WEBVTT 00:00:00.000 --> 00:00:02.395 align:middle line:90% [SQUEAKING] 00:00:02.395 --> 00:00:04.311 align:middle line:90% [RUSTLING] 00:00:04.311 --> 00:00:06.706 align:middle line:90% [CLICKING] 00:00:06.706 --> 00:00:09.380 align:middle line:90% 00:00:09.380 --> 00:00:10.880 align:middle line:84% MICHAEL CUTHBERT: OK, so today we're 00:00:10.880 --> 00:00:12.422 align:middle line:84% just going to go through some topics. 00:00:12.422 --> 00:00:17.060 align:middle line:90% And stop me when you are. 00:00:17.060 --> 00:00:18.890 align:middle line:84% I want to-- the first thing I'll do 00:00:18.890 --> 00:00:21.020 align:middle line:84% is just talk a little bit about some of the things 00:00:21.020 --> 00:00:21.930 align:middle line:90% in my research. 00:00:21.930 --> 00:00:25.340 align:middle line:84% And some of them are connected with a topic that's 00:00:25.340 --> 00:00:29.960 align:middle line:84% lingering in the back of this class that but that's not 00:00:29.960 --> 00:00:30.720 align:middle line:90% really explicit. 00:00:30.720 --> 00:00:34.430 align:middle line:84% And that is the second adjacent field 00:00:34.430 --> 00:00:41.150 align:middle line:84% of statistical and pure math, computational musicology 00:00:41.150 --> 00:00:43.920 align:middle line:84% research that is not directly computational. 00:00:43.920 --> 00:00:46.460 align:middle line:84% So we'll do a little bit with that. 00:00:46.460 --> 00:00:50.750 align:middle line:84% You'll find on the Canvas site there's a very cool-- 00:00:50.750 --> 00:00:52.890 align:middle line:90% I think it's like 9-page-- 00:00:52.890 --> 00:00:55.340 align:middle line:84% it's really short-- it has lots of pictures-- 00:00:55.340 --> 00:00:57.560 align:middle line:84% article that I'd like you to take some time 00:00:57.560 --> 00:01:02.100 align:middle line:84% to read by Leon Harkleroad, who wrote a whole book 00:01:02.100 --> 00:01:04.750 align:middle line:84% on mathematics and music, which is very cool. 00:01:04.750 --> 00:01:06.540 align:middle line:84% But I find the most cool thing about that 00:01:06.540 --> 00:01:10.590 align:middle line:84% is the final chapter, how not to mix math and music, 00:01:10.590 --> 00:01:12.930 align:middle line:84% and the ways people have mixed math and music 00:01:12.930 --> 00:01:15.640 align:middle line:90% and got things really wrong. 00:01:15.640 --> 00:01:18.220 align:middle line:84% So I might bring that up a little bit more. 00:01:18.220 --> 00:01:21.030 align:middle line:84% So we'll do a little bit with some statistical and math 00:01:21.030 --> 00:01:25.064 align:middle line:84% things that relate to my own research, too. 00:01:25.064 --> 00:01:28.710 align:middle line:90% So I'm trained as a-- 00:01:28.710 --> 00:01:30.730 align:middle line:84% actually, let me turn off this light somehow. 00:01:30.730 --> 00:01:31.530 align:middle line:90% Yep. 00:01:31.530 --> 00:01:32.340 align:middle line:90% Is that good? 00:01:32.340 --> 00:01:35.590 align:middle line:84% I'm trained as a medieval music historian, 00:01:35.590 --> 00:01:38.680 align:middle line:84% so I really, really got into medieval music. 00:01:38.680 --> 00:01:42.040 align:middle line:84% You'll hear little clips of it here and there. 00:01:42.040 --> 00:01:46.020 align:middle line:84% And that was really what I wanted 00:01:46.020 --> 00:01:49.260 align:middle line:84% to do when I programmed on the side to make some spending money 00:01:49.260 --> 00:01:50.850 align:middle line:90% and things like that. 00:01:50.850 --> 00:01:53.010 align:middle line:84% When I got into medieval music, I 00:01:53.010 --> 00:01:55.080 align:middle line:84% thought I'd be looking at things that 00:01:55.080 --> 00:01:57.340 align:middle line:84% are really beautiful like this all the time. 00:01:57.340 --> 00:02:00.250 align:middle line:84% These are people playing a little crank organ, 00:02:00.250 --> 00:02:02.260 align:middle line:84% hurdy-gurdy type thing, and stuff. 00:02:02.260 --> 00:02:05.500 align:middle line:84% And there are these beautiful, beautiful music manuscripts. 00:02:05.500 --> 00:02:10.530 align:middle line:84% This is from the early 14th century called the Novel 00:02:10.530 --> 00:02:14.140 align:middle line:84% of Fauvel, the Horse Named Fauvel, the Roman de Fauvel. 00:02:14.140 --> 00:02:17.290 align:middle line:84% And they're all really, really gorgeous. 00:02:17.290 --> 00:02:21.390 align:middle line:84% Or there's the original "Carmina Burana" 00:02:21.390 --> 00:02:24.780 align:middle line:84% that Carl Orff based his music off of. 00:02:24.780 --> 00:02:28.860 align:middle line:84% This is what music notation once looked like. 00:02:28.860 --> 00:02:35.100 align:middle line:84% And then gorgeous books in the shape of a heart. 00:02:35.100 --> 00:02:38.260 align:middle line:84% So I started focusing on the 14th century in Italy, 00:02:38.260 --> 00:02:41.050 align:middle line:84% where we have this one really amazing book. 00:02:41.050 --> 00:02:43.440 align:middle line:84% This is called the Squarcialupi Codex. 00:02:43.440 --> 00:02:48.020 align:middle line:84% Has these beautiful pictures of all the musicians 00:02:48.020 --> 00:02:49.230 align:middle line:90% who are in there. 00:02:49.230 --> 00:02:49.980 align:middle line:90% And it's a great-- 00:02:49.980 --> 00:02:52.470 align:middle line:84% I think it's valued at around $35 million 00:02:52.470 --> 00:02:53.890 align:middle line:90% or something like that. 00:02:53.890 --> 00:02:55.840 align:middle line:84% So I thought I'd be working on this. 00:02:55.840 --> 00:02:57.310 align:middle line:84% Well, it turns out people have been 00:02:57.310 --> 00:03:00.140 align:middle line:84% doing medieval music research for, I don't know, 00:03:00.140 --> 00:03:01.250 align:middle line:90% hundreds of years. 00:03:01.250 --> 00:03:02.480 align:middle line:90% And guess what? 00:03:02.480 --> 00:03:06.140 align:middle line:84% They've all studied the really pretty books. 00:03:06.140 --> 00:03:10.220 align:middle line:84% So if you wanted to go into this in around 1998, 00:03:10.220 --> 00:03:13.900 align:middle line:84% 2000, whenever I really got it started, about 25 years ago, 00:03:13.900 --> 00:03:18.160 align:middle line:84% here's what's left for us to study. 00:03:18.160 --> 00:03:19.250 align:middle line:90% Little things like that. 00:03:19.250 --> 00:03:22.730 align:middle line:84% You can kind of see the music here, and stuff like that. 00:03:22.730 --> 00:03:26.260 align:middle line:84% Or this is one of the ones I've been looking at. 00:03:26.260 --> 00:03:29.140 align:middle line:84% Some of these, worms eat them, ravages of time, 00:03:29.140 --> 00:03:32.560 align:middle line:90% or other little indignities. 00:03:32.560 --> 00:03:37.280 align:middle line:84% The music is wrapped up to keep people's sewage payment records. 00:03:37.280 --> 00:03:39.800 align:middle line:84% You have to pay somebody to clean out your chamber pots, 00:03:39.800 --> 00:03:42.440 align:middle line:84% and you want to make sure that somebody paid their bill. 00:03:42.440 --> 00:03:45.680 align:middle line:84% And so you wrap it in a piece of worthless music, 00:03:45.680 --> 00:03:46.930 align:middle line:90% and you do that. 00:03:46.930 --> 00:03:50.540 align:middle line:84% Well, when you're wrapping music on top of other documents, 00:03:50.540 --> 00:03:52.820 align:middle line:84% sometimes the document's smaller than the music. 00:03:52.820 --> 00:03:54.020 align:middle line:90% So no problem. 00:03:54.020 --> 00:03:57.660 align:middle line:84% You trim the music, and then it fits there. 00:03:57.660 --> 00:04:01.070 align:middle line:84% And some people-- there's nothing 00:04:01.070 --> 00:04:03.990 align:middle line:84% important on the left side of a score, right? 00:04:03.990 --> 00:04:08.370 align:middle line:84% Just clefs, time signatures, key signatures, nothing like that. 00:04:08.370 --> 00:04:10.850 align:middle line:84% And they used a lot of clefs back then. 00:04:10.850 --> 00:04:14.340 align:middle line:84% And then sometimes you wanted things to look really nice. 00:04:14.340 --> 00:04:18.170 align:middle line:84% So you would wipe off, wash off, or scrape off 00:04:18.170 --> 00:04:21.410 align:middle line:84% all the music that was there so that your cover looked 00:04:21.410 --> 00:04:22.380 align:middle line:90% a little nicer. 00:04:22.380 --> 00:04:24.420 align:middle line:84% And then once you've scraped everything off, 00:04:24.420 --> 00:04:26.340 align:middle line:84% it's all parchment and vellum and stuff. 00:04:26.340 --> 00:04:28.920 align:middle line:84% Then you can reuse it for, in this case, 00:04:28.920 --> 00:04:30.643 align:middle line:84% church land holdings in Florence. 00:04:30.643 --> 00:04:33.380 align:middle line:90% 00:04:33.380 --> 00:04:36.380 align:middle line:84% And then there's these little strips 00:04:36.380 --> 00:04:40.380 align:middle line:84% that you find sometimes that you weren't even sure are music. 00:04:40.380 --> 00:04:42.680 align:middle line:84% But oh, those kind of look like quarter note 00:04:42.680 --> 00:04:46.566 align:middle line:84% stems, quarter note stems, and stuff like that. 00:04:46.566 --> 00:04:48.210 align:middle line:84% And this is what was left for me. 00:04:48.210 --> 00:04:50.940 align:middle line:84% So I became a music fragment scholar. 00:04:50.940 --> 00:04:54.750 align:middle line:84% And my things are all on fragments of polyphonic music 00:04:54.750 --> 00:04:56.230 align:middle line:90% from the 14th century. 00:04:56.230 --> 00:04:58.470 align:middle line:84% So I wanted to look at these things. 00:04:58.470 --> 00:05:00.660 align:middle line:90% And how to move forward? 00:05:00.660 --> 00:05:03.720 align:middle line:84% One of the things back then with no computers 00:05:03.720 --> 00:05:05.202 align:middle line:90% is just spend a lot of time. 00:05:05.202 --> 00:05:07.410 align:middle line:84% So one of the things they were really good about then 00:05:07.410 --> 00:05:08.880 align:middle line:90% is that they-- 00:05:08.880 --> 00:05:11.200 align:middle line:84% who was told that in a music class, 00:05:11.200 --> 00:05:14.280 align:middle line:90% when you write a quarter note-- 00:05:14.280 --> 00:05:16.900 align:middle line:84% that's a very bad one-- when you write a quarter note, 00:05:16.900 --> 00:05:20.440 align:middle line:84% its stems should be exactly an octave long? 00:05:20.440 --> 00:05:23.095 align:middle line:84% And so therefore, it's kind of exactly like this. 00:05:23.095 --> 00:05:24.970 align:middle line:84% I don't know if people are still taught that. 00:05:24.970 --> 00:05:26.440 align:middle line:84% Well, they were very good at that. 00:05:26.440 --> 00:05:29.520 align:middle line:84% So you can figure out, based on the heights 00:05:29.520 --> 00:05:32.398 align:middle line:84% of the stems, what notes must have been cut off there 00:05:32.398 --> 00:05:33.190 align:middle line:90% and where they are. 00:05:33.190 --> 00:05:36.510 align:middle line:84% And you just stare for hours and hours and hours of other books 00:05:36.510 --> 00:05:40.200 align:middle line:84% until eventually you find one where every one of the 00:05:40.200 --> 00:05:41.620 align:middle line:90% stems lines up. 00:05:41.620 --> 00:05:44.080 align:middle line:84% I had to squish this by about 10% to get it, 00:05:44.080 --> 00:05:45.790 align:middle line:90% but things like that. 00:05:45.790 --> 00:05:50.200 align:middle line:84% Or for something like this, there's three parts. 00:05:50.200 --> 00:05:52.390 align:middle line:84% They wrote the parts separately back then, 00:05:52.390 --> 00:05:53.950 align:middle line:84% kind of like, I don't know, iterating 00:05:53.950 --> 00:05:56.200 align:middle line:84% through the recurse method and not the flatten method. 00:05:56.200 --> 00:05:59.590 align:middle line:84% And so part one, part two, part three. 00:05:59.590 --> 00:06:01.770 align:middle line:84% And so you just try every combination 00:06:01.770 --> 00:06:03.810 align:middle line:84% of clef and time signature and key signature 00:06:03.810 --> 00:06:08.170 align:middle line:84% until you finally find where things line up. 00:06:08.170 --> 00:06:11.640 align:middle line:84% Then use your knowledge of music theory from the 14th century 00:06:11.640 --> 00:06:14.230 align:middle line:90% to fill in the missing parts. 00:06:14.230 --> 00:06:19.530 align:middle line:84% And eventually your friends record the piece for you. 00:06:19.530 --> 00:06:21.990 align:middle line:90% [MUSIC PLAYING] 00:06:21.990 --> 00:06:26.880 align:middle line:90% 00:06:26.880 --> 00:06:30.143 align:middle line:84% Then when the notes get big, it's what we actually know. 00:06:30.143 --> 00:06:33.390 align:middle line:90% [MUSIC PLAYING] 00:06:33.390 --> 00:06:36.780 align:middle line:84% So anyhow, that was some of the things. 00:06:36.780 --> 00:06:38.850 align:middle line:84% Then the first place where computers really 00:06:38.850 --> 00:06:42.750 align:middle line:84% started coming in was about when we started getting nice color 00:06:42.750 --> 00:06:45.390 align:middle line:84% photographs, before everything was black and white photocopies 00:06:45.390 --> 00:06:45.940 align:middle line:90% and stuff. 00:06:45.940 --> 00:06:50.230 align:middle line:84% And I, with some other people and some other people 00:06:50.230 --> 00:06:53.200 align:middle line:84% independent from me, all came up about the same time 00:06:53.200 --> 00:06:56.770 align:middle line:84% with a technique that if you measured 00:06:56.770 --> 00:06:59.295 align:middle line:84% the colors of the overwriting and the colors 00:06:59.295 --> 00:07:01.670 align:middle line:84% of the underwriting, the ink would probably be different. 00:07:01.670 --> 00:07:04.820 align:middle line:84% So you could remove one and bring the other up. 00:07:04.820 --> 00:07:08.470 align:middle line:84% And so we had these various computer techniques 00:07:08.470 --> 00:07:10.450 align:middle line:84% for getting rid of the overwriting 00:07:10.450 --> 00:07:12.350 align:middle line:84% and getting to the music underneath. 00:07:12.350 --> 00:07:15.460 align:middle line:90% 00:07:15.460 --> 00:07:21.050 align:middle line:84% But everything after this was still going to be done by hand. 00:07:21.050 --> 00:07:25.270 align:middle line:84% So I started thinking about ways to use statistics and computers 00:07:25.270 --> 00:07:26.510 align:middle line:90% to do various things. 00:07:26.510 --> 00:07:29.020 align:middle line:84% So about this time we started creating music21. 00:07:29.020 --> 00:07:31.000 align:middle line:84% And if you ever wonder why there's 00:07:31.000 --> 00:07:33.970 align:middle line:84% some things that are obscure, music21's sole purpose 00:07:33.970 --> 00:07:37.160 align:middle line:84% was to try to identify music fragments like that. 00:07:37.160 --> 00:07:40.420 align:middle line:84% And everything else that this class has come about 00:07:40.420 --> 00:07:44.620 align:middle line:90% has just been of a side project. 00:07:44.620 --> 00:07:48.330 align:middle line:84% So while I was building that, I switched 00:07:48.330 --> 00:07:49.870 align:middle line:90% into a statistical mode. 00:07:49.870 --> 00:07:51.820 align:middle line:84% So we'll get back to music21 in a bit. 00:07:51.820 --> 00:07:54.450 align:middle line:84% But first, I want to think about some 00:07:54.450 --> 00:07:57.790 align:middle line:84% of the things that were coming up with all these fragments. 00:07:57.790 --> 00:08:01.180 align:middle line:84% And I was trying to figure out what they were. 00:08:01.180 --> 00:08:04.200 align:middle line:84% And that meant I would need to find another piece that 00:08:04.200 --> 00:08:05.440 align:middle line:90% was like that. 00:08:05.440 --> 00:08:08.220 align:middle line:84% But the odds that another piece would 00:08:08.220 --> 00:08:11.340 align:middle line:84% exist that matched up with the music, I was told, 00:08:11.340 --> 00:08:13.110 align:middle line:90% were really, really low. 00:08:13.110 --> 00:08:18.300 align:middle line:84% In fact, a very famous article by somebody who's very famous 00:08:18.300 --> 00:08:22.050 align:middle line:84% in my field, Nino PIrrotta, "The Oral and Written Traditions 00:08:22.050 --> 00:08:26.430 align:middle line:84% of Music," said that the surviving music from the Middle 00:08:26.430 --> 00:08:29.050 align:middle line:90% Ages is the tip of the iceberg. 00:08:29.050 --> 00:08:33.120 align:middle line:84% And that metaphor ended up being quoted and reused 00:08:33.120 --> 00:08:35.159 align:middle line:84% in a whole bunch of other articles 00:08:35.159 --> 00:08:37.710 align:middle line:90% that you don't need to see here. 00:08:37.710 --> 00:08:40.419 align:middle line:84% So this became what everybody knew. 00:08:40.419 --> 00:08:44.512 align:middle line:84% So if you're thinking about music from 600 years ago 00:08:44.512 --> 00:08:46.220 align:middle line:84% and you think about all the things you've 00:08:46.220 --> 00:08:50.690 align:middle line:84% lost in your 20 years of life, or however long, 00:08:50.690 --> 00:08:52.820 align:middle line:84% what percentage of things would have 00:08:52.820 --> 00:08:57.650 align:middle line:90% survived from 600 years ago? 00:08:57.650 --> 00:08:59.000 align:middle line:90% Or would be lost? 00:08:59.000 --> 00:08:59.930 align:middle line:90% Would be lost? 00:08:59.930 --> 00:09:01.500 align:middle line:90% About 90%? 00:09:01.500 --> 00:09:03.590 align:middle line:90% 99%? 00:09:03.590 --> 00:09:05.790 align:middle line:90% 99.9%? 00:09:05.790 --> 00:09:08.130 align:middle line:84% These are all numbers that I found people said. 00:09:08.130 --> 00:09:10.170 align:middle line:84% And then somebody said basically everything. 00:09:10.170 --> 00:09:12.020 align:middle line:84% So I have to convert everything to a number. 00:09:12.020 --> 00:09:14.605 align:middle line:84% That's pretty close to basically everything for me. 00:09:14.605 --> 00:09:17.900 align:middle line:90% 00:09:17.900 --> 00:09:18.930 align:middle line:90% Let me skip over that. 00:09:18.930 --> 00:09:20.930 align:middle line:84% We don't have all the time in the world. 00:09:20.930 --> 00:09:26.270 align:middle line:84% So I started to think about some statistical methodologies that 00:09:26.270 --> 00:09:27.360 align:middle line:90% could help in this. 00:09:27.360 --> 00:09:30.290 align:middle line:84% And one of the things that we have in some cases-- 00:09:30.290 --> 00:09:35.270 align:middle line:84% this is a table of contents for a book of music from the 14th 00:09:35.270 --> 00:09:38.360 align:middle line:84% century, where the book doesn't exist but the table of contents 00:09:38.360 --> 00:09:38.940 align:middle line:90% does. 00:09:38.940 --> 00:09:41.630 align:middle line:84% So I started looking at, OK, here's 00:09:41.630 --> 00:09:45.750 align:middle line:84% all the pieces that do not exist. 00:09:45.750 --> 00:09:49.590 align:middle line:84% And then here's all the pieces that do exist. 00:09:49.590 --> 00:09:54.180 align:middle line:84% And starting to look at the ratios. 00:09:54.180 --> 00:09:56.280 align:middle line:84% And in this particular manuscript, 00:09:56.280 --> 00:09:59.560 align:middle line:84% it looks like about 68% of them survive. 00:09:59.560 --> 00:10:04.440 align:middle line:84% So that was the first thing that maybe the 99.9999 number 00:10:04.440 --> 00:10:05.140 align:middle line:90% didn't exist. 00:10:05.140 --> 00:10:08.590 align:middle line:84% And then I looked at there's a bunch of poetry manuscripts. 00:10:08.590 --> 00:10:13.020 align:middle line:84% So this is one from about the time of Dante or Chaucer 00:10:13.020 --> 00:10:16.170 align:middle line:84% by a not very good poet named Prodenzani. 00:10:16.170 --> 00:10:18.420 align:middle line:84% But one of the things that makes him a bad poet that's 00:10:18.420 --> 00:10:20.620 align:middle line:84% really good is that when he gets into something, 00:10:20.620 --> 00:10:22.078 align:middle line:84% when he's talking about a feast, he 00:10:22.078 --> 00:10:26.020 align:middle line:84% will list for the next 50 lines everything they possibly ate. 00:10:26.020 --> 00:10:27.630 align:middle line:84% And when it gets to a concert, he 00:10:27.630 --> 00:10:31.750 align:middle line:84% lists with the viola, [SPEAKING ITALIAN] 00:10:31.750 --> 00:10:33.400 align:middle line:90% We played our May Day songs. 00:10:33.400 --> 00:10:34.473 align:middle line:90% We just had May Day. 00:10:34.473 --> 00:10:37.140 align:middle line:84% So these are the May Day songs, like the rose that never changes 00:10:37.140 --> 00:10:42.040 align:middle line:84% its color, [SPEAKING FRENCH] sweet taste, and so on. 00:10:42.040 --> 00:10:44.150 align:middle line:84% And these all look like names of songs. 00:10:44.150 --> 00:10:46.730 align:middle line:84% And so we can look at, for each one of them, 00:10:46.730 --> 00:10:50.030 align:middle line:84% do we have a song by that name, or do we not? 00:10:50.030 --> 00:10:53.210 align:middle line:84% And so we have how many are known, how many are unknown. 00:10:53.210 --> 00:10:57.820 align:middle line:84% And we eventually get to a number 00:10:57.820 --> 00:11:00.050 align:middle line:84% that looks a little bit similar to the last one. 00:11:00.050 --> 00:11:03.610 align:middle line:90% About 71% survive. 00:11:03.610 --> 00:11:06.218 align:middle line:84% So I was kind going through this. 00:11:06.218 --> 00:11:07.760 align:middle line:84% The chronology is a little bit wrong. 00:11:07.760 --> 00:11:09.320 align:middle line:90% I had to justify this later. 00:11:09.320 --> 00:11:13.450 align:middle line:84% But first I was thinking about how animal biologists, 00:11:13.450 --> 00:11:16.720 align:middle line:90% ecologists, count animals. 00:11:16.720 --> 00:11:19.900 align:middle line:84% Has anyone taken a biology class or something where 00:11:19.900 --> 00:11:23.290 align:middle line:90% you do population estimates? 00:11:23.290 --> 00:11:27.340 align:middle line:84% So one of the ways that you can do it is you 00:11:27.340 --> 00:11:29.420 align:middle line:84% want to know how many deer are in a forest. 00:11:29.420 --> 00:11:32.770 align:middle line:84% So you go, and you capture as many deer as you can 00:11:32.770 --> 00:11:33.770 align:middle line:90% in a month and a half. 00:11:33.770 --> 00:11:35.810 align:middle line:84% You come back smelling pretty bad and stuff. 00:11:35.810 --> 00:11:40.760 align:middle line:84% But every time you find a deer, you tag its ear or some way, 00:11:40.760 --> 00:11:42.380 align:middle line:84% in some way that you can identify, 00:11:42.380 --> 00:11:43.790 align:middle line:90% this is a deer that I saw. 00:11:43.790 --> 00:11:47.360 align:middle line:84% And you come back several months later or whatever, 00:11:47.360 --> 00:11:50.500 align:middle line:90% and then you count deer again. 00:11:50.500 --> 00:11:55.450 align:middle line:84% And the percentage of deer that were tagged in the first time 00:11:55.450 --> 00:11:57.580 align:middle line:90% give you some sense-- 00:11:57.580 --> 00:11:59.530 align:middle line:84% or the inverse of it gives you some sense 00:11:59.530 --> 00:12:00.980 align:middle line:90% of how big the population is. 00:12:00.980 --> 00:12:04.840 align:middle line:84% If you tagged 100 deer the first time, and you come back later 00:12:04.840 --> 00:12:06.650 align:middle line:90% and you only find-- 00:12:06.650 --> 00:12:09.580 align:middle line:84% then you capture 100 more deer, and you only see two of them 00:12:09.580 --> 00:12:11.890 align:middle line:84% are tagged, you know there's a huge population 00:12:11.890 --> 00:12:13.480 align:middle line:90% of deer out there. 00:12:13.480 --> 00:12:16.420 align:middle line:84% Similarly, if you captured 100 deer and the next time you 00:12:16.420 --> 00:12:19.220 align:middle line:84% capture 100 deer, 98 of them are tagged, 00:12:19.220 --> 00:12:20.840 align:middle line:90% you probably saw most of them. 00:12:20.840 --> 00:12:23.120 align:middle line:84% So I started thinking about, well, 00:12:23.120 --> 00:12:25.400 align:middle line:84% if a piece appears in one manuscript, 00:12:25.400 --> 00:12:27.040 align:middle line:90% we'll tag that piece. 00:12:27.040 --> 00:12:30.940 align:middle line:84% And then we'll see how often it appears in another manuscript. 00:12:30.940 --> 00:12:33.190 align:middle line:84% So I started coming up with formulas 00:12:33.190 --> 00:12:34.820 align:middle line:90% to do this type of thing. 00:12:34.820 --> 00:12:38.320 align:middle line:84% And I realized that there's an equation that tells us 00:12:38.320 --> 00:12:39.592 align:middle line:90% the number of missing pieces. 00:12:39.592 --> 00:12:41.300 align:middle line:84% All you have to do is you take the number 00:12:41.300 --> 00:12:43.350 align:middle line:90% of pieces you originally had. 00:12:43.350 --> 00:12:45.830 align:middle line:84% And you multiply by the probability 00:12:45.830 --> 00:12:47.455 align:middle line:90% that any piece would be missing. 00:12:47.455 --> 00:12:48.330 align:middle line:90% Tell me if I'm wrong. 00:12:48.330 --> 00:12:50.060 align:middle line:90% You're the MIT students. 00:12:50.060 --> 00:12:52.290 align:middle line:84% Equals the total number of missing pieces. 00:12:52.290 --> 00:12:54.510 align:middle line:84% And it's a super great, super simple formula, 00:12:54.510 --> 00:12:57.510 align:middle line:84% except that it's a formula with three unknowns. 00:12:57.510 --> 00:13:00.530 align:middle line:84% We don't know any of these three numbers. 00:13:00.530 --> 00:13:05.820 align:middle line:84% But we can kind of figure out some of these things. 00:13:05.820 --> 00:13:09.170 align:middle line:84% So we can look at, well, what's the probability that a given 00:13:09.170 --> 00:13:10.820 align:middle line:90% piece would be in a manuscript? 00:13:10.820 --> 00:13:12.320 align:middle line:84% Now, we'll start with the assumption 00:13:12.320 --> 00:13:15.450 align:middle line:84% that every piece is selected randomly. 00:13:15.450 --> 00:13:18.760 align:middle line:84% So we start with how many pieces are there in a manuscript? 00:13:18.760 --> 00:13:23.070 align:middle line:84% So just like a collection, like a box set of lots of tunes. 00:13:23.070 --> 00:13:25.080 align:middle line:84% How many pieces are there in that manuscript? 00:13:25.080 --> 00:13:26.580 align:middle line:90% We'll call that r sub i. 00:13:26.580 --> 00:13:29.990 align:middle line:84% And you divide it by the total number of pieces 00:13:29.990 --> 00:13:31.560 align:middle line:90% that were originally copied. 00:13:31.560 --> 00:13:34.490 align:middle line:84% So we know how many pieces are in a manuscript 00:13:34.490 --> 00:13:35.885 align:middle line:90% because we can count that. 00:13:35.885 --> 00:13:36.780 align:middle line:90% That survives. 00:13:36.780 --> 00:13:38.970 align:middle line:84% But we don't know that, so we just move our unknown 00:13:38.970 --> 00:13:41.040 align:middle line:90% to another place. 00:13:41.040 --> 00:13:44.760 align:middle line:84% So we can also figure out what's the probability a piece is not 00:13:44.760 --> 00:13:46.120 align:middle line:90% in a given manuscript. 00:13:46.120 --> 00:13:47.418 align:middle line:90% What's the formula? 00:13:47.418 --> 00:13:48.460 align:middle line:90% Just see if you're awake. 00:13:48.460 --> 00:13:52.050 align:middle line:84% If this is the formula it's in the manuscript, what do we do? 00:13:52.050 --> 00:13:52.990 align:middle line:90% 1 minus. 00:13:52.990 --> 00:13:55.030 align:middle line:84% Good We're all on the same page there. 00:13:55.030 --> 00:13:55.560 align:middle line:90% Great. 00:13:55.560 --> 00:13:59.746 align:middle line:84% So what's the probability that it's not in two manuscripts? 00:13:59.746 --> 00:14:02.250 align:middle line:90% 00:14:02.250 --> 00:14:04.057 align:middle line:84% You just take the first probability 00:14:04.057 --> 00:14:05.640 align:middle line:84% and you multiply it by the second one, 00:14:05.640 --> 00:14:08.500 align:middle line:84% in the assumption that these are independent. 00:14:08.500 --> 00:14:11.680 align:middle line:84% And so try to keep ones from different places, whatever. 00:14:11.680 --> 00:14:16.980 align:middle line:84% So then what's the probability that any given piece is not 00:14:16.980 --> 00:14:22.740 align:middle line:84% in any of the, we're at that point, 85 surviving manuscripts? 00:14:22.740 --> 00:14:27.540 align:middle line:84% Well, you just have something like this. 00:14:27.540 --> 00:14:29.130 align:middle line:90% And that gives us-- 00:14:29.130 --> 00:14:31.830 align:middle line:90% takes-- our two unknowns. 00:14:31.830 --> 00:14:35.940 align:middle line:84% It gives us the probability that a piece is missing. 00:14:35.940 --> 00:14:40.420 align:middle line:84% So we can go back to our original equation 00:14:40.420 --> 00:14:45.220 align:middle line:90% and plug that in. 00:14:45.220 --> 00:14:47.930 align:middle line:84% And all of these have N as a denominator. 00:14:47.930 --> 00:14:52.970 align:middle line:84% So now we've at least reduced our giant-- 00:14:52.970 --> 00:14:58.300 align:middle line:84% we've reduced our master, our main equation, 00:14:58.300 --> 00:15:00.140 align:middle line:90% into two unknowns. 00:15:00.140 --> 00:15:03.670 align:middle line:84% So we're getting a little bit better. 00:15:03.670 --> 00:15:08.390 align:middle line:84% Then we thought, how many pieces were missing? 00:15:08.390 --> 00:15:10.630 align:middle line:84% Well, the number of pieces that were missing 00:15:10.630 --> 00:15:12.460 align:middle line:84% is the number of pieces there originally 00:15:12.460 --> 00:15:17.230 align:middle line:84% were minus the number of pieces that survive. 00:15:17.230 --> 00:15:21.200 align:middle line:84% So we can count the number of pieces that survive. 00:15:21.200 --> 00:15:24.115 align:middle line:84% It takes a long time, actually, to figure out every single thing 00:15:24.115 --> 00:15:25.490 align:middle line:84% because people count differently. 00:15:25.490 --> 00:15:29.650 align:middle line:84% But we can kind of reduce this entire equation 00:15:29.650 --> 00:15:32.420 align:middle line:90% to one equation, one unknown. 00:15:32.420 --> 00:15:35.770 align:middle line:84% And at this point, I was thinking 00:15:35.770 --> 00:15:38.180 align:middle line:84% I must have screwed up something really, really bad. 00:15:38.180 --> 00:15:39.380 align:middle line:90% I have a music degree. 00:15:39.380 --> 00:15:40.730 align:middle line:90% I don't have a stats degree. 00:15:40.730 --> 00:15:43.190 align:middle line:84% This seems like a pretty fundamental equation to have. 00:15:43.190 --> 00:15:46.900 align:middle line:84% And it turns out people had been talking about equations like 00:15:46.900 --> 00:15:49.880 align:middle line:90% this a lot in the '60s or so. 00:15:49.880 --> 00:15:54.760 align:middle line:84% But back then, it was all about, what's 00:15:54.760 --> 00:15:58.600 align:middle line:84% the way that you solve an equation like this with 85-- 00:15:58.600 --> 00:16:04.060 align:middle line:84% it's an 85th power equation, or something like that. 00:16:04.060 --> 00:16:06.400 align:middle line:84% And so all of it was on the high math 00:16:06.400 --> 00:16:08.470 align:middle line:84% that I don't understand that can get 00:16:08.470 --> 00:16:11.270 align:middle line:90% you something to this answer. 00:16:11.270 --> 00:16:15.110 align:middle line:84% But this was my first computational thing. 00:16:15.110 --> 00:16:17.860 align:middle line:84% It's in a language called Perl, where if you know it, 00:16:17.860 --> 00:16:19.580 align:middle line:90% you're lying about your age. 00:16:19.580 --> 00:16:21.140 align:middle line:90% It was the big-- 00:16:21.140 --> 00:16:23.380 align:middle line:84% it was the language that built the internet 00:16:23.380 --> 00:16:25.460 align:middle line:90% in the '90s and things. 00:16:25.460 --> 00:16:30.370 align:middle line:84% And one of the things you can do is you can look at-- 00:16:30.370 --> 00:16:34.190 align:middle line:84% guess various numbers and look at the error 00:16:34.190 --> 00:16:35.810 align:middle line:84% between the left side of the equation 00:16:35.810 --> 00:16:37.227 align:middle line:84% and the right side of the equation 00:16:37.227 --> 00:16:40.500 align:middle line:84% until you find the number that comes closest to balancing it. 00:16:40.500 --> 00:16:42.080 align:middle line:84% So you just kind of try everything, 00:16:42.080 --> 00:16:44.900 align:middle line:90% and you multiply everything out. 00:16:44.900 --> 00:16:47.670 align:middle line:84% And since this isn't really a class about that, 00:16:47.670 --> 00:16:54.140 align:middle line:84% but it turned into saying that the percentage of missing pieces 00:16:54.140 --> 00:16:57.920 align:middle line:84% varied by genre, by type of piece it was. 00:16:57.920 --> 00:17:01.820 align:middle line:84% The interesting part is that the mass, the music written 00:17:01.820 --> 00:17:06.589 align:middle line:84% for sacred services, has more missing 00:17:06.589 --> 00:17:10.430 align:middle line:84% than the ones for everyday dancing and lovemaking and all 00:17:10.430 --> 00:17:11.130 align:middle line:90% that stuff. 00:17:11.130 --> 00:17:13.640 align:middle line:84% And I think that's because over time, nobody 00:17:13.640 --> 00:17:15.619 align:middle line:90% could read this music. 00:17:15.619 --> 00:17:17.180 align:middle line:84% So the only reason somebody would 00:17:17.180 --> 00:17:19.290 align:middle line:90% keep it around is for the text. 00:17:19.290 --> 00:17:22.760 align:middle line:84% And if you're running a church, you already 00:17:22.760 --> 00:17:25.440 align:middle line:84% have lots of copies of the text of the mass. 00:17:25.440 --> 00:17:30.110 align:middle line:84% But the song about we all went off into the woods, each one 00:17:30.110 --> 00:17:33.666 align:middle line:84% as a pair, and we all came back as three, 00:17:33.666 --> 00:17:36.190 align:middle line:90% that, people still keep around. 00:17:36.190 --> 00:17:41.850 align:middle line:84% So those sort of body songs have the least missing. 00:17:41.850 --> 00:17:47.640 align:middle line:84% So it turns out that our best estimates now 00:17:47.640 --> 00:17:54.880 align:middle line:84% are that about 25% of the pieces, maybe 50%. 00:17:54.880 --> 00:17:55.900 align:middle line:90% I don't know, maybe 60. 00:17:55.900 --> 00:17:57.840 align:middle line:84% Maybe I'm off by a little bit, maybe 00:17:57.840 --> 00:18:00.670 align:middle line:84% by a logarithmic order of magnitude or something. 00:18:00.670 --> 00:18:03.390 align:middle line:84% But we can actually really say something 00:18:03.390 --> 00:18:07.500 align:middle line:84% about medieval music based on the fact that much of it 00:18:07.500 --> 00:18:09.090 align:middle line:90% survives. 00:18:09.090 --> 00:18:11.760 align:middle line:84% And I was very, very scared that somehow I 00:18:11.760 --> 00:18:14.280 align:middle line:84% had made a math error and stuff until there was just 00:18:14.280 --> 00:18:19.030 align:middle line:84% a math dissertation at Yale that verified all the work and stuff. 00:18:19.030 --> 00:18:21.600 align:middle line:84% So I'm finally, finally not worried I'm 00:18:21.600 --> 00:18:26.470 align:middle line:84% going to have to do a retraction of one of my biggest papers. 00:18:26.470 --> 00:18:30.700 align:middle line:84% So now we're going to get back to these little scores. 00:18:30.700 --> 00:18:35.410 align:middle line:84% And once I had convinced myself that a good chunk of the time, 00:18:35.410 --> 00:18:38.610 align:middle line:84% 3/4 of the time or something, we're going to be able to figure 00:18:38.610 --> 00:18:42.780 align:middle line:84% out what music is on here because it's going to be in some 00:18:42.780 --> 00:18:44.240 align:middle line:90% other piece we already have. 00:18:44.240 --> 00:18:47.070 align:middle line:90% 00:18:47.070 --> 00:18:50.020 align:middle line:84% So there's this collection that I mostly use. 00:18:50.020 --> 00:18:52.270 align:middle line:84% It's called Polyphonic Music of the 14th Century, 00:18:52.270 --> 00:18:54.370 align:middle line:84% and we have it over in the Lewis Music Library. 00:18:54.370 --> 00:18:55.000 align:middle line:90% It's beautiful. 00:18:55.000 --> 00:18:55.960 align:middle line:90% It's expensive. 00:18:55.960 --> 00:18:58.450 align:middle line:84% And come in these gorgeous green volumes. 00:18:58.450 --> 00:19:02.470 align:middle line:84% And there's a lot of them, all the music from the 14th century. 00:19:02.470 --> 00:19:06.400 align:middle line:84% It's about 20-- it's 25 volumes in this series. 00:19:06.400 --> 00:19:08.680 align:middle line:84% And then there's been some others since then. 00:19:08.680 --> 00:19:11.590 align:middle line:84% So this gives you a sense of what it is. 00:19:11.590 --> 00:19:16.367 align:middle line:90% And now, MIT was able to-- 00:19:16.367 --> 00:19:17.700 align:middle line:90% I'm going to skip some of these. 00:19:17.700 --> 00:19:25.000 align:middle line:84% MIT was able to help me get some of this into a computer. 00:19:25.000 --> 00:19:26.710 align:middle line:84% So we'll get onto that in a little bit. 00:19:26.710 --> 00:19:29.010 align:middle line:84% But what if you want to do-- if you 00:19:29.010 --> 00:19:32.320 align:middle line:84% want to find if any of these pieces 00:19:32.320 --> 00:19:33.825 align:middle line:90% has a match in another thing? 00:19:33.825 --> 00:19:35.200 align:middle line:84% Because somebody has written down 00:19:35.200 --> 00:19:37.090 align:middle line:84% a lot of these little fragments, or they've 00:19:37.090 --> 00:19:39.490 align:middle line:84% put all the pieces in, and I wanted to see not just 00:19:39.490 --> 00:19:41.240 align:middle line:84% where any of these little fragments there, 00:19:41.240 --> 00:19:43.450 align:middle line:84% but at this point, are any pieces 00:19:43.450 --> 00:19:45.970 align:middle line:84% quoting or copying from or plagiarizing 00:19:45.970 --> 00:19:47.900 align:middle line:90% from anybody else's music? 00:19:47.900 --> 00:19:51.700 align:middle line:84% So what you have to do is you take all the songs, 00:19:51.700 --> 00:19:53.690 align:middle line:84% and you compare each one of them. 00:19:53.690 --> 00:19:56.990 align:middle line:84% And by N. Sorry, that's not enough. 00:19:56.990 --> 00:20:00.490 align:middle line:84% We've got to zoom out a little bit. 00:20:00.490 --> 00:20:02.660 align:middle line:90% And there we go. 00:20:02.660 --> 00:20:04.250 align:middle line:84% Yeah, so it's something like that. 00:20:04.250 --> 00:20:06.615 align:middle line:84% That's actually just comparing each of the volumes. 00:20:06.615 --> 00:20:08.740 align:middle line:84% We actually want to compare-- each of these volumes 00:20:08.740 --> 00:20:10.520 align:middle line:90% has about 150 pieces. 00:20:10.520 --> 00:20:13.960 align:middle line:84% So you have to do the square of the number of pieces. 00:20:13.960 --> 00:20:16.040 align:middle line:84% Divide by 2 because it's symmetrical. 00:20:16.040 --> 00:20:18.560 align:middle line:84% And so you have about 3.1 million comparisons. 00:20:18.560 --> 00:20:22.150 align:middle line:84% And that's the reason why nobody had done this before. 00:20:22.150 --> 00:20:23.510 align:middle line:90% I'm actually really lucky. 00:20:23.510 --> 00:20:25.790 align:middle line:84% Our best estimates, which I don't know, 00:20:25.790 --> 00:20:32.030 align:middle line:84% is that 14th century music is about 10% of the size of 15th 00:20:32.030 --> 00:20:33.030 align:middle line:90% century music. 00:20:33.030 --> 00:20:37.980 align:middle line:84% And every successive century is about tenfold more music. 00:20:37.980 --> 00:20:41.270 align:middle line:84% So I have algorithms that I've devised that I think will also 00:20:41.270 --> 00:20:42.690 align:middle line:90% work for the 15th century. 00:20:42.690 --> 00:20:44.820 align:middle line:84% And maybe if I ever had a huge research budget, 00:20:44.820 --> 00:20:45.930 align:middle line:90% I could do the 16th. 00:20:45.930 --> 00:20:48.890 align:middle line:84% But it's going to be up to you all to figure out 00:20:48.890 --> 00:20:50.840 align:middle line:84% what's the algorithm that can compare 00:20:50.840 --> 00:20:55.680 align:middle line:84% every piece of known music to every other piece and get that. 00:20:55.680 --> 00:20:59.850 align:middle line:84% And that's why I care a lot about similarity. 00:20:59.850 --> 00:21:00.350 align:middle line:90% Sorry. 00:21:00.350 --> 00:21:01.760 align:middle line:90% I got ahead of myself. 00:21:01.760 --> 00:21:05.990 align:middle line:84% So the great scholar, Anna Kathryn Grau, 00:21:05.990 --> 00:21:09.510 align:middle line:84% created the Electronic Medieval Music Score Archive Project, 00:21:09.510 --> 00:21:11.075 align:middle line:90% or EMMSAP. 00:21:11.075 --> 00:21:12.450 align:middle line:84% Slide's a little bit out of date, 00:21:12.450 --> 00:21:15.210 align:middle line:84% but back then, it had about 1.3 million notes. 00:21:15.210 --> 00:21:17.330 align:middle line:90% Now we're close to 1.8 million. 00:21:17.330 --> 00:21:20.630 align:middle line:84% And, of course, you know this one, right? 00:21:20.630 --> 00:21:25.400 align:middle line:84% So what you do is you take all the music, and you take music21. 00:21:25.400 --> 00:21:27.690 align:middle line:84% And then it does something like this. 00:21:27.690 --> 00:21:32.150 align:middle line:84% And that's how it looks when you run the matches. 00:21:32.150 --> 00:21:35.660 align:middle line:84% Now, you all know that this is what you do to get funding 00:21:35.660 --> 00:21:36.780 align:middle line:90% for your project. 00:21:36.780 --> 00:21:38.940 align:middle line:84% And that's not actually how it works, right? 00:21:38.940 --> 00:21:40.430 align:middle line:90% Only in CSI. 00:21:40.430 --> 00:21:42.530 align:middle line:84% No, the way it actually works is you go, 00:21:42.530 --> 00:21:44.597 align:middle line:84% and you take your scans that you've done. 00:21:44.597 --> 00:21:45.930 align:middle line:90% And how do you get them scanned? 00:21:45.930 --> 00:21:48.860 align:middle line:84% You spend all day putting them on a scanner. 00:21:48.860 --> 00:21:54.530 align:middle line:84% And then enter every one of these pieces into mostly 00:21:54.530 --> 00:21:57.300 align:middle line:84% MuseScore, Sibelius, Finale, whatever it is. 00:21:57.300 --> 00:22:00.780 align:middle line:84% And then we exported everything as musicXML. 00:22:00.780 --> 00:22:05.420 align:middle line:84% Some people like-- there's a specific output for musicology 00:22:05.420 --> 00:22:09.540 align:middle line:84% called MEI, which is pretty similar, but I use musicXML. 00:22:09.540 --> 00:22:13.740 align:middle line:84% And so then we have here's the musicXML for the first three-- 00:22:13.740 --> 00:22:16.940 align:middle line:84% first four notes of this one piece called-- 00:22:16.940 --> 00:22:19.350 align:middle line:84% sorry, I'll just go back called "Onques Ne Fu," 00:22:19.350 --> 00:22:24.810 align:middle line:84% which is completely only copy of it in the world. 00:22:24.810 --> 00:22:27.280 align:middle line:90% Then I wrote some programs. 00:22:27.280 --> 00:22:33.120 align:middle line:84% Python, music21, things just to take every 31-note little 00:22:33.120 --> 00:22:33.850 align:middle line:90% segment-- 00:22:33.850 --> 00:22:36.900 align:middle line:84% I don't know why I ended up with 31-- 00:22:36.900 --> 00:22:39.870 align:middle line:84% and just automatically chop it up 00:22:39.870 --> 00:22:45.010 align:middle line:84% so that there's these little segments, things. 00:22:45.010 --> 00:22:46.820 align:middle line:84% And ideally, you would chop it up 00:22:46.820 --> 00:22:50.230 align:middle line:84% and you would slide your window over one note at a time. 00:22:50.230 --> 00:22:52.680 align:middle line:84% But there's a trade-off between getting 00:22:52.680 --> 00:22:59.070 align:middle line:84% the best similarity and also not having your database explode 00:22:59.070 --> 00:23:01.390 align:middle line:90% with internal quotations. 00:23:01.390 --> 00:23:05.820 align:middle line:84% So we did this and had it go through everything here. 00:23:05.820 --> 00:23:09.510 align:middle line:84% And then once we had chopped up the pieces into these little 00:23:09.510 --> 00:23:14.680 align:middle line:84% 31-note segments, then we did what Keith was talking about, 00:23:14.680 --> 00:23:19.650 align:middle line:84% a viewpoint or a hash or an encoding system to try to reduce 00:23:19.650 --> 00:23:21.370 align:middle line:90% the complexity of it. 00:23:21.370 --> 00:23:24.080 align:middle line:84% So the complexity of the system that I used, 00:23:24.080 --> 00:23:25.930 align:middle line:90% you're going to laugh at. 00:23:25.930 --> 00:23:28.480 align:middle line:84% If a note was the same duration as the previous, 00:23:28.480 --> 00:23:30.830 align:middle line:84% it got the ASCII letter A, B, C, D, E, F, 00:23:30.830 --> 00:23:35.050 align:middle line:84% G. I dropped sharps and flats because different copies 00:23:35.050 --> 00:23:36.610 align:middle line:84% of the same piece in the Middle Ages 00:23:36.610 --> 00:23:38.450 align:middle line:90% sometimes write it as B-flat. 00:23:38.450 --> 00:23:39.890 align:middle line:84% Sometimes they don't write a flat. 00:23:39.890 --> 00:23:41.870 align:middle line:84% You're just supposed to hear that. 00:23:41.870 --> 00:23:44.030 align:middle line:84% Well, obviously there was an augmented fourth. 00:23:44.030 --> 00:23:46.730 align:middle line:84% I'm going to sing that flat so they don't always put that in. 00:23:46.730 --> 00:23:48.500 align:middle line:90% So we get rid of accidentals. 00:23:48.500 --> 00:23:52.660 align:middle line:84% And then if the note's longer than the previous note, 00:23:52.660 --> 00:23:55.660 align:middle line:84% then we use H through N. And if it's shorter, 00:23:55.660 --> 00:24:01.390 align:middle line:84% then it's O through U. So P is a B that is 00:24:01.390 --> 00:24:03.490 align:middle line:90% shorter than the previous note. 00:24:03.490 --> 00:24:07.000 align:middle line:84% You just go through and put everything in like that. 00:24:07.000 --> 00:24:09.850 align:middle line:84% And the first note, I always just assume it's the same. 00:24:09.850 --> 00:24:12.310 align:middle line:84% So we take all of these things and put it 00:24:12.310 --> 00:24:14.200 align:middle line:90% into a giant database. 00:24:14.200 --> 00:24:15.140 align:middle line:90% It's not that big. 00:24:15.140 --> 00:24:19.800 align:middle line:84% It's about 188,000 of these little segments at that time. 00:24:19.800 --> 00:24:23.600 align:middle line:90% 00:24:23.600 --> 00:24:28.850 align:middle line:84% And so this is the segment for the opening of "Onques Ne Fu." 00:24:28.850 --> 00:24:31.040 align:middle line:84% I always think it's kind of unceremoniously 00:24:31.040 --> 00:24:34.190 align:middle line:84% stored there, like the Ark at the end of the Indiana Jones 00:24:34.190 --> 00:24:35.550 align:middle line:90% film, if you've ever seen it. 00:24:35.550 --> 00:24:38.120 align:middle line:84% You just can't really tell where it is. 00:24:38.120 --> 00:24:42.980 align:middle line:84% So then we have to compare every one of these 188,000 sequences 00:24:42.980 --> 00:24:44.490 align:middle line:90% against every other one. 00:24:44.490 --> 00:24:49.530 align:middle line:84% So we take the first one, the "Onques Ne Fu" melody, 00:24:49.530 --> 00:24:51.630 align:middle line:90% and just some random other one. 00:24:51.630 --> 00:24:54.770 align:middle line:84% And we can figure out what are all the things we 00:24:54.770 --> 00:24:58.200 align:middle line:84% have to do in Earth Mover, Levinstein, 00:24:58.200 --> 00:25:00.170 align:middle line:84% or some other distance thing in order 00:25:00.170 --> 00:25:02.460 align:middle line:84% to transform the first one to the second one. 00:25:02.460 --> 00:25:05.393 align:middle line:84% So you have to-- well, you insert a whole bunch of things, 00:25:05.393 --> 00:25:06.810 align:middle line:84% and then some things are the same. 00:25:06.810 --> 00:25:07.970 align:middle line:90% Delete, whatever. 00:25:07.970 --> 00:25:13.530 align:middle line:84% In the end, you get a ratio from 0 to 1 of how similar they are. 00:25:13.530 --> 00:25:17.820 align:middle line:84% I always like to store integers in databases. 00:25:17.820 --> 00:25:19.290 align:middle line:90% It saves a lot of space. 00:25:19.290 --> 00:25:23.090 align:middle line:84% So I just multiplied by 10,000 so I get a number between 0 00:25:23.090 --> 00:25:24.860 align:middle line:90% and 10,000 to store. 00:25:24.860 --> 00:25:27.510 align:middle line:90% These ones are 17% similar. 00:25:27.510 --> 00:25:31.040 align:middle line:84% These are actually a surprisingly bad amount 00:25:31.040 --> 00:25:31.830 align:middle line:90% of similarity. 00:25:31.830 --> 00:25:36.380 align:middle line:84% Random pieces tend to be more similar. 00:25:36.380 --> 00:25:38.520 align:middle line:90% So this is not a match, right? 00:25:38.520 --> 00:25:42.480 align:middle line:84% Nobody's going to say that those two lines are the same piece. 00:25:42.480 --> 00:25:43.560 align:middle line:90% Slightly different. 00:25:43.560 --> 00:25:45.650 align:middle line:90% No. 00:25:45.650 --> 00:25:50.550 align:middle line:84% But that's OK because we do it 188,000 by 188,000 times, 00:25:50.550 --> 00:25:52.340 align:middle line:90% or 35 billion. 00:25:52.340 --> 00:25:54.620 align:middle line:84% Divide by 2, since it's symmetrical. 00:25:54.620 --> 00:25:57.054 align:middle line:90% 16 billion. 00:25:57.054 --> 00:25:59.160 align:middle line:90% 18 billion, right? 00:25:59.160 --> 00:26:02.420 align:middle line:84% But then I went through and stored every single time 00:26:02.420 --> 00:26:06.030 align:middle line:84% there was something that was more than 50% similar. 00:26:06.030 --> 00:26:10.410 align:middle line:84% So there's two IDs and the ratio of how similar they are. 00:26:10.410 --> 00:26:15.810 align:middle line:84% And over 50% similar ended up with 814,000 things. 00:26:15.810 --> 00:26:17.550 align:middle line:84% I'm never going to look at those. 00:26:17.550 --> 00:26:18.970 align:middle line:90% That's just way too many. 00:26:18.970 --> 00:26:22.990 align:middle line:84% So I started going to-- at around 65% similar, 00:26:22.990 --> 00:26:24.540 align:middle line:84% I started to suspect these tended 00:26:24.540 --> 00:26:29.470 align:middle line:84% to be pieces by the same composer or quite often, 00:26:29.470 --> 00:26:31.390 align:middle line:84% if we knew or I suspected they would be, 00:26:31.390 --> 00:26:32.380 align:middle line:90% or something like that. 00:26:32.380 --> 00:26:35.020 align:middle line:84% At 70% similar, you're like, wow. 00:26:35.020 --> 00:26:38.560 align:middle line:84% These aren't the same piece, but they're a lot like it. 00:26:38.560 --> 00:26:45.580 align:middle line:84% But definitely over 80% similar, they're always the same piece. 00:26:45.580 --> 00:26:48.490 align:middle line:84% And how can something be the same piece and be 20% off? 00:26:48.490 --> 00:26:51.550 align:middle line:84% It could just be that they were sliced at different points. 00:26:51.550 --> 00:26:54.900 align:middle line:84% So they're the exact same thing, but the first third 00:26:54.900 --> 00:26:58.020 align:middle line:84% of one segment is in some other one. 00:26:58.020 --> 00:27:02.740 align:middle line:84% So this is what the actual workflow looks like. 00:27:02.740 --> 00:27:04.470 align:middle line:90% I used to use Eclipse. 00:27:04.470 --> 00:27:06.880 align:middle line:84% And just running through all these pieces. 00:27:06.880 --> 00:27:10.020 align:middle line:84% And occasionally it finds a match, and it puts it up. 00:27:10.020 --> 00:27:13.300 align:middle line:84% And I get to see, OK, does that look like that? 00:27:13.300 --> 00:27:16.780 align:middle line:84% Yeah, that one kind of looks like that one. 00:27:16.780 --> 00:27:18.740 align:middle line:84% And sometimes we already knew them. 00:27:18.740 --> 00:27:22.750 align:middle line:84% The computer does not read what pieces we already knew 00:27:22.750 --> 00:27:23.720 align:middle line:90% were quoted. 00:27:23.720 --> 00:27:25.940 align:middle line:84% But we ended up with some interesting things. 00:27:25.940 --> 00:27:28.580 align:middle line:84% This is a piece by a guy named Johannes Ciconia. 00:27:28.580 --> 00:27:30.020 align:middle line:90% This is unpublished yet. 00:27:30.020 --> 00:27:32.170 align:middle line:84% Don't put it all over everywhere. 00:27:32.170 --> 00:27:35.270 align:middle line:84% A guy by the name of Johannes Ciconia, 00:27:35.270 --> 00:27:37.360 align:middle line:84% one of the most important composers around 1400. 00:27:37.360 --> 00:27:40.420 align:middle line:84% And one of his pieces, it's a part of the mass, 00:27:40.420 --> 00:27:41.990 align:middle line:90% patrem omnipotentem. 00:27:41.990 --> 00:27:45.130 align:middle line:84% And it turns out that a big chunk of it 00:27:45.130 --> 00:27:49.645 align:middle line:90% was taken from an unknown-- 00:27:49.645 --> 00:27:53.660 align:middle line:84% an anonymous, never recorded by anybody, German song. 00:27:53.660 --> 00:27:57.160 align:middle line:90% [SINGING IN LATIN] 00:27:57.160 --> 00:27:58.330 align:middle line:90% Let me see if I can do the-- 00:27:58.330 --> 00:28:01.060 align:middle line:90% 00:28:01.060 --> 00:28:02.905 align:middle line:84% Here we are, if you've never read it. 00:28:02.905 --> 00:28:05.056 align:middle line:90% [SINGING IN LATIN] 00:28:05.056 --> 00:28:16.270 align:middle line:90% 00:28:16.270 --> 00:28:20.770 align:middle line:84% So we can find that there was a lot more copying than we ever 00:28:20.770 --> 00:28:21.850 align:middle line:90% expected. 00:28:21.850 --> 00:28:23.150 align:middle line:90% This is one of my favorites. 00:28:23.150 --> 00:28:25.640 align:middle line:84% Here's a French piece, an Italian piece. 00:28:25.640 --> 00:28:28.210 align:middle line:84% Nobody ever suspected they had anything in common 00:28:28.210 --> 00:28:29.017 align:middle line:90% because whoever-- 00:28:29.017 --> 00:28:30.850 align:middle line:84% and I don't know which direction the copying 00:28:30.850 --> 00:28:33.760 align:middle line:84% happened-- whoever did the copying did a good chance 00:28:33.760 --> 00:28:35.240 align:middle line:90% of covering their tracks. 00:28:35.240 --> 00:28:38.690 align:middle line:84% The colored parts represent the same music. 00:28:38.690 --> 00:28:43.580 align:middle line:84% And then down here, stole something from up there. 00:28:43.580 --> 00:28:45.940 align:middle line:84% And then up here, we stole something 00:28:45.940 --> 00:28:47.690 align:middle line:90% from over there, and so on. 00:28:47.690 --> 00:28:52.480 align:middle line:84% So it's just two that are pastiches of each other. 00:28:52.480 --> 00:28:54.740 align:middle line:84% And then if this were a musicology class, 00:28:54.740 --> 00:28:57.820 align:middle line:84% people would actually care about which one this-- 00:28:57.820 --> 00:28:59.510 align:middle line:90% what all these other things. 00:28:59.510 --> 00:29:03.820 align:middle line:84% But eventually, we got to start reading these erased pieces 00:29:03.820 --> 00:29:06.800 align:middle line:84% and figuring out where they came from. 00:29:06.800 --> 00:29:13.030 align:middle line:84% So that's the big reason why I created music21 00:29:13.030 --> 00:29:16.700 align:middle line:84% and why you will find that there are lots of weird little things 00:29:16.700 --> 00:29:22.130 align:middle line:84% that are only useful for music, for medieval music, hidden 00:29:22.130 --> 00:29:27.470 align:middle line:84% around deep inside the various libraries and stuff. 00:29:27.470 --> 00:29:31.730 align:middle line:84% So that's what I do when I'm not enjoying being in your company. 00:29:31.730 --> 00:29:34.520 align:middle line:90% Any questions? 00:29:34.520 --> 00:29:36.100 align:middle line:84% Or anything you want to see again? 00:29:36.100 --> 00:29:41.720 align:middle line:90% 00:29:41.720 --> 00:29:43.640 align:middle line:90% There are, by the way-- 00:29:43.640 --> 00:29:47.480 align:middle line:84% lots of places do want historians 00:29:47.480 --> 00:29:48.750 align:middle line:90% who can do this type of work. 00:29:48.750 --> 00:29:51.840 align:middle line:84% So if you're all interested, humanities in general. 00:29:51.840 --> 00:29:54.540 align:middle line:84% But you're like, but I also want to program and stuff. 00:29:54.540 --> 00:29:56.340 align:middle line:84% People are dying for things like that. 00:29:56.340 --> 00:29:57.260 align:middle line:90% Yeah? 00:29:57.260 --> 00:30:02.240 align:middle line:84% AUDIENCE: So what made you want to expand music21? 00:30:02.240 --> 00:30:04.290 align:middle line:84% MICHAEL CUTHBERT: You all, your predecessors, 00:30:04.290 --> 00:30:08.010 align:middle line:84% people from about 10, 15 years before you from here at MIT. 00:30:08.010 --> 00:30:11.880 align:middle line:84% It just felt like, people wanted to do 00:30:11.880 --> 00:30:15.150 align:middle line:84% interesting things with composition, with analysis. 00:30:15.150 --> 00:30:21.450 align:middle line:84% Everybody wanted to solve their first-year theory homework 00:30:21.450 --> 00:30:22.770 align:middle line:90% by computer. 00:30:22.770 --> 00:30:23.680 align:middle line:90% And why not? 00:30:23.680 --> 00:30:25.570 align:middle line:84% If you can program the computer to do it 00:30:25.570 --> 00:30:28.865 align:middle line:84% and it's not a complete black box AI, 00:30:28.865 --> 00:30:30.240 align:middle line:84% you're probably teaching yourself 00:30:30.240 --> 00:30:32.260 align:middle line:90% how to do it better also. 00:30:32.260 --> 00:30:34.390 align:middle line:90% So it was things like that. 00:30:34.390 --> 00:30:38.430 align:middle line:84% And over time, I've taken out a lot of the most egregious that 00:30:38.430 --> 00:30:44.160 align:middle line:84% only a person working on 14th century Italy would want to do 00:30:44.160 --> 00:30:46.180 align:middle line:84% this and put this in a separate project. 00:30:46.180 --> 00:30:49.170 align:middle line:84% So there's no longer an automatic "change medieval 00:30:49.170 --> 00:30:51.820 align:middle line:84% notation into modern notation" tool. 00:30:51.820 --> 00:30:53.680 align:middle line:84% You have to install that separately. 00:30:53.680 --> 00:30:58.140 align:middle line:84% But yeah, it's just felt like I was having too much fun. 00:30:58.140 --> 00:31:00.100 align:middle line:84% And other people wanted to share in it, 00:31:00.100 --> 00:31:03.190 align:middle line:84% and that meant eventually docs would have to happen. 00:31:03.190 --> 00:31:06.540 align:middle line:84% And then a very generous funding organization 00:31:06.540 --> 00:31:09.690 align:middle line:84% called The Seaver Institute selected music21 00:31:09.690 --> 00:31:14.620 align:middle line:84% to be MIT's representative project for their funding 00:31:14.620 --> 00:31:16.160 align:middle line:90% organization for three years. 00:31:16.160 --> 00:31:20.140 align:middle line:84% And that allowed me to do a little bit more than one person 00:31:20.140 --> 00:31:22.070 align:middle line:90% can do at their desk. 00:31:22.070 --> 00:31:25.060 align:middle line:84% And now the thing that helps me do more than one person can 00:31:25.060 --> 00:31:27.550 align:middle line:84% do at the desk is community of a lot 00:31:27.550 --> 00:31:32.180 align:middle line:84% of people who keep adding to it and doing cool things with it. 00:31:32.180 --> 00:31:34.660 align:middle line:90% So thanks. 00:31:34.660 --> 00:31:36.670 align:middle line:90% Other Qs? 00:31:36.670 --> 00:31:38.440 align:middle line:84% AUDIENCE: Why is it called music21? 00:31:38.440 --> 00:31:40.405 align:middle line:90% MICHAEL CUTHBERT: Course 21M. 00:31:40.405 --> 00:31:44.560 align:middle line:84% I wanted something that connected itself 00:31:44.560 --> 00:31:49.000 align:middle line:84% to MIT in some way but wasn't MIT music 00:31:49.000 --> 00:31:52.730 align:middle line:84% because your trademark office would probably get against me. 00:31:52.730 --> 00:31:55.670 align:middle line:84% And also, I was a second-year professor without tenure, 00:31:55.670 --> 00:31:57.850 align:middle line:84% so I might have been denied tenure and needed 00:31:57.850 --> 00:32:01.100 align:middle line:84% to be able to take it with me if I went someplace else. 00:32:01.100 --> 00:32:03.440 align:middle line:84% And then somebody later was like oh, 00:32:03.440 --> 00:32:04.940 align:middle line:84% it's the thing for the 21st century? 00:32:04.940 --> 00:32:09.050 align:middle line:84% I said, I actually never thought of that connotation. 00:32:09.050 --> 00:32:11.770 align:middle line:84% If I had, there's no way I would have called it 21 because that 00:32:11.770 --> 00:32:18.003 align:middle line:84% sounds very A, arrogant, and B, a little obsolete in 2006, 00:32:18.003 --> 00:32:19.670 align:middle line:84% when you're already in the 21st century. 00:32:19.670 --> 00:32:21.980 align:middle line:84% It's perfect for 1980 or something. 00:32:21.980 --> 00:32:23.560 align:middle line:90% Yeah. 00:32:23.560 --> 00:32:25.660 align:middle line:84% AUDIENCE: What was it called before music21? 00:32:25.660 --> 00:32:29.620 align:middle line:84% MICHAEL CUTHBERT: It was called PMusic first for Perl music 00:32:29.620 --> 00:32:30.980 align:middle line:90% when I was writing it in Perl. 00:32:30.980 --> 00:32:32.980 align:middle line:90% And then the fact-- 00:32:32.980 --> 00:32:36.730 align:middle line:84% then as soon as the Intro to CS class 00:32:36.730 --> 00:32:40.010 align:middle line:84% switched from your older language scheme to Python, 00:32:40.010 --> 00:32:41.740 align:middle line:84% I was like, well, if all of MIT is 00:32:41.740 --> 00:32:44.480 align:middle line:84% going to move to a new language at the same time, 00:32:44.480 --> 00:32:49.060 align:middle line:84% then it'll be easier for me to learn a new language 00:32:49.060 --> 00:32:52.510 align:middle line:84% than to have the rest of my life teach my students how to 00:32:52.510 --> 00:32:53.990 align:middle line:90% program in Perl. 00:32:53.990 --> 00:32:56.950 align:middle line:90% And I'm very glad I did. 00:32:56.950 --> 00:33:01.310 align:middle line:84% The other thing is the work on it began in 2004. 00:33:01.310 --> 00:33:04.490 align:middle line:84% The work really began around 2006. 00:33:04.490 --> 00:33:08.720 align:middle line:84% And at the time, I predicted that it would have a 20-year 00:33:08.720 --> 00:33:16.640 align:middle line:84% lifespan, that it would be five or six years of getting people 00:33:16.640 --> 00:33:21.080 align:middle line:84% to notice it and start using it, seven or eight years of it being 00:33:21.080 --> 00:33:25.490 align:middle line:84% the main thing out there, and five to seven years 00:33:25.490 --> 00:33:28.780 align:middle line:84% of the decline while something else better came out. 00:33:28.780 --> 00:33:30.780 align:middle line:84% And I'm still looking for that something better. 00:33:30.780 --> 00:33:33.840 align:middle line:90% You guys can do that. 00:33:33.840 --> 00:33:36.920 align:middle line:84% There are things we've learned from using it 00:33:36.920 --> 00:33:41.030 align:middle line:84% that I think have made me realize that there are 00:33:41.030 --> 00:33:44.660 align:middle line:84% some pretty poor design decisions, such as having 00:33:44.660 --> 00:33:47.880 align:middle line:84% to copy everything all the time and things like that. 00:33:47.880 --> 00:33:54.080 align:middle line:84% And so I'd really love it if somebody else would create 00:33:54.080 --> 00:33:55.800 align:middle line:90% something new and better. 00:33:55.800 --> 00:33:58.770 align:middle line:84% So whoever's here or watching it, 00:33:58.770 --> 00:34:03.295 align:middle line:84% you have my blessing to try to knock this off its shelf. 00:34:03.295 --> 00:34:04.670 align:middle line:84% And maybe the new thing will have 00:34:04.670 --> 00:34:06.840 align:middle line:84% a lot of machine learning built in 00:34:06.840 --> 00:34:10.179 align:middle line:84% or something to be able to do better analysis. 00:34:10.179 --> 00:34:11.489 align:middle line:90% Yeah. 00:34:11.489 --> 00:34:14.699 align:middle line:84% But Python has been enduring a lot longer 00:34:14.699 --> 00:34:16.389 align:middle line:90% than I thought it would be. 00:34:16.389 --> 00:34:21.429 align:middle line:84% It's been 15 years as a major language, 00:34:21.429 --> 00:34:22.989 align:middle line:84% and it seems to be still growing, 00:34:22.989 --> 00:34:25.560 align:middle line:90% so that probably will stop. 00:34:25.560 --> 00:34:26.620 align:middle line:90% AUDIENCE: Julia is next. 00:34:26.620 --> 00:34:28.102 align:middle line:90% MICHAEL CUTHBERT: Julia is next. 00:34:28.102 --> 00:34:30.060 align:middle line:84% People have been saying that about Julia and R. 00:34:30.060 --> 00:34:33.280 align:middle line:84% There is a Julia port of music21, if you'd like that. 00:34:33.280 --> 00:34:35.620 align:middle line:90% I don't know how good it works. 00:34:35.620 --> 00:34:38.490 align:middle line:90% So that's a perfect transition. 00:34:38.490 --> 00:34:40.929 align:middle line:84% We can keep going more to a second topic. 00:34:40.929 --> 00:34:43.210 align:middle line:84% So this one, get out your laptops. 00:34:43.210 --> 00:34:44.460 align:middle line:90% We're going to have-- 00:34:44.460 --> 00:34:50.159 align:middle line:84% because I couldn't have scripted a better transition to-- 00:34:50.159 --> 00:34:52.449 align:middle line:90% OK, so now more grab bag. 00:34:52.449 --> 00:34:54.600 align:middle line:84% And these are more requested from previous years 00:34:54.600 --> 00:34:55.420 align:middle line:90% than anything. 00:34:55.420 --> 00:34:55.920 align:middle line:90% Sorry. 00:34:55.920 --> 00:34:57.503 align:middle line:90% I can't stand all that dust. 00:34:57.503 --> 00:35:00.220 align:middle line:90% 00:35:00.220 --> 00:35:00.720 align:middle line:90% Oops. 00:35:00.720 --> 00:35:02.830 align:middle line:84% Did pushing all this shut it down? 00:35:02.830 --> 00:35:03.780 align:middle line:90% No. 00:35:03.780 --> 00:35:06.060 align:middle line:90% Here we go. 00:35:06.060 --> 00:35:07.590 align:middle line:90% OK. 00:35:07.590 --> 00:35:09.010 align:middle line:90% So here are some of the things. 00:35:09.010 --> 00:35:14.620 align:middle line:84% Go ahead and go to this website, m21sand2. 00:35:14.620 --> 00:35:18.630 align:middle line:84% If you leave off the 2, you get to use a three-year-old version 00:35:18.630 --> 00:35:20.370 align:middle line:90% of this. 00:35:20.370 --> 00:35:23.430 align:middle line:84% You should be seeing something that looks a bit like this 00:35:23.430 --> 00:35:26.190 align:middle line:90% when you get there. 00:35:26.190 --> 00:35:31.020 align:middle line:90% 21m-- 21-- m21sand2. 00:35:31.020 --> 00:35:33.480 align:middle line:90% m21sand2. 00:35:33.480 --> 00:35:37.985 align:middle line:84% sand Sandbox, the place where you play around. 00:35:37.985 --> 00:35:44.070 align:middle line:90% 00:35:44.070 --> 00:35:48.300 align:middle line:84% So the thing I've always hated most about music21 00:35:48.300 --> 00:35:52.230 align:middle line:90% is that you can't see anything. 00:35:52.230 --> 00:35:53.070 align:middle line:90% There's two things. 00:35:53.070 --> 00:35:54.250 align:middle line:90% You can't see anything. 00:35:54.250 --> 00:35:56.865 align:middle line:90% You can't hear anything unless-- 00:35:56.865 --> 00:35:59.702 align:middle line:84% we didn't even have Jupyter notebooks or something back 00:35:59.702 --> 00:36:00.910 align:middle line:90% then, so we didn't have that. 00:36:00.910 --> 00:36:03.490 align:middle line:84% And number three, it's so hard to install. 00:36:03.490 --> 00:36:05.060 align:middle line:84% That's getting easier, but still. 00:36:05.060 --> 00:36:06.580 align:middle line:84% So I thought that something where 00:36:06.580 --> 00:36:10.070 align:middle line:84% people can start playing with it immediately online would work. 00:36:10.070 --> 00:36:15.570 align:middle line:84% And so I've been working in parallel for the past five 00:36:15.570 --> 00:36:21.080 align:middle line:84% or six years, there's a TypeScript or JavaScript port. 00:36:21.080 --> 00:36:25.090 align:middle line:84% Who has done JavaScript here in some ways? 00:36:25.090 --> 00:36:27.110 align:middle line:90% OK, a little bit more than half. 00:36:27.110 --> 00:36:31.000 align:middle line:84% So the big difference if you're new to JavaScript 00:36:31.000 --> 00:36:34.120 align:middle line:84% is that you're going to put new in front of any time you 00:36:34.120 --> 00:36:36.080 align:middle line:90% want to instantiate something. 00:36:36.080 --> 00:36:38.830 align:middle line:84% And I've imported music21 without importing 00:36:38.830 --> 00:36:40.160 align:middle line:90% all of the things. 00:36:40.160 --> 00:36:44.200 align:middle line:84% So you're going to have to type that quite a bit. 00:36:44.200 --> 00:36:49.000 align:middle line:84% But what's kind of nice is you can go through and change a note 00:36:49.000 --> 00:36:53.720 align:middle line:84% and immediately see the stream there, or octave, 00:36:53.720 --> 00:36:55.577 align:middle line:84% things like that, or put everything down. 00:36:55.577 --> 00:36:57.410 align:middle line:84% What happens if we put everything down here? 00:36:57.410 --> 00:36:59.470 align:middle line:84% Doesn't it automatically give me the good clef? 00:36:59.470 --> 00:37:00.340 align:middle line:90% No. 00:37:00.340 --> 00:37:01.290 align:middle line:90% Did I put it in? 00:37:01.290 --> 00:37:03.690 align:middle line:84% OK, well, we can put in a proper clef. 00:37:03.690 --> 00:37:04.190 align:middle line:90% s. 00:37:04.190 --> 00:37:09.060 align:middle line:84% So we'll append to the stream a new music21.clef.BassClef. 00:37:09.060 --> 00:37:13.190 align:middle line:90% 00:37:13.190 --> 00:37:15.120 align:middle line:84% And now we can see our notes again. 00:37:15.120 --> 00:37:19.833 align:middle line:84% And by default, if you click the thing by default-- 00:37:19.833 --> 00:37:26.747 align:middle line:90% 00:37:26.747 --> 00:37:28.190 align:middle line:90% [NOTES PLAYING] 00:37:28.190 --> 00:37:28.860 align:middle line:90% There we go. 00:37:28.860 --> 00:37:31.740 align:middle line:84% OK, well, I've lost all my changes, but you can see. 00:37:31.740 --> 00:37:33.950 align:middle line:84% And so some of the things you can do 00:37:33.950 --> 00:37:36.530 align:middle line:84% is create interactive little systems 00:37:36.530 --> 00:37:38.720 align:middle line:84% where you're scrolling things up and down, where 00:37:38.720 --> 00:37:40.890 align:middle line:90% you're hearing everything. 00:37:40.890 --> 00:37:43.950 align:middle line:84% But it's still absolutely a work in progress. 00:37:43.950 --> 00:37:51.270 align:middle line:84% So if you do analyze key, you get analyze is not a function. 00:37:51.270 --> 00:37:55.020 align:middle line:84% So there's still a lot of things missing there. 00:37:55.020 --> 00:37:58.100 align:middle line:84% But there's something really nice to being able to manipulate 00:37:58.100 --> 00:38:00.380 align:middle line:90% with scores in a browser. 00:38:00.380 --> 00:38:03.380 align:middle line:84% The alternatives that people are doing right now 00:38:03.380 --> 00:38:08.672 align:middle line:84% tend to be about actually using HTML elements to represent 00:38:08.672 --> 00:38:10.380 align:middle line:84% notes, now that you have custom elements. 00:38:10.380 --> 00:38:12.500 align:middle line:84% And that lets you use your browser's 00:38:12.500 --> 00:38:16.400 align:middle line:84% built-in getElementsByClass and all these things 00:38:16.400 --> 00:38:18.030 align:middle line:90% to move around a score. 00:38:18.030 --> 00:38:22.170 align:middle line:84% And in theory, it should be substantially faster than this, 00:38:22.170 --> 00:38:25.250 align:middle line:90% or at least more powerful. 00:38:25.250 --> 00:38:27.020 align:middle line:84% I don't know if anybody wants to-- 00:38:27.020 --> 00:38:30.780 align:middle line:84% you can play around with any of this for a little bit. 00:38:30.780 --> 00:38:35.240 align:middle line:84% You can make this a dotted quarter. 00:38:35.240 --> 00:38:39.635 align:middle line:84% What I hate is duration.dots equals 1. 00:38:39.635 --> 00:38:41.510 align:middle line:84% And nothing's going to happen until I get rid 00:38:41.510 --> 00:38:43.680 align:middle line:90% of this analyze thing here. 00:38:43.680 --> 00:38:44.180 align:middle line:90% Yep. 00:38:44.180 --> 00:38:45.380 align:middle line:90% Play it around. 00:38:45.380 --> 00:38:49.860 align:middle line:90% Give it a 7/8 time signature. 00:38:49.860 --> 00:38:54.210 align:middle line:90% And then-- here let's do this. 00:38:54.210 --> 00:38:59.470 align:middle line:84% Let's create p equals stream.Part. 00:38:59.470 --> 00:39:00.120 align:middle line:90% Oops. 00:39:00.120 --> 00:39:03.960 align:middle line:84% I'm totally-- just being in this class with you 00:39:03.960 --> 00:39:07.772 align:middle line:84% all, I can't not be in Python mode. 00:39:07.772 --> 00:39:10.230 align:middle line:84% So I'm just going to keep typing Python and then correcting 00:39:10.230 --> 00:39:12.220 align:middle line:90% it to JavaScript until it runs. 00:39:12.220 --> 00:39:19.860 align:middle line:84% But we can do something like for let i equals 0, 00:39:19.860 --> 00:39:24.340 align:middle line:90% i is less than 4, i plus plus. 00:39:24.340 --> 00:39:27.903 align:middle line:84% And then-- oh, this pains me as a Python-- 00:39:27.903 --> 00:39:30.810 align:middle line:90% 00:39:30.810 --> 00:39:33.850 align:middle line:84% as a Python person to not have indented code. 00:39:33.850 --> 00:39:38.940 align:middle line:84% But actually do we have to call that? 00:39:38.940 --> 00:39:40.710 align:middle line:90% We have to call that Measure. 00:39:40.710 --> 00:39:45.030 align:middle line:84% Music21j is a lot more strict about such things. 00:39:45.030 --> 00:39:51.300 align:middle line:90% Did I-- Hmm. 00:39:51.300 --> 00:39:53.910 align:middle line:90% What did I do wrong? 00:39:53.910 --> 00:39:55.690 align:middle line:84% It's so hard to tell without indentations. 00:39:55.690 --> 00:40:00.255 align:middle line:84% But this editor doesn't allow me to hit Tab to indent things. 00:40:00.255 --> 00:40:07.150 align:middle line:90% 00:40:07.150 --> 00:40:09.040 align:middle line:90% Always make your life easier. 00:40:09.040 --> 00:40:12.420 align:middle line:84% Get rid of that so you can see everything on one page. 00:40:12.420 --> 00:40:17.318 align:middle line:90% 00:40:17.318 --> 00:40:18.860 align:middle line:84% Anybody know what I'm mistyping here? 00:40:18.860 --> 00:40:22.450 align:middle line:84% I have a fully baked version over here somewhere 00:40:22.450 --> 00:40:23.610 align:middle line:90% on another tab. 00:40:23.610 --> 00:40:26.590 align:middle line:90% 00:40:26.590 --> 00:40:29.710 align:middle line:84% Here, we'll go over to the fully baked one that already works 00:40:29.710 --> 00:40:33.800 align:middle line:90% so you can play around with it. 00:40:33.800 --> 00:40:40.850 align:middle line:84% Just saying first note of each measure will be a random number. 00:40:40.850 --> 00:40:44.510 align:middle line:84% And as we go through, we'll just change them. 00:40:44.510 --> 00:40:48.460 align:middle line:84% And if I make any changes here, it will automatically 00:40:48.460 --> 00:40:51.310 align:middle line:90% give me a new random number. 00:40:51.310 --> 00:40:53.020 align:middle line:90% I thought I had it. 00:40:53.020 --> 00:40:55.220 align:middle line:90% Oh, this. 00:40:55.220 --> 00:40:58.400 align:middle line:84% OK, I think I have to copy and paste. 00:40:58.400 --> 00:41:00.235 align:middle line:90% What I think happens is-- 00:41:00.235 --> 00:41:02.840 align:middle line:90% 00:41:02.840 --> 00:41:03.930 align:middle line:90% there we go. 00:41:03.930 --> 00:41:06.470 align:middle line:90% [MUSIC PLAYING] 00:41:06.470 --> 00:41:08.820 align:middle line:90% You can do overlapping things. 00:41:08.820 --> 00:41:11.700 align:middle line:90% [MUSIC PLAYING] 00:41:11.700 --> 00:41:18.920 align:middle line:90% 00:41:18.920 --> 00:41:22.100 align:middle line:84% Anyhow, so it can be kind of fun for a live coding environment 00:41:22.100 --> 00:41:24.940 align:middle line:84% if you don't care about the quality of the music coming. 00:41:24.940 --> 00:41:26.940 align:middle line:84% If you don't care about the quality of the sound 00:41:26.940 --> 00:41:30.150 align:middle line:84% because it's not really optimized for sound quality, 00:41:30.150 --> 00:41:34.460 align:middle line:84% but you could put it out through other things. 00:41:34.460 --> 00:41:38.150 align:middle line:84% Let's grab bag topic number one, how to do interactive-- 00:41:38.150 --> 00:41:39.960 align:middle line:84% how to do interactive programming. 00:41:39.960 --> 00:41:41.810 align:middle line:90% So if you can do everything-- 00:41:41.810 --> 00:41:42.630 align:middle line:90% sorry, John. 00:41:42.630 --> 00:41:44.767 align:middle line:84% You just came back in, and I'm going to just say, 00:41:44.767 --> 00:41:45.600 align:middle line:90% you're the only one. 00:41:45.600 --> 00:41:48.530 align:middle line:84% Has anyone else taken Interactive Music Systems? 00:41:48.530 --> 00:41:49.160 align:middle line:90% Oh, you are? 00:41:49.160 --> 00:41:49.660 align:middle line:90% OK. 00:41:49.660 --> 00:41:52.820 align:middle line:84% So you have-- yeah, so you can put everything into-- 00:41:52.820 --> 00:41:56.010 align:middle line:84% you guys usually use Kivy, right, as your toolkit? 00:41:56.010 --> 00:41:59.000 align:middle line:84% So you know there are things you can do on the Python side that 00:41:59.000 --> 00:42:02.630 align:middle line:84% connect up music21 to things to get better 00:42:02.630 --> 00:42:05.040 align:middle line:90% sounding interactive things. 00:42:05.040 --> 00:42:08.960 align:middle line:84% But I often find sometimes just the easiest little thing 00:42:08.960 --> 00:42:10.730 align:middle line:90% can be all you need. 00:42:10.730 --> 00:42:11.700 align:middle line:90% OK. 00:42:11.700 --> 00:42:13.970 align:middle line:84% I'm going to close these things because otherwise it 00:42:13.970 --> 00:42:16.280 align:middle line:84% will eventually just start playing again. 00:42:16.280 --> 00:42:19.860 align:middle line:84% And we've just enough time for, I think, for one more topic, 00:42:19.860 --> 00:42:22.220 align:middle line:84% and then I might finally keep my promise 00:42:22.220 --> 00:42:25.880 align:middle line:84% and let you all go a little bit earlier. 00:42:25.880 --> 00:42:28.640 align:middle line:84% OK, so the last thing I want to talk about a little bit 00:42:28.640 --> 00:42:30.420 align:middle line:90% is music visualization. 00:42:30.420 --> 00:42:33.380 align:middle line:84% And we're going to listen to a piece of music 00:42:33.380 --> 00:42:36.890 align:middle line:84% by a contemporary Estonian composer, Arvo Part. 00:42:36.890 --> 00:42:39.650 align:middle line:84% And I'm going to ask you afterwards 00:42:39.650 --> 00:42:43.220 align:middle line:84% to say something about the structure or the form 00:42:43.220 --> 00:42:45.270 align:middle line:84% of this piece and how it works musically. 00:42:45.270 --> 00:42:48.780 align:middle line:84% First, it's a piece for choir, and so it has a text. 00:42:48.780 --> 00:42:51.810 align:middle line:84% It's actually high, high medieval today. 00:42:51.810 --> 00:42:54.130 align:middle line:90% It's based on a Gregorian chant. 00:42:54.130 --> 00:42:56.310 align:middle line:90% It's sung in German translation. 00:42:56.310 --> 00:42:57.856 align:middle line:90% [SPEAKING GERMAN] 00:42:57.856 --> 00:43:07.840 align:middle line:90% 00:43:07.840 --> 00:43:11.470 align:middle line:84% And the German texts can be slightly important for that. 00:43:11.470 --> 00:43:15.828 align:middle line:84% So it's about a two-minute piece and wrong time 00:43:15.828 --> 00:43:16.870 align:middle line:90% of the year for doing it. 00:43:16.870 --> 00:43:21.330 align:middle line:90% But with that, here we go. 00:43:21.330 --> 00:43:23.934 align:middle line:90% [MUSIC PLAYING] 00:43:23.934 --> 00:43:52.480 align:middle line:90% 00:43:52.480 --> 00:43:59.800 align:middle line:84% 1988, I think, was one of my favorites. 00:43:59.800 --> 00:44:03.020 align:middle line:84% Anybody catch anything about the structure? 00:44:03.020 --> 00:44:07.730 align:middle line:84% You have seen the entire score, every single note. 00:44:07.730 --> 00:44:12.560 align:middle line:90% So we can get something. 00:44:12.560 --> 00:44:13.060 align:middle line:90% Yeah? 00:44:13.060 --> 00:44:15.265 align:middle line:84% AUDIENCE: The measures always switch between 1/2 and 3/2. 00:44:15.265 --> 00:44:17.598 align:middle line:84% MICHAEL CUTHBERT: The measures always switch between 1/2 00:44:17.598 --> 00:44:18.850 align:middle line:90% and 3/2, 1/2 and 3/2. 00:44:18.850 --> 00:44:24.610 align:middle line:90% 00:44:24.610 --> 00:44:29.252 align:middle line:84% How many sections did the piece have? 00:44:29.252 --> 00:44:30.100 align:middle line:90% Yeah? 00:44:30.100 --> 00:44:31.430 align:middle line:90% AUDIENCE: Into three. 00:44:31.430 --> 00:44:32.560 align:middle line:90% MICHAEL CUTHBERT: Sure. 00:44:32.560 --> 00:44:33.220 align:middle line:90% Nice. 00:44:33.220 --> 00:44:34.220 align:middle line:90% That's actually correct. 00:44:34.220 --> 00:44:35.480 align:middle line:90% How many people knew that? 00:44:35.480 --> 00:44:38.330 align:middle line:84% And how many people were like me when they heard this once, 00:44:38.330 --> 00:44:43.070 align:middle line:84% twice, three times, and didn't fully catch the structure? 00:44:43.070 --> 00:44:44.025 align:middle line:90% I was-- yeah, yeah. 00:44:44.025 --> 00:44:46.900 align:middle line:90% 00:44:46.900 --> 00:44:48.460 align:middle line:90% Fantastic, fantastic. 00:44:48.460 --> 00:44:51.020 align:middle line:84% Usually-- so yeah, there's some things. 00:44:51.020 --> 00:44:54.250 align:middle line:90% And what voice is most-- 00:44:54.250 --> 00:44:58.190 align:middle line:84% what two voices were most melodically active? 00:44:58.190 --> 00:44:58.690 align:middle line:90% Yeah? 00:44:58.690 --> 00:45:00.670 align:middle line:90% AUDIENCE: Middle two, I think? 00:45:00.670 --> 00:45:02.030 align:middle line:90% MICHAEL CUTHBERT: Good ear. 00:45:02.030 --> 00:45:04.300 align:middle line:90% Good ear. 00:45:04.300 --> 00:45:06.130 align:middle line:90% Y'all are really getting-- 00:45:06.130 --> 00:45:08.440 align:middle line:84% we should have been doing more music analysis in class 00:45:08.440 --> 00:45:10.648 align:middle line:84% because you're getting a lot of things I thought were 00:45:10.648 --> 00:45:11.870 align:middle line:90% going to be extremely hard. 00:45:11.870 --> 00:45:15.830 align:middle line:84% And at least throughout the room, we've had correct answers. 00:45:15.830 --> 00:45:20.900 align:middle line:84% But I want to spend a little bit of time on music visualization. 00:45:20.900 --> 00:45:22.900 align:middle line:90% By the way, there are a few-- 00:45:22.900 --> 00:45:27.190 align:middle line:84% out of almost exactly, there is one measure of 5/2. 00:45:27.190 --> 00:45:30.680 align:middle line:84% But yeah, there's a couple other things, but yep. 00:45:30.680 --> 00:45:32.750 align:middle line:90% So are we up there? 00:45:32.750 --> 00:45:33.250 align:middle line:90% Yeah. 00:45:33.250 --> 00:45:35.020 align:middle line:90% Go ahead and download. 00:45:35.020 --> 00:45:41.720 align:middle line:84% There is the XML file, musicXML file, of this piece on Canvas. 00:45:41.720 --> 00:45:43.100 align:middle line:90% And take a minute. 00:45:43.100 --> 00:45:45.070 align:middle line:84% It's under copyright, but I'm going 00:45:45.070 --> 00:45:47.570 align:middle line:84% to assert a claim of fair use for us 00:45:47.570 --> 00:45:51.680 align:middle line:90% to be able to analyze with it. 00:45:51.680 --> 00:45:55.260 align:middle line:84% Should show you just the first page if you're in Jupyter, 00:45:55.260 --> 00:45:58.345 align:middle line:84% and more than that if you're not. 00:45:58.345 --> 00:46:05.870 align:middle line:90% 00:46:05.870 --> 00:46:13.890 align:middle line:84% So some of these things might be helpful for what we're doing. 00:46:13.890 --> 00:46:16.620 align:middle line:90% So a little bit more. 00:46:16.620 --> 00:46:23.096 align:middle line:84% We're going to be going through the various ways of visualizing. 00:46:23.096 --> 00:46:33.200 align:middle line:90% 00:46:33.200 --> 00:46:35.330 align:middle line:84% I don't think we've maybe I've done 00:46:35.330 --> 00:46:38.600 align:middle line:84% a tiny bit of visualization, but mostly just on slides. 00:46:38.600 --> 00:46:39.823 align:middle line:90% I don't think I've shown-- 00:46:39.823 --> 00:46:43.400 align:middle line:90% 00:46:43.400 --> 00:46:45.580 align:middle line:84% are we feeling in a good place to move on now? 00:46:45.580 --> 00:46:46.879 align:middle line:90% OK. 00:46:46.879 --> 00:46:53.230 align:middle line:84% So we can do all the things that we normally would do. 00:46:53.230 --> 00:46:58.740 align:middle line:84% We can get the key of the piece, which I believe changes 00:46:58.740 --> 00:46:59.830 align:middle line:90% quite a bit. 00:46:59.830 --> 00:47:05.620 align:middle line:84% I think if we do measures 1 through 20, analyze key, 00:47:05.620 --> 00:47:08.110 align:middle line:90% we get something very different. 00:47:08.110 --> 00:47:10.110 align:middle line:90% No, we don't. 00:47:10.110 --> 00:47:11.520 align:middle line:90% Still get-- interesting. 00:47:11.520 --> 00:47:14.400 align:middle line:90% Just the key signature changes. 00:47:14.400 --> 00:47:15.546 align:middle line:90% OK. 00:47:15.546 --> 00:47:17.830 align:middle line:84% But now we'll get into some visualization things. 00:47:17.830 --> 00:47:21.330 align:middle line:84% So the easiest thing you can do with a stream 00:47:21.330 --> 00:47:23.680 align:middle line:90% is to do something called plot. 00:47:23.680 --> 00:47:29.250 align:middle line:84% And plot just gives you whatever you-- 00:47:29.250 --> 00:47:34.890 align:middle line:90% a standard, ready-made-- oops. 00:47:34.890 --> 00:47:36.660 align:middle line:90% That's why I never do this here. 00:47:36.660 --> 00:47:38.980 align:middle line:90% Ready-made image. 00:47:38.980 --> 00:47:39.480 align:middle line:90% Sorry. 00:47:39.480 --> 00:47:42.040 align:middle line:84% It doesn't zoom the image in here, 00:47:42.040 --> 00:47:44.600 align:middle line:84% but you might be able to see something like that. 00:47:44.600 --> 00:47:47.170 align:middle line:84% And so you can see a relationship 00:47:47.170 --> 00:47:54.470 align:middle line:84% of the various parts colored in different colors 00:47:54.470 --> 00:47:59.080 align:middle line:90% and which ones are singing what. 00:47:59.080 --> 00:48:01.280 align:middle line:90% So here are the three-part-- 00:48:01.280 --> 00:48:02.673 align:middle line:90% the three-fold relationships. 00:48:02.673 --> 00:48:04.840 align:middle line:84% Sorry, I'm going to have to zoom this out a tiny bit 00:48:04.840 --> 00:48:06.930 align:middle line:90% so we can see this again. 00:48:06.930 --> 00:48:09.760 align:middle line:90% 00:48:09.760 --> 00:48:12.970 align:middle line:84% The three-part relation-- three-section relationship 00:48:12.970 --> 00:48:14.780 align:middle line:84% of the piece becomes very clear, right? 00:48:14.780 --> 00:48:17.080 align:middle line:84% You can see that something happens 00:48:17.080 --> 00:48:21.160 align:middle line:84% at the beginning, this increase up here 00:48:21.160 --> 00:48:22.820 align:middle line:90% up until a certain point. 00:48:22.820 --> 00:48:26.140 align:middle line:90% And then a lot of things change. 00:48:26.140 --> 00:48:31.853 align:middle line:84% So what measure does the third section begin on? 00:48:31.853 --> 00:48:35.562 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:48:35.562 --> 00:48:37.520 align:middle line:84% MICHAEL CUTHBERT: Yeah, somewhere around there. 00:48:37.520 --> 00:48:42.520 align:middle line:84% So you can-- 45, I think, 46, 44, 45. 00:48:42.520 --> 00:48:45.860 align:middle line:84% So you can see something substantial changes. 00:48:45.860 --> 00:48:49.996 align:middle line:84% And here's what Jason pointed out, 00:48:49.996 --> 00:48:54.010 align:middle line:84% that the inner voices in the second and third sections 00:48:54.010 --> 00:49:02.020 align:middle line:84% are the ones that are very, very active. 00:49:02.020 --> 00:49:04.510 align:middle line:84% So where does the second section begin? 00:49:04.510 --> 00:49:10.130 align:middle line:90% Measure 13 to measure 45. 00:49:10.130 --> 00:49:12.260 align:middle line:90% So let's get this. 00:49:12.260 --> 00:49:17.350 align:middle line:90% sec2 equals arvo.measures. 00:49:17.350 --> 00:49:20.690 align:middle line:90% Let's say 14 to 45. 00:49:20.690 --> 00:49:25.090 align:middle line:90% 44, we'll say sec2.plot. 00:49:25.090 --> 00:49:27.910 align:middle line:84% I think the default is piano roll because that's 00:49:27.910 --> 00:49:29.030 align:middle line:90% what most people want. 00:49:29.030 --> 00:49:32.440 align:middle line:90% So we can look at Section 2. 00:49:32.440 --> 00:49:38.290 align:middle line:84% And we'll say section 3 was measures, what, 45 to 76. 00:49:38.290 --> 00:49:47.540 align:middle line:84% Section 3 equals arvo.measures 45 to 76. 00:49:47.540 --> 00:49:48.550 align:middle line:90% We can plot that. 00:49:48.550 --> 00:49:56.270 align:middle line:90% 00:49:56.270 --> 00:49:58.010 align:middle line:84% And there's a lot of similarities 00:49:58.010 --> 00:50:02.785 align:middle line:84% here between section 2 and section 3. 00:50:02.785 --> 00:50:05.300 align:middle line:90% 00:50:05.300 --> 00:50:09.080 align:middle line:84% What's the biggest difference musically 00:50:09.080 --> 00:50:12.710 align:middle line:84% that you can tell from these charts between section 00:50:12.710 --> 00:50:14.520 align:middle line:90% 2 and section three? 00:50:14.520 --> 00:50:17.070 align:middle line:84% You'll probably want to go all the way back up to your bigger 00:50:17.070 --> 00:50:17.570 align:middle line:90% roll. 00:50:17.570 --> 00:50:21.528 align:middle line:90% 00:50:21.528 --> 00:50:22.320 align:middle line:90% Over here? 00:50:22.320 --> 00:50:24.200 align:middle line:90% This side's been mostly quiet. 00:50:24.200 --> 00:50:24.920 align:middle line:90% Yeah? 00:50:24.920 --> 00:50:26.180 align:middle line:90% AUDIENCE: Section 2. 00:50:26.180 --> 00:50:29.475 align:middle line:84% Section 2 and section 3 close, but section 2 is up. 00:50:29.475 --> 00:50:32.100 align:middle line:84% MICHAEL CUTHBERT: Section 2 and Section 3 are almost identical, 00:50:32.100 --> 00:50:33.330 align:middle line:90% but section 2 is up. 00:50:33.330 --> 00:50:34.102 align:middle line:90% Good. 00:50:34.102 --> 00:50:38.670 align:middle line:84% Can we figure out about how much up it is? 00:50:38.670 --> 00:50:42.180 align:middle line:90% Look at the key on this side. 00:50:42.180 --> 00:50:45.310 align:middle line:84% Yeah, the E to the A and the E to the A 00:50:45.310 --> 00:50:48.750 align:middle line:84% So it's about a fifth off in a lot of things, 00:50:48.750 --> 00:50:51.070 align:middle line:90% except for on the extremes. 00:50:51.070 --> 00:50:57.870 align:middle line:84% But what about the notes in between these moving parts? 00:50:57.870 --> 00:51:01.170 align:middle line:90% Where are they off? 00:51:01.170 --> 00:51:02.675 align:middle line:90% What's the relationship there? 00:51:02.675 --> 00:51:07.384 align:middle line:90% 00:51:07.384 --> 00:51:08.728 align:middle line:90% AUDIENCE: An octave up? 00:51:08.728 --> 00:51:10.020 align:middle line:90% MICHAEL CUTHBERT: Yeah, about-- 00:51:10.020 --> 00:51:11.200 align:middle line:90% exactly an octave up. 00:51:11.200 --> 00:51:12.660 align:middle line:90% So we have things moving. 00:51:12.660 --> 00:51:18.940 align:middle line:84% Now, we'll go-- I'll open up the score one more time. 00:51:18.940 --> 00:51:21.180 align:middle line:84% I know why I wanted the score open, 00:51:21.180 --> 00:51:24.060 align:middle line:84% so I could keep going to back to this. 00:51:24.060 --> 00:51:25.140 align:middle line:90% Let me get a-- 00:51:25.140 --> 00:51:26.070 align:middle line:90% yep. 00:51:26.070 --> 00:51:27.930 align:middle line:90% There we go. 00:51:27.930 --> 00:51:29.960 align:middle line:84% So I'll just put this in front for a second. 00:51:29.960 --> 00:51:33.540 align:middle line:90% 00:51:33.540 --> 00:51:38.700 align:middle line:84% sorry, now I've lost my train of thought. 00:51:38.700 --> 00:51:43.260 align:middle line:84% How easy is it to see which parts are static 00:51:43.260 --> 00:51:48.000 align:middle line:84% and which parts are in motion in this? 00:51:48.000 --> 00:51:49.720 align:middle line:90% Quite a bit harder. 00:51:49.720 --> 00:51:52.570 align:middle line:84% So what kind of motion is happening? 00:51:52.570 --> 00:51:58.650 align:middle line:84% We've identified that it's the inner voices that are in motion. 00:51:58.650 --> 00:52:01.050 align:middle line:90% What's the pattern? 00:52:01.050 --> 00:52:03.180 align:middle line:84% Now go back to your visualization 00:52:03.180 --> 00:52:05.750 align:middle line:84% and see if you can figure it out. 00:52:05.750 --> 00:52:08.340 align:middle line:90% 00:52:08.340 --> 00:52:09.680 align:middle line:90% In any of the inner voices. 00:52:09.680 --> 00:52:12.360 align:middle line:90% 00:52:12.360 --> 00:52:15.820 align:middle line:84% Maybe it's easier if you just look at one of the sections. 00:52:15.820 --> 00:52:18.960 align:middle line:84% So you can zoom in a little bit more. 00:52:18.960 --> 00:52:20.440 align:middle line:90% John, do you want to? 00:52:20.440 --> 00:52:22.650 align:middle line:84% AUDIENCE: They move in parallel sections. 00:52:22.650 --> 00:52:24.940 align:middle line:84% MICHAEL CUTHBERT: They move in parallel first, yeah. 00:52:24.940 --> 00:52:25.810 align:middle line:90% That looks good. 00:52:25.810 --> 00:52:29.525 align:middle line:84% And within any given voice, what's it doing? 00:52:29.525 --> 00:52:32.730 align:middle line:90% 00:52:32.730 --> 00:52:35.400 align:middle line:84% Is it playing, "Mary had a little lamb, bop, bop, bop, bop, 00:52:35.400 --> 00:52:35.900 align:middle line:90% bop, bop? 00:52:35.900 --> 00:52:39.280 align:middle line:84% Is it jumping around a huge octave 00:52:39.280 --> 00:52:40.935 align:middle line:90% and then coming back down? 00:52:40.935 --> 00:52:41.435 align:middle line:90% Adam? 00:52:41.435 --> 00:52:42.760 align:middle line:84% AUDIENCE: They're just playing the same note. 00:52:42.760 --> 00:52:44.320 align:middle line:84% MICHAEL CUTHBERT: They're just playing the same note. 00:52:44.320 --> 00:52:46.070 align:middle line:84% Not all of them are playing the same note. 00:52:46.070 --> 00:52:48.491 align:middle line:84% These ones are playing the same note. 00:52:48.491 --> 00:52:53.737 align:middle line:84% But what are the other voices doing, these inner voices? 00:52:53.737 --> 00:52:55.570 align:middle line:84% That go all the way up and then all the way? 00:52:55.570 --> 00:52:55.930 align:middle line:90% Yeah? 00:52:55.930 --> 00:52:57.050 align:middle line:84% AUDIENCE: Are you saying they're repeating? 00:52:57.050 --> 00:52:59.000 align:middle line:84% MICHAEL CUTHBERT: They're repeating, but what do they do? 00:52:59.000 --> 00:53:00.080 align:middle line:90% What's the pattern? 00:53:00.080 --> 00:53:00.610 align:middle line:90% Yeah? 00:53:00.610 --> 00:53:01.370 align:middle line:90% AUDIENCE: Stepwise? 00:53:01.370 --> 00:53:02.170 align:middle line:90% MICHAEL CUTHBERT: Stepwise. 00:53:02.170 --> 00:53:02.670 align:middle line:90% Good. 00:53:02.670 --> 00:53:05.610 align:middle line:84% It's all stepwise, which is the hard part about the piano roll, 00:53:05.610 --> 00:53:06.110 align:middle line:90% right? 00:53:06.110 --> 00:53:09.490 align:middle line:84% You would want a diatonic piano roll at some point. 00:53:09.490 --> 00:53:11.530 align:middle line:90% I think we have that somewhere. 00:53:11.530 --> 00:53:14.210 align:middle line:90% And it's all stepwise. 00:53:14.210 --> 00:53:16.130 align:middle line:90% And it's even more than that. 00:53:16.130 --> 00:53:16.630 align:middle line:90% Yeah? 00:53:16.630 --> 00:53:17.418 align:middle line:90% Go ahead, Vincent. 00:53:17.418 --> 00:53:19.460 align:middle line:84% AUDIENCE: Neighbor tone's around a certain pitch, 00:53:19.460 --> 00:53:21.370 align:middle line:84% just like the top voices around the C. 00:53:21.370 --> 00:53:22.450 align:middle line:84% MICHAEL CUTHBERT: They're all neighbor tones 00:53:22.450 --> 00:53:23.660 align:middle line:90% around a certain pitch, yeah. 00:53:23.660 --> 00:53:25.580 align:middle line:84% So you can-- top one, I can't reach, 00:53:25.580 --> 00:53:28.360 align:middle line:84% so we'll do the middle one, I guess around 00:53:28.360 --> 00:53:33.190 align:middle line:84% E. And is there a pattern that you do three ups and then a 00:53:33.190 --> 00:53:36.290 align:middle line:90% down, and then what is it? 00:53:36.290 --> 00:53:37.880 align:middle line:90% Up, then down. 00:53:37.880 --> 00:53:39.230 align:middle line:90% Up, then down. 00:53:39.230 --> 00:53:40.200 align:middle line:90% Up and down. 00:53:40.200 --> 00:53:44.400 align:middle line:84% So you could almost have a formula with this. 00:53:44.400 --> 00:53:51.390 align:middle line:84% In fact, one of the other Python-based music packages, 00:53:51.390 --> 00:53:55.130 align:middle line:84% which is more about creating algorithmically generatable 00:53:55.130 --> 00:54:00.510 align:middle line:84% music, is called arvo, based on Arvo Part's ability to do this. 00:54:00.510 --> 00:54:03.240 align:middle line:84% So you can download and install arvo, 00:54:03.240 --> 00:54:07.770 align:middle line:84% and it makes it much easier than music21 does to generate. 00:54:07.770 --> 00:54:08.910 align:middle line:90% Here's a motif. 00:54:08.910 --> 00:54:11.300 align:middle line:84% Now spin it out over a certain amount of time while 00:54:11.300 --> 00:54:13.080 align:middle line:90% doing something else. 00:54:13.080 --> 00:54:16.430 align:middle line:84% So we have this thing going up and down and up and down 00:54:16.430 --> 00:54:18.680 align:middle line:90% and things like that. 00:54:18.680 --> 00:54:20.750 align:middle line:84% By the way, some of the other interesting things 00:54:20.750 --> 00:54:23.930 align:middle line:84% about the piece that we're not going to visualize in music21 00:54:23.930 --> 00:54:31.040 align:middle line:84% are, when does it change notes on any multi-syllable, accented 00:54:31.040 --> 00:54:32.930 align:middle line:90% German word? 00:54:32.930 --> 00:54:36.150 align:middle line:84% Which I think is interesting here. 00:54:36.150 --> 00:54:41.580 align:middle line:84% So the accent always gets the whole note. 00:54:41.580 --> 00:54:46.580 align:middle line:84% And it's always the opposite of whatever it was before. 00:54:46.580 --> 00:54:50.270 align:middle line:84% And then you can see, well, in section 2, all 00:54:50.270 --> 00:54:53.480 align:middle line:84% of the voices kind of play at once, and they all rest at once. 00:54:53.480 --> 00:54:56.840 align:middle line:84% But in section 3, the top and the bottom ones 00:54:56.840 --> 00:54:58.710 align:middle line:90% only come in at certain times. 00:54:58.710 --> 00:55:01.830 align:middle line:84% And the visualization of this helped me in figuring out, 00:55:01.830 --> 00:55:03.420 align:middle line:90% well, when are those times? 00:55:03.420 --> 00:55:07.640 align:middle line:84% And it turns out, also very strictly generated, 00:55:07.640 --> 00:55:12.320 align:middle line:84% that it is just every other word. 00:55:12.320 --> 00:55:14.670 align:middle line:90% du Hoffnung, they do. 00:55:14.670 --> 00:55:15.680 align:middle line:90% That's two words. 00:55:15.680 --> 00:55:18.170 align:middle line:90% und Heiland, we don't sing. 00:55:18.170 --> 00:55:19.640 align:middle line:90% Next. 00:55:19.640 --> 00:55:22.460 align:middle line:90% Two words, der völker, we sing. 00:55:22.460 --> 00:55:25.260 align:middle line:90% o komm, we don't. 00:55:25.260 --> 00:55:28.430 align:middle line:90% And there's one exception to it. 00:55:28.430 --> 00:55:30.570 align:middle line:84% No, sorry, there isn't an exception on this one. 00:55:30.570 --> 00:55:32.860 align:middle line:84% Someplace else, there's an exception on things. 00:55:32.860 --> 00:55:36.540 align:middle line:84% But I think probably set up so that just the number of words 00:55:36.540 --> 00:55:39.660 align:middle line:84% makes it so that God stands alone at the end 00:55:39.660 --> 00:55:41.290 align:middle line:90% without accompaniment. 00:55:41.290 --> 00:55:43.360 align:middle line:90% So interesting piece. 00:55:43.360 --> 00:55:48.330 align:middle line:84% Now let's do a tiny bit more analysis on it. 00:55:48.330 --> 00:55:51.210 align:middle line:90% There's a plot that-- 00:55:51.210 --> 00:55:54.180 align:middle line:90% I could call this a cook plot. 00:55:54.180 --> 00:55:58.800 align:middle line:84% Cook, because I saw this now in the reading for Nicholas Cook 00:55:58.800 --> 00:56:03.150 align:middle line:84% article on computational and comparative music-- 00:56:03.150 --> 00:56:05.710 align:middle line:84% computational and comparative musicology. 00:56:05.710 --> 00:56:09.970 align:middle line:84% But I first saw this in a book by somebody named Emily Dolan. 00:56:09.970 --> 00:56:13.530 align:middle line:84% So I call it a Dolan graph, even though-- 00:56:13.530 --> 00:56:17.310 align:middle line:84% and it shows you who is singing where, 00:56:17.310 --> 00:56:20.770 align:middle line:84% at what point, which parts are performing. 00:56:20.770 --> 00:56:24.430 align:middle line:84% And do you remember this from the Cook? 00:56:24.430 --> 00:56:26.040 align:middle line:84% It's slightly different graph that he 00:56:26.040 --> 00:56:30.340 align:middle line:84% had, a slightly different shape, size, but same type of thing. 00:56:30.340 --> 00:56:33.910 align:middle line:90% What's being depicted here? 00:56:33.910 --> 00:56:34.780 align:middle line:90% Take a guess. 00:56:34.780 --> 00:56:35.380 align:middle line:90% What's that? 00:56:35.380 --> 00:56:35.770 align:middle line:90% AUDIENCE: Dynamics? 00:56:35.770 --> 00:56:36.895 align:middle line:90% MICHAEL CUTHBERT: Dynamics. 00:56:36.895 --> 00:56:40.040 align:middle line:84% Yeah, so it's a who's playing when, and what are the dynamics? 00:56:40.040 --> 00:56:41.990 align:middle line:84% And if you zoom in really closely, 00:56:41.990 --> 00:56:44.950 align:middle line:84% you can see that soprano is always singing a tiny bit 00:56:44.950 --> 00:56:46.520 align:middle line:90% before the other parts. 00:56:46.520 --> 00:56:52.030 align:middle line:84% But yeah, so the piece just sort of builds up to about 2/3 point, 00:56:52.030 --> 00:56:56.730 align:middle line:84% then drops off and just very quiet, everything after that. 00:56:56.730 --> 00:56:59.560 align:middle line:90% 00:56:59.560 --> 00:57:02.710 align:middle line:84% So there's quite often, I think, for people 00:57:02.710 --> 00:57:06.800 align:middle line:84% who can read music notation, graphs and plotting, 00:57:06.800 --> 00:57:09.500 align:middle line:84% visualization isn't too much of a help. 00:57:09.500 --> 00:57:13.060 align:middle line:84% But for getting a sense of the form of a large piece 00:57:13.060 --> 00:57:18.490 align:middle line:84% very quickly, these tools can be very, very helpful. 00:57:18.490 --> 00:57:22.340 align:middle line:84% We can see, what notes does he use the most? 00:57:22.340 --> 00:57:25.420 align:middle line:84% Well, obviously those that are going to be-- 00:57:25.420 --> 00:57:29.600 align:middle line:84% that those sustained notes are going to come quite a bit. 00:57:29.600 --> 00:57:35.150 align:middle line:84% But we can see that of the various pitch classes, 00:57:35.150 --> 00:57:42.310 align:middle line:84% basically, there's a reason why it was coming out as A major, 00:57:42.310 --> 00:57:44.890 align:middle line:90% as our analysis. 00:57:44.890 --> 00:57:47.470 align:middle line:90% Because A, definitely winning. 00:57:47.470 --> 00:57:49.030 align:middle line:90% E, C-sharp. 00:57:49.030 --> 00:57:53.080 align:middle line:90% 00:57:53.080 --> 00:57:55.930 align:middle line:84% I guess every-- surprisingly for a piece that 00:57:55.930 --> 00:57:59.030 align:middle line:84% sounds so consonant in many ways, 00:57:59.030 --> 00:58:02.595 align:middle line:84% every pitch class is represented at least once there. 00:58:02.595 --> 00:58:06.130 align:middle line:90% 00:58:06.130 --> 00:58:06.920 align:middle line:90% Let me see which-- 00:58:06.920 --> 00:58:09.640 align:middle line:84% I have a whole bunch of ones that are maybe a little bit less 00:58:09.640 --> 00:58:10.640 align:middle line:90% interesting. 00:58:10.640 --> 00:58:19.090 align:middle line:84% But we can look at certain pitches use 00:58:19.090 --> 00:58:20.380 align:middle line:90% different notes more. 00:58:20.380 --> 00:58:23.330 align:middle line:90% So we can plot a scatter plot. 00:58:23.330 --> 00:58:24.970 align:middle line:84% And then what we haven't seen yet 00:58:24.970 --> 00:58:29.600 align:middle line:84% is the second and third element here 00:58:29.600 --> 00:58:35.693 align:middle line:90% is quarter length versus pitch. 00:58:35.693 --> 00:58:43.700 align:middle line:90% 00:58:43.700 --> 00:58:45.510 align:middle line:84% I think there's other things you can do. 00:58:45.510 --> 00:58:47.370 align:middle line:84% You can play around with octave and stuff. 00:58:47.370 --> 00:58:52.250 align:middle line:84% So a plot gives you a ready-made take in a score 00:58:52.250 --> 00:58:54.930 align:middle line:90% and get some kind of analysis. 00:58:54.930 --> 00:58:57.710 align:middle line:84% There's two slightly lower level things 00:58:57.710 --> 00:59:00.870 align:middle line:84% if you want to-- if you're thinking of doing visualization 00:59:00.870 --> 00:59:01.370 align:middle line:90% in there. 00:59:01.370 --> 00:59:05.120 align:middle line:84% One, the graph, which is underlying the plot, which 00:59:05.120 --> 00:59:10.140 align:middle line:84% is what you're trying to do and what data you want to extract. 00:59:10.140 --> 00:59:12.360 align:middle line:84% So it's a feature extraction again. 00:59:12.360 --> 00:59:14.520 align:middle line:84% And what do you want to put on each axis? 00:59:14.520 --> 00:59:17.120 align:middle line:84% So there's axes that are defined that you can-- 00:59:17.120 --> 00:59:18.920 align:middle line:90% I don't know, we can do-- 00:59:18.920 --> 00:59:24.240 align:middle line:84% let's plot pitch against dynamic. 00:59:24.240 --> 00:59:25.680 align:middle line:90% You know What? 00:59:25.680 --> 00:59:27.850 align:middle line:90% Yeah, dynamics. 00:59:27.850 --> 00:59:28.475 align:middle line:90% Does that work? 00:59:28.475 --> 00:59:36.115 align:middle line:90% 00:59:36.115 --> 00:59:37.690 align:middle line:90% You know what? 00:59:37.690 --> 00:59:40.810 align:middle line:90% Who puts pitch on the x-axis? 00:59:40.810 --> 00:59:45.550 align:middle line:84% We'll put pitch on the y-axis versus dynamics. 00:59:45.550 --> 00:59:48.437 align:middle line:90% Swap that around. 00:59:48.437 --> 00:59:49.895 align:middle line:84% That's why I was having so trouble. 00:59:49.895 --> 00:59:53.520 align:middle line:90% 00:59:53.520 --> 00:59:55.590 align:middle line:90% So you can see that the-- 00:59:55.590 --> 01:00:02.490 align:middle line:84% oops-- that the lowest notes in the pieces only 01:00:02.490 --> 01:00:06.160 align:middle line:90% appear on the quietest things. 01:00:06.160 --> 01:00:12.420 align:middle line:84% And you can also look at this terraced initial motion 01:00:12.420 --> 01:00:18.840 align:middle line:84% of the piece as the notes were going up, both going up in pitch 01:00:18.840 --> 01:00:20.500 align:middle line:90% and getting higher in volume. 01:00:20.500 --> 01:00:23.800 align:middle line:84% And then the very highest volumes 01:00:23.800 --> 01:00:27.070 align:middle line:84% are scattered all throughout, but everything down here 01:00:27.070 --> 01:00:33.130 align:middle line:84% shifted up a little bit, just as we saw. 01:00:33.130 --> 01:00:35.110 align:middle line:84% I think the best thing to do would 01:00:35.110 --> 01:00:36.920 align:middle line:84% be now that we've thought about the piece, 01:00:36.920 --> 01:00:42.160 align:middle line:84% thought about its structure, listen to it one more time. 01:00:42.160 --> 01:00:50.500 align:middle line:84% Maybe with the-- we'll listen to it with the piano roll and see 01:00:50.500 --> 01:00:52.870 align:middle line:90% if we can-- 01:00:52.870 --> 01:00:53.930 align:middle line:90% oops, not that one. 01:00:53.930 --> 01:00:55.930 align:middle line:90% The big one. 01:00:55.930 --> 01:00:59.980 align:middle line:84% And see if we can hear the various parts of the piece 01:00:59.980 --> 01:01:05.050 align:middle line:84% just as well as we could on with the score. 01:01:05.050 --> 01:01:06.533 align:middle line:90% Words are harder to tell. 01:01:06.533 --> 01:01:07.575 align:middle line:90% There's no plot for that. 01:01:07.575 --> 01:01:10.960 align:middle line:90% 01:01:10.960 --> 01:01:12.680 align:middle line:90% You're mostly colorblind. 01:01:12.680 --> 01:01:16.810 align:middle line:84% Professor just realized that I used a version of the plot that 01:01:16.810 --> 01:01:19.460 align:middle line:84% does colors not based on the part 01:01:19.460 --> 01:01:23.960 align:middle line:84% but just as a way of being able to see which pitches are which. 01:01:23.960 --> 01:01:24.950 align:middle line:90% So I apologize. 01:01:24.950 --> 01:01:27.680 align:middle line:84% I made a mistake and said you can tell the lines by color. 01:01:27.680 --> 01:01:32.510 align:middle line:84% But I have to strain to see color, so sorry about that. 01:01:32.510 --> 01:01:36.020 align:middle line:84% But I did, just while listening to it, make one observation. 01:01:36.020 --> 01:01:39.460 align:middle line:84% This interesting line that the E is the very first thing 01:01:39.460 --> 01:01:40.490 align:middle line:90% that you hear. 01:01:40.490 --> 01:01:43.990 align:middle line:84% And it just after a little absence comes back. 01:01:43.990 --> 01:01:46.390 align:middle line:84% And it's one of the few lines that's 01:01:46.390 --> 01:01:49.550 align:middle line:90% so prominent throughout there. 01:01:49.550 --> 01:01:56.530 align:middle line:84% So maybe E is the true root point of this piece. 01:01:56.530 --> 01:02:00.250 align:middle line:84% Well, thanks, everybody, for going through grab bag. 01:02:00.250 --> 01:02:02.450 align:middle line:84% I have more topics that are interest to me, 01:02:02.450 --> 01:02:06.240 align:middle line:84% but anything that's of interest to you, let me know. 01:02:06.240 --> 01:02:21.000 align:middle line:90%