WEBVTT 00:00:00.000 --> 00:00:01.996 align:middle line:90% [SQUEAKING] 00:00:01.996 --> 00:00:03.992 align:middle line:90% [RUSTLING] 00:00:03.992 --> 00:00:07.485 align:middle line:90% [CLICKING] 00:00:07.485 --> 00:00:10.127 align:middle line:90% 00:00:10.127 --> 00:00:11.460 align:middle line:90% MICHAEL CUTHBERT: Hi, everybody. 00:00:11.460 --> 00:00:15.140 align:middle line:84% Today we're going to spend the bulk of our time 00:00:15.140 --> 00:00:21.140 align:middle line:84% making up for lost lab time, lost time coding and doing-- 00:00:21.140 --> 00:00:24.180 align:middle line:84% implementing some of the ideas that we have, but first, 00:00:24.180 --> 00:00:28.680 align:middle line:84% we're going to step back to just a little bit on the quiz. 00:00:28.680 --> 00:00:30.870 align:middle line:84% Apologies for taking a while to get it back to you, 00:00:30.870 --> 00:00:32.100 align:middle line:90% but now you have it. 00:00:32.100 --> 00:00:37.080 align:middle line:84% And the quiz is the opposite of the practical side. 00:00:37.080 --> 00:00:38.820 align:middle line:84% It's more of the theoretical side. 00:00:38.820 --> 00:00:43.093 align:middle line:84% So I wanted to talk about a couple aspects of that. 00:00:43.093 --> 00:00:45.510 align:middle line:84% Somebody's going to remind me to put the screen back down. 00:00:45.510 --> 00:00:47.000 align:middle line:90% Paul's not here today. 00:00:47.000 --> 00:00:48.740 align:middle line:90% So please do that. 00:00:48.740 --> 00:00:53.960 align:middle line:84% Some of the practical aspects on the quiz in space. 00:00:53.960 --> 00:00:59.330 align:middle line:84% First, why are authors and articles important? 00:00:59.330 --> 00:01:02.405 align:middle line:84% Why am I really sensing that not just you 00:01:02.405 --> 00:01:06.140 align:middle line:84% know what the three contexts are or what optic is, but really 00:01:06.140 --> 00:01:07.950 align:middle line:90% whose idea this is? 00:01:07.950 --> 00:01:09.750 align:middle line:90% And there's really two reasons. 00:01:09.750 --> 00:01:12.990 align:middle line:90% One, the field is small. 00:01:12.990 --> 00:01:14.190 align:middle line:90% The field is small. 00:01:14.190 --> 00:01:17.840 align:middle line:84% And if you're working in it-- and it's young. 00:01:17.840 --> 00:01:22.670 align:middle line:84% Not young as y'all or-- it's even older than me, but young, 00:01:22.670 --> 00:01:26.465 align:middle line:84% like almost everyone who has come up with the great ideas 00:01:26.465 --> 00:01:29.090 align:middle line:84% that have changed the field are still living and people you can 00:01:29.090 --> 00:01:31.370 align:middle line:90% meet. 00:01:31.370 --> 00:01:33.410 align:middle line:90% But more importantly-- 00:01:33.410 --> 00:01:36.620 align:middle line:84% And so some of the guest speakers that we've had 00:01:36.620 --> 00:01:40.380 align:middle line:84% recently have appeared-- it's campus preview weekend, 00:01:40.380 --> 00:01:43.910 align:middle line:90% so we got to close this. 00:01:43.910 --> 00:01:46.372 align:middle line:90% Otherwise, it'll get loud. 00:01:46.372 --> 00:01:48.410 align:middle line:84% But some of the speakers that we've seen 00:01:48.410 --> 00:01:51.740 align:middle line:84% have actually already appeared in articles 00:01:51.740 --> 00:01:53.550 align:middle line:84% that we've been reading and things. 00:01:53.550 --> 00:01:57.880 align:middle line:84% So these are names that will keep popping up again. 00:01:57.880 --> 00:02:01.430 align:middle line:84% And when David Huron talks about Carol Krumhansl, who 00:02:01.430 --> 00:02:03.540 align:middle line:90% was after the quiz. 00:02:03.540 --> 00:02:06.990 align:middle line:84% But this is a name that, oh, I've already read that. 00:02:06.990 --> 00:02:10.520 align:middle line:90% The other first reason is that-- 00:02:10.520 --> 00:02:13.610 align:middle line:84% I don't know if you saw on one of our guest speakers 00:02:13.610 --> 00:02:15.540 align:middle line:90% on music cognition. 00:02:15.540 --> 00:02:18.028 align:middle line:84% A lot of times, there were these nice, pretty pictures of-- 00:02:18.028 --> 00:02:18.570 align:middle line:90% I don't know. 00:02:18.570 --> 00:02:21.660 align:middle line:84% Can I draw a light bulb or something like that? 00:02:21.660 --> 00:02:23.370 align:middle line:90% And some idea and things. 00:02:23.370 --> 00:02:25.370 align:middle line:84% And over in the corner, you would 00:02:25.370 --> 00:02:31.860 align:middle line:90% see Devin's 2019 or whatever. 00:02:31.860 --> 00:02:35.750 align:middle line:90% And those are just ways-- 00:02:35.750 --> 00:02:39.440 align:middle line:84% they're industry shortcuts for how you can learn more 00:02:39.440 --> 00:02:40.770 align:middle line:90% about a particular topic. 00:02:40.770 --> 00:02:43.830 align:middle line:84% So I don't tend to talk with footnotes. 00:02:43.830 --> 00:02:45.710 align:middle line:90% Maybe I should more-- 00:02:45.710 --> 00:02:50.600 align:middle line:90% Strunk and White, 2004-- 00:02:50.600 --> 00:02:53.700 align:middle line:84% but these are things that people do quite often. 00:02:53.700 --> 00:02:55.010 align:middle line:90% And it's because-- 00:02:55.010 --> 00:02:59.200 align:middle line:84% Here's the worst thing about almost every article 00:02:59.200 --> 00:03:01.490 align:middle line:84% you'll read, whether in science, engineering, 00:03:01.490 --> 00:03:05.230 align:middle line:90% humanities, arts that-- 00:03:05.230 --> 00:03:08.420 align:middle line:84% I'm telling you to read these articles and things, 00:03:08.420 --> 00:03:11.260 align:middle line:84% but then the articles aren't actually written for you 00:03:11.260 --> 00:03:12.560 align:middle line:90% to read. 00:03:12.560 --> 00:03:14.830 align:middle line:90% It's so ironic. 00:03:14.830 --> 00:03:17.180 align:middle line:84% Why do we write and publish research? 00:03:17.180 --> 00:03:22.120 align:middle line:84% For the most part, we're publishing research to talk to 00:03:22.120 --> 00:03:27.280 align:middle line:84% or to argue with or push back on or develop the theory 00:03:27.280 --> 00:03:29.330 align:middle line:90% of somebody else who's living. 00:03:29.330 --> 00:03:34.993 align:middle line:84% So these scholars tend to talk to each other quite a bit. 00:03:34.993 --> 00:03:36.910 align:middle line:84% And so what they're doing when they're putting 00:03:36.910 --> 00:03:39.085 align:middle line:90% these names down is really-- 00:03:39.085 --> 00:03:42.360 align:middle line:84% there's a seat here today, if you'd like-- 00:03:42.360 --> 00:03:47.530 align:middle line:84% and what they're really doing is trying 00:03:47.530 --> 00:03:50.870 align:middle line:84% to argue against something that you might not already know. 00:03:50.870 --> 00:03:54.430 align:middle line:84% So when somebody is presenting an idea, they're really saying, 00:03:54.430 --> 00:03:57.972 align:middle line:84% hey, I've got a better idea than this other person. 00:03:57.972 --> 00:03:59.680 align:middle line:84% And so they're always going to be talking 00:03:59.680 --> 00:04:01.910 align:middle line:90% about names of other people. 00:04:01.910 --> 00:04:03.680 align:middle line:84% And so it's just kind of good to get that. 00:04:03.680 --> 00:04:07.210 align:middle line:90% So that's something there. 00:04:07.210 --> 00:04:09.310 align:middle line:84% The other question I think that can come up 00:04:09.310 --> 00:04:12.190 align:middle line:84% in the context of these quizzes based primarily 00:04:12.190 --> 00:04:14.750 align:middle line:84% on the readings and these abstract things 00:04:14.750 --> 00:04:18.800 align:middle line:84% is, why are there so many darn old articles in this class? 00:04:18.800 --> 00:04:21.670 align:middle line:84% Why are you doing a lot of citations of things that 00:04:21.670 --> 00:04:24.020 align:middle line:90% are 10 years old, 25 years old? 00:04:24.020 --> 00:04:26.960 align:middle line:84% And then you got the Illiac Suite. 00:04:26.960 --> 00:04:27.620 align:middle line:90% What is that? 00:04:27.620 --> 00:04:30.970 align:middle line:90% 70-- 77 years old now? 00:04:30.970 --> 00:04:35.830 align:middle line:84% So what's the point of getting into it? 00:04:35.830 --> 00:04:38.980 align:middle line:84% So I've been teaching for a while, and one of the-- there's 00:04:38.980 --> 00:04:43.070 align:middle line:84% one lecture that I love the topic, 00:04:43.070 --> 00:04:45.350 align:middle line:84% and I hope you'll love it too when we get to it, 00:04:45.350 --> 00:04:46.970 align:middle line:90% but I hate giving this lecture. 00:04:46.970 --> 00:04:53.360 align:middle line:84% It's the lecture on practical AI in music. 00:04:53.360 --> 00:04:54.920 align:middle line:90% And why is that? 00:04:54.920 --> 00:04:58.120 align:middle line:84% It's because the various techniques 00:04:58.120 --> 00:05:01.810 align:middle line:84% that I've been teaching have changed 00:05:01.810 --> 00:05:06.110 align:middle line:84% so often that they're not really relevant two years later. 00:05:06.110 --> 00:05:10.570 align:middle line:84% So I'm going to be thinking about, oh, OK, 00:05:10.570 --> 00:05:13.180 align:middle line:84% this weekend, it's time to update everything 00:05:13.180 --> 00:05:15.790 align:middle line:84% from TensorFlow, which was so state of the art 00:05:15.790 --> 00:05:19.390 align:middle line:84% three years ago, and I wrote a whole lecture around it 00:05:19.390 --> 00:05:23.960 align:middle line:84% for those who know this, PyTorch, which I'm using now. 00:05:23.960 --> 00:05:27.100 align:middle line:84% And it really means that there's a lot of things 00:05:27.100 --> 00:05:29.800 align:middle line:84% that we'll be spending time in that class. 00:05:29.800 --> 00:05:33.868 align:middle line:84% That if PyTorch ends up not being the super great thing 00:05:33.868 --> 00:05:36.160 align:middle line:84% that you're going to be using for the rest of your life 00:05:36.160 --> 00:05:40.220 align:middle line:84% because of GPT or whatever else that's coming out, 00:05:40.220 --> 00:05:44.510 align:middle line:84% those types of information will get stale pretty fast. 00:05:44.510 --> 00:05:49.120 align:middle line:84% But the notion of things like equality and equivalence 00:05:49.120 --> 00:05:51.880 align:middle line:84% and how you can put equivalence classes, I hope, 00:05:51.880 --> 00:05:54.670 align:middle line:84% will stay with you even if you're not 00:05:54.670 --> 00:05:58.485 align:middle line:84% doing anything with music or even anything with computation. 00:05:58.485 --> 00:05:59.860 align:middle line:84% I hope there are things that will 00:05:59.860 --> 00:06:02.390 align:middle line:84% stay with you for the rest of your life, 00:06:02.390 --> 00:06:06.890 align:middle line:84% and that it'll change how you make an outlook on the world. 00:06:06.890 --> 00:06:12.800 align:middle line:84% So that's a little bit why this class has a good amount of it. 00:06:12.800 --> 00:06:16.480 align:middle line:84% I figure if it's something that inspired me 15 years ago, 00:06:16.480 --> 00:06:18.380 align:middle line:84% and it's still inspiring me today, 00:06:18.380 --> 00:06:20.170 align:middle line:84% it has a good chance that it'll still 00:06:20.170 --> 00:06:24.500 align:middle line:84% be relevant inspirational in 10, 20, or 30 years from now. 00:06:24.500 --> 00:06:32.810 align:middle line:84% For those who did the work on the global rule, somebody 00:06:32.810 --> 00:06:37.780 align:middle line:84% remind us what the global rule is and what-- first, 00:06:37.780 --> 00:06:38.970 align:middle line:90% where does it apply? 00:06:38.970 --> 00:06:42.640 align:middle line:90% 00:06:42.640 --> 00:06:44.380 align:middle line:90% Anyone want to take a guess? 00:06:44.380 --> 00:06:47.210 align:middle line:84% Matthew, do you want to take a guess or call on somebody else? 00:06:47.210 --> 00:06:47.710 align:middle line:90% AUDIENCE: Counterpoint? 00:06:47.710 --> 00:06:48.470 align:middle line:90% MICHAEL CUTHBERT: Counterpoint. 00:06:48.470 --> 00:06:48.970 align:middle line:90% Great. 00:06:48.970 --> 00:06:49.840 align:middle line:90% Super. 00:06:49.840 --> 00:06:54.780 align:middle line:90% So it's counterpoint rule, rule. 00:06:54.780 --> 00:07:00.120 align:middle line:84% And what's it trying to maximize in counterpoint? 00:07:00.120 --> 00:07:05.900 align:middle line:90% So I'm just trying to think. 00:07:05.900 --> 00:07:08.610 align:middle line:90% 00:07:08.610 --> 00:07:11.160 align:middle line:84% What's it trying to maximize in counterpoint? 00:07:11.160 --> 00:07:12.562 align:middle line:90% What's that? 00:07:12.562 --> 00:07:15.690 align:middle line:90% 00:07:15.690 --> 00:07:17.370 align:middle line:90% You want to try it? 00:07:17.370 --> 00:07:20.010 align:middle line:84% AUDIENCE: I guess it's trying to maximize the musical notes 00:07:20.010 --> 00:07:22.090 align:middle line:90% or how good it sounds. 00:07:22.090 --> 00:07:23.590 align:middle line:84% MICHAEL CUTHBERT: Max musicality. 00:07:23.590 --> 00:07:24.360 align:middle line:90% Absolutely. 00:07:24.360 --> 00:07:24.960 align:middle line:90% Great. 00:07:24.960 --> 00:07:25.460 align:middle line:90% Super. 00:07:25.460 --> 00:07:29.280 align:middle line:90% 00:07:29.280 --> 00:07:31.140 align:middle line:90% And it does this-- 00:07:31.140 --> 00:07:34.110 align:middle line:84% ironically, trying to maximize musicality 00:07:34.110 --> 00:07:40.080 align:middle line:84% came down to giving a formula or giving a set of formulas. 00:07:40.080 --> 00:07:42.245 align:middle line:84% And where do we begin with the global rule? 00:07:42.245 --> 00:07:44.880 align:middle line:90% 00:07:44.880 --> 00:07:45.393 align:middle line:90% [INAUDIBLE]? 00:07:45.393 --> 00:07:46.560 align:middle line:90% AUDIENCE: From the last one? 00:07:46.560 --> 00:07:48.060 align:middle line:84% MICHAEL CUTHBERT: Start from the end 00:07:48.060 --> 00:07:53.230 align:middle line:84% and go backwards and look at specifically, do you have what? 00:07:53.230 --> 00:07:56.060 align:middle line:84% Three possibilities for the last one? 00:07:56.060 --> 00:07:59.400 align:middle line:90% 00:07:59.400 --> 00:08:00.566 align:middle line:90% If you're going backwards? 00:08:00.566 --> 00:08:03.990 align:middle line:90% 00:08:03.990 --> 00:08:06.540 align:middle line:84% No, you have two possibilities because you can't repeat notes 00:08:06.540 --> 00:08:07.450 align:middle line:90% in this context. 00:08:07.450 --> 00:08:13.150 align:middle line:84% So you can be trying here and here against some other thing. 00:08:13.150 --> 00:08:15.580 align:middle line:84% David Lewin would actually not be happy with me. 00:08:15.580 --> 00:08:18.160 align:middle line:84% He always did his counterpoints in alto clef, 00:08:18.160 --> 00:08:21.160 align:middle line:84% but we'll do it in treble and bass. 00:08:21.160 --> 00:08:25.560 align:middle line:84% So yeah, you're trying to figure out, OK, if we ended here 00:08:25.560 --> 00:08:28.530 align:middle line:84% and the previous note is here, what 00:08:28.530 --> 00:08:30.460 align:middle line:84% are the other notes that we can do? 00:08:30.460 --> 00:08:32.710 align:middle line:84% So we have traditional counterpoint rules, 00:08:32.710 --> 00:08:36.419 align:middle line:84% but we also have this notion that every note that 00:08:36.419 --> 00:08:44.373 align:middle line:84% appears in the line must at some point find what? 00:08:44.373 --> 00:08:44.915 align:middle line:90% You remember? 00:08:44.915 --> 00:08:50.170 align:middle line:90% 00:08:50.170 --> 00:08:52.930 align:middle line:84% Everybody quiet because they all know this so easily 00:08:52.930 --> 00:08:55.810 align:middle line:90% or because it's a little foggy? 00:08:55.810 --> 00:08:57.510 align:middle line:90% Easy? 00:08:57.510 --> 00:08:58.440 align:middle line:90% Foggy? 00:08:58.440 --> 00:08:59.410 align:middle line:90% OK, good. 00:08:59.410 --> 00:09:00.010 align:middle line:90% That's good. 00:09:00.010 --> 00:09:00.510 align:middle line:90% Good. 00:09:00.510 --> 00:09:02.670 align:middle line:84% I prefer silence when it's foggy because then I 00:09:02.670 --> 00:09:04.360 align:middle line:90% know what to do next. 00:09:04.360 --> 00:09:07.510 align:middle line:84% So in order to get maximum musicality, 00:09:07.510 --> 00:09:10.920 align:middle line:90% you talked about smoo-- 00:09:10.920 --> 00:09:13.980 align:middle line:90% what begins with smoo--? 00:09:13.980 --> 00:09:15.893 align:middle line:90% He wants what kind of lines? 00:09:15.893 --> 00:09:16.560 align:middle line:90% AUDIENCE: Smooth 00:09:16.560 --> 00:09:17.350 align:middle line:90% MICHAEL CUTHBERT: Smooth lines. 00:09:17.350 --> 00:09:18.490 align:middle line:90% So we want smooth lines. 00:09:18.490 --> 00:09:22.270 align:middle line:84% So if at some point, you have a d here, a low d-- 00:09:22.270 --> 00:09:24.165 align:middle line:90% and we're going to get to c-- 00:09:24.165 --> 00:09:26.770 align:middle line:84% what are the notes that we need to see after this? 00:09:26.770 --> 00:09:32.910 align:middle line:90% Oops, just turned red. 00:09:32.910 --> 00:09:37.410 align:middle line:84% What are the notes that we need to see after this? 00:09:37.410 --> 00:09:40.240 align:middle line:84% What's a note we need to see after d? 00:09:40.240 --> 00:09:40.740 align:middle line:90% AUDIENCE: E? 00:09:40.740 --> 00:09:42.180 align:middle line:90% MICHAEL CUTHBERT: What's that? 00:09:42.180 --> 00:09:42.680 align:middle line:90% AUDIENCE: E? 00:09:42.680 --> 00:09:43.722 align:middle line:90% MICHAEL CUTHBERT: E. Good. 00:09:43.722 --> 00:09:44.222 align:middle line:90% Good. 00:09:44.222 --> 00:09:48.090 align:middle line:84% So if we have an e, then what happens if we 00:09:48.090 --> 00:09:51.210 align:middle line:90% have another d after that? 00:09:51.210 --> 00:09:55.850 align:middle line:84% What are we going to need after the d at some point? 00:09:55.850 --> 00:09:56.350 align:middle line:90% Go ahead. 00:09:56.350 --> 00:09:56.800 align:middle line:90% AUDIENCE: Another e. 00:09:56.800 --> 00:09:57.967 align:middle line:90% MICHAEL CUTHBERT: Another e. 00:09:57.967 --> 00:09:58.680 align:middle line:90% Good. 00:09:58.680 --> 00:10:02.770 align:middle line:84% So basically, whenever you have a note, 00:10:02.770 --> 00:10:07.695 align:middle line:84% you have to have after it every note between here-- 00:10:07.695 --> 00:10:09.708 align:middle line:90% every diatonic note. 00:10:09.708 --> 00:10:10.750 align:middle line:90% Not every chromatic note. 00:10:10.750 --> 00:10:12.910 align:middle line:84% You're not going to need a d sharp at some point. 00:10:12.910 --> 00:10:17.350 align:middle line:84% Every diatonic note between here and the final cadence note. 00:10:17.350 --> 00:10:19.960 align:middle line:84% And that's why it was a little bit easier to work backwards. 00:10:19.960 --> 00:10:24.613 align:middle line:84% Now, why was this rule important for this class? 00:10:24.613 --> 00:10:26.725 align:middle line:90% 00:10:26.725 --> 00:10:28.350 align:middle line:84% This one might be a silent because it's 00:10:28.350 --> 00:10:32.400 align:middle line:84% pretty easy, because almost everything in this class. 00:10:32.400 --> 00:10:33.275 align:middle line:90% Who can do it? 00:10:33.275 --> 00:10:36.540 align:middle line:90% 00:10:36.540 --> 00:10:37.380 align:middle line:90% [INAUDIBLE]? 00:10:37.380 --> 00:10:40.740 align:middle line:90% 00:10:40.740 --> 00:10:43.578 align:middle line:84% What kind of thing can apply this rule? 00:10:43.578 --> 00:10:44.370 align:middle line:90% AUDIENCE: Computer. 00:10:44.370 --> 00:10:45.495 align:middle line:90% MICHAEL CUTHBERT: Computer. 00:10:45.495 --> 00:10:46.980 align:middle line:90% So you can have an-- 00:10:46.980 --> 00:10:48.690 align:middle line:90% it can all be done. 00:10:48.690 --> 00:10:50.850 align:middle line:84% The ironic thing, we're maximizing musicality 00:10:50.850 --> 00:10:54.310 align:middle line:90% through algorithms. 00:10:54.310 --> 00:10:54.810 align:middle line:90% Great. 00:10:54.810 --> 00:10:58.770 align:middle line:84% So that's about all I want on that. 00:10:58.770 --> 00:11:01.650 align:middle line:84% And people whose chose that problem, those 00:11:01.650 --> 00:11:03.310 align:middle line:90% tended to do pretty well. 00:11:03.310 --> 00:11:11.250 align:middle line:84% Now let's get to second, equality and equivalence. 00:11:11.250 --> 00:11:14.690 align:middle line:84% And almost everybody chose to do this one. 00:11:14.690 --> 00:11:17.662 align:middle line:90% 00:11:17.662 --> 00:11:21.270 align:middle line:84% What's the name associated with this, without looking down? 00:11:21.270 --> 00:11:23.388 align:middle line:90% Dmitri is the first name-- 00:11:23.388 --> 00:11:24.180 align:middle line:90% AUDIENCE: Tymoczko. 00:11:24.180 --> 00:11:25.540 align:middle line:90% MICHAEL CUTHBERT: Tymoczko. 00:11:25.540 --> 00:11:27.100 align:middle line:90% Let's try to spell it together. 00:11:27.100 --> 00:11:27.988 align:middle line:90% Give me a-- 00:11:27.988 --> 00:11:28.530 align:middle line:90% AUDIENCE: T-- 00:11:28.530 --> 00:11:30.060 align:middle line:84% MICHAEL CUTHBERT: T-- give me a-- 00:11:30.060 --> 00:11:30.330 align:middle line:90% AUDIENCE: Y-- 00:11:30.330 --> 00:11:31.784 align:middle line:84% MICHAEL CUTHBERT: Y-- give me a-- 00:11:31.784 --> 00:11:32.712 align:middle line:90% AUDIENCE: M-- 00:11:32.712 --> 00:11:34.318 align:middle line:84% MICHAEL CUTHBERT: M-- give me a-- 00:11:34.318 --> 00:11:34.860 align:middle line:90% AUDIENCE: O-- 00:11:34.860 --> 00:11:35.981 align:middle line:90% MICHAEL CUTHBERT: O-- 00:11:35.981 --> 00:11:36.689 align:middle line:90% AUDIENCE: C-Z-K-- 00:11:36.689 --> 00:11:39.525 align:middle line:90% 00:11:39.525 --> 00:11:40.786 align:middle line:90% MICHAEL CUTHBERT: K-- 00:11:40.786 --> 00:11:41.328 align:middle line:90% AUDIENCE: Q-- 00:11:41.328 --> 00:11:43.790 align:middle line:90% MICHAEL CUTHBERT: Q, Tymoczkq. 00:11:43.790 --> 00:11:45.060 align:middle line:90% He'd like that. 00:11:45.060 --> 00:11:47.930 align:middle line:90% No, Tymoczko. 00:11:47.930 --> 00:11:51.140 align:middle line:84% So this one's a little bit hard, and I would not-- 00:11:51.140 --> 00:11:52.130 align:middle line:90% whatever. 00:11:52.130 --> 00:11:57.290 align:middle line:84% Basically, one of the things I try to do is I put in optic 00:11:57.290 --> 00:12:02.090 align:middle line:84% and whatever you put and see if Google could find the author 00:12:02.090 --> 00:12:04.400 align:middle line:90% on the first thing so that-- 00:12:04.400 --> 00:12:05.880 align:middle line:90% on the first page. 00:12:05.880 --> 00:12:11.430 align:middle line:84% And just remember that, if you put in Wolfgang Mustard, 00:12:11.430 --> 00:12:12.420 align:middle line:90% it finds Mozart. 00:12:12.420 --> 00:12:14.900 align:middle line:84% So Google is pretty good at this, but-- 00:12:14.900 --> 00:12:17.910 align:middle line:90% OK, so Dmitri Tymoczko's optic. 00:12:17.910 --> 00:12:21.530 align:middle line:90% Almost everybody got optic-- 00:12:21.530 --> 00:12:23.345 align:middle line:90% octave-- P-T-I-C-- 00:12:23.345 --> 00:12:27.993 align:middle line:90% 00:12:27.993 --> 00:12:28.910 align:middle line:90% AUDIENCE: Cardinality. 00:12:28.910 --> 00:12:29.520 align:middle line:90% MICHAEL CUTHBERT: Cardinality. 00:12:29.520 --> 00:12:30.020 align:middle line:90% Good. 00:12:30.020 --> 00:12:31.200 align:middle line:90% I know this back of my hand. 00:12:31.200 --> 00:12:33.290 align:middle line:84% I just don't know how to spell the word optic. 00:12:33.290 --> 00:12:35.420 align:middle line:84% And then most people, thank you for including 00:12:35.420 --> 00:12:37.400 align:middle line:84% my little contribution of spelling 00:12:37.400 --> 00:12:39.210 align:middle line:90% on the list, a lot of people. 00:12:39.210 --> 00:12:40.300 align:middle line:90% Great. 00:12:40.300 --> 00:12:42.400 align:middle line:84% So people did really, really great on that. 00:12:42.400 --> 00:12:44.460 align:middle line:84% Here's some of the things that, though, 00:12:44.460 --> 00:12:46.500 align:middle line:90% were a little bit harder. 00:12:46.500 --> 00:12:49.300 align:middle line:84% I think I might have thrown some people for a loop, 00:12:49.300 --> 00:12:51.515 align:middle line:84% and I didn't try to grade too hard 00:12:51.515 --> 00:12:52.890 align:middle line:84% on this, because I realized, ooh, 00:12:52.890 --> 00:12:55.570 align:middle line:84% I didn't do the greatest job on this in lecture. 00:12:55.570 --> 00:13:01.030 align:middle line:84% So it was the difference between equality and equivalence. 00:13:01.030 --> 00:13:03.630 align:middle line:84% When we talk about sameness, which one 00:13:03.630 --> 00:13:05.770 align:middle line:84% do you think we're most likely talking about? 00:13:05.770 --> 00:13:08.670 align:middle line:90% Votes for equality? 00:13:08.670 --> 00:13:11.460 align:middle line:90% Same, equivalence. 00:13:11.460 --> 00:13:13.210 align:middle line:90% Oh, we have more on equivalence. 00:13:13.210 --> 00:13:17.140 align:middle line:84% I might not have done as well on this. 00:13:17.140 --> 00:13:20.940 align:middle line:84% I think of sameness as having more 00:13:20.940 --> 00:13:24.210 align:middle line:84% to do with equality in some sense 00:13:24.210 --> 00:13:28.783 align:middle line:84% and equivalence meaning can be grouped together. 00:13:28.783 --> 00:13:35.400 align:middle line:90% 00:13:35.400 --> 00:13:37.320 align:middle line:84% And we could say it can be grouped together 00:13:37.320 --> 00:13:40.170 align:middle line:84% in some logical connection or can be grouped together, 00:13:40.170 --> 00:13:42.810 align:middle line:90% connected in some logical way. 00:13:42.810 --> 00:13:47.090 align:middle line:84% And the other thing that I think probably falls a little bit 00:13:47.090 --> 00:13:51.800 align:middle line:84% on me because didn't come out as clearly is that, 00:13:51.800 --> 00:13:54.260 align:middle line:84% when we're talking about same, some people-- 00:13:54.260 --> 00:13:56.310 align:middle line:84% and you got full credit if you did this-- 00:13:56.310 --> 00:13:58.500 align:middle line:90% talked about the big picture. 00:13:58.500 --> 00:14:02.490 align:middle line:84% This note is same in every conceivable way. 00:14:02.490 --> 00:14:05.450 align:middle line:84% So are this piece is the same as this other piece 00:14:05.450 --> 00:14:08.360 align:middle line:90% in every conceivable way? 00:14:08.360 --> 00:14:12.680 align:middle line:84% And that's one way that we can think of a grand scale 00:14:12.680 --> 00:14:16.710 align:middle line:84% equality of problem, is that you all are really smart 00:14:16.710 --> 00:14:21.152 align:middle line:84% and you all know how to conceive of things that can break that. 00:14:21.152 --> 00:14:24.950 align:middle line:84% I hit Play on this recording and then I 00:14:24.950 --> 00:14:27.080 align:middle line:84% hit Play on this recording again, but one of them 00:14:27.080 --> 00:14:29.930 align:middle line:84% happened 10 minutes later, and one of them 00:14:29.930 --> 00:14:35.600 align:middle line:84% was played through on speakers that had 10 minutes more of wear 00:14:35.600 --> 00:14:37.440 align:middle line:90% and tear on them or something. 00:14:37.440 --> 00:14:39.690 align:middle line:84% So you can always conceive of the way it's different. 00:14:39.690 --> 00:14:42.860 align:middle line:84% So maybe that's not as good, but we 00:14:42.860 --> 00:14:47.750 align:middle line:84% might think of equality of aspects of something, equality 00:14:47.750 --> 00:14:50.640 align:middle line:90% of aspects of-- 00:14:50.640 --> 00:14:52.137 align:middle line:90% that-- 00:14:52.137 --> 00:14:52.970 align:middle line:90% I'm trying to think. 00:14:52.970 --> 00:14:55.980 align:middle line:84% You all are sitting down, so I'm trying to think. 00:14:55.980 --> 00:14:56.840 align:middle line:90% Maybe Jake is. 00:14:56.840 --> 00:14:59.040 align:middle line:84% That we are not exactly the same, 00:14:59.040 --> 00:15:01.290 align:middle line:84% but I think we're approximately the same height. 00:15:01.290 --> 00:15:02.130 align:middle line:90% Maybe we're the same height. 00:15:02.130 --> 00:15:03.047 align:middle line:90% Let's say that we are. 00:15:03.047 --> 00:15:06.930 align:middle line:84% So we are same in heightness or something like that. 00:15:06.930 --> 00:15:12.600 align:middle line:84% So two notes could be same in frequency, equal in frequency. 00:15:12.600 --> 00:15:18.650 align:middle line:84% So that's tend to use equality for some sort of attribute 00:15:18.650 --> 00:15:25.010 align:middle line:84% of something that is identical or not cannot be distinguished 00:15:25.010 --> 00:15:26.420 align:middle line:90% from each other. 00:15:26.420 --> 00:15:31.070 align:middle line:84% Whereas equivalence, we tend to think of as things 00:15:31.070 --> 00:15:33.330 align:middle line:90% that we can group together. 00:15:33.330 --> 00:15:42.830 align:middle line:84% None of us are the same in any real, deep, great way, 00:15:42.830 --> 00:15:49.120 align:middle line:84% but we all could be lumped under the equivalence class of MIT 00:15:49.120 --> 00:15:54.185 align:middle line:90% 21M.383 students. 00:15:54.185 --> 00:15:57.250 align:middle line:84% And it kind of tells you also that equivalence classes might 00:15:57.250 --> 00:15:59.500 align:middle line:84% be overlapping, because some of you 00:15:59.500 --> 00:16:05.480 align:middle line:84% might be also MIT 6.042 students together, 00:16:05.480 --> 00:16:07.550 align:middle line:84% or you could be in something else. 00:16:07.550 --> 00:16:09.970 align:middle line:90% So they could be overlapping. 00:16:09.970 --> 00:16:13.900 align:middle line:84% Then the hardest part, I think, on this problem that snagged 00:16:13.900 --> 00:16:17.560 align:middle line:90% a bunch of people is where-- 00:16:17.560 --> 00:16:26.620 align:middle line:84% in what contexts equivalence classes might be used 00:16:26.620 --> 00:16:27.320 align:middle line:90% and might not. 00:16:27.320 --> 00:16:36.160 align:middle line:84% That we might think of [PLAYING INSTRUMENT] as one 00:16:36.160 --> 00:16:41.950 align:middle line:84% chord, arpeggiated, and [PLAYING INSTRUMENT] as the same 00:16:41.950 --> 00:16:43.150 align:middle line:90% chord or-- 00:16:43.150 --> 00:16:45.890 align:middle line:84% I guess I just use same in an equivalent sense. 00:16:45.890 --> 00:16:50.990 align:middle line:84% So maybe I'm less dogmatic there-- as an equivalent chord, 00:16:50.990 --> 00:16:57.490 align:middle line:84% even though one of them was going up 00:16:57.490 --> 00:16:59.630 align:middle line:84% and the other one was going down. 00:16:59.630 --> 00:17:03.220 align:middle line:84% So we might think that the permutation doesn't matter 00:17:03.220 --> 00:17:05.470 align:middle line:84% in that particular class when we're talking about, 00:17:05.470 --> 00:17:07.780 align:middle line:90% what chord did I arpeggiate? 00:17:07.780 --> 00:17:09.819 align:middle line:84% And then later, we might say, well, 00:17:09.819 --> 00:17:11.839 align:middle line:84% direction is another equivalence class. 00:17:11.839 --> 00:17:16.030 align:middle line:90% Did it go up or did it go down? 00:17:16.030 --> 00:17:19.119 align:middle line:84% And contexts for when you might use one 00:17:19.119 --> 00:17:21.069 align:middle line:90% and when you might not use one. 00:17:21.069 --> 00:17:24.849 align:middle line:84% A lot of times the context where equivalence classes come 00:17:24.849 --> 00:17:28.270 align:middle line:84% in, it's a little kind of too obvious in a class 00:17:28.270 --> 00:17:31.160 align:middle line:84% called computational music theory and analysis. 00:17:31.160 --> 00:17:34.480 align:middle line:84% The equivalence classes tend to not come in very-- 00:17:34.480 --> 00:17:39.910 align:middle line:84% as often in performance than in analysis. 00:17:39.910 --> 00:17:46.540 align:middle line:84% So I think more than one person wrote, well, 00:17:46.540 --> 00:17:48.850 align:middle line:84% that you can think of a performance 00:17:48.850 --> 00:17:52.310 align:middle line:84% where cardinality doesn't matter. 00:17:52.310 --> 00:17:55.670 align:middle line:84% And I might have written something like, well, 00:17:55.670 --> 00:17:57.555 align:middle line:84% if you play that measure three times 00:17:57.555 --> 00:17:59.930 align:middle line:84% because that's what's written-- and I only play it once-- 00:17:59.930 --> 00:18:02.450 align:middle line:84% it's going to matter for a performance class play, 00:18:02.450 --> 00:18:06.040 align:middle line:84% but we might not think of the cardinality as mattering. 00:18:06.040 --> 00:18:08.290 align:middle line:84% If we're trying to do a search on, 00:18:08.290 --> 00:18:12.080 align:middle line:84% does this piece have any diminished triads? 00:18:12.080 --> 00:18:15.010 align:middle line:84% We don't really care how many major triads 00:18:15.010 --> 00:18:17.360 align:middle line:84% and how many minor, but in that case, 00:18:17.360 --> 00:18:19.330 align:middle line:84% we might just be lumping everything 00:18:19.330 --> 00:18:22.570 align:middle line:84% under the type of triad equivalence class 00:18:22.570 --> 00:18:25.690 align:middle line:90% and not counting how many. 00:18:25.690 --> 00:18:30.530 align:middle line:84% A particular one, but we use these all the time in real life. 00:18:30.530 --> 00:18:34.000 align:middle line:84% So the example that popped into my head today 00:18:34.000 --> 00:18:40.910 align:middle line:84% is, if you're going to Taylor Swift-- 00:18:40.910 --> 00:18:44.590 align:middle line:84% if you're going to be analyzing a Taylor Swift song 00:18:44.590 --> 00:18:48.140 align:middle line:84% and you're going to look at the harmonic structure of it, 00:18:48.140 --> 00:18:52.840 align:middle line:84% does it matter, presumably, if you're 00:18:52.840 --> 00:18:55.030 align:middle line:84% listening to Taylor Swift's recording 00:18:55.030 --> 00:18:56.590 align:middle line:84% or if you're listening to a cover 00:18:56.590 --> 00:19:01.566 align:middle line:84% band, one that's trying to be faithful for harmonic structure? 00:19:01.566 --> 00:19:04.270 align:middle line:90% 00:19:04.270 --> 00:19:05.030 align:middle line:90% Not really. 00:19:05.030 --> 00:19:07.270 align:middle line:84% You hope a good cover band is trying 00:19:07.270 --> 00:19:09.970 align:middle line:84% to sound like that, trying to use the same harmonies. 00:19:09.970 --> 00:19:18.110 align:middle line:84% So we could come up with a cover band equivalence class cover. 00:19:18.110 --> 00:19:20.600 align:middle line:84% Maybe we just call it the cover equivalence class, 00:19:20.600 --> 00:19:23.980 align:middle line:84% which applies if you're doing harmonic analysis. 00:19:23.980 --> 00:19:27.250 align:middle line:84% Does it matter whether you're seeing Taylor Swift or a cover 00:19:27.250 --> 00:19:31.210 align:middle line:84% band if you just paid $900 for front row tickets? 00:19:31.210 --> 00:19:32.540 align:middle line:90% Yeah, it does. 00:19:32.540 --> 00:19:35.500 align:middle line:84% So we can think of live performance as a place 00:19:35.500 --> 00:19:38.210 align:middle line:84% where cover equivalence doesn't exist. 00:19:38.210 --> 00:19:40.580 align:middle line:84% Now, we mostly talked about pitch equivalence. 00:19:40.580 --> 00:19:43.720 align:middle line:90% So that's a big thing there. 00:19:43.720 --> 00:19:47.590 align:middle line:84% So that we might be thinking too much about pitch and not enough 00:19:47.590 --> 00:19:51.640 align:middle line:84% about duration equivalence, not enough about bigger things. 00:19:51.640 --> 00:19:54.340 align:middle line:84% The other thing just to talk about 00:19:54.340 --> 00:19:57.220 align:middle line:84% is that, often, when we're talking about these pitch 00:19:57.220 --> 00:20:00.080 align:middle line:84% equivalences, like octave or cardinality or things, 00:20:00.080 --> 00:20:04.504 align:middle line:84% we're not really thinking about the sort of-- 00:20:04.504 --> 00:20:08.190 align:middle line:84% I don't know-- the scale of the piece. 00:20:08.190 --> 00:20:11.020 align:middle line:84% We're not really thinking, does this piece 00:20:11.020 --> 00:20:13.870 align:middle line:84% have the same number of notes as this piece 00:20:13.870 --> 00:20:16.700 align:middle line:84% if we apply cardinality equivalence or something? 00:20:16.700 --> 00:20:20.140 align:middle line:84% But we might be thinking about, does this chord 00:20:20.140 --> 00:20:23.620 align:middle line:84% have the same number of unique pitch classes 00:20:23.620 --> 00:20:28.110 align:middle line:84% if we're applying octave, permutation, transposition, 00:20:28.110 --> 00:20:30.630 align:middle line:90% and cardinality? 00:20:30.630 --> 00:20:34.270 align:middle line:84% So that level comes up quite a bit. 00:20:34.270 --> 00:20:39.900 align:middle line:84% I think there's one place where we 00:20:39.900 --> 00:20:43.540 align:middle line:84% do tend to think of equivalence classes on a piece level 00:20:43.540 --> 00:20:46.020 align:middle line:90% sometimes. 00:20:46.020 --> 00:20:49.080 align:middle line:90% That's when you have-- 00:20:49.080 --> 00:20:50.580 align:middle line:90% I don't know-- 00:20:50.580 --> 00:20:57.598 align:middle line:90% Beethoven's third symphony in-- 00:20:57.598 --> 00:20:59.710 align:middle line:90% I don't know-- E-flat major. 00:20:59.710 --> 00:21:02.310 align:middle line:84% Sorry, of course, this isn't a music history class 00:21:02.310 --> 00:21:04.380 align:middle line:84% on the history of Beethoven, but that we do 00:21:04.380 --> 00:21:09.000 align:middle line:84% tend to group pieces in classical music by key. 00:21:09.000 --> 00:21:11.380 align:middle line:84% The other place that immediately comes to head, 00:21:11.380 --> 00:21:15.660 align:middle line:84% where there might be equivalence classes of pieces 00:21:15.660 --> 00:21:19.200 align:middle line:84% is a DJ might have a beats per minute equivalence class, where 00:21:19.200 --> 00:21:23.080 align:middle line:84% you want to group together all songs with the same BPM 00:21:23.080 --> 00:21:24.610 align:middle line:90% so you can switch between them. 00:21:24.610 --> 00:21:27.840 align:middle line:90% So think on that. 00:21:27.840 --> 00:21:33.480 align:middle line:84% Any thoughts or questions on this? 00:21:33.480 --> 00:21:36.030 align:middle line:84% And thank you to the person who gave me the opportunity 00:21:36.030 --> 00:21:39.390 align:middle line:84% to explore the permutation equivalence class 00:21:39.390 --> 00:21:40.150 align:middle line:90% on happy birthday. 00:21:40.150 --> 00:21:44.130 align:middle line:90% 00:21:44.130 --> 00:21:50.080 align:middle line:84% OK last ones to talk about, the three contexts. 00:21:50.080 --> 00:21:54.700 align:middle line:84% This one was a little bit harder. 00:21:54.700 --> 00:21:56.610 align:middle line:90% Some people got. 00:21:56.610 --> 00:21:58.560 align:middle line:84% It was by Eleanor Selfridge-Field. 00:21:58.560 --> 00:22:02.438 align:middle line:84% And some people thought it was the decently 00:22:02.438 --> 00:22:04.230 align:middle line:84% similar about the same time in the semester 00:22:04.230 --> 00:22:05.740 align:middle line:90% article by Nicholas Cook. 00:22:05.740 --> 00:22:08.880 align:middle line:84% And if you wrote that, you are getting some credit 00:22:08.880 --> 00:22:12.540 align:middle line:84% because you were really in the right ballpark. 00:22:12.540 --> 00:22:18.300 align:middle line:84% So she talks about the three main contexts talks about are-- 00:22:18.300 --> 00:22:20.680 align:middle line:84% you can read them off or better sing them out. 00:22:20.680 --> 00:22:22.830 align:middle line:90% First one? 00:22:22.830 --> 00:22:23.760 align:middle line:90% AUDIENCE: Symbolic? 00:22:23.760 --> 00:22:25.710 align:middle line:84% MICHAEL CUTHBERT: So symbolic is-- 00:22:25.710 --> 00:22:29.250 align:middle line:84% well, we'll get-- is there but not one of her terms. 00:22:29.250 --> 00:22:31.060 align:middle line:84% And that ends up being the problematic one. 00:22:31.060 --> 00:22:32.780 align:middle line:90% But yeah, we'll keep that one. 00:22:32.780 --> 00:22:33.280 align:middle line:90% Else? 00:22:33.280 --> 00:22:33.970 align:middle line:90% What's that? 00:22:33.970 --> 00:22:34.290 align:middle line:90% AUDIENCE: Graphical? 00:22:34.290 --> 00:22:35.457 align:middle line:90% MICHAEL CUTHBERT: Graphical. 00:22:35.457 --> 00:22:37.410 align:middle line:90% Yep. 00:22:37.410 --> 00:22:38.220 align:middle line:90% Graphical. 00:22:38.220 --> 00:22:40.110 align:middle line:84% And what's the opposite-- what do we 00:22:40.110 --> 00:22:42.353 align:middle line:90% contrast graphical things with? 00:22:42.353 --> 00:22:43.020 align:middle line:90% AUDIENCE: Sound. 00:22:43.020 --> 00:22:44.020 align:middle line:90% MICHAEL CUTHBERT: Sound. 00:22:44.020 --> 00:22:46.230 align:middle line:90% Good. 00:22:46.230 --> 00:22:50.685 align:middle line:84% And then the logical is what she has. 00:22:50.685 --> 00:22:54.810 align:middle line:84% And so symbolic will be in there, things. 00:22:54.810 --> 00:22:58.320 align:middle line:84% One of the things that came up a lot in the quiz 00:22:58.320 --> 00:23:04.470 align:middle line:84% was that people were immediately going to a higher level 00:23:04.470 --> 00:23:06.430 align:middle line:90% than what she was intending. 00:23:06.430 --> 00:23:09.990 align:middle line:84% So when we think about graphical, 00:23:09.990 --> 00:23:14.820 align:middle line:84% this is a graphical context for representing music, 00:23:14.820 --> 00:23:18.090 align:middle line:84% but in her mind, what is the graphical thing 00:23:18.090 --> 00:23:20.580 align:middle line:90% I just created here? 00:23:20.580 --> 00:23:22.290 align:middle line:90% Anyone want to take a guess? 00:23:22.290 --> 00:23:25.263 align:middle line:90% If you don't go to high-- 00:23:25.263 --> 00:23:26.430 align:middle line:90% AUDIENCE: Circle and a line? 00:23:26.430 --> 00:23:27.930 align:middle line:84% MICHAEL CUTHBERT: Circle and a line. 00:23:27.930 --> 00:23:31.020 align:middle line:84% Going to say-- great, a circle and a line. 00:23:31.020 --> 00:23:36.900 align:middle line:84% So by the time you move that to, Professor, you drew a quarter 00:23:36.900 --> 00:23:41.250 align:middle line:84% note with a stem down, stem down, 00:23:41.250 --> 00:23:46.050 align:middle line:84% on the third space with this context, you draw a C, 00:23:46.050 --> 00:23:50.010 align:middle line:84% you've already been moving to the logical domain. 00:23:50.010 --> 00:23:53.980 align:middle line:84% Similarly, when you hear a sound-- 00:23:53.980 --> 00:23:56.140 align:middle line:84% I can only represent sound right now. 00:23:56.140 --> 00:23:58.660 align:middle line:84% Well, duh, I can do it in the sound domain 00:23:58.660 --> 00:24:02.700 align:middle line:84% but in the graphic domain of sound. 00:24:02.700 --> 00:24:08.590 align:middle line:84% You don't necessarily yet hear, oh, I hear a C. 00:24:08.590 --> 00:24:12.270 align:middle line:84% Maybe you can say-- or I hear an A. Maybe you can say-- 00:24:12.270 --> 00:24:14.860 align:middle line:84% if you're an oscillator in your head, you can say, 00:24:14.860 --> 00:24:18.790 align:middle line:84% I hear something oscillating at 4:40 times per second. 00:24:18.790 --> 00:24:23.070 align:middle line:84% But then to move that to an A4, octave 4, 00:24:23.070 --> 00:24:25.690 align:middle line:84% is a motion to the logical domain. 00:24:25.690 --> 00:24:27.960 align:middle line:84% So this, I don't think I was clear enough 00:24:27.960 --> 00:24:31.200 align:middle line:84% on and maybe Eleanor Selfridge-Field wasn't enough 00:24:31.200 --> 00:24:34.720 align:middle line:84% or we just need to read it a little bit more closely. 00:24:34.720 --> 00:24:38.550 align:middle line:84% And similarly, even things like instrument, 00:24:38.550 --> 00:24:41.160 align:middle line:84% I hear an instrument, you're already 00:24:41.160 --> 00:24:43.330 align:middle line:90% moving to the logical domain. 00:24:43.330 --> 00:24:48.010 align:middle line:84% You might, if you're a signal processor, be saying, 00:24:48.010 --> 00:24:53.370 align:middle line:84% oh, I'm hearing a waveform where only the odd partial harmonics 00:24:53.370 --> 00:24:58.620 align:middle line:84% are present, and then your memory bank is saying, 00:24:58.620 --> 00:25:01.140 align:middle line:90% oh, I'm hearing a clarinet. 00:25:01.140 --> 00:25:05.470 align:middle line:84% So those are the odd [INAUDIBLE] I don't teach that class. 00:25:05.470 --> 00:25:08.286 align:middle line:90% I think that's right. 00:25:08.286 --> 00:25:13.140 align:middle line:84% So because elements of the logical domain, 00:25:13.140 --> 00:25:15.150 align:middle line:84% a lot of our answers were transferring 00:25:15.150 --> 00:25:17.860 align:middle line:84% to the sound or the graphical domain, 00:25:17.860 --> 00:25:27.500 align:middle line:84% the logical domain got sort of tangled up with the next higher 00:25:27.500 --> 00:25:31.310 align:middle line:84% domain, here, the next, more abstract thing, which 00:25:31.310 --> 00:25:34.613 align:middle line:84% in this case, I'm going to call it the meaning domain. 00:25:34.613 --> 00:25:37.610 align:middle line:90% 00:25:37.610 --> 00:25:41.265 align:middle line:90% We can call it the her-- 00:25:41.265 --> 00:25:42.890 align:middle line:84% I'm going to actually try to write this 00:25:42.890 --> 00:25:43.807 align:middle line:90% without looking down-- 00:25:43.807 --> 00:25:48.920 align:middle line:84% --menutic domain, which is the study of the construction 00:25:48.920 --> 00:25:51.510 align:middle line:84% of meaning or the conceptualization of meaning. 00:25:51.510 --> 00:25:54.150 align:middle line:84% It's actually a pretty cool word if you don't know it, 00:25:54.150 --> 00:25:56.930 align:middle line:84% but I don't like it too much because my whole life, 00:25:56.930 --> 00:26:02.030 align:middle line:84% I've had blowhards, if I say that word. 00:26:02.030 --> 00:26:04.320 align:middle line:84% Who use hermenutic and throw it around everywhere? 00:26:04.320 --> 00:26:06.362 align:middle line:84% I'm having a hermeneutic construction of meaning. 00:26:06.362 --> 00:26:09.380 align:middle line:84% It's like, well, no, that's just what that means. 00:26:09.380 --> 00:26:11.970 align:middle line:84% If you [INAUDIBLE] up, learn your hermenutics [INAUDIBLE]. 00:26:11.970 --> 00:26:14.460 align:middle line:84% So I'll often just call it the meaning domain. 00:26:14.460 --> 00:26:19.800 align:middle line:84% And so you might be that your logical sound domain, 00:26:19.800 --> 00:26:22.220 align:middle line:84% you've heard [MAKING TONGUE CLICKING SOUNDS] 00:26:22.220 --> 00:26:25.580 align:middle line:84% And your graphical domain, you saw a whole bunch of things 00:26:25.580 --> 00:26:29.000 align:middle line:84% on page and your logical domain said, oh, 00:26:29.000 --> 00:26:33.320 align:middle line:84% there's a whole bunch of randomly spaced staccato 8th 00:26:33.320 --> 00:26:37.430 align:middle line:84% notes, or even randomly spaced might be too far down. 00:26:37.430 --> 00:26:40.940 align:middle line:84% So at this level, you might say, oh, the title of the piece 00:26:40.940 --> 00:26:44.690 align:middle line:84% is fireflies, and this is a depiction 00:26:44.690 --> 00:26:47.070 align:middle line:84% of how the fireflies are coming in and out. 00:26:47.070 --> 00:26:53.060 align:middle line:84% So there is a next level of domain to have there. 00:26:53.060 --> 00:26:59.060 align:middle line:84% Difficulty is that-- there's this word semantic that came up 00:26:59.060 --> 00:27:03.050 align:middle line:90% a lot, semantic-- 00:27:03.050 --> 00:27:05.180 align:middle line:84% sorry, I'm writing over it, but I'm writing there 00:27:05.180 --> 00:27:06.230 align:middle line:90% for a particular reason-- 00:27:06.230 --> 00:27:11.420 align:middle line:90% 00:27:11.420 --> 00:27:14.750 align:middle line:84% that Eleanor Selfridge-Field uses 00:27:14.750 --> 00:27:19.550 align:middle line:84% to imply this level of understanding. 00:27:19.550 --> 00:27:22.050 align:middle line:84% That that's the greater meaning of things. 00:27:22.050 --> 00:27:24.690 align:middle line:90% So it's a fourth context there. 00:27:24.690 --> 00:27:29.390 align:middle line:84% But over time, it's kind of been migrated up 00:27:29.390 --> 00:27:33.110 align:middle line:84% in music information retrieval to be 00:27:33.110 --> 00:27:35.760 align:middle line:90% closer to the logical domain. 00:27:35.760 --> 00:27:39.710 align:middle line:84% So people will say, oh, I don't want to-- 00:27:39.710 --> 00:27:42.320 align:middle line:84% I don't want to know exactly how you're 00:27:42.320 --> 00:27:44.520 align:middle line:90% going to draw it on the page. 00:27:44.520 --> 00:27:50.910 align:middle line:84% I want to know it's semantically a quarter note C5 or something. 00:27:50.910 --> 00:27:53.840 align:middle line:84% And so this term, I'm going to try 00:27:53.840 --> 00:27:58.190 align:middle line:84% to avoid too much because it's being used in two 00:27:58.190 --> 00:28:04.294 align:middle line:90% very different contexts here. 00:28:04.294 --> 00:28:06.796 align:middle line:84% Questions on this or more discussion? 00:28:06.796 --> 00:28:14.760 align:middle line:90% 00:28:14.760 --> 00:28:17.510 align:middle line:84% I know we want to get to some coding 00:28:17.510 --> 00:28:20.480 align:middle line:84% and get to some other things, but thanks 00:28:20.480 --> 00:28:22.440 align:middle line:90% for sticking with all of this. 00:28:22.440 --> 00:28:24.560 align:middle line:84% Oh, and there was one thing that came up 00:28:24.560 --> 00:28:26.210 align:middle line:84% and a really good answer that made 00:28:26.210 --> 00:28:29.880 align:middle line:84% me realize that I definitely didn't say this in class. 00:28:29.880 --> 00:28:36.890 align:middle line:84% That she says, most notation formats focus on one of these-- 00:28:36.890 --> 00:28:40.080 align:middle line:84% or music representations focus on one of these things. 00:28:40.080 --> 00:28:45.500 align:middle line:84% So yeah, definitely the CD focused on sound 00:28:45.500 --> 00:28:53.520 align:middle line:84% and the PDF of music focuses on graphics and things like that. 00:28:53.520 --> 00:28:57.380 align:middle line:84% But the one way that that article has aged 00:28:57.380 --> 00:29:00.560 align:middle line:84% is that nowadays, we have so many formats that 00:29:00.560 --> 00:29:04.950 align:middle line:84% try to do-- encode two or more of these things together. 00:29:04.950 --> 00:29:07.220 align:middle line:84% So that you might have MusicXML, which 00:29:07.220 --> 00:29:11.690 align:middle line:84% is encoding some pixel placements of notes 00:29:11.690 --> 00:29:14.380 align:middle line:90% also and also encoding-- 00:29:14.380 --> 00:29:18.550 align:middle line:84% you can do links to the waveform of something. 00:29:18.550 --> 00:29:22.790 align:middle line:84% And even going from CD to MP3 in modern formats, 00:29:22.790 --> 00:29:25.090 align:middle line:84% yes, it encodes the sound but also encodes 00:29:25.090 --> 00:29:28.630 align:middle line:84% some of the metadata, the year it was proposed 00:29:28.630 --> 00:29:29.960 align:middle line:90% and things like that. 00:29:29.960 --> 00:29:33.400 align:middle line:84% And nowadays, they can even be putting recommendations 00:29:33.400 --> 00:29:35.480 align:middle line:84% to other songs or something like that. 00:29:35.480 --> 00:29:38.020 align:middle line:90% Cool. 00:29:38.020 --> 00:29:41.720 align:middle line:84% Let's come back because want to make some things. 00:29:41.720 --> 00:29:44.430 align:middle line:84% We've been in theory mode for too long. 00:29:44.430 --> 00:29:48.910 align:middle line:90% 00:29:48.910 --> 00:29:52.930 align:middle line:84% Last class, we ended by doing some algorithmic composition 00:29:52.930 --> 00:29:55.990 align:middle line:90% with random walks. 00:29:55.990 --> 00:30:00.500 align:middle line:84% Here's a random walk composition that I wrote in 10 minutes once, 00:30:00.500 --> 00:30:03.020 align:middle line:84% and I just want to say one or two things on it. 00:30:03.020 --> 00:30:03.800 align:middle line:90% Maybe you hate it. 00:30:03.800 --> 00:30:04.760 align:middle line:90% Maybe you like it. 00:30:04.760 --> 00:30:08.211 align:middle line:90% [MUSIC PLAYING] 00:30:08.211 --> 00:30:37.300 align:middle line:90% 00:30:37.300 --> 00:30:41.470 align:middle line:84% So one of the things I did in my aesthetic on the piece, just 00:30:41.470 --> 00:30:43.640 align:middle line:84% to say a few little things on it, 00:30:43.640 --> 00:30:49.538 align:middle line:84% is that I gave a large amount of gravity toward whatever note, 00:30:49.538 --> 00:30:51.830 align:middle line:84% which is a kind of transpose to make it more dissonant, 00:30:51.830 --> 00:30:53.620 align:middle line:84% whatever note something started on. 00:30:53.620 --> 00:30:56.860 align:middle line:84% When it went away, it was really, really likely 00:30:56.860 --> 00:30:59.750 align:middle line:84% to get pulled back to where it came from. 00:30:59.750 --> 00:31:02.650 align:middle line:84% So that's why you'll see just a few things that 00:31:02.650 --> 00:31:04.880 align:middle line:90% get perturbed out of way. 00:31:04.880 --> 00:31:08.030 align:middle line:84% And then, as the piece goes on within each section, 00:31:08.030 --> 00:31:09.590 align:middle line:84% the gravity got weaker and weaker. 00:31:09.590 --> 00:31:11.798 align:middle line:84% And so that kind of let it have-- 00:31:11.798 --> 00:31:13.840 align:middle line:84% I don't know-- kind of the opposite of a Lewinian 00:31:13.840 --> 00:31:17.500 align:middle line:84% global rule that things got a little bit farther out 00:31:17.500 --> 00:31:18.530 align:middle line:90% as it went. 00:31:18.530 --> 00:31:20.800 align:middle line:84% The other thing that I couldn't believe when I first 00:31:20.800 --> 00:31:23.050 align:middle line:84% saw, I was like, oh, I think this will be a good idea, 00:31:23.050 --> 00:31:24.850 align:middle line:84% write the code or the code, generate 00:31:24.850 --> 00:31:28.000 align:middle line:84% put, and it sounded just a mess, totally. 00:31:28.000 --> 00:31:30.491 align:middle line:84% Maybe it still sounded like a mess to you. 00:31:30.491 --> 00:31:34.600 align:middle line:84% But putting in these staccato marks 00:31:34.600 --> 00:31:36.760 align:middle line:84% made all the difference for making it 00:31:36.760 --> 00:31:38.720 align:middle line:90% more of a percussive piece. 00:31:38.720 --> 00:31:42.490 align:middle line:84% So you can do things like that if you want your pieces to be 00:31:42.490 --> 00:31:44.210 align:middle line:90% a little bit more interesting. 00:31:44.210 --> 00:31:44.710 align:middle line:90% Yeah. 00:31:44.710 --> 00:31:46.960 align:middle line:84% AUDIENCE: Is there some form of articulation 00:31:46.960 --> 00:31:48.670 align:middle line:84% label that you could use to avoid 00:31:48.670 --> 00:31:50.055 align:middle line:90% having to staccato every note? 00:31:50.055 --> 00:31:52.900 align:middle line:90% 00:31:52.900 --> 00:31:54.655 align:middle line:90% MICHAEL CUTHBERT: You could-- 00:31:54.655 --> 00:31:56.560 align:middle line:90% in modern thing you would say-- 00:31:56.560 --> 00:31:58.360 align:middle line:84% you dot, dot, dot, dot, and then you 00:31:58.360 --> 00:32:02.080 align:middle line:84% probably say staccat sim staccato-- similarly, 00:32:02.080 --> 00:32:03.050 align:middle line:90% staccato throughout. 00:32:03.050 --> 00:32:06.400 align:middle line:84% Or probably you would just tell a performer, 00:32:06.400 --> 00:32:08.540 align:middle line:84% if you're talking to actual humans, 00:32:08.540 --> 00:32:11.290 align:middle line:84% all notes smaller than whole notes 00:32:11.290 --> 00:32:14.818 align:middle line:90% are staccatissimo or something. 00:32:14.818 --> 00:32:16.360 align:middle line:84% AUDIENCE: Is it possible to implement 00:32:16.360 --> 00:32:20.140 align:middle line:84% that in this graphical software or does 00:32:20.140 --> 00:32:21.307 align:middle line:90% the MIDI play not recognize? 00:32:21.307 --> 00:32:23.182 align:middle line:84% MICHAEL CUTHBERT: Yeah, it doesn't recognize. 00:32:23.182 --> 00:32:25.210 align:middle line:84% When you start talking, you think, ever 00:32:25.210 --> 00:32:27.640 align:middle line:84% more expressive as it goes, the MIDI 00:32:27.640 --> 00:32:30.320 align:middle line:84% just ignores that, for the most part. 00:32:30.320 --> 00:32:37.485 align:middle line:84% I mean, maybe that's the great large language model thing too. 00:32:37.485 --> 00:32:39.790 align:middle line:84% The first thing that takes a Mahler score 00:32:39.790 --> 00:32:42.840 align:middle line:84% is MIDI and give it all of his rehearsal marks, 00:32:42.840 --> 00:32:46.880 align:middle line:84% the [SPEAKING GERMAN], all that stuff. 00:32:46.880 --> 00:32:49.480 align:middle line:84% It's like, oh, I must turn myself into fire 00:32:49.480 --> 00:32:51.830 align:middle line:90% and perform this in this way. 00:32:51.830 --> 00:32:54.958 align:middle line:84% And yeah, maybe that would be kind of interesting. 00:32:54.958 --> 00:32:56.000 align:middle line:90% I hadn't thought of that. 00:32:56.000 --> 00:32:59.170 align:middle line:90% Thanks for the idea. 00:32:59.170 --> 00:33:01.453 align:middle line:84% Yeah, so we don't have that type of thing. 00:33:01.453 --> 00:33:03.370 align:middle line:84% Besides, when you're doing computation things, 00:33:03.370 --> 00:33:07.300 align:middle line:84% one of the things is it's pretty cheap to, 00:33:07.300 --> 00:33:11.380 align:middle line:84% in a loop, put staccatos on every single thing. 00:33:11.380 --> 00:33:12.650 align:middle line:90% Yeah, great. 00:33:12.650 --> 00:33:14.710 align:middle line:84% So anyhow, I want to spend time on that, just 00:33:14.710 --> 00:33:18.850 align:middle line:84% a little amuse-bouche before getting to go ahead and open up 00:33:18.850 --> 00:33:21.564 align:middle line:90% Jupyter. 00:33:21.564 --> 00:33:23.470 align:middle line:90% I'll give you a second or two. 00:33:23.470 --> 00:33:28.000 align:middle line:90% 00:33:28.000 --> 00:33:34.000 align:middle line:84% We have a bunch of little things that we haven't gotten to yet 00:33:34.000 --> 00:33:39.460 align:middle line:84% that I want to make sure that we can get to. 00:33:39.460 --> 00:33:44.770 align:middle line:84% Reminder that the problem set is a Russian nesting doll 00:33:44.770 --> 00:33:49.570 align:middle line:84% of unlocking tools, so that please pay very close attention 00:33:49.570 --> 00:33:53.690 align:middle line:84% on each of the questions on what tools have been unlocked. 00:33:53.690 --> 00:33:57.232 align:middle line:84% But if I'm telling you, well, you now have access to chord, 00:33:57.232 --> 00:33:58.940 align:middle line:84% and now you have access to Roman numeral, 00:33:58.940 --> 00:34:00.950 align:middle line:84% I should at least introduce these to you. 00:34:00.950 --> 00:34:08.870 align:middle line:84% I can't remember if I introduced chord very briefly, 00:34:08.870 --> 00:34:10.380 align:middle line:90% or if we didn't. 00:34:10.380 --> 00:34:12.980 align:middle line:90% Maybe-- I don't think we did. 00:34:12.980 --> 00:34:14.920 align:middle line:84% I probably need some other things. 00:34:14.920 --> 00:34:19.770 align:middle line:84% I'm going to import chord note pitch for now, so go ahead 00:34:19.770 --> 00:34:21.600 align:middle line:90% and do that. 00:34:21.600 --> 00:34:23.469 align:middle line:90% Did I put the screen down even? 00:34:23.469 --> 00:34:24.659 align:middle line:90% It's all good. 00:34:24.659 --> 00:34:30.239 align:middle line:84% OK, so the hardest way that you can create a chord 00:34:30.239 --> 00:34:34.542 align:middle line:84% is, let's say, C equals note.Note C. I'm giving you 00:34:34.542 --> 00:34:36.000 align:middle line:84% the hardest way, so maybe you don't 00:34:36.000 --> 00:34:37.375 align:middle line:84% want to do this because I'm going 00:34:37.375 --> 00:34:41.699 align:middle line:84% to give you the easier way in a bit, or if you just get behind. 00:34:41.699 --> 00:34:44.679 align:middle line:84% Note G-- oh, I should probably give them octaves, shouldn't I? 00:34:44.679 --> 00:34:47.580 align:middle line:90% C4, E4, G4. 00:34:47.580 --> 00:34:51.719 align:middle line:84% And then we'll say ch for chord, "cha." 00:34:51.719 --> 00:34:54.659 align:middle line:84% Remember that chord is a bad name 00:34:54.659 --> 00:34:58.080 align:middle line:84% for a variable-- chord.pitch-- chord.Chord. 00:34:58.080 --> 00:35:00.762 align:middle line:84% Lowercase chord indicates it is a-- 00:35:00.762 --> 00:35:01.470 align:middle line:90% AUDIENCE: Module. 00:35:01.470 --> 00:35:02.895 align:middle line:90% MICHAEL CUTHBERT: Module. 00:35:02.895 --> 00:35:03.653 align:middle line:90% Uppercase means-- 00:35:03.653 --> 00:35:04.320 align:middle line:90% AUDIENCE: Class. 00:35:04.320 --> 00:35:05.550 align:middle line:84% MICHAEL CUTHBERT: Class, good, and so we're 00:35:05.550 --> 00:35:06.675 align:middle line:90% getting the object to that. 00:35:06.675 --> 00:35:08.560 align:middle line:90% So we could do c-- 00:35:08.560 --> 00:35:10.740 align:middle line:90% oops. 00:35:10.740 --> 00:35:14.220 align:middle line:84% Apparently there's a button for Google Search-- 00:35:14.220 --> 00:35:15.437 align:middle line:90% c, e, g. 00:35:15.437 --> 00:35:24.210 align:middle line:90% 00:35:24.210 --> 00:35:27.660 align:middle line:90% And do that. 00:35:27.660 --> 00:35:29.970 align:middle line:84% The other thing that you can do, and you can actually 00:35:29.970 --> 00:35:33.790 align:middle line:84% thank Dmitri Tymoczko for bugging me on, Mike, 00:35:33.790 --> 00:35:35.140 align:middle line:90% why can't I just do this? 00:35:35.140 --> 00:35:38.040 align:middle line:90% OK. 00:35:38.040 --> 00:35:41.490 align:middle line:84% That's more often how you're going to be doing things 00:35:41.490 --> 00:35:42.850 align:middle line:90% when you're coding here. 00:35:42.850 --> 00:35:46.860 align:middle line:84% But obviously, when you're doing something algorithmically, 00:35:46.860 --> 00:35:48.670 align:middle line:84% quite often you're going to have notes. 00:35:48.670 --> 00:35:52.620 align:middle line:84% You can also start with pitches here. 00:35:52.620 --> 00:35:55.410 align:middle line:84% Some of the things to say-- chords, 00:35:55.410 --> 00:35:57.120 align:middle line:90% you can iterate over them. 00:35:57.120 --> 00:36:02.190 align:middle line:90% For thing in ch, print thing. 00:36:02.190 --> 00:36:07.540 align:middle line:84% And you get the notes and that each of the nodes are there. 00:36:07.540 --> 00:36:10.560 align:middle line:84% You can change the duration of one note 00:36:10.560 --> 00:36:13.650 align:middle line:84% in a chord and not the other, but that doesn't work too, too, 00:36:13.650 --> 00:36:15.360 align:middle line:90% too well. 00:36:15.360 --> 00:36:18.990 align:middle line:90% Let's create a second chord. 00:36:18.990 --> 00:36:24.510 align:middle line:84% Weird equals chord.Chord-- oh, I don't know-- 00:36:24.510 --> 00:36:26.888 align:middle line:90% E3, G5. 00:36:26.888 --> 00:36:30.570 align:middle line:90% 00:36:30.570 --> 00:36:31.780 align:middle line:90% What are we going to do? 00:36:31.780 --> 00:36:39.820 align:middle line:90% Let's put in D7, C-sharp 8. 00:36:39.820 --> 00:36:42.030 align:middle line:90% That's a pretty weird chord. 00:36:42.030 --> 00:36:42.730 align:middle line:90% I don't know. 00:36:42.730 --> 00:36:45.810 align:middle line:84% I'll put in a B9 in there, just because I know 00:36:45.810 --> 00:36:47.380 align:middle line:90% exactly what that will put in. 00:36:47.380 --> 00:36:49.380 align:middle line:84% This is the function that you're going 00:36:49.380 --> 00:36:53.693 align:middle line:84% to wish you had access to on one of them, the root function. 00:36:53.693 --> 00:36:59.910 align:middle line:90% 00:36:59.910 --> 00:37:01.830 align:middle line:90% We all get that. 00:37:01.830 --> 00:37:05.070 align:middle line:90% This one might not have a name-- 00:37:05.070 --> 00:37:06.420 align:middle line:90% commonName. 00:37:06.420 --> 00:37:11.250 align:middle line:84% Diminished-minor ninth chord-- is that correct? 00:37:11.250 --> 00:37:14.730 align:middle line:90% Weird.show. 00:37:14.730 --> 00:37:15.540 align:middle line:90% Woo. 00:37:15.540 --> 00:37:16.930 align:middle line:90% That one went too high. 00:37:16.930 --> 00:37:19.193 align:middle line:84% OK, let's-- oh, because it's an E3. 00:37:19.193 --> 00:37:20.610 align:middle line:84% No, that actually might be correct 00:37:20.610 --> 00:37:23.410 align:middle line:84% because it has to fit it all into one staff when you do this. 00:37:23.410 --> 00:37:31.560 align:middle line:84% Maybe instead of E3, let's say E4, 5, 6-- 00:37:31.560 --> 00:37:35.530 align:middle line:84% octaves don't matter-- 5, 5, 6, 6. 00:37:35.530 --> 00:37:36.800 align:middle line:90% It'll sort it for us. 00:37:36.800 --> 00:37:39.480 align:middle line:90% 00:37:39.480 --> 00:37:42.210 align:middle line:84% Yeah, that looks a little bit better. 00:37:42.210 --> 00:37:47.610 align:middle line:84% Easier, though, is close_and_weird-- 00:37:47.610 --> 00:37:49.140 align:middle line:90% I guess I'll call it-- 00:37:49.140 --> 00:37:51.585 align:middle line:90% equals weird.closedPosition. 00:37:51.585 --> 00:37:58.100 align:middle line:90% 00:37:58.100 --> 00:37:59.420 align:middle line:90% Oops. 00:37:59.420 --> 00:38:02.300 align:middle line:90% OK. 00:38:02.300 --> 00:38:06.560 align:middle line:84% So who remembers what closed position is from 301 00:38:06.560 --> 00:38:07.525 align:middle line:90% or something like that? 00:38:07.525 --> 00:38:11.480 align:middle line:90% 00:38:11.480 --> 00:38:12.020 align:middle line:90% Yeah? 00:38:12.020 --> 00:38:13.228 align:middle line:90% AUDIENCE: It's in one octave. 00:38:13.228 --> 00:38:16.730 align:middle line:84% MICHAEL CUTHBERT: Yeah, it's all within one octave. 00:38:16.730 --> 00:38:19.770 align:middle line:84% There's actually two different things. 00:38:19.770 --> 00:38:23.030 align:middle line:84% Some definitions allow the bass note 00:38:23.030 --> 00:38:30.230 align:middle line:84% to be in a different octave, but the top nodes are all as close 00:38:30.230 --> 00:38:31.290 align:middle line:90% together as you can get. 00:38:31.290 --> 00:38:33.110 align:middle line:84% Yeah, and that can be pretty useful 00:38:33.110 --> 00:38:37.360 align:middle line:90% for an analysis type of task. 00:38:37.360 --> 00:38:43.590 align:middle line:84% So we'll choose a different Bach piece today. 00:38:43.590 --> 00:38:46.220 align:middle line:84% I'm sorry I'm not keeping up my promise 00:38:46.220 --> 00:38:48.720 align:middle line:90% to do a bit more than just Bach. 00:38:48.720 --> 00:38:52.670 align:middle line:84% But it does make things go a little bit faster. 00:38:52.670 --> 00:38:55.950 align:middle line:84% And this will say, bach equals corpus-- 00:38:55.950 --> 00:38:57.180 align:middle line:90% so I'm importing corpus. 00:38:57.180 --> 00:38:57.770 align:middle line:90% Sorry. 00:38:57.770 --> 00:39:00.080 align:middle line:90% I should be talking around-- 00:39:00.080 --> 00:39:03.720 align:middle line:90% corpus bwv269. 00:39:03.720 --> 00:39:06.020 align:middle line:84% This is going to be one of our favorite ones 00:39:06.020 --> 00:39:08.976 align:middle line:90% coming up for a bit. 00:39:08.976 --> 00:39:10.260 align:middle line:90% I think it's 269. 00:39:10.260 --> 00:39:11.840 align:middle line:90% Do I have the right template? 00:39:11.840 --> 00:39:13.030 align:middle line:90% Yep, great. 00:39:13.030 --> 00:39:17.750 align:middle line:90% 00:39:17.750 --> 00:39:19.940 align:middle line:90% [SPEAKING GERMAN] 00:39:19.940 --> 00:39:21.710 align:middle line:90% 00:39:21.710 --> 00:39:24.560 align:middle line:90% Great. 00:39:24.560 --> 00:39:30.763 align:middle line:84% And so one of the things we can do is we can get-- 00:39:30.763 --> 00:39:31.680 align:middle line:90% so what did I call it? 00:39:31.680 --> 00:39:34.595 align:middle line:84% Bach-- let's do bach.chordify.show. 00:39:34.595 --> 00:39:37.970 align:middle line:90% 00:39:37.970 --> 00:39:40.550 align:middle line:84% I think we've encountered this, but we haven't really 00:39:40.550 --> 00:39:42.570 align:middle line:90% talked about it very much. 00:39:42.570 --> 00:39:45.090 align:middle line:84% And I'm going to need to zoom out for a second, 00:39:45.090 --> 00:39:47.690 align:middle line:90% or you can do this on your own. 00:39:47.690 --> 00:39:51.390 align:middle line:84% Or maybe I'll just do this-- bach.measures-- 00:39:51.390 --> 00:39:52.295 align:middle line:90% so we remember this. 00:39:52.295 --> 00:39:53.520 align:middle line:90% It begins with pickup? 00:39:53.520 --> 00:39:57.645 align:middle line:90% Yep-- 0 through 4 .show. 00:39:57.645 --> 00:40:00.020 align:middle line:84% Chordify is slow enough so you probably shouldn't call it 00:40:00.020 --> 00:40:01.130 align:middle line:90% every single time. 00:40:01.130 --> 00:40:04.070 align:middle line:90% bach.chord-- bach... 00:40:04.070 --> 00:40:08.600 align:middle line:84% Might as well make the part that's faster go first. 00:40:08.600 --> 00:40:12.110 align:middle line:84% bach.measures, 0 to 4, .chordify.show. 00:40:12.110 --> 00:40:13.190 align:middle line:90% You don't have to-- 00:40:13.190 --> 00:40:15.320 align:middle line:90% am I going too fast today? 00:40:15.320 --> 00:40:16.120 align:middle line:90% Yes, I am? 00:40:16.120 --> 00:40:16.620 align:middle line:90% Good. 00:40:16.620 --> 00:40:19.020 align:middle line:84% Thank you for having the courage to nod when you do it. 00:40:19.020 --> 00:40:20.850 align:middle line:84% So we're going to do the same thing, 00:40:20.850 --> 00:40:26.570 align:middle line:84% and I just want to make sure that we can get-- 00:40:26.570 --> 00:40:28.770 align:middle line:84% I can't really tell if that's a G, 00:40:28.770 --> 00:40:33.900 align:middle line:84% but it does look about an octave below that note, 00:40:33.900 --> 00:40:36.570 align:middle line:84% and I do know that that's a G. And so yep. 00:40:36.570 --> 00:40:39.800 align:middle line:84% So it's taking at every moment what's sometimes 00:40:39.800 --> 00:40:43.530 align:middle line:84% called a salami slice, which is to say, 00:40:43.530 --> 00:40:48.570 align:middle line:84% every time something changes, there is a new chord created. 00:40:48.570 --> 00:40:52.980 align:middle line:84% So we can see here that there's nothing that changes here 00:40:52.980 --> 00:40:54.348 align:middle line:90% in between here and here. 00:40:54.348 --> 00:40:55.140 align:middle line:90% So this is a chord. 00:40:55.140 --> 00:40:55.807 align:middle line:90% This is a chord. 00:40:55.807 --> 00:40:59.750 align:middle line:84% But here, this will need to be made into two chords in order 00:40:59.750 --> 00:41:02.400 align:middle line:90% to deal with it. 00:41:02.400 --> 00:41:07.850 align:middle line:84% And we can see here that this works. 00:41:07.850 --> 00:41:11.787 align:middle line:84% It's rather hard to figure out what chords these things are. 00:41:11.787 --> 00:41:12.870 align:middle line:90% So what did we just learn? 00:41:12.870 --> 00:41:13.370 align:middle line:90% Yeah? 00:41:13.370 --> 00:41:15.650 align:middle line:90% AUDIENCE: What's MXL? 00:41:15.650 --> 00:41:20.906 align:middle line:84% MICHAEL CUTHBERT: It's a MusicXML format 00:41:20.906 --> 00:41:23.310 align:middle line:90% that is compressed MusicXML. 00:41:23.310 --> 00:41:25.890 align:middle line:84% So it's kind of nice that it's MusicXML all compressed. 00:41:25.890 --> 00:41:33.040 align:middle line:84% So MusicXML takes up a lot for notation format 00:41:33.040 --> 00:41:35.870 align:middle line:84% and not a lot for video format or something-- 00:41:35.870 --> 00:41:38.310 align:middle line:84% not a lot for something in the sound domain, 00:41:38.310 --> 00:41:42.030 align:middle line:84% but a lot for something in the logical domain of things. 00:41:42.030 --> 00:41:43.980 align:middle line:84% But it compresses incredibly well. 00:41:43.980 --> 00:41:47.780 align:middle line:84% Anybody who works on compression algorithms 00:41:47.780 --> 00:41:49.410 align:middle line:90% might find that interesting. 00:41:49.410 --> 00:41:51.910 align:middle line:84% So a lot of people compress their MusicXML. 00:41:51.910 --> 00:41:52.660 align:middle line:90% Good question. 00:41:52.660 --> 00:41:55.440 align:middle line:84% OK, so what's something we just learned 00:41:55.440 --> 00:42:02.203 align:middle line:84% that we can do to help make this a little bit easier to read, 00:42:02.203 --> 00:42:03.870 align:middle line:84% to figure out what chords are happening? 00:42:03.870 --> 00:42:04.860 align:middle line:90% Yeah, John? 00:42:04.860 --> 00:42:06.640 align:middle line:84% AUDIENCE: After [INAUDIBLE] to compress. 00:42:06.640 --> 00:42:06.960 align:middle line:90% MICHAEL CUTHBERT: Yeah. 00:42:06.960 --> 00:42:07.540 align:middle line:90% Yep. 00:42:07.540 --> 00:42:09.000 align:middle line:90% Did somebody want to-- 00:42:09.000 --> 00:42:11.502 align:middle line:84% what was it that we used to compress the chords? 00:42:11.502 --> 00:42:12.210 align:middle line:90% We just learned-- 00:42:12.210 --> 00:42:12.720 align:middle line:90% AUDIENCE: Closed position. 00:42:12.720 --> 00:42:14.550 align:middle line:84% MICHAEL CUTHBERT: Closed position, good. 00:42:14.550 --> 00:42:22.320 align:middle line:84% So let's say chf, or chordified, is bach.-- 00:42:22.320 --> 00:42:24.450 align:middle line:84% here, we'll just do a little excerpt-- 00:42:24.450 --> 00:42:28.410 align:middle line:90% 0 through 4 .chordify. 00:42:28.410 --> 00:42:32.352 align:middle line:84% And I'll make sure that that's the same as before, 00:42:32.352 --> 00:42:33.490 align:middle line:90% that I did type it right. 00:42:33.490 --> 00:42:33.990 align:middle line:90% Yep. 00:42:33.990 --> 00:42:38.280 align:middle line:84% OK, so how am I going to do this? 00:42:38.280 --> 00:42:43.330 align:middle line:84% Actually, before I do that, let's just look at it in text-- 00:42:43.330 --> 00:42:45.660 align:middle line:90% show.text. 00:42:45.660 --> 00:42:47.080 align:middle line:90% Instrument 3, 4. 00:42:47.080 --> 00:42:47.580 align:middle line:90% Yep. 00:42:47.580 --> 00:42:51.020 align:middle line:84% And we have all these chords within measure. 00:42:51.020 --> 00:42:55.660 align:middle line:84% So we want to put all of these chords into closed position. 00:42:55.660 --> 00:42:58.060 align:middle line:84% What's our favorite three-letter word 00:42:58.060 --> 00:42:59.390 align:middle line:90% that we're going to start with? 00:42:59.390 --> 00:43:00.095 align:middle line:90% AUDIENCE: Four. 00:43:00.095 --> 00:43:00.800 align:middle line:90% MICHAEL CUTHBERT: Four. 00:43:00.800 --> 00:43:01.300 align:middle line:90% Great. 00:43:01.300 --> 00:43:04.240 align:middle line:90% So let's do this. 00:43:04.240 --> 00:43:10.040 align:middle line:84% For my_chord in-- what do we call that? 00:43:10.040 --> 00:43:13.490 align:middle line:84% We call that chf or chf.-something. 00:43:13.490 --> 00:43:15.647 align:middle line:84% Whisper to your neighbor what the answer should be, 00:43:15.647 --> 00:43:16.980 align:middle line:90% and then we'll all shout it out. 00:43:16.980 --> 00:43:21.700 align:middle line:90% 00:43:21.700 --> 00:43:24.790 align:middle line:90% [SIDE CONVERSATION] 00:43:24.790 --> 00:43:28.750 align:middle line:90% 00:43:28.750 --> 00:43:32.835 align:middle line:84% Who votes for the next thing being a colon? 00:43:32.835 --> 00:43:37.480 align:middle line:90% 00:43:37.480 --> 00:43:38.830 align:middle line:90% No, nobody? 00:43:38.830 --> 00:43:41.890 align:middle line:90% Who votes for recurse? 00:43:41.890 --> 00:43:43.035 align:middle line:90% Who votes for flatten? 00:43:43.035 --> 00:43:45.670 align:middle line:90% 00:43:45.670 --> 00:43:47.950 align:middle line:90% Who votes for something else? 00:43:47.950 --> 00:43:49.990 align:middle line:90% OK, something else? 00:43:49.990 --> 00:43:51.940 align:middle line:84% AUDIENCE: A bracket in the chord class. 00:43:51.940 --> 00:43:53.830 align:middle line:90% MICHAEL CUTHBERT: Ah, yeah-- 00:43:53.830 --> 00:43:58.100 align:middle line:84% bracket on the chord class, which is equivalent to-- 00:43:58.100 --> 00:43:59.560 align:middle line:90% anyone remember? 00:43:59.560 --> 00:44:00.310 align:middle line:90% AUDIENCE: Recurse. 00:44:00.310 --> 00:44:02.020 align:middle line:90% MICHAEL CUTHBERT: Recurse and? 00:44:02.020 --> 00:44:02.320 align:middle line:90% AUDIENCE: Get elements... 00:44:02.320 --> 00:44:03.770 align:middle line:84% MICHAEL CUTHBERT: Get elements by class. 00:44:03.770 --> 00:44:05.600 align:middle line:84% So yeah, that would be really, really great. 00:44:05.600 --> 00:44:07.017 align:middle line:84% The other thing-- by the way, this 00:44:07.017 --> 00:44:09.970 align:middle line:84% is a case where flatten isn't going to be too bad either 00:44:09.970 --> 00:44:12.950 align:middle line:84% because we don't really care what order we're getting them. 00:44:12.950 --> 00:44:17.170 align:middle line:84% We're going to put them all into closed position. 00:44:17.170 --> 00:44:19.660 align:middle line:84% So for my_chord chord in this thing, 00:44:19.660 --> 00:44:23.200 align:middle line:90% we can do something like this. 00:44:23.200 --> 00:44:26.290 align:middle line:90% We say, closedPosition. 00:44:26.290 --> 00:44:27.380 align:middle line:90% Oh, shoot. 00:44:27.380 --> 00:44:29.920 align:middle line:84% But that returns a new thing, and we don't 00:44:29.920 --> 00:44:31.750 align:middle line:90% have a stream to put it in. 00:44:31.750 --> 00:44:33.970 align:middle line:84% A lot of these things that change 00:44:33.970 --> 00:44:36.370 align:middle line:84% streams and change chords and stuff like that 00:44:36.370 --> 00:44:40.480 align:middle line:90% has an in-place option. 00:44:40.480 --> 00:44:44.260 align:middle line:84% It also has something-- forceOctave, 00:44:44.260 --> 00:44:46.120 align:middle line:84% and we'll say forceOctave equals 4. 00:44:46.120 --> 00:44:47.870 align:middle line:84% And that's something that's pretty useful. 00:44:47.870 --> 00:44:50.050 align:middle line:84% That says, now you're shrinking everything 00:44:50.050 --> 00:44:51.530 align:middle line:90% to be within one octave. 00:44:51.530 --> 00:44:54.300 align:middle line:84% Let's not have you do your own transpose function or something 00:44:54.300 --> 00:44:54.800 align:middle line:90% after that. 00:44:54.800 --> 00:44:56.860 align:middle line:90% Let's just put it all into four. 00:44:56.860 --> 00:44:59.230 align:middle line:84% So hopefully this works so I don't-- 00:44:59.230 --> 00:45:01.570 align:middle line:84% AUDIENCE: Should be running closedPosition 00:45:01.570 --> 00:45:02.720 align:middle line:90% on my_chord, not c? 00:45:02.720 --> 00:45:04.220 align:middle line:90% MICHAEL CUTHBERT: Oh, thank you. 00:45:04.220 --> 00:45:05.210 align:middle line:90% Thank you. 00:45:05.210 --> 00:45:10.120 align:middle line:84% This class is like a running example 00:45:10.120 --> 00:45:15.250 align:middle line:84% of how two people coding code faster than two people coding 00:45:15.250 --> 00:45:19.060 align:middle line:84% together code more code faster than two people coding 00:45:19.060 --> 00:45:21.070 align:middle line:90% separately-- maybe not 17. 00:45:21.070 --> 00:45:22.190 align:middle line:90% That's probably too many. 00:45:22.190 --> 00:45:24.970 align:middle line:90% But yeah. 00:45:24.970 --> 00:45:28.720 align:middle line:84% So I haven't ever figured out the time 00:45:28.720 --> 00:45:32.660 align:middle line:84% to fix the tie algorithm when you do closed position 00:45:32.660 --> 00:45:35.620 align:middle line:84% because obviously it's kind of cool that it finds that, 00:45:35.620 --> 00:45:37.675 align:middle line:84% oh, there's a tie that was opened, 00:45:37.675 --> 00:45:39.550 align:middle line:84% but then this got moved to here or something. 00:45:39.550 --> 00:45:40.310 align:middle line:90% So great. 00:45:40.310 --> 00:45:44.800 align:middle line:84% So now we have a certain number of chords 00:45:44.800 --> 00:45:46.720 align:middle line:90% that are happening here. 00:45:46.720 --> 00:45:48.760 align:middle line:84% What key do we think the piece is in now 00:45:48.760 --> 00:45:51.970 align:middle line:90% that we can see it more easily? 00:45:51.970 --> 00:45:52.757 align:middle line:90% AUDIENCE: G major. 00:45:52.757 --> 00:45:54.340 align:middle line:84% MICHAEL CUTHBERT: G major, good, good. 00:45:54.340 --> 00:45:57.740 align:middle line:84% And so now we can start putting Roman numerals on things. 00:45:57.740 --> 00:45:59.213 align:middle line:90% What do we call this in G major? 00:45:59.213 --> 00:46:00.130 align:middle line:90% AUDIENCE: The first... 00:46:00.130 --> 00:46:01.630 align:middle line:90% MICHAEL CUTHBERT: I. 00:46:01.630 --> 00:46:03.630 align:middle line:90% AUDIENCE: I. 00:46:03.630 --> 00:46:04.172 align:middle line:90% AUDIENCE: IV. 00:46:04.172 --> 00:46:04.713 align:middle line:90% AUDIENCE: IV. 00:46:04.713 --> 00:46:05.590 align:middle line:90% MICHAEL CUTHBERT: IV. 00:46:05.590 --> 00:46:06.050 align:middle line:90% What-- 00:46:06.050 --> 00:46:06.633 align:middle line:90% AUDIENCE: IV6. 00:46:06.633 --> 00:46:09.220 align:middle line:84% MICHAEL CUTHBERT: IV6-- IV in first inversion? 00:46:09.220 --> 00:46:10.920 align:middle line:90% AUDIENCE: VI. 00:46:10.920 --> 00:46:12.890 align:middle line:90% MICHAEL CUTHBERT: VI, yep. 00:46:12.890 --> 00:46:13.390 align:middle line:90% AUDIENCE: V. 00:46:13.390 --> 00:46:15.170 align:middle line:84% AUDIENCE: VI-- or first inversion. 00:46:15.170 --> 00:46:16.670 align:middle line:84% MICHAEL CUTHBERT: V first inversion. 00:46:16.670 --> 00:46:19.253 align:middle line:84% Now, then there's certain things that we have to be like, ooh, 00:46:19.253 --> 00:46:21.250 align:middle line:90% but was that-- 00:46:21.250 --> 00:46:24.800 align:middle line:84% we go all the way back up to here-- 00:46:24.800 --> 00:46:25.300 align:middle line:90% no. 00:46:25.300 --> 00:46:26.740 align:middle line:90% OK, good. 00:46:26.740 --> 00:46:29.110 align:middle line:84% What's hard to tell is if that was a passing tone 00:46:29.110 --> 00:46:31.150 align:middle line:84% or if that was-- which one of these two 00:46:31.150 --> 00:46:34.190 align:middle line:84% was the passing tone in that case-- can you see my pointer? 00:46:34.190 --> 00:46:36.660 align:middle line:84% Yeah-- which one of those two was the passing tone there. 00:46:36.660 --> 00:46:37.160 align:middle line:90% Great. 00:46:37.160 --> 00:46:40.910 align:middle line:84% So we can go there, and we can do this here. 00:46:40.910 --> 00:46:44.730 align:middle line:84% We'll get to how we can have the computer do all of this for us 00:46:44.730 --> 00:46:46.205 align:middle line:90% in just a bit. 00:46:46.205 --> 00:46:48.960 align:middle line:90% 00:46:48.960 --> 00:46:50.328 align:middle line:90% Questions or anything? 00:46:50.328 --> 00:46:51.870 align:middle line:84% I should go a little bit more slowly. 00:46:51.870 --> 00:46:52.560 align:middle line:90% Yeah, John? 00:46:52.560 --> 00:46:54.373 align:middle line:84% AUDIENCE: If we force octave to be four, 00:46:54.373 --> 00:46:56.290 align:middle line:84% why do we have some notes in the fifth octave? 00:46:56.290 --> 00:46:59.040 align:middle line:84% MICHAEL CUTHBERT: Why do we have some notes in the fifth octave? 00:46:59.040 --> 00:47:03.210 align:middle line:84% What it says is that forced the lowest note to be an octave 4, 00:47:03.210 --> 00:47:09.030 align:middle line:84% and so since it can go up to an octave-- 00:47:09.030 --> 00:47:13.060 align:middle line:84% yeah, so that's the case where it's the highest here. 00:47:13.060 --> 00:47:16.200 align:middle line:84% It does mean, if you do compositions 00:47:16.200 --> 00:47:18.450 align:middle line:84% where you're putting chords in closed positions 00:47:18.450 --> 00:47:22.270 align:middle line:84% and jumping them around, it can sound very jumpy. 00:47:22.270 --> 00:47:26.410 align:middle line:90% So that's one example here. 00:47:26.410 --> 00:47:26.910 align:middle line:90% Great. 00:47:26.910 --> 00:47:29.782 align:middle line:90% Anything else? 00:47:29.782 --> 00:47:31.240 align:middle line:84% I should have been going with this. 00:47:31.240 --> 00:47:34.740 align:middle line:90% Let me-- OK. 00:47:34.740 --> 00:47:38.610 align:middle line:84% Let's dir the chord class for a second-- 00:47:38.610 --> 00:47:41.190 align:middle line:90% chord.Chord. 00:47:41.190 --> 00:47:41.910 align:middle line:90% Oops. 00:47:41.910 --> 00:47:47.430 align:middle line:84% Actually, I should be just diring one of the chords. 00:47:47.430 --> 00:47:51.960 align:middle line:84% So some of the things are things that you've already 00:47:51.960 --> 00:47:54.157 align:middle line:84% seen because chords are music21 objects. 00:47:54.157 --> 00:47:55.490 align:middle line:90% Obviously, they have a duration. 00:47:55.490 --> 00:47:57.040 align:middle line:90% You know how to deal with it. 00:47:57.040 --> 00:48:00.520 align:middle line:84% They don't have a .pitch attribute. 00:48:00.520 --> 00:48:04.000 align:middle line:84% They have a .pitches, which gives you all the pitches there. 00:48:04.000 --> 00:48:05.850 align:middle line:84% But there's some kind of things-- 00:48:05.850 --> 00:48:07.390 align:middle line:90% canBeTonic. 00:48:07.390 --> 00:48:10.710 align:middle line:84% Can this chord be a tonic in some key? 00:48:10.710 --> 00:48:12.050 align:middle line:90% What chords can be tonics? 00:48:12.050 --> 00:48:14.730 align:middle line:90% 00:48:14.730 --> 00:48:15.910 align:middle line:90% What kinds of chords? 00:48:15.910 --> 00:48:19.292 align:middle line:84% What equivalence class of chords? 00:48:19.292 --> 00:48:20.250 align:middle line:90% AUDIENCE: Major chords. 00:48:20.250 --> 00:48:21.870 align:middle line:84% MICHAEL CUTHBERT: Major chords and-- 00:48:21.870 --> 00:48:22.200 align:middle line:90% AUDIENCE: Minor. 00:48:22.200 --> 00:48:23.460 align:middle line:84% MICHAEL CUTHBERT: Minor chords, great. 00:48:23.460 --> 00:48:24.100 align:middle line:90% Super. 00:48:24.100 --> 00:48:27.360 align:middle line:90% So that's some of the things. 00:48:27.360 --> 00:48:29.440 align:middle line:84% Does the chord contain a seventh? 00:48:29.440 --> 00:48:31.050 align:middle line:90% I think weird does. 00:48:31.050 --> 00:48:36.180 align:middle line:90% .containsSeventh-- True. 00:48:36.180 --> 00:48:39.270 align:middle line:84% But do we still have that first one? 00:48:39.270 --> 00:48:40.110 align:middle line:90% Yep. 00:48:40.110 --> 00:48:42.040 align:middle line:90% ch.containsSeventh. 00:48:42.040 --> 00:48:45.780 align:middle line:84% So you'll find that there's all these slightly useful things 00:48:45.780 --> 00:48:47.760 align:middle line:90% in here. 00:48:47.760 --> 00:48:50.010 align:middle line:90% I don't know what C-- 00:48:50.010 --> 00:48:51.580 align:middle line:90% is it an augmented triad? 00:48:51.580 --> 00:48:52.750 align:middle line:90% Is it an augmented sixth? 00:48:52.750 --> 00:48:54.310 align:middle line:90% Is it a French augmented sixth? 00:48:54.310 --> 00:48:56.340 align:middle line:84% It's a half-diminished augmented sixth? 00:48:56.340 --> 00:48:58.020 align:middle line:84% A lot of these things here-- is it 00:48:58.020 --> 00:49:00.000 align:middle line:90% transpositionally symmetrical? 00:49:00.000 --> 00:49:03.160 align:middle line:84% These things come up quite a bit. 00:49:03.160 --> 00:49:07.120 align:middle line:84% And you can put the same pitch more than once into a chord. 00:49:07.120 --> 00:49:10.530 align:middle line:84% So sometimes you want to remove the redundant pitches, 00:49:10.530 --> 00:49:15.600 align:middle line:84% redundant pitch classes, and so on. 00:49:15.600 --> 00:49:17.700 align:middle line:84% Sometimes you might have weird chords 00:49:17.700 --> 00:49:20.080 align:middle line:84% that you want to respell and so on. 00:49:20.080 --> 00:49:23.110 align:middle line:84% So these are some of the things that are of useful in here. 00:49:23.110 --> 00:49:28.860 align:middle line:84% And if you want to talk about ontology errors here, 00:49:28.860 --> 00:49:30.810 align:middle line:90% ch.third gives you the third. 00:49:30.810 --> 00:49:33.000 align:middle line:90% ch.fifth gives you the fifth. 00:49:33.000 --> 00:49:38.290 align:middle line:84% And ch.base gives you a bound method of something. 00:49:38.290 --> 00:49:39.990 align:middle line:90% So that's something I wish-- 00:49:39.990 --> 00:49:43.320 align:middle line:84% I wish I could figure out how to change that these were done 00:49:43.320 --> 00:49:47.070 align:middle line:84% differently early on, and it's a little too late 00:49:47.070 --> 00:49:50.130 align:middle line:84% sometimes to change things, just like it's a little too 00:49:50.130 --> 00:49:55.740 align:middle line:84% late to change how certain words in English are spelled. 00:49:55.740 --> 00:49:56.290 align:middle line:90% Cool. 00:49:56.290 --> 00:49:59.640 align:middle line:84% So that's the end of the introduction to chords, 00:49:59.640 --> 00:50:03.995 align:middle line:84% unless people want to do something with this. 00:50:03.995 --> 00:50:06.908 align:middle line:90% 00:50:06.908 --> 00:50:07.950 align:middle line:90% AUDIENCE: Roman numerals? 00:50:07.950 --> 00:50:08.710 align:middle line:90% MICHAEL CUTHBERT: What's that? 00:50:08.710 --> 00:50:09.390 align:middle line:90% AUDIENCE: Roman numerals. 00:50:09.390 --> 00:50:10.150 align:middle line:84% MICHAEL CUTHBERT: Roman numerals-- 00:50:10.150 --> 00:50:12.400 align:middle line:84% we'll get to Roman numerals in just a second. 00:50:12.400 --> 00:50:13.065 align:middle line:90% So great. 00:50:13.065 --> 00:50:15.190 align:middle line:84% So we're definitely going to get to Roman numerals. 00:50:15.190 --> 00:50:22.890 align:middle line:84% But first, a small leftover from our work on cognition 00:50:22.890 --> 00:50:26.520 align:middle line:84% and keys and the probe tone method by-- 00:50:26.520 --> 00:50:30.075 align:middle line:84% anyone know, if you know the author? 00:50:30.075 --> 00:50:30.962 align:middle line:90% AUDIENCE: Carol-- 00:50:30.962 --> 00:50:31.920 align:middle line:90% MICHAEL CUTHBERT: What? 00:50:31.920 --> 00:50:32.550 align:middle line:90% AUDIENCE: Carol Krumhansl. 00:50:32.550 --> 00:50:33.967 align:middle line:84% MICHAEL CUTHBERT: Carol Krumhansl. 00:50:33.967 --> 00:50:34.540 align:middle line:90% Great! 00:50:34.540 --> 00:50:35.040 align:middle line:90% well done. 00:50:35.040 --> 00:50:37.110 align:middle line:90% Yep. 00:50:37.110 --> 00:50:40.840 align:middle line:84% Who was one of the people who referenced this. 00:50:40.840 --> 00:50:45.960 align:middle line:84% Yeah, the probe tone message by Krumhansl, Carol Krumhansl. 00:50:45.960 --> 00:50:48.300 align:middle line:84% And so what we're going to do is I'm going 00:50:48.300 --> 00:50:52.260 align:middle line:90% to get us to two pieces here. 00:50:52.260 --> 00:50:56.423 align:middle line:84% You don't have to do this part if you don't-- 00:50:56.423 --> 00:50:58.090 align:middle line:84% actually, at this point in the semester, 00:50:58.090 --> 00:51:00.570 align:middle line:84% you don't have to type anything that I'm typing 00:51:00.570 --> 00:51:02.860 align:middle line:90% unless it's helpful for you. 00:51:02.860 --> 00:51:04.960 align:middle line:84% Maybe in the first part, it's good. 00:51:04.960 --> 00:51:08.760 align:middle line:84% So this is a particular little jig. 00:51:08.760 --> 00:51:12.120 align:middle line:84% We're going to be working with a lot of jigs in the next time 00:51:12.120 --> 00:51:13.930 align:middle line:90% that we do some coding together. 00:51:13.930 --> 00:51:18.040 align:middle line:84% So that's a nice little 9/8 jig, a little bit unusual. 00:51:18.040 --> 00:51:20.100 align:middle line:84% What key does it look like it's in? 00:51:20.100 --> 00:51:21.060 align:middle line:90% AUDIENCE: D major. 00:51:21.060 --> 00:51:22.018 align:middle line:90% MICHAEL CUTHBERT: Yeah. 00:51:22.018 --> 00:51:24.600 align:middle line:84% You always have to-- you can let people give us 00:51:24.600 --> 00:51:26.080 align:middle line:90% a chance to do it. 00:51:26.080 --> 00:51:27.380 align:middle line:90% Yep, D major here. 00:51:27.380 --> 00:51:30.090 align:middle line:90% 00:51:30.090 --> 00:51:34.160 align:middle line:84% And then we'll get a piece by the 20th century composer Arnold 00:51:34.160 --> 00:51:40.330 align:middle line:90% Schoenberg, Schoenberg opus. 00:51:40.330 --> 00:51:46.740 align:middle line:84% S-C-H-O-E-N-B-E-R-G slash O-P-U-S 19/movement6-- 00:51:46.740 --> 00:51:47.780 align:middle line:90% all one word. 00:51:47.780 --> 00:51:49.030 align:middle line:90% I know it's a little bit hard. 00:51:49.030 --> 00:51:52.190 align:middle line:90% 00:51:52.190 --> 00:51:56.120 align:middle line:84% I wish I had another title that we can do. 00:51:56.120 --> 00:51:57.430 align:middle line:90% It's a little piano piece. 00:51:57.430 --> 00:52:01.050 align:middle line:90% 00:52:01.050 --> 00:52:01.550 align:middle line:90% Great. 00:52:01.550 --> 00:52:03.710 align:middle line:90% And Adam, what key is it in? 00:52:03.710 --> 00:52:05.810 align:middle line:90% AUDIENCE: No one knows. 00:52:05.810 --> 00:52:07.760 align:middle line:90% MICHAEL CUTHBERT: OK. 00:52:07.760 --> 00:52:11.720 align:middle line:84% Yeah, so this is a rather ambiguous piece. 00:52:11.720 --> 00:52:16.160 align:middle line:84% Just so you can get a tiny bit in your ear, just 00:52:16.160 --> 00:52:19.335 align:middle line:90% the first couple chords. 00:52:19.335 --> 00:52:23.295 align:middle line:90% [PIANO CHORDS] 00:52:23.295 --> 00:52:32.210 align:middle line:90% 00:52:32.210 --> 00:52:37.752 align:middle line:84% So something wrong on-- there's a cleft change missing. 00:52:37.752 --> 00:52:41.640 align:middle line:90% [PIANO MELODY] 00:52:41.640 --> 00:52:42.620 align:middle line:90% 00:52:42.620 --> 00:52:45.500 align:middle line:84% Yeah, I know there's something a little bit wrong in this 00:52:45.500 --> 00:52:46.170 align:middle line:90% encoding. 00:52:46.170 --> 00:52:49.590 align:middle line:84% Anyhow, a little bit ambiguous piece. 00:52:49.590 --> 00:52:52.940 align:middle line:84% So what I want to do is let's get into unlocking 00:52:52.940 --> 00:52:56.840 align:middle line:90% some key analysis things. 00:52:56.840 --> 00:53:03.490 align:middle line:84% So what we can do is-- we called it a jig, right? 00:53:03.490 --> 00:53:04.170 align:middle line:90% Yep. 00:53:04.170 --> 00:53:11.173 align:middle line:84% k1-- our first key will be jig.analyze key. 00:53:11.173 --> 00:53:17.750 align:middle line:90% 00:53:17.750 --> 00:53:20.600 align:middle line:90% So that's pretty good. 00:53:20.600 --> 00:53:26.630 align:middle line:84% Now, in addition to analyzing key, there's specific-- 00:53:26.630 --> 00:53:31.900 align:middle line:84% a number of people have implemented their own analysis 00:53:31.900 --> 00:53:32.400 align:middle line:90% things. 00:53:32.400 --> 00:53:35.690 align:middle line:84% So you'll have to get this-- so we're going to run through 00:53:35.690 --> 00:53:38.330 align:middle line:90% a bunch of different methods-- 00:53:38.330 --> 00:53:47.490 align:middle line:84% the standard key method and Simple. 00:53:47.490 --> 00:53:55.790 align:middle line:84% So key is something I put a guarantee to people using 00:53:55.790 --> 00:53:58.850 align:middle line:84% music21 that that will be whatever I think 00:53:58.850 --> 00:54:00.360 align:middle line:90% is giving the best results. 00:54:00.360 --> 00:54:02.850 align:middle line:84% And I'll try to keep improving it and get that. 00:54:02.850 --> 00:54:07.700 align:middle line:84% Krumhansl is exactly Carol Krumhansl's probe tone method 00:54:07.700 --> 00:54:12.090 align:middle line:84% with the exact same things, which was learned-- 00:54:12.090 --> 00:54:15.200 align:middle line:84% we learned the different weights, the different amounts, 00:54:15.200 --> 00:54:17.827 align:middle line:84% how important the tonic is, how important the third is, 00:54:17.827 --> 00:54:19.410 align:middle line:84% how important the fifth is in the key. 00:54:19.410 --> 00:54:23.210 align:middle line:90% How did she learn that? 00:54:23.210 --> 00:54:23.960 align:middle line:90% AUDIENCE: ProTone. 00:54:23.960 --> 00:54:25.043 align:middle line:90% MICHAEL CUTHBERT: ProTone. 00:54:25.043 --> 00:54:33.710 align:middle line:84% So she was asking people, just getting people's reaction 00:54:33.710 --> 00:54:35.280 align:middle line:90% to how far and out. 00:54:35.280 --> 00:54:38.010 align:middle line:90% So it's based on cognition. 00:54:38.010 --> 00:54:42.410 align:middle line:84% The Essen one was based on labeled keys 00:54:42.410 --> 00:54:46.655 align:middle line:84% for the entire Essen folk song repertory, which 00:54:46.655 --> 00:54:49.080 align:middle line:84% we've used a couple times on things, 00:54:49.080 --> 00:54:51.240 align:middle line:84% and it's come up in this class quite a bit. 00:54:51.240 --> 00:54:54.440 align:middle line:84% And so people use that database on the ones that 00:54:54.440 --> 00:55:00.980 align:middle line:84% were labeled in the key to learn not from people, but from what 00:55:00.980 --> 00:55:04.880 align:middle line:84% number of notes were in a piece that was labeled as in F, what's 00:55:04.880 --> 00:55:06.900 align:middle line:84% the number of things were labeled as in E? 00:55:06.900 --> 00:55:08.730 align:middle line:84% And all of these weights, by the way, 00:55:08.730 --> 00:55:16.400 align:middle line:84% have these weird numbers, like the tonic 6.238-- 00:55:16.400 --> 00:55:19.680 align:middle line:84% don't make it too much like pi, 2 pi or something-- 00:55:19.680 --> 00:55:26.750 align:middle line:84% so these really long, complex numbers on things like that. 00:55:26.750 --> 00:55:29.000 align:middle line:84% Where Craig Sapp, who has come up 00:55:29.000 --> 00:55:31.250 align:middle line:84% in this class a couple of times for making the Rosetta 00:55:31.250 --> 00:55:32.280 align:middle line:90% Stone and things-- 00:55:32.280 --> 00:55:35.510 align:middle line:84% I think it was Craig Sapp who came up with a very simple-- 00:55:35.510 --> 00:55:41.040 align:middle line:84% he's like, no, we can just use 1, 0, 1, 0 1, 0.5. 00:55:41.040 --> 00:55:44.160 align:middle line:84% And I think everything in his weighting is either 0 or 0.5. 00:55:44.160 --> 00:55:46.380 align:middle line:84% And he's like, it's much easier to remember, 00:55:46.380 --> 00:55:50.070 align:middle line:84% much easier to program, and it works, he thought, even better. 00:55:50.070 --> 00:55:51.720 align:middle line:90% So we have all these in here. 00:55:51.720 --> 00:55:55.710 align:middle line:90% So we'll do this here. 00:55:55.710 --> 00:55:59.970 align:middle line:84% You don't need to know Python f-string formats, 00:55:59.970 --> 00:56:02.400 align:middle line:84% but I'm going to give 20 letters for the method. 00:56:02.400 --> 00:56:07.050 align:middle line:84% And then we'll analyze using that method here. 00:56:07.050 --> 00:56:10.490 align:middle line:90% Actually, we'll just do this-- 00:56:10.490 --> 00:56:11.480 align:middle line:90% key_out. 00:56:11.480 --> 00:56:15.810 align:middle line:84% I'll make this a little bit easier to read. 00:56:15.810 --> 00:56:25.015 align:middle line:84% And so we'll call key_out equals jig.analyze using the method. 00:56:25.015 --> 00:56:29.660 align:middle line:90% 00:56:29.660 --> 00:56:30.160 align:middle line:90% Oops. 00:56:30.160 --> 00:56:31.395 align:middle line:84% AUDIENCE: You put method in a string. 00:56:31.395 --> 00:56:32.937 align:middle line:84% MICHAEL CUTHBERT: Method-- thank you. 00:56:32.937 --> 00:56:39.070 align:middle line:84% I put method in a string, a string of Methodists. 00:56:39.070 --> 00:56:42.470 align:middle line:84% So when you put the jig into there, 00:56:42.470 --> 00:56:45.890 align:middle line:90% everybody agrees it's D major. 00:56:45.890 --> 00:56:47.390 align:middle line:84% That makes pretty good sense, right? 00:56:47.390 --> 00:56:50.020 align:middle line:84% You would not trust any algorithm 00:56:50.020 --> 00:56:53.860 align:middle line:84% that came up with a result other than D major 00:56:53.860 --> 00:56:55.220 align:middle line:90% for this entire piece. 00:56:55.220 --> 00:56:56.720 align:middle line:90% This is the whole piece. 00:56:56.720 --> 00:56:58.970 align:middle line:84% But let's see what happens when we give it Schoenberg. 00:56:58.970 --> 00:57:02.290 align:middle line:84% So I'm going to just copy and paste, the copy and paste method 00:57:02.290 --> 00:57:04.490 align:middle line:90% for coding quickly in class. 00:57:04.490 --> 00:57:09.520 align:middle line:90% And did I call it sch, I think? 00:57:09.520 --> 00:57:15.640 align:middle line:84% And here, we end up with quite a bit of distinctions. 00:57:15.640 --> 00:57:19.310 align:middle line:84% Maybe E minor and A minor aren't too far apart, 00:57:19.310 --> 00:57:21.950 align:middle line:84% but we even have a major key in there. 00:57:21.950 --> 00:57:24.400 align:middle line:84% So depending on how you do your weighting, 00:57:24.400 --> 00:57:26.300 align:middle line:84% different things could be better. 00:57:26.300 --> 00:57:30.640 align:middle line:84% There's always the goal of trying to come up with a better 00:57:30.640 --> 00:57:33.050 align:middle line:90% key analysis routine. 00:57:33.050 --> 00:57:39.580 align:middle line:84% And the other main unsolved task in this domain 00:57:39.580 --> 00:57:42.557 align:middle line:84% is, pieces aren't always just in one key. 00:57:42.557 --> 00:57:44.140 align:middle line:84% And I'm not talking about Charles Ives 00:57:44.140 --> 00:57:46.240 align:middle line:90% with multi-tonality and things. 00:57:46.240 --> 00:57:49.400 align:middle line:84% I'm talking about pieces change keys throughout the piece. 00:57:49.400 --> 00:57:51.320 align:middle line:90% And sometimes it's easy. 00:57:51.320 --> 00:57:53.720 align:middle line:84% They change the key signature at that moment. 00:57:53.720 --> 00:57:55.570 align:middle line:84% But quite often, pieces change keys 00:57:55.570 --> 00:57:57.200 align:middle line:84% without giving you a key signature. 00:57:57.200 --> 00:58:00.860 align:middle line:84% Can you have a method that says, well, it begins in E, 00:58:00.860 --> 00:58:03.470 align:middle line:84% and then it goes to A, then it goes to C major, 00:58:03.470 --> 00:58:05.270 align:middle line:84% and then it goes some other place? 00:58:05.270 --> 00:58:08.470 align:middle line:84% Can you detect where all those key changes are? 00:58:08.470 --> 00:58:10.120 align:middle line:90% So that's something that-- 00:58:10.120 --> 00:58:11.810 align:middle line:84% people have worked on it a little bit, 00:58:11.810 --> 00:58:13.935 align:middle line:84% but it's still an unsolved general problem. 00:58:13.935 --> 00:58:18.790 align:middle line:90% 00:58:18.790 --> 00:58:23.350 align:middle line:84% Any questions on these types of things? 00:58:23.350 --> 00:58:25.070 align:middle line:90% By the way, you can-- 00:58:25.070 --> 00:58:28.400 align:middle line:84% there's a bunch of other things you can use on analyzing. 00:58:28.400 --> 00:58:31.100 align:middle line:84% You can get the pitch range and stuff like that. 00:58:31.100 --> 00:58:34.130 align:middle line:90% But that works. 00:58:34.130 --> 00:58:38.950 align:middle line:84% Oh, and I'll just say, on this last one, key_out.alternative-- 00:58:38.950 --> 00:58:42.370 align:middle line:90% 00:58:42.370 --> 00:58:43.000 align:middle line:90% what is it? 00:58:43.000 --> 00:58:45.760 align:middle line:84% I can never-- alternateInterpretations 00:58:45.760 --> 00:58:49.660 align:middle line:84% interpretations gives you a list of-- 00:58:49.660 --> 00:58:51.400 align:middle line:90% so this is one, C major. 00:58:51.400 --> 00:58:55.540 align:middle line:84% It gives you a list from the next most likely to 00:58:55.540 --> 00:58:56.860 align:middle line:90% by far the least likely. 00:58:56.860 --> 00:58:58.870 align:middle line:84% In fact, let's do that on the jig. 00:58:58.870 --> 00:59:02.110 align:middle line:90% We'll run the jig one more time. 00:59:02.110 --> 00:59:03.180 align:middle line:90% What did we call it, k1? 00:59:03.180 --> 00:59:03.680 align:middle line:90% Yeah. 00:59:03.680 --> 00:59:10.240 align:middle line:84% So k1 is the jig's key, and k1.alternateInterpretations. 00:59:10.240 --> 00:59:13.210 align:middle line:90% 00:59:13.210 --> 00:59:14.320 align:middle line:90% Yep. 00:59:14.320 --> 00:59:16.955 align:middle line:84% So if it's not in D major, it might be in B minor. 00:59:16.955 --> 00:59:19.330 align:middle line:84% Yeah, it might be, depending on what the second section-- 00:59:19.330 --> 00:59:21.480 align:middle line:84% it's very unlikely to be in A-flat major. 00:59:21.480 --> 00:59:25.210 align:middle line:90% 00:59:25.210 --> 00:59:25.960 align:middle line:90% Great. 00:59:25.960 --> 00:59:29.710 align:middle line:84% With the last 10 minutes-- but I'm always happy to slow down-- 00:59:29.710 --> 00:59:32.440 align:middle line:90% questions, come back, talk. 00:59:32.440 --> 00:59:33.230 align:middle line:90% No? 00:59:33.230 --> 00:59:35.510 align:middle line:90% OK, sure. 00:59:35.510 --> 00:59:36.010 align:middle line:90% Great. 00:59:36.010 --> 00:59:44.590 align:middle line:84% So let's get what we all want, which is Roman numerals. 00:59:44.590 --> 00:59:48.150 align:middle line:84% So go ahead and, from music21, import roman. 00:59:48.150 --> 00:59:54.550 align:middle line:90% 00:59:54.550 --> 01:00:00.615 align:middle line:84% And I'm trying to find where I have this part broken up. 01:00:00.615 --> 01:00:03.160 align:middle line:90% 01:00:03.160 --> 01:00:04.070 align:middle line:90% Here we go. 01:00:04.070 --> 01:00:11.930 align:middle line:84% OK, within roman, we can say rn equals roman.RomanNumeral. 01:00:11.930 --> 01:00:14.110 align:middle line:84% What are the two parts of a Roman numeral 01:00:14.110 --> 01:00:22.290 align:middle line:84% the computer is going to need in order to figure out 01:00:22.290 --> 01:00:23.730 align:middle line:90% what pitches there are? 01:00:23.730 --> 01:00:25.000 align:middle line:90% Sorry, I-- 01:00:25.000 --> 01:00:27.280 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:00:27.280 --> 01:00:28.400 align:middle line:90% MICHAEL CUTHBERT: Yep? 01:00:28.400 --> 01:00:30.523 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:00:30.523 --> 01:00:31.440 align:middle line:90% MICHAEL CUTHBERT: Yep. 01:00:31.440 --> 01:00:34.950 align:middle line:84% We'll call that the figure, the string representing things 01:00:34.950 --> 01:00:37.210 align:middle line:90% like I, V things and the key. 01:00:37.210 --> 01:00:39.630 align:middle line:84% So what we can do is, if you had a key object-- 01:00:39.630 --> 01:00:42.280 align:middle line:90% I think we still have one, k1-- 01:00:42.280 --> 01:00:47.020 align:middle line:84% we can pass that in and get this IV in D major. 01:00:47.020 --> 01:00:49.200 align:middle line:84% The other thing-- what we'll often 01:00:49.200 --> 01:00:53.730 align:middle line:84% do when we're coding in class is I'll just give it 01:00:53.730 --> 01:00:55.530 align:middle line:90% a capital D for D major. 01:00:55.530 --> 01:00:57.340 align:middle line:90% Lowercase d would be D minor. 01:00:57.340 --> 01:00:59.460 align:middle line:90% And that works just as well. 01:00:59.460 --> 01:01:01.660 align:middle line:84% If you're actually writing a program, 01:01:01.660 --> 01:01:04.080 align:middle line:84% unfortunately one of the least-optimized things 01:01:04.080 --> 01:01:06.520 align:middle line:90% is creating a new key object. 01:01:06.520 --> 01:01:08.670 align:middle line:84% It's about an order of magnitude slower 01:01:08.670 --> 01:01:11.110 align:middle line:84% than it should be in an idealized world. 01:01:11.110 --> 01:01:13.680 align:middle line:84% So it is helpful to reuse your key object 01:01:13.680 --> 01:01:17.070 align:middle line:84% if you're going to keep using it over and over again. 01:01:17.070 --> 01:01:23.050 align:middle line:84% OK, so we have Roman numeral IV in D major. 01:01:23.050 --> 01:01:27.480 align:middle line:84% Somebody this side of the room, what pitches 01:01:27.480 --> 01:01:29.970 align:middle line:84% are we going to be expecting with Roman numeral 01:01:29.970 --> 01:01:31.160 align:middle line:90% IV in D major? 01:01:31.160 --> 01:01:33.720 align:middle line:90% 01:01:33.720 --> 01:01:34.620 align:middle line:90% Yep, go ahead. 01:01:34.620 --> 01:01:35.427 align:middle line:90% AUDIENCE: G, B, D. 01:01:35.427 --> 01:01:37.510 align:middle line:84% MICHAEL CUTHBERT: G, B, D. Were you going to that? 01:01:37.510 --> 01:01:37.825 align:middle line:90% AUDIENCE: Yeah. 01:01:37.825 --> 01:01:39.033 align:middle line:90% MICHAEL CUTHBERT: Good, good. 01:01:39.033 --> 01:01:46.740 align:middle line:84% So what we can do is G, B, D. And what octave should they 01:01:46.740 --> 01:01:47.240 align:middle line:90% be in? 01:01:47.240 --> 01:01:50.670 align:middle line:90% 01:01:50.670 --> 01:01:53.460 align:middle line:84% Do that more gesturally so that we can get that. 01:01:53.460 --> 01:01:54.015 align:middle line:90% You went-- 01:01:54.015 --> 01:01:55.030 align:middle line:90% AUDIENCE: It doesn't matter. 01:01:55.030 --> 01:01:55.900 align:middle line:84% MICHAEL CUTHBERT: It doesn't matter. 01:01:55.900 --> 01:01:57.412 align:middle line:90% It doesn't matter, right? 01:01:57.412 --> 01:01:59.940 align:middle line:84% So there's this weird thing that happens 01:01:59.940 --> 01:02:07.000 align:middle line:84% that, when we want to put a pitch onto a staff or something, 01:02:07.000 --> 01:02:08.350 align:middle line:90% we need to give it an octave. 01:02:08.350 --> 01:02:10.180 align:middle line:84% We need to reify it at that moment. 01:02:10.180 --> 01:02:12.930 align:middle line:90% But it doesn't matter. 01:02:12.930 --> 01:02:18.450 align:middle line:84% So here's the first question on this 01:02:18.450 --> 01:02:24.960 align:middle line:84% is, what kinds of-- when we say that we have the same Roman 01:02:24.960 --> 01:02:28.480 align:middle line:84% numeral here as the same Roman numeral here, 01:02:28.480 --> 01:02:31.050 align:middle line:84% what kinds of equivalence classes 01:02:31.050 --> 01:02:36.750 align:middle line:84% are we talking about if I say that Roman numeral IV equals 01:02:36.750 --> 01:02:37.760 align:middle line:90% Roman numeral IV? 01:02:37.760 --> 01:02:40.350 align:middle line:90% 01:02:40.350 --> 01:02:44.405 align:middle line:84% I want to throw some equivalence classes on pitches or notes. 01:02:44.405 --> 01:02:48.960 align:middle line:90% 01:02:48.960 --> 01:02:51.852 align:middle line:84% Somebody throw out an easy one because we just said one. 01:02:51.852 --> 01:02:52.560 align:middle line:90% AUDIENCE: Octave. 01:02:52.560 --> 01:02:53.852 align:middle line:90% MICHAEL CUTHBERT: Octave, good. 01:02:53.852 --> 01:02:55.710 align:middle line:90% So that's definitely one. 01:02:55.710 --> 01:02:56.550 align:middle line:90% Yeah, go ahead. 01:02:56.550 --> 01:02:57.240 align:middle line:90% AUDIENCE: Permutation. 01:02:57.240 --> 01:02:58.490 align:middle line:90% MICHAEL CUTHBERT: Permutation. 01:02:58.490 --> 01:03:01.590 align:middle line:84% Yeah, it doesn't really matter what order they are. 01:03:01.590 --> 01:03:04.200 align:middle line:84% I'll come back with octave on just a little bit 01:03:04.200 --> 01:03:06.610 align:middle line:84% because there's a caveat, but later. 01:03:06.610 --> 01:03:09.810 align:middle line:84% So everyone should try to figure out the caveat on that. 01:03:09.810 --> 01:03:11.323 align:middle line:90% What else? 01:03:11.323 --> 01:03:12.240 align:middle line:90% AUDIENCE: Cardinality. 01:03:12.240 --> 01:03:13.782 align:middle line:84% MICHAEL CUTHBERT: Cardinality, right? 01:03:13.782 --> 01:03:16.110 align:middle line:90% I mean, is-- 01:03:16.110 --> 01:03:17.200 align:middle line:90% I almost wrote on that. 01:03:17.200 --> 01:03:20.040 align:middle line:90% 01:03:20.040 --> 01:03:30.480 align:middle line:84% Yeah, because this is I in C major, but so is this, and so 01:03:30.480 --> 01:03:32.770 align:middle line:90% is this, and so is this. 01:03:32.770 --> 01:03:35.320 align:middle line:84% It doesn't really matter how many notes we have. 01:03:35.320 --> 01:03:36.990 align:middle line:90% Good. 01:03:36.990 --> 01:03:40.480 align:middle line:84% Now, when we're just talking about a Roman numeral like IV, 01:03:40.480 --> 01:03:46.080 align:middle line:84% what's the other thing that we're in there for? 01:03:46.080 --> 01:03:47.080 align:middle line:90% What do you think about? 01:03:47.080 --> 01:03:47.767 align:middle line:90% Yeah? 01:03:47.767 --> 01:03:49.350 align:middle line:84% AUDIENCE: Whether it's major or minor. 01:03:49.350 --> 01:03:52.440 align:middle line:84% MICHAEL CUTHBERT: Whether it's major or minor, yep. 01:03:52.440 --> 01:03:54.513 align:middle line:90% So we have something on-- 01:03:54.513 --> 01:03:57.510 align:middle line:90% 01:03:57.510 --> 01:03:59.470 align:middle line:84% let's try to think some of these things. 01:03:59.470 --> 01:04:06.930 align:middle line:84% And do we have the same blanket octave equivalence, the one 01:04:06.930 --> 01:04:09.580 align:middle line:84% that we've been thinking of that you've already coded? 01:04:09.580 --> 01:04:11.690 align:middle line:90% What's my caveat on octave? 01:04:11.690 --> 01:04:15.765 align:middle line:90% 01:04:15.765 --> 01:04:16.265 align:middle line:90% Yeah? 01:04:16.265 --> 01:04:18.543 align:middle line:84% AUDIENCE: I would think the second chord inversion. 01:04:18.543 --> 01:04:19.960 align:middle line:84% MICHAEL CUTHBERT: Chord inversion. 01:04:19.960 --> 01:04:23.070 align:middle line:84% Yeah, we have this different kind of inversion 01:04:23.070 --> 01:04:34.800 align:middle line:84% where this is I, and this is I first inversion. 01:04:34.800 --> 01:04:35.842 align:middle line:90% What is it? 01:04:35.842 --> 01:04:40.150 align:middle line:84% Ib if you're British, I6 if you're American. 01:04:40.150 --> 01:04:42.510 align:middle line:90% Yep. 01:04:42.510 --> 01:04:50.250 align:middle line:84% Yeah, so we have this unusual thing, 01:04:50.250 --> 01:04:53.565 align:middle line:84% which is very usual for us as musicians or as people 01:04:53.565 --> 01:04:54.940 align:middle line:84% who have taken traditional class, 01:04:54.940 --> 01:04:56.515 align:middle line:90% but a little bit different for-- 01:04:56.515 --> 01:04:59.620 align:middle line:90% 01:04:59.620 --> 01:05:03.450 align:middle line:84% well, the octave of this doesn't matter in itself. 01:05:03.450 --> 01:05:06.000 align:middle line:90% We can move this up to-- 01:05:06.000 --> 01:05:08.070 align:middle line:84% sorry, this is all over in the corner-- 01:05:08.070 --> 01:05:12.930 align:middle line:90% G, E, G, C, and it's still I6. 01:05:12.930 --> 01:05:15.690 align:middle line:84% So there's something about the octave that doesn't matter. 01:05:15.690 --> 01:05:24.600 align:middle line:84% But we don't have, we might say, a bass pitch equivalence. 01:05:24.600 --> 01:05:28.940 align:middle line:84% So we're always going to be creating new equivalence classes 01:05:28.940 --> 01:05:29.610 align:middle line:90% on things. 01:05:29.610 --> 01:05:32.970 align:middle line:84% And so there's a very unusual equivalence class. 01:05:32.970 --> 01:05:38.930 align:middle line:84% We also have a kind of limited transposition equivalence class 01:05:38.930 --> 01:05:45.200 align:middle line:84% that I can write C, E, G and say it's I. 01:05:45.200 --> 01:05:57.950 align:middle line:84% But I can also write D, F-sharp, A and call it I, 01:05:57.950 --> 01:06:04.680 align:middle line:84% as long as I say that I is I in C major, and I is I in D major, 01:06:04.680 --> 01:06:09.980 align:middle line:84% so that there's this abstraction out of-- 01:06:09.980 --> 01:06:13.010 align:middle line:84% that transposition, it's measured according 01:06:13.010 --> 01:06:15.745 align:middle line:90% to distance from what note? 01:06:15.745 --> 01:06:19.280 align:middle line:90% 01:06:19.280 --> 01:06:23.173 align:middle line:84% Not a note like C or something, a conceptual note. 01:06:23.173 --> 01:06:23.840 align:middle line:90% AUDIENCE: Tonic. 01:06:23.840 --> 01:06:25.090 align:middle line:90% MICHAEL CUTHBERT: Tonic, yeah. 01:06:25.090 --> 01:06:27.650 align:middle line:84% So we want to have things that are 01:06:27.650 --> 01:06:30.800 align:middle line:90% the difference from the tonic. 01:06:30.800 --> 01:06:32.630 align:middle line:84% So I think this might actually be 01:06:32.630 --> 01:06:36.488 align:middle line:84% different on yours than on mine because I'm 01:06:36.488 --> 01:06:38.030 align:middle line:84% running a beta version that I haven't 01:06:38.030 --> 01:06:40.340 align:middle line:90% still haven't got the bugs out. 01:06:40.340 --> 01:06:45.080 align:middle line:84% So you can see, Roman numeral comes from some abstract class 01:06:45.080 --> 01:06:48.150 align:middle line:84% called Harmony, which also represents chord symbols, 01:06:48.150 --> 01:06:50.100 align:middle line:90% which I will not get to today. 01:06:50.100 --> 01:06:52.740 align:middle line:90% And it comes from Chord. 01:06:52.740 --> 01:06:56.540 align:middle line:84% I think you're missing ChordBase probably, for most people. 01:06:56.540 --> 01:06:57.850 align:middle line:90% Or maybe-- no, it's there? 01:06:57.850 --> 01:06:58.350 align:middle line:90% It's there? 01:06:58.350 --> 01:06:59.845 align:middle line:90% OK, great. 01:06:59.845 --> 01:07:02.640 align:middle line:84% I couldn't remember what version got that in. 01:07:02.640 --> 01:07:03.770 align:middle line:90% Great. 01:07:03.770 --> 01:07:10.590 align:middle line:84% So with our Roman numeral IV, we can get back, its figure is IV. 01:07:10.590 --> 01:07:13.320 align:middle line:84% Well, that's not telling you too much. 01:07:13.320 --> 01:07:14.490 align:middle line:90% Let's get another one. 01:07:14.490 --> 01:07:23.210 align:middle line:84% We'll call it rn1 equals roman.RomanNumeral flat II6 01:07:23.210 --> 01:07:24.810 align:middle line:90% in C major. 01:07:24.810 --> 01:07:28.240 align:middle line:84% What's another word for flat II6? 01:07:28.240 --> 01:07:31.970 align:middle line:84% Anyone remember-- flat major II6? 01:07:31.970 --> 01:07:34.700 align:middle line:84% Don't worry if you don't know this because this is something 01:07:34.700 --> 01:07:36.710 align:middle line:84% that some people may know, but it's 01:07:36.710 --> 01:07:38.250 align:middle line:84% the next semester beyond the prereq. 01:07:38.250 --> 01:07:38.960 align:middle line:90% Yep? 01:07:38.960 --> 01:07:40.835 align:middle line:84% AUDIENCE: [INAUDIBLE] augmented sixth chords. 01:07:40.835 --> 01:07:42.335 align:middle line:84% MICHAEL CUTHBERT: It's traditionally 01:07:42.335 --> 01:07:44.570 align:middle line:84% taught the same week as augmented sixth chord, so 01:07:44.570 --> 01:07:48.830 align:middle line:84% everybody-- or the week before it. 01:07:48.830 --> 01:07:51.560 align:middle line:84% That's the type of stuff-- it's named after an emperor-- 01:07:51.560 --> 01:07:52.710 align:middle line:90% or no it's not. 01:07:52.710 --> 01:07:55.380 align:middle line:84% It's named after a city-- a Neapolitan chord. 01:07:55.380 --> 01:07:58.100 align:middle line:84% So it's named-- not Napoleon chord, sorry-- named 01:07:58.100 --> 01:07:59.930 align:middle line:90% after the city of Naples. 01:07:59.930 --> 01:08:01.710 align:middle line:90% Very, very cool chord. 01:08:01.710 --> 01:08:04.220 align:middle line:84% If we had two more minutes, I would play it. 01:08:04.220 --> 01:08:06.110 align:middle line:90% So here's something here. 01:08:06.110 --> 01:08:10.160 align:middle line:84% It has a VI at the end, so what do we call it? 01:08:10.160 --> 01:08:12.156 align:middle line:90% What's the inversion? 01:08:12.156 --> 01:08:12.890 align:middle line:90% AUDIENCE: First. 01:08:12.890 --> 01:08:14.307 align:middle line:84% MICHAEL CUTHBERT: First inversion. 01:08:14.307 --> 01:08:17.090 align:middle line:84% So you can call inversion and put it 01:08:17.090 --> 01:08:22.790 align:middle line:84% as I. You can see it's a little bit strange that it has-- 01:08:22.790 --> 01:08:25.010 align:middle line:84% inversion takes some time to calculate 01:08:25.010 --> 01:08:26.819 align:middle line:90% on very complex chords. 01:08:26.819 --> 01:08:28.740 align:middle line:90% So it's method. 01:08:28.740 --> 01:08:33.330 align:middle line:84% But we can get that its romanNumeralAlone-- 01:08:33.330 --> 01:08:34.649 align:middle line:90% this is a little bit wordy. 01:08:34.649 --> 01:08:36.399 align:middle line:84% I should have come up with another thing-- 01:08:36.399 --> 01:08:43.550 align:middle line:84% is II and its frontAlterationAccidental-- 01:08:43.550 --> 01:08:48.319 align:middle line:90% woo-- is a flat. 01:08:48.319 --> 01:08:54.130 align:middle line:84% So it's a II with a flat in front of it. 01:08:54.130 --> 01:08:57.500 align:middle line:90% 01:08:57.500 --> 01:09:00.500 align:middle line:84% So one of the things we can do, just 01:09:00.500 --> 01:09:05.560 align:middle line:84% looking at the last moment, what you'll probably be wanting 01:09:05.560 --> 01:09:07.854 align:middle line:90% is roman.romanNumeralFromChord. 01:09:07.854 --> 01:09:11.569 align:middle line:90% 01:09:11.569 --> 01:09:15.350 align:middle line:84% So given a chord and a key, what's the Roman numeral? 01:09:15.350 --> 01:09:17.920 align:middle line:90% So we still have weird-- 01:09:17.920 --> 01:09:22.960 align:middle line:84% no, let's start with ch in C major. 01:09:22.960 --> 01:09:24.590 align:middle line:90% My CEG is still there. 01:09:24.590 --> 01:09:25.090 align:middle line:90% Great. 01:09:25.090 --> 01:09:26.899 align:middle line:90% What would that be in-- 01:09:26.899 --> 01:09:28.510 align:middle line:90% here, let's just do this-- 01:09:28.510 --> 01:09:32.380 align:middle line:90% for s in ABCDEFG? 01:09:32.380 --> 01:09:35.920 align:middle line:90% 01:09:35.920 --> 01:09:38.350 align:middle line:90% We'll print this. 01:09:38.350 --> 01:09:41.350 align:middle line:90% Print the Roman numeral in the-- 01:09:41.350 --> 01:09:42.554 align:middle line:90% I'm using s for step. 01:09:42.554 --> 01:09:46.609 align:middle line:90% 01:09:46.609 --> 01:09:49.720 align:middle line:90% Does that makes sense? 01:09:49.720 --> 01:09:51.974 align:middle line:90% Some odd, odd chords in there. 01:09:51.974 --> 01:09:54.920 align:middle line:84% But you can figure out these types of things here. 01:09:54.920 --> 01:09:59.620 align:middle line:84% And so we can even do roman.RomanNumeralFromChord. 01:09:59.620 --> 01:10:03.740 align:middle line:84% I almost always, when I'm using this a lot, abbreviate this. 01:10:03.740 --> 01:10:09.490 align:middle line:84% So rnfc equals that, so I can just 01:10:09.490 --> 01:10:11.895 align:middle line:84% do that. romanNumeralFromChord, weird. 01:10:11.895 --> 01:10:14.920 align:middle line:90% 01:10:14.920 --> 01:10:15.782 align:middle line:90% Oops. 01:10:15.782 --> 01:10:16.740 align:middle line:90% I should give it a key. 01:10:16.740 --> 01:10:20.440 align:middle line:90% 01:10:20.440 --> 01:10:21.380 align:middle line:90% There we go. 01:10:21.380 --> 01:10:29.500 align:middle line:84% Sharp I, half-diminished flat VII, VI, flat V, flat III. 01:10:29.500 --> 01:10:34.090 align:middle line:84% So music21 will try to find all these things for you. 01:10:34.090 --> 01:10:36.160 align:middle line:84% I've kept you over, so I'm not going 01:10:36.160 --> 01:10:43.090 align:middle line:84% to show you how you can run this on every chord in a Bach piece, 01:10:43.090 --> 01:10:47.030 align:middle line:84% put it as the dot lyric, and then reshow the piece. 01:10:47.030 --> 01:10:49.870 align:middle line:84% We'll leave that as an exercise for take home 01:10:49.870 --> 01:10:53.330 align:middle line:84% and might come into a class later. 01:10:53.330 --> 01:10:55.830 align:middle line:90% So thanks, everybody. 01:10:55.830 --> 01:11:04.000 align:middle line:90%