. 00:44:33.790 --> 00:44:34.540 align:middle line:90% AUDIENCE: Seconds. 00:44:34.540 --> 00:44:35.623 align:middle line:90% MICHAEL CUTHBERT: Seconds. 00:44:35.623 --> 00:44:41.290 align:middle line:84% So we have to have a second, and then a second. 00:44:41.290 --> 00:44:46.830 align:middle line:84% Do the seconds have to be ascending? 00:44:46.830 --> 00:44:48.520 align:middle line:90% No. 00:44:48.520 --> 00:44:51.748 align:middle line:84% Can they be in opposite directions? 00:44:51.748 --> 00:44:52.290 align:middle line:90% AUDIENCE: No. 00:44:52.290 --> 00:44:53.165 align:middle line:90% MICHAEL CUTHBERT: No. 00:44:53.165 --> 00:44:54.180 align:middle line:90% Why not? 00:44:54.180 --> 00:44:55.080 align:middle line:84% AUDIENCE: Because then you have a neighbor. 00:44:55.080 --> 00:44:57.288 align:middle line:84% MICHAEL CUTHBERT: Then you have a neighbor tone, yep. 00:44:57.288 --> 00:45:01.470 align:middle line:84% So 2, 2, second, second equals passing tone. 00:45:01.470 --> 00:45:05.210 align:middle line:84% Negative 2, negative 2 equals passing tone. 00:45:05.210 --> 00:45:09.000 align:middle line:84% 2, negative 2 equals neighbor tone. 00:45:09.000 --> 00:45:12.540 align:middle line:84% And negative 2, 2 is neighbor tone. 00:45:12.540 --> 00:45:15.200 align:middle line:84% I know some of you are already trying to pass your LeetCode 00:45:15.200 --> 00:45:17.360 align:middle line:84% things and thinking, what's the bitwise operation 00:45:17.360 --> 00:45:19.730 align:middle line:84% that's going to make it so I don't have to put all four 00:45:19.730 --> 00:45:20.640 align:middle line:90% of those? 00:45:20.640 --> 00:45:22.440 align:middle line:90% No, it's OK, it's only four. 00:45:22.440 --> 00:45:26.580 align:middle line:84% So you can look-- find these in here. 00:45:26.580 --> 00:45:27.980 align:middle line:84% So yeah, you might be doing that. 00:45:27.980 --> 00:45:29.960 align:middle line:84% Then anything else that you think 00:45:29.960 --> 00:45:34.520 align:middle line:84% is important for saying that something is a passing tone? 00:45:34.520 --> 00:45:37.220 align:middle line:90% So I have this format. 00:45:37.220 --> 00:45:38.300 align:middle line:90% Yeah, John? 00:45:38.300 --> 00:45:40.925 align:middle line:84% AUDIENCE: Making sure the notes surrounding it are chord tones. 00:45:40.925 --> 00:45:43.175 align:middle line:84% MICHAEL CUTHBERT: Making sure the notes surrounding it 00:45:43.175 --> 00:45:43.860 align:middle line:90% are chord tones. 00:45:43.860 --> 00:45:44.360 align:middle line:90% Yeah. 00:45:44.360 --> 00:45:48.060 align:middle line:84% So these things have to fit into this. 00:45:48.060 --> 00:45:52.220 align:middle line:84% And this is why I was saying that diminished fifth might 00:45:52.220 --> 00:45:53.900 align:middle line:90% be a-- 00:45:53.900 --> 00:45:59.430 align:middle line:84% might not be a non-chord tone if the surrounding chord happens 00:45:59.430 --> 00:46:00.495 align:middle line:90% to be a diminished triad. 00:46:00.495 --> 00:46:03.030 align:middle line:84% And you might say, well, then all of these might be chord 00:46:03.030 --> 00:46:05.220 align:middle line:84% tones, because maybe the surrounding chord really is 00:46:05.220 --> 00:46:09.120 align:middle line:90% 4-7-6-3, but probably not. 00:46:09.120 --> 00:46:13.150 align:middle line:84% What do we-- so now there's two ways to look at this. 00:46:13.150 --> 00:46:16.540 align:middle line:84% We can do this on the individual voice level. 00:46:16.540 --> 00:46:18.957 align:middle line:84% And so that's what we're doing-- or individual part level. 00:46:18.957 --> 00:46:20.540 align:middle line:84% If you're looking at a chorale, that's 00:46:20.540 --> 00:46:22.540 align:middle line:84% what you're going to do before chordifying. 00:46:22.540 --> 00:46:24.480 align:middle line:84% The other thing you can do-- what do you think 00:46:24.480 --> 00:46:25.630 align:middle line:90% is happening here? 00:46:25.630 --> 00:46:30.100 align:middle line:84% You can't even really see what's happening. 00:46:30.100 --> 00:46:35.160 align:middle line:84% But you can see that we have iv6, something weird happening, 00:46:35.160 --> 00:46:37.740 align:middle line:90% and then iv. 00:46:37.740 --> 00:46:40.170 align:middle line:84% So we're going-- something's happening here, 00:46:40.170 --> 00:46:42.540 align:middle line:84% where we're going from the first inversion of a chord 00:46:42.540 --> 00:46:46.620 align:middle line:84% to the root position of the chord. 00:46:46.620 --> 00:46:51.040 align:middle line:84% And these, there might be a lot of passing motion in there. 00:46:51.040 --> 00:46:55.110 align:middle line:84% So you might be able to identify these non-chord tones 00:46:55.110 --> 00:46:58.820 align:middle line:84% at the chord level, or you might be working 00:46:58.820 --> 00:47:02.720 align:middle line:90% on the individual voice level. 00:47:02.720 --> 00:47:04.710 align:middle line:84% Which one do you think works better? 00:47:04.710 --> 00:47:08.030 align:middle line:84% Individual voice level, chord level? 00:47:08.030 --> 00:47:10.040 align:middle line:90% Individual voice? 00:47:10.040 --> 00:47:11.990 align:middle line:90% Chords? 00:47:11.990 --> 00:47:13.220 align:middle line:90% Yeah. 00:47:13.220 --> 00:47:14.460 align:middle line:90% And the answer? 00:47:14.460 --> 00:47:15.860 align:middle line:90% We don't really know. 00:47:15.860 --> 00:47:18.410 align:middle line:84% I try to do both, because some things 00:47:18.410 --> 00:47:20.820 align:middle line:84% are easier to get from one than the other. 00:47:20.820 --> 00:47:22.470 align:middle line:90% So great. 00:47:22.470 --> 00:47:29.610 align:middle line:84% We've gone through, and we've done a question-- outline 1 00:47:29.610 --> 00:47:32.150 align:middle line:90% and most of outline 3 on here. 00:47:32.150 --> 00:47:34.430 align:middle line:84% I jumped around because I realized 00:47:34.430 --> 00:47:37.580 align:middle line:84% that a different ordering was going to be better. 00:47:37.580 --> 00:47:42.230 align:middle line:84% So we're going to gone through 3 A and B, 00:47:42.230 --> 00:47:47.960 align:middle line:84% and then I'll leave C and D for a little bit later. 00:47:47.960 --> 00:47:51.330 align:middle line:84% What I want to do, since we have our jigs loaded up, 00:47:51.330 --> 00:47:52.765 align:middle line:90% I want to do a little bit of 2. 00:47:52.765 --> 00:47:55.810 align:middle line:90% 00:47:55.810 --> 00:47:57.400 align:middle line:84% We'll say take two if we're doing it. 00:47:57.400 --> 00:47:59.150 align:middle line:84% No, we're not doing that level of editing. 00:47:59.150 --> 00:48:01.498 align:middle line:84% But one last little thing-- problem set 9, 00:48:01.498 --> 00:48:03.290 align:middle line:84% you're going to be getting in a little bit. 00:48:03.290 --> 00:48:05.410 align:middle line:84% And what you're going to be doing in problem 00:48:05.410 --> 00:48:12.740 align:middle line:84% set 9 is this kind of chord tone identification and removal. 00:48:12.740 --> 00:48:15.610 align:middle line:84% So you're going to be given various-- 00:48:15.610 --> 00:48:19.910 align:middle line:84% you're going to be given various four-part chorales. 00:48:19.910 --> 00:48:23.890 align:middle line:84% And what I want to see is instead of things 00:48:23.890 --> 00:48:26.600 align:middle line:84% like this that look really hilarious, 00:48:26.600 --> 00:48:33.820 align:middle line:84% something pretty clear out, and a nice reduction of that. 00:48:33.820 --> 00:48:36.580 align:middle line:84% One of the things you might start thinking about 00:48:36.580 --> 00:48:39.820 align:middle line:84% is that Roman numerals are a type of equivalence class 00:48:39.820 --> 00:48:41.600 align:middle line:90% on a set of pitches. 00:48:41.600 --> 00:48:43.940 align:middle line:90% That's not only about-- 00:48:43.940 --> 00:48:47.120 align:middle line:84% well, it helps to say that this is the same chord-- 00:48:47.120 --> 00:48:49.850 align:middle line:84% the same chordal function in different keys. 00:48:49.850 --> 00:48:56.940 align:middle line:84% It's also an equivalence class on the cloud of notes, 00:48:56.940 --> 00:49:00.980 align:middle line:84% including non-chord tones that we can say, 00:49:00.980 --> 00:49:03.540 align:middle line:84% these two things are the same Roman numeral, 00:49:03.540 --> 00:49:06.290 align:middle line:84% even though one of them has filled in all the passing tones 00:49:06.290 --> 00:49:08.960 align:middle line:90% or neighbor tones-- 00:49:08.960 --> 00:49:09.680 align:middle line:90% suspensions. 00:49:09.680 --> 00:49:10.520 align:middle line:90% Did we get them all? 00:49:10.520 --> 00:49:11.870 align:middle line:90% Escape tones. 00:49:11.870 --> 00:49:13.160 align:middle line:90% That's a pretty hard one. 00:49:13.160 --> 00:49:16.170 align:middle line:90% There are a bunch of other ones. 00:49:16.170 --> 00:49:19.380 align:middle line:84% But yeah, so these are things that you're going to be doing. 00:49:19.380 --> 00:49:21.570 align:middle line:84% So I'll be giving it to you in just a little bit. 00:49:21.570 --> 00:49:25.580 align:middle line:84% So you want to be able to take something and make it 00:49:25.580 --> 00:49:26.640 align:middle line:90% quite a bit nicer. 00:49:26.640 --> 00:49:29.520 align:middle line:84% You're going to have help on this. 00:49:29.520 --> 00:49:30.770 align:middle line:90% A couple of things that help-- 00:49:30.770 --> 00:49:33.210 align:middle line:84% you're going to have at least a week. 00:49:33.210 --> 00:49:35.600 align:middle line:90% I'm thinking next Friday. 00:49:35.600 --> 00:49:39.860 align:middle line:84% There's the danger between I don't want to give too 00:49:39.860 --> 00:49:41.930 align:middle line:84% little time, but I also don't want 00:49:41.930 --> 00:49:44.600 align:middle line:84% to go so late that you can't have your full attention 00:49:44.600 --> 00:49:45.840 align:middle line:90% on the final projects. 00:49:45.840 --> 00:49:47.245 align:middle line:90% So what's your thing? 00:49:47.245 --> 00:49:48.620 align:middle line:84% What I'd like you to do is you're 00:49:48.620 --> 00:49:52.750 align:middle line:84% going to be doing problem set 9 with your partner 00:49:52.750 --> 00:49:59.390 align:middle line:84% that you're working on the final project with and one other team. 00:49:59.390 --> 00:50:00.650 align:middle line:90% So groups of four. 00:50:00.650 --> 00:50:04.250 align:middle line:84% The team of four, I think you're a natural group of four. 00:50:04.250 --> 00:50:06.250 align:middle line:90% So why don't you put them there? 00:50:06.250 --> 00:50:10.240 align:middle line:84% But what I'd like you to do is there are different steps 00:50:10.240 --> 00:50:12.790 align:middle line:90% along the process. 00:50:12.790 --> 00:50:15.700 align:middle line:84% Here, I'll just-- I'll pop up PSet 9 right now, so you 00:50:15.700 --> 00:50:17.860 align:middle line:84% can see it while it's here, even though I'm 00:50:17.860 --> 00:50:20.440 align:middle line:84% doing some last second tweaks, depending 00:50:20.440 --> 00:50:23.765 align:middle line:90% on what we get through today. 00:50:23.765 --> 00:50:24.265 align:middle line:90% Great. 00:50:24.265 --> 00:50:28.765 align:middle line:90% 00:50:28.765 --> 00:50:31.780 align:middle line:84% PSet 9, you're going to be doing reduction and key analysis 00:50:31.780 --> 00:50:34.600 align:middle line:90% of tonal music. 00:50:34.600 --> 00:50:36.700 align:middle line:90% And I want you to say-- 00:50:36.700 --> 00:50:37.610 align:middle line:90% note this. 00:50:37.610 --> 00:50:39.590 align:middle line:84% You need not get every chord right. 00:50:39.590 --> 00:50:41.570 align:middle line:84% It need not work on every chorale. 00:50:41.570 --> 00:50:43.750 align:middle line:84% I'm asking for a decent amount of work 00:50:43.750 --> 00:50:46.940 align:middle line:84% toward a solution, not a complete solution in itself. 00:50:46.940 --> 00:50:48.350 align:middle line:90% Great. 00:50:48.350 --> 00:50:51.180 align:middle line:84% So you're not going to be doing that. 00:50:51.180 --> 00:50:56.230 align:middle line:84% So what you'd probably like to do is-- 00:50:56.230 --> 00:51:00.780 align:middle line:84% what you're going to do is I'm going to call vocabulary_reduce 00:51:00.780 --> 00:51:03.960 align:middle line:84% on a score, and you're going to give me 00:51:03.960 --> 00:51:06.600 align:middle line:84% either a score or a part, depending on how you 00:51:06.600 --> 00:51:09.550 align:middle line:90% try to choose to represent it. 00:51:09.550 --> 00:51:12.600 align:middle line:90% That is the reduced one. 00:51:12.600 --> 00:51:16.380 align:middle line:84% You have four people on your team. 00:51:16.380 --> 00:51:19.290 align:middle line:84% You probably do not want to implement-- you definitely 00:51:19.290 --> 00:51:21.210 align:middle line:84% do not want to implement your entire solution 00:51:21.210 --> 00:51:25.950 align:middle line:84% inside this vocabulary_reduce programming in a Jupyter 00:51:25.950 --> 00:51:26.920 align:middle line:90% Notebook. 00:51:26.920 --> 00:51:30.150 align:middle line:84% Take this, divide it up, and share it 00:51:30.150 --> 00:51:35.700 align:middle line:84% among your favorite collaborative coding tools. 00:51:35.700 --> 00:51:40.320 align:middle line:84% I'm starting you with a chorale that's easier than the one 00:51:40.320 --> 00:51:43.270 align:middle line:84% we've been working on in class 66.6. 00:51:43.270 --> 00:51:46.290 align:middle line:84% And here are the four I'm going to test you 00:51:46.290 --> 00:51:48.160 align:middle line:90% on for 90% of your points. 00:51:48.160 --> 00:51:50.080 align:middle line:90% So I'm going to tell you that. 00:51:50.080 --> 00:51:50.630 align:middle line:90% Oops. 00:51:50.630 --> 00:51:52.540 align:middle line:84% So this is why I'm still editing. 00:51:52.540 --> 00:51:56.650 align:middle line:84% You have key analysis unlocked because we 00:51:56.650 --> 00:51:58.940 align:middle line:90% lost four classes this year. 00:51:58.940 --> 00:52:02.793 align:middle line:84% So you'll be allowed to analyze the key using analysis things. 00:52:02.793 --> 00:52:03.793 align:middle line:90% We're going to chordify. 00:52:03.793 --> 00:52:06.520 align:middle line:90% 00:52:06.520 --> 00:52:08.920 align:middle line:84% This addPartIdAsGroup is something 00:52:08.920 --> 00:52:12.340 align:middle line:84% that lets you figure out for each pitch 00:52:12.340 --> 00:52:16.250 align:middle line:84% in your chordified score what part it originally came from, 00:52:16.250 --> 00:52:19.250 align:middle line:84% which can be very useful for figuring out what to delete. 00:52:19.250 --> 00:52:25.360 align:middle line:84% And yeah, we'll just show the first-- 00:52:25.360 --> 00:52:27.820 align:middle line:84% put it in-- actually, I'll show different steps 00:52:27.820 --> 00:52:29.960 align:middle line:90% that might happen here. 00:52:29.960 --> 00:52:32.170 align:middle line:84% So what I've done is I've gone through one chord 00:52:32.170 --> 00:52:34.900 align:middle line:90% that if you load these things-- 00:52:34.900 --> 00:52:36.615 align:middle line:90% sorry-- one choral-- oops! 00:52:36.615 --> 00:52:39.290 align:middle line:90% 00:52:39.290 --> 00:52:39.790 align:middle line:90% Sorry. 00:52:39.790 --> 00:52:43.270 align:middle line:84% I forgot I have to restart and run all. 00:52:43.270 --> 00:52:44.480 align:middle line:90% Yep, here we go. 00:52:44.480 --> 00:52:49.530 align:middle line:84% So here's the original chorale I'm asking you to work on. 00:52:49.530 --> 00:52:53.080 align:middle line:84% And then I'm unlocking something called implode(), 00:52:53.080 --> 00:52:57.390 align:middle line:84% which you might find useful, just for seeing a chorale on two 00:52:57.390 --> 00:52:58.270 align:middle line:90% staves. 00:52:58.270 --> 00:53:01.600 align:middle line:84% It might not be too useful for you analytically. 00:53:01.600 --> 00:53:06.180 align:middle line:84% And then what I've done is given you 00:53:06.180 --> 00:53:08.620 align:middle line:90% the first part of the answer-- 00:53:08.620 --> 00:53:14.220 align:middle line:84% how an answer, how I think this might work with all 00:53:14.220 --> 00:53:18.150 align:middle line:90% the non-chord tones labeled. 00:53:18.150 --> 00:53:25.720 align:middle line:84% And then, second one, here is after they've been removed. 00:53:25.720 --> 00:53:27.060 align:middle line:90% So you have them all labeled. 00:53:27.060 --> 00:53:29.650 align:middle line:90% Now you have all them removed. 00:53:29.650 --> 00:53:33.090 align:middle line:84% And then the last step, you might 00:53:33.090 --> 00:53:35.370 align:middle line:84% be trying to figure out that, actually, there's 00:53:35.370 --> 00:53:36.760 align:middle line:90% some key changes in here. 00:53:36.760 --> 00:53:42.720 align:middle line:84% So we move from A major to D major to A major and so on. 00:53:42.720 --> 00:53:47.157 align:middle line:84% Why have I given you these intermediate steps, if this is 00:53:47.157 --> 00:53:48.365 align:middle line:90% what you're trying to get to? 00:53:48.365 --> 00:53:51.540 align:middle line:84% It's because you have a larger team. 00:53:51.540 --> 00:53:54.950 align:middle line:84% And so what I would like is that somebody 00:53:54.950 --> 00:53:59.210 align:middle line:84% can be working on part 4 while somebody else is working 00:53:59.210 --> 00:54:03.300 align:middle line:84% on part 3, while somebody else is working on part 2 and part 1. 00:54:03.300 --> 00:54:07.640 align:middle line:84% So then what I'll say, the last little thing 00:54:07.640 --> 00:54:11.060 align:middle line:84% is just to show a little preview of some of the things 00:54:11.060 --> 00:54:14.790 align:middle line:90% that we might be doing later. 00:54:14.790 --> 00:54:18.030 align:middle line:84% And I know it's not on the right screen. 00:54:18.030 --> 00:54:19.140 align:middle line:90% I can make that bigger. 00:54:19.140 --> 00:54:24.800 align:middle line:84% This is something I've been working on an automatic-- 00:54:24.800 --> 00:54:29.750 align:middle line:84% well, let's let it run first-- on an AI-based automatically 00:54:29.750 --> 00:54:32.720 align:middle line:84% trying to do labeling of Roman numerals 00:54:32.720 --> 00:54:37.680 align:middle line:84% based on sets of pitches and training data. 00:54:37.680 --> 00:54:40.310 align:middle line:84% What I've done is, right now, I'm 00:54:40.310 --> 00:54:44.890 align:middle line:84% only having it work with a few Roman numerals. 00:54:44.890 --> 00:54:47.290 align:middle line:84% And always take a guess when you're trying 00:54:47.290 --> 00:54:48.850 align:middle line:90% to figure out what things are. 00:54:48.850 --> 00:54:53.180 align:middle line:84% These, how many entries are there in each of these arrays? 00:54:53.180 --> 00:54:56.210 align:middle line:84% 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 00:54:56.210 --> 00:55:02.720 align:middle line:84% So these are the pitch classes above the tonic thing, 00:55:02.720 --> 00:55:04.780 align:middle line:90% so that one has-- 00:55:04.780 --> 00:55:07.000 align:middle line:90% I can't even reach up there. 00:55:07.000 --> 00:55:13.390 align:middle line:84% So one has the most entries in, if you call that, C, C-sharp, D, 00:55:13.390 --> 00:55:16.390 align:middle line:90% E-flat, E-- that's quite a bit-- 00:55:16.390 --> 00:55:20.240 align:middle line:84% F, F-sharp, almost nothing, G, quite a bit. 00:55:20.240 --> 00:55:21.910 align:middle line:84% And so this is how many times you 00:55:21.910 --> 00:55:24.580 align:middle line:84% see that chord tone in everything 00:55:24.580 --> 00:55:28.420 align:middle line:84% in our labeled training data was labeled I, and so on. 00:55:28.420 --> 00:55:33.820 align:middle line:84% For V, you see a lot of V, scale degree 5, scale degree 7, 00:55:33.820 --> 00:55:37.840 align:middle line:84% and scale degree 2, kind of what you would expect. 00:55:37.840 --> 00:55:41.320 align:middle line:84% And put everything into a neural net 00:55:41.320 --> 00:55:44.820 align:middle line:84% that I'm still trying to make this a little bit better, 00:55:44.820 --> 00:55:45.960 align:middle line:90% a little bit better. 00:55:45.960 --> 00:55:47.220 align:middle line:90% Run it. 00:55:47.220 --> 00:55:49.490 align:middle line:90% Hopefully, it's running. 00:55:49.490 --> 00:55:51.780 align:middle line:84% You can see run it through one time. 00:55:51.780 --> 00:55:54.300 align:middle line:84% It's starting to get 62% accurate. 00:55:54.300 --> 00:55:55.650 align:middle line:90% Keep going up. 00:55:55.650 --> 00:55:59.440 align:middle line:84% It stays at 62, 62, 62 quite a long time. 00:55:59.440 --> 00:56:01.470 align:middle line:90% It jumps up to 67, 68. 00:56:01.470 --> 00:56:03.840 align:middle line:84% Hopefully, it's going pretty well. 00:56:03.840 --> 00:56:07.770 align:middle line:84% Eventually, it gets 87, 88, 90, and so on. 00:56:07.770 --> 00:56:11.150 align:middle line:84% So it is possible to do this kind of thing 00:56:11.150 --> 00:56:15.290 align:middle line:84% with today's computational resources 00:56:15.290 --> 00:56:17.270 align:middle line:90% kind of ending at around-- 00:56:17.270 --> 00:56:20.720 align:middle line:84% are we going to be able to get to 99 today? 00:56:20.720 --> 00:56:21.720 align:middle line:90% AUDIENCE: How big is it? 00:56:21.720 --> 00:56:23.470 align:middle line:84% MICHAEL CUTHBERT: So that's what I'm going 00:56:23.470 --> 00:56:24.600 align:middle line:90% to get to in just a second. 00:56:24.600 --> 00:56:27.140 align:middle line:84% So this-- oh, of course, my computer 00:56:27.140 --> 00:56:29.150 align:middle line:84% can barely handle this while projecting. 00:56:29.150 --> 00:56:31.580 align:middle line:90% I think I did 400. 00:56:31.580 --> 00:56:34.950 align:middle line:84% Well, while it tries to scroll down to the bottom, 00:56:34.950 --> 00:56:41.060 align:middle line:84% the danger is this data set took me years to get. 00:56:41.060 --> 00:56:42.410 align:middle line:90% And it took years to put in. 00:56:42.410 --> 00:56:45.710 align:middle line:84% This is the complete piano sonatas of Mozart. 00:56:45.710 --> 00:56:47.450 align:middle line:90% [VOCALIZING] 00:56:47.450 --> 00:56:51.800 align:middle line:84% Complete piano sonatas of Mozart, all labeled. 00:56:51.800 --> 00:56:57.350 align:middle line:84% And when I divided it up into half training, half test, 00:56:57.350 --> 00:57:00.130 align:middle line:84% I still didn't have enough information for it 00:57:00.130 --> 00:57:01.610 align:middle line:90% to be able to get on. 00:57:01.610 --> 00:57:05.360 align:middle line:84% So I'm dividing it into 90% training, 10% test. 00:57:05.360 --> 00:57:07.190 align:middle line:84% And that seems to be about what's there. 00:57:07.190 --> 00:57:11.290 align:middle line:84% So the other thing was when I decided, 00:57:11.290 --> 00:57:13.180 align:middle line:84% oh, this sounded like a fun project 00:57:13.180 --> 00:57:15.832 align:middle line:84% for over the holiday break, so I thought 00:57:15.832 --> 00:57:18.040 align:middle line:84% I'd be able to present this on the first day of class 00:57:18.040 --> 00:57:18.770 align:middle line:90% or something. 00:57:18.770 --> 00:57:23.590 align:middle line:84% I went in, and the entire Roman numeral set could not 00:57:23.590 --> 00:57:27.110 align:middle line:84% be trusted compared to the encoding of the things, 00:57:27.110 --> 00:57:29.110 align:middle line:84% because people slightly disagreed 00:57:29.110 --> 00:57:33.550 align:middle line:84% on where measure 14 was, or where measure 113 was, 00:57:33.550 --> 00:57:38.000 align:middle line:84% or this edition had this part of the minuet. 00:57:38.000 --> 00:57:39.520 align:middle line:90% The repeats were written out. 00:57:39.520 --> 00:57:41.500 align:middle line:84% And they weren't-- so I was going through. 00:57:41.500 --> 00:57:44.010 align:middle line:84% And when I was spot checking, the Roman numerals just 00:57:44.010 --> 00:57:46.710 align:middle line:84% looked totally wrong to me, or it would say, 00:57:46.710 --> 00:57:50.220 align:middle line:84% Roman numeral placed after end of piece. 00:57:50.220 --> 00:57:53.918 align:middle line:90% And so, again, it was about-- 00:57:53.918 --> 00:57:54.460 align:middle line:90% I don't know. 00:57:54.460 --> 00:58:00.130 align:middle line:84% It was about 3 hours a night for about 3 weeks of just, 00:58:00.130 --> 00:58:01.390 align:middle line:90% well, let's realign this one. 00:58:01.390 --> 00:58:02.020 align:middle line:90% Let's realign. 00:58:02.020 --> 00:58:03.687 align:middle line:84% Now, it was a little bit less than that, 00:58:03.687 --> 00:58:05.550 align:middle line:90% but about 2 weeks maybe. 00:58:05.550 --> 00:58:10.060 align:middle line:84% So this ends up being one of the dangers and why I'm pushing-- 00:58:10.060 --> 00:58:11.580 align:middle line:84% even though, I think we're starting 00:58:11.580 --> 00:58:13.540 align:middle line:84% to get-- how many epochs did I do this time? 00:58:13.540 --> 00:58:14.740 align:middle line:90% I must have changed it. 00:58:14.740 --> 00:58:17.400 align:middle line:90% But we're getting pretty close. 00:58:17.400 --> 00:58:20.400 align:middle line:84% And it takes a very long time before the computer 00:58:20.400 --> 00:58:23.160 align:middle line:90% is being able to get things up. 00:58:23.160 --> 00:58:26.850 align:middle line:84% So these are some of the reasons why 00:58:26.850 --> 00:58:28.960 align:middle line:84% I'm going to teach you some of these techniques. 00:58:28.960 --> 00:58:30.990 align:middle line:84% But then I'm going to encourage you not 00:58:30.990 --> 00:58:33.130 align:middle line:84% to use them on your final projects, 00:58:33.130 --> 00:58:37.270 align:middle line:84% even though they are kind of the coolest new thing going. 00:58:37.270 --> 00:58:38.160 align:middle line:90% Great. 00:58:38.160 --> 00:58:39.180 align:middle line:90% Any questions? 00:58:39.180 --> 00:58:39.680 align:middle line:90% And sorry. 00:58:39.680 --> 00:58:41.055 align:middle line:84% I'm not getting-- oh, here we go. 00:58:41.055 --> 00:58:43.480 align:middle line:90% Finally, we get to the done. 00:58:43.480 --> 00:58:45.560 align:middle line:84% And my computer is still so slow. 00:58:45.560 --> 00:58:48.980 align:middle line:84% Here's the mistakes that it was making. 00:58:48.980 --> 00:58:50.710 align:middle line:90% Oh, this time it only got there. 00:58:50.710 --> 00:58:55.210 align:middle line:84% Last time, it got to all but one correct. 00:58:55.210 --> 00:58:56.200 align:middle line:90% Yep. 00:58:56.200 --> 00:59:00.490 align:middle line:84% 177 times it saw I. It predicted it one. 00:59:00.490 --> 00:59:02.350 align:middle line:84% One time it saw it, and predicted 00:59:02.350 --> 00:59:08.240 align:middle line:84% V. You can imagine that IV and II have some confusion 00:59:08.240 --> 00:59:08.990 align:middle line:90% with the computer. 00:59:08.990 --> 00:59:13.370 align:middle line:84% And V and VII also had some confusion. 00:59:13.370 --> 00:59:16.130 align:middle line:84% VI, VI and IV have some confusion. 00:59:16.130 --> 00:59:18.760 align:middle line:84% So then the nice thing was actually 00:59:18.760 --> 00:59:23.710 align:middle line:84% going back the last time I did this and looking at every place 00:59:23.710 --> 00:59:29.680 align:middle line:84% that there was a confusion and saying, oh, about half the time 00:59:29.680 --> 00:59:32.830 align:middle line:84% I agreed with the neural net and not 00:59:32.830 --> 00:59:35.430 align:middle line:90% with the professional encoder. 00:59:35.430 --> 00:59:39.000 align:middle line:90%