WEBVTT 00:00:00.000 --> 00:00:02.976 align:middle line:90% [SQUEAKING] 00:00:02.976 --> 00:00:04.464 align:middle line:90% [RUSTLING] 00:00:04.464 --> 00:00:05.952 align:middle line:90% [CLICKING] 00:00:05.952 --> 00:00:10.220 align:middle line:90% 00:00:10.220 --> 00:00:13.350 align:middle line:84% MICHAEL CUTHBERT: Let's get started. 00:00:13.350 --> 00:00:14.430 align:middle line:90% We're moving on. 00:00:14.430 --> 00:00:16.590 align:middle line:84% This is week four, so we're on Topic 4. 00:00:16.590 --> 00:00:19.170 align:middle line:84% They're not always going to line up so neatly with a week, 00:00:19.170 --> 00:00:20.960 align:middle line:84% but as long as we can do it, it just makes 00:00:20.960 --> 00:00:22.230 align:middle line:90% the mind a little better. 00:00:22.230 --> 00:00:27.920 align:middle line:84% And week four is about equality, equivalence and intervals. 00:00:27.920 --> 00:00:33.170 align:middle line:84% So first things first, any questions on problem 00:00:33.170 --> 00:00:38.030 align:middle line:84% set three, those who have started working on it? 00:00:38.030 --> 00:00:38.843 align:middle line:90% Yeah, Jake. 00:00:38.843 --> 00:00:40.760 align:middle line:84% AUDIENCE: One of the scores we're going to do, 00:00:40.760 --> 00:00:44.612 align:middle line:84% 10.7, just behaved weird when I was testing. 00:00:44.612 --> 00:00:46.070 align:middle line:84% MICHAEL CUTHBERT: Yeah, anyone else 00:00:46.070 --> 00:00:47.910 align:middle line:90% see anything weird about 10.7? 00:00:47.910 --> 00:00:49.813 align:middle line:90% Did you show the score? 00:00:49.813 --> 00:00:51.230 align:middle line:84% AUDIENCE: Yeah, I showed the score 00:00:51.230 --> 00:00:52.647 align:middle line:84% and I counted the number of notes, 00:00:52.647 --> 00:00:54.752 align:middle line:90% and then I actually used-- 00:00:54.752 --> 00:00:56.210 align:middle line:84% MICHAEL CUTHBERT: Oh, maybe I'm not 00:00:56.210 --> 00:00:59.850 align:middle line:84% thinking of 10.7 then if it didn't immediately-- 00:00:59.850 --> 00:01:02.060 align:middle line:84% AUDIENCE: I got like three times as many notes 00:01:02.060 --> 00:01:04.662 align:middle line:84% when I did score analysis, but it 00:01:04.662 --> 00:01:06.120 align:middle line:84% didn't happen on any of the pieces, 00:01:06.120 --> 00:01:08.460 align:middle line:84% but I actually physically counted them on my hand. 00:01:08.460 --> 00:01:09.710 align:middle line:90% MICHAEL CUTHBERT: Interesting. 00:01:09.710 --> 00:01:11.250 align:middle line:90% I'll have to look at that one. 00:01:11.250 --> 00:01:11.750 align:middle line:90% Yeah. 00:01:11.750 --> 00:01:14.092 align:middle line:84% AUDIENCE: I doesn't show the entire score. 00:01:14.092 --> 00:01:16.550 align:middle line:84% MICHAEL CUTHBERT: Yeah. so it doesn't show the entire score 00:01:16.550 --> 00:01:17.360 align:middle line:90% in Jupyter. 00:01:17.360 --> 00:01:18.950 align:middle line:90% That's a feature. 00:01:18.950 --> 00:01:21.120 align:middle line:90% Thank you for reminding me. 00:01:21.120 --> 00:01:23.863 align:middle line:84% That's a feature in Version 9, which 00:01:23.863 --> 00:01:26.280 align:middle line:84% was supposed to be released before the beginning of class, 00:01:26.280 --> 00:01:28.370 align:middle line:84% but we found bugs in that where you'll 00:01:28.370 --> 00:01:30.330 align:middle line:84% be able to look at the other parts. 00:01:30.330 --> 00:01:33.630 align:middle line:84% Yeah, 10.9 is one of the longer scores. 00:01:33.630 --> 00:01:34.680 align:middle line:90% Thank you, Thank you. 00:01:34.680 --> 00:01:37.280 align:middle line:84% One of the other scores has something a little bit 00:01:37.280 --> 00:01:41.010 align:middle line:84% different, too, about it that's worth looking at. 00:01:41.010 --> 00:01:42.260 align:middle line:90% Cool. 00:01:42.260 --> 00:01:46.190 align:middle line:84% Yeah, so especially if it doesn't 00:01:46.190 --> 00:01:49.940 align:middle line:84% seem to conclude with a nice authentic cadence or something 00:01:49.940 --> 00:01:52.800 align:middle line:90% like that, then probably not. 00:01:52.800 --> 00:01:57.300 align:middle line:84% And actually, for anybody nice, I don't have any prizes. 00:01:57.300 --> 00:01:59.760 align:middle line:84% I didn't bring any candy or anything. 00:01:59.760 --> 00:02:02.030 align:middle line:84% 66.6, the one we're working on, does 00:02:02.030 --> 00:02:06.320 align:middle line:84% it end with an authentic cadence or something else? 00:02:06.320 --> 00:02:08.930 align:middle line:84% That'll be an interesting point when we get around 00:02:08.930 --> 00:02:12.350 align:middle line:84% to automatic Roman numeral analysis, which 00:02:12.350 --> 00:02:14.360 align:middle line:90% we will get to later. 00:02:14.360 --> 00:02:18.303 align:middle line:84% The preview, I think that's piece set seven. 00:02:18.303 --> 00:02:19.470 align:middle line:90% It might be piece set eight. 00:02:19.470 --> 00:02:23.520 align:middle line:84% That's the other one, and I'll give you some notice in advance. 00:02:23.520 --> 00:02:27.080 align:middle line:84% That's the other piece set that takes a little bit more time, 00:02:27.080 --> 00:02:31.880 align:middle line:84% though, that one, you have a group for that. 00:02:31.880 --> 00:02:33.560 align:middle line:90% Great. 00:02:33.560 --> 00:02:37.610 align:middle line:84% I can see most people are doing a very good job of keeping up 00:02:37.610 --> 00:02:39.500 align:middle line:90% with the videos and things. 00:02:39.500 --> 00:02:41.690 align:middle line:84% This weekend, by the way, you won't have any. 00:02:41.690 --> 00:02:44.210 align:middle line:84% You all need a break from that, definitely. 00:02:44.210 --> 00:02:46.200 align:middle line:84% But most people keeping up with videos. 00:02:46.200 --> 00:02:48.210 align:middle line:84% Anything about the sound to score, 00:02:48.210 --> 00:02:50.790 align:middle line:84% the thing I had hoped to get into class, 00:02:50.790 --> 00:02:54.660 align:middle line:84% but that we instead watched me, not blabber live, 00:02:54.660 --> 00:02:56.910 align:middle line:90% but blabber on video? 00:02:56.910 --> 00:02:58.030 align:middle line:90% Anything about that? 00:02:58.030 --> 00:03:00.940 align:middle line:84% There were some really cool other examples. 00:03:00.940 --> 00:03:04.810 align:middle line:84% Anybody want to share theirs on there? 00:03:04.810 --> 00:03:08.680 align:middle line:84% That one I did give sometimes just one to two words feedback. 00:03:08.680 --> 00:03:11.710 align:middle line:84% But what were some of the things that you could use? 00:03:11.710 --> 00:03:13.770 align:middle line:90% What are some of the steps? 00:03:13.770 --> 00:03:21.790 align:middle line:84% Do you remember in going from an audio file, audio to a score? 00:03:21.790 --> 00:03:23.800 align:middle line:84% What were some of the things you needed to do? 00:03:23.800 --> 00:03:24.622 align:middle line:90% Anyone remember? 00:03:24.622 --> 00:03:25.830 align:middle line:90% AUDIENCE: Frequency analysis? 00:03:25.830 --> 00:03:26.400 align:middle line:90% MICHAEL CUTHBERT: What's that? 00:03:26.400 --> 00:03:27.460 align:middle line:90% Frequency analysis. 00:03:27.460 --> 00:03:28.260 align:middle line:90% Good, good. 00:03:28.260 --> 00:03:30.640 align:middle line:84% More toward the end or toward the beginning? 00:03:30.640 --> 00:03:31.200 align:middle line:90% AUDIENCE: Toward the beginning. 00:03:31.200 --> 00:03:31.630 align:middle line:84% MICHAEL CUTHBERT: Toward the beginning. 00:03:31.630 --> 00:03:33.970 align:middle line:84% So somewhere over here with frequency analysis. 00:03:33.970 --> 00:03:35.670 align:middle line:90% Yeah. 00:03:35.670 --> 00:03:37.140 align:middle line:90% Pitch connections. 00:03:37.140 --> 00:03:40.440 align:middle line:90% What did we mean by that? 00:03:40.440 --> 00:03:44.040 align:middle line:84% AUDIENCE: I guess that's technically analyzing the notes 00:03:44.040 --> 00:03:46.507 align:middle line:84% or what notes are being produced in frequency. 00:03:46.507 --> 00:03:48.090 align:middle line:84% MICHAEL CUTHBERT: What notes are being 00:03:48.090 --> 00:03:49.257 align:middle line:90% produced in the frequencies. 00:03:49.257 --> 00:03:52.402 align:middle line:84% Yeah, what's slightly different about frequency? 00:03:52.402 --> 00:03:54.610 align:middle line:84% I think you started to say, oh, that's actually the-- 00:03:54.610 --> 00:03:56.818 align:middle line:84% and then you're like, no, it's not actually the same. 00:03:56.818 --> 00:04:01.750 align:middle line:84% What's the difference between frequency analysis and pitches, 00:04:01.750 --> 00:04:02.720 align:middle line:90% musical pitches? 00:04:02.720 --> 00:04:05.760 align:middle line:90% 00:04:05.760 --> 00:04:07.953 align:middle line:84% And what's the thing we need to do, Misha? 00:04:07.953 --> 00:04:09.870 align:middle line:84% AUDIENCE: I guess, some pitches or notes, they 00:04:09.870 --> 00:04:11.890 align:middle line:84% have multiple frequencies, like overtones. 00:04:11.890 --> 00:04:14.650 align:middle line:84% So we're trying to analyze that and create an instrument loop. 00:04:14.650 --> 00:04:17.649 align:middle line:84% MICHAEL CUTHBERT: Yeah, yeah, when you play a really low note. 00:04:17.649 --> 00:04:19.800 align:middle line:90% [LOW NOTE] 00:04:19.800 --> 00:04:22.260 align:middle line:84% You can hear some of them, especially 00:04:22.260 --> 00:04:26.490 align:middle line:90% if I take one of the notes. 00:04:26.490 --> 00:04:28.320 align:middle line:90% [LOW NOTE] 00:04:28.320 --> 00:04:28.950 align:middle line:90% And you-- 00:04:28.950 --> 00:04:30.600 align:middle line:90% [LOW NOTE] 00:04:30.600 --> 00:04:33.630 align:middle line:84% Get rid of the really low frequencies, you can-- 00:04:33.630 --> 00:04:35.280 align:middle line:90% [LOW NOTE] 00:04:35.280 --> 00:04:37.270 align:middle line:90% Start hearing the thing. 00:04:37.270 --> 00:04:39.120 align:middle line:84% If you ever are writing a piano piece 00:04:39.120 --> 00:04:40.985 align:middle line:84% and you need some bells in the background, 00:04:40.985 --> 00:04:42.110 align:middle line:90% that's always a good trick. 00:04:42.110 --> 00:04:45.930 align:middle line:90% 00:04:45.930 --> 00:04:49.965 align:middle line:84% Not too many composers writing for piano and wanting bells. 00:04:49.965 --> 00:04:51.580 align:middle line:90% So good. 00:04:51.580 --> 00:04:55.320 align:middle line:84% Yeah, so we're taking out the harmonic spectrum 00:04:55.320 --> 00:04:58.690 align:middle line:84% and we're getting the pitches and things from that. 00:04:58.690 --> 00:05:01.775 align:middle line:84% What's the byproduct if we're thinking of nuclear fission? 00:05:01.775 --> 00:05:03.150 align:middle line:84% We have all these energies and we 00:05:03.150 --> 00:05:04.890 align:middle line:84% have this radioactive byproduct, what 00:05:04.890 --> 00:05:08.590 align:middle line:84% did we learn when we strip out the overtones? 00:05:08.590 --> 00:05:12.840 align:middle line:84% What might we be able to learn and get down to the notes 00:05:12.840 --> 00:05:20.850 align:middle line:84% themselves, if you do that with a whole bunch of notes 00:05:20.850 --> 00:05:24.006 align:middle line:84% or a whole bunch of sets of frequencies? 00:05:24.006 --> 00:05:27.990 align:middle line:90% 00:05:27.990 --> 00:05:30.910 align:middle line:84% I think it was already said, but it wasn't super explicit. 00:05:30.910 --> 00:05:34.415 align:middle line:84% The word already appeared in what you said. 00:05:34.415 --> 00:05:45.163 align:middle line:90% 00:05:45.163 --> 00:05:47.140 align:middle line:90% Anyone, take a stab. 00:05:47.140 --> 00:05:49.140 align:middle line:84% What are we talking about when we're talking 00:05:49.140 --> 00:05:51.806 align:middle line:90% about overtones and harmonics? 00:05:51.806 --> 00:05:54.540 align:middle line:90% 00:05:54.540 --> 00:05:55.930 align:middle line:90% Are they always the same? 00:05:55.930 --> 00:05:57.690 align:middle line:90% Yeah, Vanessa. 00:05:57.690 --> 00:06:00.467 align:middle line:84% AUDIENCE: Are you talking about, sometimes you don't necessarily 00:06:00.467 --> 00:06:02.550 align:middle line:84% want to consider overtones when you're considering 00:06:02.550 --> 00:06:04.830 align:middle line:84% the individual pitch, because they're 00:06:04.830 --> 00:06:07.483 align:middle line:84% kind of present for all of the different individual pitches 00:06:07.483 --> 00:06:08.400 align:middle line:90% that you'd be playing. 00:06:08.400 --> 00:06:09.942 align:middle line:84% To So you could when that's something 00:06:09.942 --> 00:06:11.400 align:middle line:84% that you should be paying attention 00:06:11.400 --> 00:06:13.410 align:middle line:84% to, as opposed to if it's in a chord or not. 00:06:13.410 --> 00:06:14.660 align:middle line:90% MICHAEL CUTHBERT: Yeah, super. 00:06:14.660 --> 00:06:17.320 align:middle line:84% So chords definitely an issue, problem. 00:06:17.320 --> 00:06:19.320 align:middle line:90% We'll leave that off. 00:06:19.320 --> 00:06:24.240 align:middle line:84% If I can just follow up, does every D that you analyze, 00:06:24.240 --> 00:06:26.580 align:middle line:84% let's say, D octave four, does it always 00:06:26.580 --> 00:06:27.988 align:middle line:90% have the same overtone spectrum? 00:06:27.988 --> 00:06:28.530 align:middle line:90% AUDIENCE: No. 00:06:28.530 --> 00:06:30.626 align:middle line:84% MICHAEL CUTHBERT: What determines the difference? 00:06:30.626 --> 00:06:34.020 align:middle line:90% 00:06:34.020 --> 00:06:34.720 align:middle line:90% It's OK. 00:06:34.720 --> 00:06:35.970 align:middle line:90% Great, John. 00:06:35.970 --> 00:06:37.170 align:middle line:90% AUDIENCE: The instrument. 00:06:37.170 --> 00:06:37.720 align:middle line:84% MICHAEL CUTHBERT: The instrument. 00:06:37.720 --> 00:06:39.550 align:middle line:90% Yeah, so I said this was there. 00:06:39.550 --> 00:06:42.370 align:middle line:84% So one of the things, while we're going from frequency-- 00:06:42.370 --> 00:06:44.040 align:middle line:84% I should have had something up here 00:06:44.040 --> 00:06:47.810 align:middle line:84% while we're going from frequency to pitches, 00:06:47.810 --> 00:06:54.313 align:middle line:84% the byproduct is determining what instrument is being played. 00:06:54.313 --> 00:06:54.980 align:middle line:90% So we have that. 00:06:54.980 --> 00:06:55.480 align:middle line:90% Good. 00:06:55.480 --> 00:07:01.275 align:middle line:84% What are some other parts of the process that we remember? 00:07:01.275 --> 00:07:03.880 align:middle line:90% 00:07:03.880 --> 00:07:04.660 align:middle line:90% Hannah. 00:07:04.660 --> 00:07:06.050 align:middle line:84% AUDIENCE: The duration and tempo. 00:07:06.050 --> 00:07:07.610 align:middle line:84% MICHAEL CUTHBERT: The duration and tempo. 00:07:07.610 --> 00:07:07.900 align:middle line:90% Great. 00:07:07.900 --> 00:07:09.370 align:middle line:84% Does duration tell you the tempo, 00:07:09.370 --> 00:07:11.060 align:middle line:84% or does tempo tell you-- who votes 00:07:11.060 --> 00:07:13.000 align:middle line:90% duration tells you the tempo? 00:07:13.000 --> 00:07:16.480 align:middle line:84% Who votes tempo tells you the duration? 00:07:16.480 --> 00:07:20.330 align:middle line:84% Who votes, something else, something more complex? 00:07:20.330 --> 00:07:22.880 align:middle line:84% Yeah, you could also have raised your hand on both of them. 00:07:22.880 --> 00:07:25.540 align:middle line:84% There's kind of that weird feedback loop 00:07:25.540 --> 00:07:28.540 align:middle line:84% that you can't tell the tempo unless you 00:07:28.540 --> 00:07:31.450 align:middle line:84% have a whole bunch of durations, but then the tempo 00:07:31.450 --> 00:07:35.150 align:middle line:84% will also tell you something about, is that a quarter note. 00:07:35.150 --> 00:07:36.810 align:middle line:90% So you have second duration. 00:07:36.810 --> 00:07:37.310 align:middle line:90% Good. 00:07:37.310 --> 00:07:40.180 align:middle line:90% Any other parts that stood out? 00:07:40.180 --> 00:07:43.150 align:middle line:90% 00:07:43.150 --> 00:07:45.820 align:middle line:90% What's somebody else's? 00:07:45.820 --> 00:07:48.910 align:middle line:84% People gave great, great examples of something 00:07:48.910 --> 00:07:50.080 align:middle line:90% that you could-- 00:07:50.080 --> 00:07:53.300 align:middle line:84% once you think you have a score, once you're at some part, 00:07:53.300 --> 00:07:56.590 align:middle line:84% you could use something from music theory or history 00:07:56.590 --> 00:07:58.530 align:middle line:90% to bring back. 00:07:58.530 --> 00:08:00.280 align:middle line:84% I'm going to put you on the spot because I 00:08:00.280 --> 00:08:01.880 align:middle line:90% remember yours was very good. 00:08:01.880 --> 00:08:03.255 align:middle line:84% AUDIENCE: I don't remember what-- 00:08:03.255 --> 00:08:05.980 align:middle line:90% MICHAEL CUTHBERT: OK, good. 00:08:05.980 --> 00:08:11.590 align:middle line:84% Y'all do your work early in the weekend, and it's out of mind. 00:08:11.590 --> 00:08:14.290 align:middle line:84% Anyone want to make up something? 00:08:14.290 --> 00:08:17.450 align:middle line:84% I think yours was on articulations, was it not? 00:08:17.450 --> 00:08:19.463 align:middle line:90% Spiccato? 00:08:19.463 --> 00:08:21.130 align:middle line:84% Yeah, that you could find that there's-- 00:08:21.130 --> 00:08:22.503 align:middle line:90% go ahead. 00:08:22.503 --> 00:08:23.920 align:middle line:84% AUDIENCE: Oh, no, I was just going 00:08:23.920 --> 00:08:26.200 align:middle line:84% to say that sometimes you might hear it 00:08:26.200 --> 00:08:28.780 align:middle line:84% as a lot of notes that can be followed by short rests 00:08:28.780 --> 00:08:30.340 align:middle line:90% and notated that way. 00:08:30.340 --> 00:08:32.690 align:middle line:84% But then based on the piece or style, 00:08:32.690 --> 00:08:34.840 align:middle line:84% you might go back and mark it as spiccato. 00:08:34.840 --> 00:08:38.409 align:middle line:84% MICHAEL CUTHBERT: Yeah, based on having a whole bunch of notes 00:08:38.409 --> 00:08:41.450 align:middle line:84% that always have this large amount of rests, 00:08:41.450 --> 00:08:43.890 align:middle line:84% you might say it's spiccato, or staccato, or something 00:08:43.890 --> 00:08:45.890 align:middle line:84% where the notes are all running into each other. 00:08:45.890 --> 00:08:47.420 align:middle line:90% You might say this is legato. 00:08:47.420 --> 00:08:49.520 align:middle line:90% You might get out slurs, things. 00:08:49.520 --> 00:08:50.020 align:middle line:90% Good. 00:08:50.020 --> 00:08:54.400 align:middle line:84% Anybody else either remember theirs or something else 00:08:54.400 --> 00:08:55.125 align:middle line:90% come to mind? 00:08:55.125 --> 00:09:00.670 align:middle line:90% 00:09:00.670 --> 00:09:02.110 align:middle line:90% I'm trying to remember. 00:09:02.110 --> 00:09:06.970 align:middle line:84% There were at least three that I've never seen, that I never 00:09:06.970 --> 00:09:08.920 align:middle line:84% thought of that I was like, wow, and then 00:09:08.920 --> 00:09:10.510 align:middle line:84% about seven more that I'm like, we're 00:09:10.510 --> 00:09:15.400 align:middle line:84% on the same wavelength with each other. 00:09:15.400 --> 00:09:18.350 align:middle line:84% OK, I'll come back to that later. 00:09:18.350 --> 00:09:21.220 align:middle line:84% One of the things you'll find, the end of problem 00:09:21.220 --> 00:09:24.920 align:middle line:84% set three asks you to write your own question. 00:09:24.920 --> 00:09:27.340 align:middle line:84% It asks you, hey, if you had a whole bunch of chorales 00:09:27.340 --> 00:09:30.910 align:middle line:84% and based on the tools you have for statistical analysis, what 00:09:30.910 --> 00:09:33.440 align:middle line:84% kinds of questions you could ask. 00:09:33.440 --> 00:09:36.580 align:middle line:84% And it doesn't ask you to answer that, 00:09:36.580 --> 00:09:41.000 align:middle line:84% but you're going to find that as the semester goes on, 00:09:41.000 --> 00:09:44.230 align:middle line:84% those become bigger and bigger parts of the problem sets, 00:09:44.230 --> 00:09:45.710 align:middle line:90% taking more time. 00:09:45.710 --> 00:09:48.130 align:middle line:84% You'll be asked to pose your own question 00:09:48.130 --> 00:09:52.610 align:middle line:84% and answer them, and both the quality of the answer, 00:09:52.610 --> 00:09:56.560 align:middle line:84% but also, the interest of the question 00:09:56.560 --> 00:09:58.130 align:middle line:90% becomes really important. 00:09:58.130 --> 00:09:59.570 align:middle line:90% And why is that important? 00:09:59.570 --> 00:10:02.380 align:middle line:84% What are we going to do at the end of the semester? 00:10:02.380 --> 00:10:05.536 align:middle line:84% We're going to pose our own question and try to solve it. 00:10:05.536 --> 00:10:10.510 align:middle line:84% And what do researchers do in the world for the most part? 00:10:10.510 --> 00:10:12.040 align:middle line:84% They pose an interesting question, 00:10:12.040 --> 00:10:12.950 align:middle line:90% and they try to solve it. 00:10:12.950 --> 00:10:14.408 align:middle line:84% So we're going to try to make it so 00:10:14.408 --> 00:10:18.490 align:middle line:84% that by the end of the semester, you're not just students who 00:10:18.490 --> 00:10:20.290 align:middle line:84% are given an assignment to do, but also 00:10:20.290 --> 00:10:22.430 align:middle line:90% posing your own questions. 00:10:22.430 --> 00:10:25.000 align:middle line:84% And so you'll probably get sick of the fact 00:10:25.000 --> 00:10:28.180 align:middle line:84% that I'm asking you to document, write docstrings, 00:10:28.180 --> 00:10:30.560 align:middle line:84% and all that stuff in your problem sets now. 00:10:30.560 --> 00:10:32.860 align:middle line:84% And at first, it's pretty silly because I'm asking you 00:10:32.860 --> 00:10:36.580 align:middle line:90% specifically to do one task. 00:10:36.580 --> 00:10:42.330 align:middle line:84% But then as it goes on, the more and more complex problems, 00:10:42.330 --> 00:10:44.700 align:middle line:84% you're going to be making your own subproblems. 00:10:44.700 --> 00:10:47.180 align:middle line:84% P set four is the first one where 00:10:47.180 --> 00:10:50.840 align:middle line:84% I suggest that you might write some helper functions that 00:10:50.840 --> 00:10:51.990 align:middle line:90% won't be graded. 00:10:51.990 --> 00:10:53.690 align:middle line:84% It'll be the first time where I think 00:10:53.690 --> 00:10:55.370 align:middle line:84% you probably shouldn't try to solve 00:10:55.370 --> 00:10:58.550 align:middle line:90% everything right in the answer. 00:10:58.550 --> 00:11:00.770 align:middle line:84% And so that's a good time to practice 00:11:00.770 --> 00:11:04.400 align:middle line:90% doing that type of thing. 00:11:04.400 --> 00:11:10.610 align:middle line:84% Anything else before moving on to the third little topic 00:11:10.610 --> 00:11:14.810 align:middle line:84% from the weekend discussion, musicxml? 00:11:14.810 --> 00:11:17.220 align:middle line:90% Any thoughts? 00:11:17.220 --> 00:11:19.880 align:middle line:84% Anybody watch the interview with Michael Good 00:11:19.880 --> 00:11:23.830 align:middle line:84% and take away anything you want to share with us? 00:11:23.830 --> 00:11:29.180 align:middle line:90% 00:11:29.180 --> 00:11:33.900 align:middle line:84% He's going to drop into this class in a couple weeks, 00:11:33.900 --> 00:11:34.740 align:middle line:90% I think. 00:11:34.740 --> 00:11:37.470 align:middle line:90% He's visiting campus. 00:11:37.470 --> 00:11:38.860 align:middle line:90% Yeah, go ahead. 00:11:38.860 --> 00:11:40.970 align:middle line:84% AUDIENCE: I had one thing that I kind of took away 00:11:40.970 --> 00:11:41.595 align:middle line:90% from the video. 00:11:41.595 --> 00:11:46.160 align:middle line:84% It was just how much effort goes into creating something and then 00:11:46.160 --> 00:11:47.330 align:middle line:90% trying to-- 00:11:47.330 --> 00:11:50.090 align:middle line:84% in order to ensure its like survivability 00:11:50.090 --> 00:11:52.010 align:middle line:84% into the future, how much of your own effort 00:11:52.010 --> 00:11:53.870 align:middle line:84% has to go into advocating for something 00:11:53.870 --> 00:11:55.132 align:middle line:90% when there is nothing to show. 00:11:55.132 --> 00:11:56.340 align:middle line:90% MICHAEL CUTHBERT: Yeah, yeah. 00:11:56.340 --> 00:11:58.550 align:middle line:84% So he did this huge-- he said, well, I 00:11:58.550 --> 00:12:01.710 align:middle line:84% came up with this format, and then I had to market it. 00:12:01.710 --> 00:12:05.130 align:middle line:84% And I don't know if everybody knows Finale and Sibelius. 00:12:05.130 --> 00:12:07.610 align:middle line:84% Some of you all know MuseScore, and Noteflight, and things. 00:12:07.610 --> 00:12:10.770 align:middle line:84% Flat might be the things now as much. 00:12:10.770 --> 00:12:14.310 align:middle line:84% But yeah, but those were the two big leaders, 00:12:14.310 --> 00:12:16.850 align:middle line:84% and he just felt like if he couldn't get one of them 00:12:16.850 --> 00:12:19.890 align:middle line:84% to use his product, he might as well not have made it. 00:12:19.890 --> 00:12:24.140 align:middle line:84% And then just going around trying to make more, and more, 00:12:24.140 --> 00:12:27.290 align:middle line:84% and more things out of it, and it's 00:12:27.290 --> 00:12:30.590 align:middle line:90% been a super successful legacy. 00:12:30.590 --> 00:12:36.770 align:middle line:84% Michael Good finally retired from running the a musicxml spec 00:12:36.770 --> 00:12:39.840 align:middle line:84% from taking charge, and making sure it was all working. 00:12:39.840 --> 00:12:41.330 align:middle line:90% After doing that for-- 00:12:41.330 --> 00:12:42.882 align:middle line:90% what was it? 00:12:42.882 --> 00:12:45.410 align:middle line:90% 24 years of doing it. 00:12:45.410 --> 00:12:50.720 align:middle line:84% But he finally found some poor schmuck to take on that role 00:12:50.720 --> 00:12:53.965 align:middle line:84% and agree to do it for the next couple of years. 00:12:53.965 --> 00:12:55.340 align:middle line:84% He also mentions in there there's 00:12:55.340 --> 00:12:58.970 align:middle line:84% something called MNX, which is interesting 00:12:58.970 --> 00:13:03.060 align:middle line:84% that it's really beginning to pick up some steam. 00:13:03.060 --> 00:13:07.410 align:middle line:84% And so what musicxml was primarily about, if you recall, 00:13:07.410 --> 00:13:12.380 align:middle line:84% it was about, you have data in one application and you 00:13:12.380 --> 00:13:14.310 align:middle line:84% want to get data in some other application, 00:13:14.310 --> 00:13:17.540 align:middle line:84% and you don't want to convert it down to MIDI and loose spelling 00:13:17.540 --> 00:13:20.990 align:middle line:84% and lose all the things about tempo estimation, 00:13:20.990 --> 00:13:24.830 align:middle line:84% and beat, and staccatos, and all these other things. 00:13:24.830 --> 00:13:28.740 align:middle line:84% You want to transfer over into musicxml, was really great, 00:13:28.740 --> 00:13:31.410 align:middle line:84% is really great for transferring documents. 00:13:31.410 --> 00:13:34.410 align:middle line:84% But once you get it into your application, 00:13:34.410 --> 00:13:37.970 align:middle line:84% almost every application you use has some of internal memory 00:13:37.970 --> 00:13:39.030 align:middle line:90% representation. 00:13:39.030 --> 00:13:41.940 align:middle line:84% You've coded things that you store. 00:13:41.940 --> 00:13:44.962 align:middle line:84% I'm going to store the name here as a string. 00:13:44.962 --> 00:13:46.670 align:middle line:84% And somebody else's, well, I'm storing it 00:13:46.670 --> 00:13:49.050 align:middle line:84% as an array of characters so I can manipulate it. 00:13:49.050 --> 00:13:52.590 align:middle line:84% Whatever it is, everybody has a different representation. 00:13:52.590 --> 00:13:55.938 align:middle line:84% And musicxml was not good for that. 00:13:55.938 --> 00:13:57.480 align:middle line:84% That wasn't what it was designed for. 00:13:57.480 --> 00:13:59.990 align:middle line:84% But now more and more people want that, 00:13:59.990 --> 00:14:00.990 align:middle line:90% and they want something. 00:14:00.990 --> 00:14:05.490 align:middle line:84% And so MNX, something like music notation next or something. 00:14:05.490 --> 00:14:07.740 align:middle line:84% The X doesn't really mean anything. 00:14:07.740 --> 00:14:11.490 align:middle line:84% The next format was coming out, and the encoding format, 00:14:11.490 --> 00:14:16.190 align:middle line:84% the final decision on that it's going to be entirely JSON based. 00:14:16.190 --> 00:14:18.110 align:middle line:90% Who has heard of JSON? 00:14:18.110 --> 00:14:20.970 align:middle line:90% Who has not? 00:14:20.970 --> 00:14:24.920 align:middle line:84% Yeah, so it's the data format, interchange format originally 00:14:24.920 --> 00:14:25.950 align:middle line:90% for JavaScript. 00:14:25.950 --> 00:14:30.050 align:middle line:84% That's what the J, JS stands for, but now used 00:14:30.050 --> 00:14:33.450 align:middle line:90% by in almost every language. 00:14:33.450 --> 00:14:37.380 align:middle line:84% It's where XML was 20 years ago, that this is 00:14:37.380 --> 00:14:38.800 align:middle line:90% the thing that everybody knows. 00:14:38.800 --> 00:14:40.240 align:middle line:90% That's the thing now. 00:14:40.240 --> 00:14:44.530 align:middle line:84% And so trying to figure out exactly how it's going to work. 00:14:44.530 --> 00:14:48.600 align:middle line:84% But this is pretty exciting things 00:14:48.600 --> 00:14:52.800 align:middle line:84% that the next 20, 25 years, 30 years of music notation 00:14:52.800 --> 00:14:58.110 align:middle line:90% was finally decided yesterday. 00:14:58.110 --> 00:15:01.150 align:middle line:90% So that's pretty good. 00:15:01.150 --> 00:15:03.190 align:middle line:84% It's an exciting, exciting world. 00:15:03.190 --> 00:15:07.080 align:middle line:84% And if you get very into notation and representation 00:15:07.080 --> 00:15:10.440 align:middle line:84% and things, you can jump onto the GitHub repository 00:15:10.440 --> 00:15:14.490 align:middle line:84% and start saying, no, if you represent 00:15:14.490 --> 00:15:18.000 align:middle line:84% accordion symbols in this way, it 00:15:18.000 --> 00:15:20.710 align:middle line:84% will never be useful for what I like to do with accordion. 00:15:20.710 --> 00:15:22.210 align:middle line:84% It doesn't have to be that esoteric. 00:15:22.210 --> 00:15:24.190 align:middle line:90% It could even be on octaves. 00:15:24.190 --> 00:15:28.200 align:middle line:84% The question is, we all like writing things 00:15:28.200 --> 00:15:34.840 align:middle line:84% like pitch C4, something like that. 00:15:34.840 --> 00:15:47.640 align:middle line:84% But, boy, should it be, like, name C and octave four? 00:15:47.640 --> 00:15:49.800 align:middle line:84% And therefore, you have one less thing 00:15:49.800 --> 00:15:54.070 align:middle line:84% that you have to convert from a string to an int there. 00:15:54.070 --> 00:16:00.300 align:middle line:84% And so that your program won't crash on octave negative two or 00:16:00.300 --> 00:16:02.370 align:middle line:84% whatever happens, octave 10, all the things 00:16:02.370 --> 00:16:05.310 align:middle line:90% that we always forget to do. 00:16:05.310 --> 00:16:07.440 align:middle line:84% So anyhow, that's what's been happening 00:16:07.440 --> 00:16:09.690 align:middle line:90% a little bit in the world. 00:16:09.690 --> 00:16:14.070 align:middle line:84% OK, let's get to the main topics today. 00:16:14.070 --> 00:16:16.630 align:middle line:84% Let's start with the concept of equality. 00:16:16.630 --> 00:16:20.220 align:middle line:84% What does it mean for something in music 00:16:20.220 --> 00:16:22.180 align:middle line:90% to be equal to something else? 00:16:22.180 --> 00:16:22.930 align:middle line:90% What does it mean? 00:16:22.930 --> 00:16:27.081 align:middle line:84% What does it mean for two notes to be equal? 00:16:27.081 --> 00:16:28.431 align:middle line:90% We're a little bit less-- 00:16:28.431 --> 00:16:31.450 align:middle line:90% 00:16:31.450 --> 00:16:35.120 align:middle line:84% I don't know-- vigorous today than we have in the past, 00:16:35.120 --> 00:16:37.960 align:middle line:84% so I'm going to call on some people, 00:16:37.960 --> 00:16:43.480 align:middle line:84% just because there's not really a right, wrong answer on this. 00:16:43.480 --> 00:16:45.530 align:middle line:84% The first person I'm going to call on is Jason. 00:16:45.530 --> 00:16:47.715 align:middle line:90% Then I'm going to call on-- 00:16:47.715 --> 00:16:50.800 align:middle line:90% 00:16:50.800 --> 00:16:56.380 align:middle line:84% then I'll call on Hannah, then Paul. 00:16:56.380 --> 00:17:01.400 align:middle line:84% So what would you say means for two notes to be equal? 00:17:01.400 --> 00:17:02.920 align:middle line:84% AUDIENCE: I guess abstractly, maybe 00:17:02.920 --> 00:17:04.337 align:middle line:84% just that the pitches are the same 00:17:04.337 --> 00:17:05.750 align:middle line:90% and the durations are the same. 00:17:05.750 --> 00:17:07.670 align:middle line:84% MICHAEL CUTHBERT: OK, so pitches are the same. 00:17:07.670 --> 00:17:10.270 align:middle line:84% AUDIENCE: At least for single notes. 00:17:10.270 --> 00:17:12.490 align:middle line:90% MICHAEL CUTHBERT: Pitch, same. 00:17:12.490 --> 00:17:15.075 align:middle line:90% Duration, the same. 00:17:15.075 --> 00:17:19.329 align:middle line:90% 00:17:19.329 --> 00:17:21.105 align:middle line:84% What do we mean by pitches, the same? 00:17:21.105 --> 00:17:24.400 align:middle line:90% 00:17:24.400 --> 00:17:27.930 align:middle line:84% AUDIENCE: Abstractly, mostly, if you really 00:17:27.930 --> 00:17:30.790 align:middle line:84% want to compare the frequencies, like the overtones and stuff, 00:17:30.790 --> 00:17:32.440 align:middle line:90% that might cause some issues. 00:17:32.440 --> 00:17:37.830 align:middle line:84% So I guess abstractly, just maybe going down 00:17:37.830 --> 00:17:43.663 align:middle line:84% to MIDI is a little too simple, but just name and accidentals. 00:17:43.663 --> 00:17:44.830 align:middle line:90% MICHAEL CUTHBERT: OK, great. 00:17:44.830 --> 00:17:49.180 align:middle line:84% The name and accidental are the same. 00:17:49.180 --> 00:17:51.040 align:middle line:90% This is a very good definition. 00:17:51.040 --> 00:17:54.540 align:middle line:84% So we could completely go with that. 00:17:54.540 --> 00:17:58.690 align:middle line:84% And do you want to change anything, go with it? 00:17:58.690 --> 00:18:00.940 align:middle line:84% AUDIENCE: I was going to say something really similar. 00:18:00.940 --> 00:18:03.570 align:middle line:84% Probably also consider the octave. 00:18:03.570 --> 00:18:07.505 align:middle line:84% MICHAEL CUTHBERT: So octave has to be the same. 00:18:07.505 --> 00:18:17.550 align:middle line:90% 00:18:17.550 --> 00:18:19.210 align:middle line:90% Anybody else want to jump in? 00:18:19.210 --> 00:18:20.447 align:middle line:90% Do you want to? 00:18:20.447 --> 00:18:22.530 align:middle line:84% AUDIENCE: I wouldn't say that the accidentals have 00:18:22.530 --> 00:18:23.180 align:middle line:90% to be the same. 00:18:23.180 --> 00:18:25.680 align:middle line:84% MICHAEL CUTHBERT: You wouldn't say that the accidentals have 00:18:25.680 --> 00:18:26.560 align:middle line:90% to be the same. 00:18:26.560 --> 00:18:30.910 align:middle line:84% So give me an example of something 00:18:30.910 --> 00:18:32.743 align:middle line:90% that would be the same without. 00:18:32.743 --> 00:18:40.660 align:middle line:90% 00:18:40.660 --> 00:18:42.280 align:middle line:90% AUDIENCE: D-flat 00:18:42.280 --> 00:18:46.610 align:middle line:84% MICHAEL CUTHBERT: D-flat and C-sharp. 00:18:46.610 --> 00:18:47.710 align:middle line:90% Great. 00:18:47.710 --> 00:18:51.980 align:middle line:84% So in this case, not only is the accidental different. 00:18:51.980 --> 00:18:53.500 align:middle line:90% What else is different? 00:18:53.500 --> 00:18:54.380 align:middle line:90% The name. 00:18:54.380 --> 00:18:54.880 align:middle line:90% Good. 00:18:54.880 --> 00:18:57.630 align:middle line:84% So what can we put instead for that? 00:18:57.630 --> 00:19:04.030 align:middle line:90% 00:19:04.030 --> 00:19:08.553 align:middle line:84% What's a representation that allows these to be equal? 00:19:08.553 --> 00:19:13.480 align:middle line:90% 00:19:13.480 --> 00:19:15.910 align:middle line:84% AUDIENCE: The request in the [INAUDIBLE]. 00:19:15.910 --> 00:19:17.935 align:middle line:84% MICHAEL CUTHBERT: The pitch class 00:19:17.935 --> 00:19:19.310 align:middle line:84% is what you might be thinking of. 00:19:19.310 --> 00:19:24.830 align:middle line:84% Yeah, pitch class, or pitch class plus octave. 00:19:24.830 --> 00:19:28.670 align:middle line:84% What's another thing that encodes pitch class plus octave? 00:19:28.670 --> 00:19:31.910 align:middle line:84% I've heard this four letter acronym used a couple of times. 00:19:31.910 --> 00:19:32.872 align:middle line:90% John? 00:19:32.872 --> 00:19:34.330 align:middle line:84% AUDIENCE: I was going to say space, 00:19:34.330 --> 00:19:35.720 align:middle line:90% but it's not four letters. 00:19:35.720 --> 00:19:36.400 align:middle line:84% MICHAEL CUTHBERT: It's not four letters. 00:19:36.400 --> 00:19:37.400 align:middle line:90% Space is good. 00:19:37.400 --> 00:19:37.900 align:middle line:90% Yeah, Adam. 00:19:37.900 --> 00:19:38.290 align:middle line:90% AUDIENCE: MIDI. 00:19:38.290 --> 00:19:39.248 align:middle line:90% MICHAEL CUTHBERT: MIDI. 00:19:39.248 --> 00:19:41.680 align:middle line:90% So it's MIDI number. 00:19:41.680 --> 00:19:42.190 align:middle line:90% Good. 00:19:42.190 --> 00:19:44.160 align:middle line:90% So we could do this. 00:19:44.160 --> 00:19:47.050 align:middle line:90% 00:19:47.050 --> 00:19:54.370 align:middle line:84% So when you turn in your homework for your tonal harmony 00:19:54.370 --> 00:20:03.270 align:middle line:84% class, and it says F major, 5 to 1, write this, and you put in-- 00:20:03.270 --> 00:20:16.780 align:middle line:90% 00:20:16.780 --> 00:20:19.450 align:middle line:84% and you get it wrong, marked wrong 00:20:19.450 --> 00:20:23.900 align:middle line:84% by your teacher that wasn't 5 to 1, I think I got-- no. 00:20:23.900 --> 00:20:25.930 align:middle line:84% Well, that wouldn't be 5 to 1 anyhow. 00:20:25.930 --> 00:20:27.235 align:middle line:90% That's what I'm looking for. 00:20:27.235 --> 00:20:31.975 align:middle line:90% 00:20:31.975 --> 00:20:36.530 align:middle line:84% Do all of these notes have the same MIDI number as this? 00:20:36.530 --> 00:20:37.990 align:middle line:90% Yeah. 00:20:37.990 --> 00:20:38.840 align:middle line:90% Good. 00:20:38.840 --> 00:20:43.520 align:middle line:84% So maybe we don't want to go with that, 00:20:43.520 --> 00:20:47.422 align:middle line:84% because there's a place where your teacher says it's wrong. 00:20:47.422 --> 00:20:49.300 align:middle line:84% On the other hand, what are the consequences 00:20:49.300 --> 00:20:52.840 align:middle line:84% of that, of not saying that MIDI? 00:20:52.840 --> 00:20:55.572 align:middle line:90% Are these two notes the same? 00:20:55.572 --> 00:20:57.730 align:middle line:90% [MUSICAL NOTES] 00:20:57.730 --> 00:21:00.430 align:middle line:84% Of course, when I do this, it's always a trick question. 00:21:00.430 --> 00:21:03.670 align:middle line:84% What do you think the answer should be? 00:21:03.670 --> 00:21:06.162 align:middle line:84% Yes, but we already said we're not 00:21:06.162 --> 00:21:07.370 align:middle line:90% going to count that the same. 00:21:07.370 --> 00:21:09.530 align:middle line:90% And I played a C and a B sharp. 00:21:09.530 --> 00:21:11.390 align:middle line:84% You all you all knew that, right? 00:21:11.390 --> 00:21:14.150 align:middle line:84% I conceptually flipped the n harmonic between the two. 00:21:14.150 --> 00:21:19.880 align:middle line:84% So we've worked ourselves into a real bind. 00:21:19.880 --> 00:21:21.770 align:middle line:84% I think this is a useful exercise, 00:21:21.770 --> 00:21:28.990 align:middle line:84% but the answer really comes with, we don't really, really 00:21:28.990 --> 00:21:29.690 align:middle line:90% know. 00:21:29.690 --> 00:21:32.620 align:middle line:84% And we can define different cases 00:21:32.620 --> 00:21:35.740 align:middle line:84% where we use the words-- we don't use the word equal 00:21:35.740 --> 00:21:38.130 align:middle line:84% too much, but let's say the same, the same. 00:21:38.130 --> 00:21:40.960 align:middle line:90% 00:21:40.960 --> 00:21:42.520 align:middle line:90% Yeah, go ahead. 00:21:42.520 --> 00:21:44.410 align:middle line:84% AUDIENCE: I had a good question about what 00:21:44.410 --> 00:21:48.940 align:middle line:84% cases would the details of the meaning of musical equality 00:21:48.940 --> 00:21:50.250 align:middle line:90% really matter? 00:21:50.250 --> 00:21:51.250 align:middle line:90% MICHAEL CUTHBERT: Great. 00:21:51.250 --> 00:21:52.958 align:middle line:84% We're about we're about to get into that. 00:21:52.958 --> 00:21:53.930 align:middle line:90% What cases? 00:21:53.930 --> 00:21:58.270 align:middle line:84% Let's we'll open that up as a topic to think about there. 00:21:58.270 --> 00:22:00.670 align:middle line:84% I have some in my head, and it's going 00:22:00.670 --> 00:22:04.010 align:middle line:84% to be-- you're one slide ahead of me. 00:22:04.010 --> 00:22:11.696 align:middle line:84% But maybe everybody sing this with me. 00:22:11.696 --> 00:22:15.119 align:middle line:90% [MUSICAL NOTES] 00:22:15.119 --> 00:22:16.100 align:middle line:90% 00:22:16.100 --> 00:22:19.355 align:middle line:90% [SINGING] 00:22:19.355 --> 00:22:21.260 align:middle line:90% 00:22:21.260 --> 00:22:28.640 align:middle line:84% Well, the man sang with me, but the woman didn't, unless we have 00:22:28.640 --> 00:22:32.020 align:middle line:84% a saying, "sing this" doesn't include the octave. 00:22:32.020 --> 00:22:35.948 align:middle line:90% 00:22:35.948 --> 00:22:41.450 align:middle line:84% But also, we can think of a lot of different things 00:22:41.450 --> 00:22:44.900 align:middle line:84% that might be slightly different with each other. 00:22:44.900 --> 00:22:49.250 align:middle line:84% We can also say that here are two notes. 00:22:49.250 --> 00:22:51.590 align:middle line:90% Bom, bom. 00:22:51.590 --> 00:22:53.060 align:middle line:90% Are they the same? 00:22:53.060 --> 00:22:55.450 align:middle line:84% Yeah, in some ways, but also, no. 00:22:55.450 --> 00:22:56.700 align:middle line:90% The first one was on beat one. 00:22:56.700 --> 00:22:58.500 align:middle line:90% The second one was on beat two. 00:22:58.500 --> 00:23:01.670 align:middle line:84% There might be cases where we want to not just consider 00:23:01.670 --> 00:23:03.590 align:middle line:84% the duration, which we didn't even talk about, 00:23:03.590 --> 00:23:07.070 align:middle line:84% because I already began this semester with the trick question 00:23:07.070 --> 00:23:08.360 align:middle line:90% of how many notes. 00:23:08.360 --> 00:23:09.570 align:middle line:90% Do we remember that? 00:23:09.570 --> 00:23:10.350 align:middle line:90% Good, good. 00:23:10.350 --> 00:23:13.333 align:middle line:84% I'm starting to see smiles and things and not just scared, 00:23:13.333 --> 00:23:14.250 align:middle line:90% he's going to call me. 00:23:14.250 --> 00:23:15.330 align:middle line:90% But yeah. 00:23:15.330 --> 00:23:18.890 align:middle line:84% But not only duration, but we might also 00:23:18.890 --> 00:23:23.270 align:middle line:84% consider what beat it's on, that we might not 00:23:23.270 --> 00:23:27.320 align:middle line:90% say that to be the same. 00:23:27.320 --> 00:23:30.140 align:middle line:84% So there might be different cases like that. 00:23:30.140 --> 00:23:32.970 align:middle line:84% Here's an example from one of these. 00:23:32.970 --> 00:23:33.602 align:middle line:90% Oops. 00:23:33.602 --> 00:23:35.060 align:middle line:84% Well, it's even more complex than I 00:23:35.060 --> 00:23:37.940 align:middle line:90% expected it to be without that. 00:23:37.940 --> 00:23:38.450 align:middle line:90% Great. 00:23:38.450 --> 00:23:43.130 align:middle line:84% Who is my designated "tell professor when he's projecting 00:23:43.130 --> 00:23:44.378 align:middle line:90% without projecting"? 00:23:44.378 --> 00:23:45.420 align:middle line:90% That's all of you, right? 00:23:45.420 --> 00:23:48.510 align:middle line:84% You'll all you'll all take it on yourselves to say and save time. 00:23:48.510 --> 00:23:49.220 align:middle line:90% Good. 00:23:49.220 --> 00:23:52.340 align:middle line:84% So this is one of these weird experimental pieces from 00:23:52.340 --> 00:23:56.630 align:middle line:84% the '60s and '70s and things called Burdocks by a composer 00:23:56.630 --> 00:23:59.460 align:middle line:84% who's a Dartmouth professor of philosophy, actually, 00:23:59.460 --> 00:24:03.330 align:middle line:84% Christian Wolff, a friend of John Cage's. 00:24:03.330 --> 00:24:04.980 align:middle line:90% And this is typical things. 00:24:04.980 --> 00:24:06.480 align:middle line:84% It's in a whole bunch of movements. 00:24:06.480 --> 00:24:13.070 align:middle line:84% But very famously, for me, is the opposite of equal, 00:24:13.070 --> 00:24:16.590 align:middle line:84% is the instructions for number three. 00:24:16.590 --> 00:24:21.630 align:middle line:84% Each player is to make about 400, 511 sounds. 00:24:21.630 --> 00:24:23.940 align:middle line:84% Each sound different in some way. 00:24:23.940 --> 00:24:28.490 align:middle line:84% And I remember talking with Professor Wolff. 00:24:28.490 --> 00:24:31.678 align:middle line:84% He was a guest speaker in one of my composition classes once, 00:24:31.678 --> 00:24:33.470 align:middle line:84% and he was talking about the interpretation 00:24:33.470 --> 00:24:36.990 align:middle line:84% that this movement ended up being one of his favorite ones, 00:24:36.990 --> 00:24:40.460 align:middle line:84% watching it performed to see what people did. 00:24:40.460 --> 00:24:46.250 align:middle line:84% And in one case, a player had a bucket, 00:24:46.250 --> 00:24:48.590 align:middle line:84% and then had another bucket filled with water, 00:24:48.590 --> 00:24:52.100 align:middle line:84% and took an eyedropper, and dropped one drip of water 00:24:52.100 --> 00:24:54.030 align:middle line:84% into the other bucket, and hit it, 00:24:54.030 --> 00:24:56.052 align:middle line:84% dropped one, hit it, dropped one, 00:24:56.052 --> 00:24:57.510 align:middle line:84% because the frequency would change. 00:24:57.510 --> 00:24:59.730 align:middle line:90% And after 511, it changed a lot. 00:24:59.730 --> 00:25:01.430 align:middle line:90% And so he thought-- 00:25:01.430 --> 00:25:03.560 align:middle line:84% the composer was saying, oh, I thought 00:25:03.560 --> 00:25:04.680 align:middle line:90% this was very interesting. 00:25:04.680 --> 00:25:06.450 align:middle line:84% And other people did all kinds of things. 00:25:06.450 --> 00:25:09.890 align:middle line:84% But as you can imagine, you get your piece 00:25:09.890 --> 00:25:11.762 align:middle line:90% played with a larger ensemble. 00:25:11.762 --> 00:25:14.220 align:middle line:84% And some people are really, really into this kind of music. 00:25:14.220 --> 00:25:15.270 align:middle line:90% I can find it. 00:25:15.270 --> 00:25:17.488 align:middle line:84% If you've never performed a piece like this, 00:25:17.488 --> 00:25:18.780 align:middle line:90% don't knock it till you try it. 00:25:18.780 --> 00:25:20.907 align:middle line:84% It always sounds kind of, I won't enjoy it. 00:25:20.907 --> 00:25:23.240 align:middle line:84% Then you go and do it, and you're with all your friends, 00:25:23.240 --> 00:25:25.380 align:middle line:84% and you're trying to follow these instructions, 00:25:25.380 --> 00:25:27.090 align:middle line:90% and it can be quite wonderful. 00:25:27.090 --> 00:25:28.875 align:middle line:84% But there's always somebody who's 00:25:28.875 --> 00:25:30.000 align:middle line:90% not going to want to do it. 00:25:30.000 --> 00:25:31.042 align:middle line:90% And they said there was-- 00:25:31.042 --> 00:25:36.980 align:middle line:84% I think it was a trombone player who just sat there, bap, bap, 00:25:36.980 --> 00:25:38.760 align:middle line:90% bap, bap. 00:25:38.760 --> 00:25:40.710 align:middle line:84% And the composer only came to the performance, 00:25:40.710 --> 00:25:41.880 align:middle line:90% not any of the rehearsals. 00:25:41.880 --> 00:25:45.290 align:middle line:84% And he said he got so furious at first, 00:25:45.290 --> 00:25:48.440 align:middle line:84% because the only thing, the only constraint he 00:25:48.440 --> 00:25:52.160 align:middle line:84% put on him, on the performer, was 00:25:52.160 --> 00:25:54.990 align:middle line:84% that each note had to be different in some other way. 00:25:54.990 --> 00:25:56.780 align:middle line:84% And so the only thing, you can do anything 00:25:56.780 --> 00:25:59.040 align:middle line:90% you want, choosing not to. 00:25:59.040 --> 00:26:00.920 align:middle line:84% Then he said, but of course, it's 00:26:00.920 --> 00:26:04.050 align:middle line:84% 511 notes, so I had a long time to think about it. 00:26:04.050 --> 00:26:06.720 align:middle line:84% And after a while, I began to really, 00:26:06.720 --> 00:26:09.120 align:middle line:84% really like what he was doing, because every one of them 00:26:09.120 --> 00:26:10.000 align:middle line:90% was different. 00:26:10.000 --> 00:26:13.540 align:middle line:84% Because first, it was a bap out of the blue. 00:26:13.540 --> 00:26:17.290 align:middle line:84% Then it was a bap that had been preceded by a bap. 00:26:17.290 --> 00:26:20.200 align:middle line:84% Then it was a bap that had been preceded by two other ones. 00:26:20.200 --> 00:26:23.320 align:middle line:84% And the one that you hear in the 100th time is very different. 00:26:23.320 --> 00:26:28.470 align:middle line:84% So this is all to say that we can think of equality 00:26:28.470 --> 00:26:31.770 align:middle line:84% in many, many different ways, and that there could 00:26:31.770 --> 00:26:36.210 align:middle line:84% be different cases where you want to do something different 00:26:36.210 --> 00:26:37.650 align:middle line:90% than the other. 00:26:37.650 --> 00:26:40.420 align:middle line:84% Let's go ahead and start a Jupyter Notebook. 00:26:40.420 --> 00:26:43.050 align:middle line:84% You guys seem to be pretty fast at getting this. 00:26:43.050 --> 00:26:47.790 align:middle line:84% And we want to figure out some definitions of equal 00:26:47.790 --> 00:26:51.570 align:middle line:84% that Music21 has used, but just only 00:26:51.570 --> 00:26:55.410 align:middle line:84% to think of what kinds of assumptions 00:26:55.410 --> 00:26:59.610 align:middle line:84% were built into the system, even though they're not-- 00:26:59.610 --> 00:27:02.950 align:middle line:84% you could have just about any one. 00:27:02.950 --> 00:27:04.510 align:middle line:90% So I'm over here. 00:27:04.510 --> 00:27:11.670 align:middle line:84% And just to review, how do we test in Python that x equals 5? 00:27:11.670 --> 00:27:12.550 align:middle line:90% What's that? 00:27:12.550 --> 00:27:13.380 align:middle line:90% Just shout it. 00:27:13.380 --> 00:27:14.760 align:middle line:90% AUDIENCE: Assert. 00:27:14.760 --> 00:27:19.320 align:middle line:90% MICHAEL CUTHBERT: Assert x, 5. 00:27:19.320 --> 00:27:19.820 align:middle line:90% No. 00:27:19.820 --> 00:27:25.367 align:middle line:90% 00:27:25.367 --> 00:27:27.700 align:middle line:84% If you were doing in an if statement, what would you do? 00:27:27.700 --> 00:27:29.520 align:middle line:90% If? 00:27:29.520 --> 00:27:30.750 align:middle line:90% AUDIENCE: x equals, equals 5. 00:27:30.750 --> 00:27:32.292 align:middle line:84% MICHAEL CUTHBERT: x equals, equals 5. 00:27:32.292 --> 00:27:32.950 align:middle line:90% Good, good. 00:27:32.950 --> 00:27:35.220 align:middle line:84% Yeah, problem is I have to remember where my trick 00:27:35.220 --> 00:27:38.472 align:middle line:84% questions are and where we're going to the real ones 00:27:38.472 --> 00:27:39.180 align:middle line:90% so you can do it. 00:27:39.180 --> 00:27:41.550 align:middle line:90% Good. 00:27:41.550 --> 00:27:44.400 align:middle line:84% And Python's a little bit interesting 00:27:44.400 --> 00:27:47.560 align:middle line:84% that we can create two mutable arrays. 00:27:47.560 --> 00:27:51.960 align:middle line:84% We'll say A is 3, comma 4 B is 3, comma 4. 00:27:51.960 --> 00:27:53.450 align:middle line:90% Does A equal B? 00:27:53.450 --> 00:27:56.130 align:middle line:90% 00:27:56.130 --> 00:27:58.463 align:middle line:90% AUDIENCE: Yes. 00:27:58.463 --> 00:27:59.880 align:middle line:84% MICHAEL CUTHBERT: You say yes, no. 00:27:59.880 --> 00:28:02.610 align:middle line:84% We can hit Shift Enter and get it. 00:28:02.610 --> 00:28:04.462 align:middle line:90% In this case, yes. 00:28:04.462 --> 00:28:07.390 align:middle line:84% I think I can do this up here without anything going. 00:28:07.390 --> 00:28:08.530 align:middle line:90% Can I make this any bigger? 00:28:08.530 --> 00:28:09.690 align:middle line:90% Yep, I can. 00:28:09.690 --> 00:28:11.650 align:middle line:90% Let's do this in JavaScript. 00:28:11.650 --> 00:28:15.250 align:middle line:90% Let x equals 3, comma 4. 00:28:15.250 --> 00:28:18.990 align:middle line:90% Let y, B equals 3, comma 4. 00:28:18.990 --> 00:28:24.090 align:middle line:90% A equals, equals B, false. 00:28:24.090 --> 00:28:28.380 align:middle line:84% So two very well often used languages, both kind 00:28:28.380 --> 00:28:30.102 align:middle line:90% of scripting type languages. 00:28:30.102 --> 00:28:32.435 align:middle line:84% This is the first time I've shown my console in a while. 00:28:32.435 --> 00:28:36.921 align:middle line:90% 00:28:36.921 --> 00:28:42.480 align:middle line:84% Yeah, that end up with very different results on that. 00:28:42.480 --> 00:28:47.635 align:middle line:84% Let me just make a note for myself to make sure to do that. 00:28:47.635 --> 00:28:48.135 align:middle line:90% Yeah. 00:28:48.135 --> 00:28:51.210 align:middle line:90% 00:28:51.210 --> 00:28:54.210 align:middle line:84% This is, by the way, one of the first mistakes I always 00:28:54.210 --> 00:28:56.680 align:middle line:84% make when switching over to JavaScript. 00:28:56.680 --> 00:29:00.670 align:middle line:84% Now, Python has a second equality operator. 00:29:00.670 --> 00:29:05.650 align:middle line:84% So there's equals, equals, and there's is. 00:29:05.650 --> 00:29:12.933 align:middle line:90% Yeah, so A is B, false. 00:29:12.933 --> 00:29:15.520 align:middle line:90% 00:29:15.520 --> 00:29:21.110 align:middle line:90% So x is 5, yes or no? 00:29:21.110 --> 00:29:24.420 align:middle line:90% 00:29:24.420 --> 00:29:27.270 align:middle line:84% You get all kinds of warnings now 00:29:27.270 --> 00:29:29.550 align:middle line:84% if you're on a new Python saying, that's not really 00:29:29.550 --> 00:29:31.570 align:middle line:84% a great way to do it, that's not really a great way to do it. 00:29:31.570 --> 00:29:32.710 align:middle line:90% Hey, stop doing this, Michael. 00:29:32.710 --> 00:29:33.293 align:middle line:90% Stop doing it. 00:29:33.293 --> 00:29:35.760 align:middle line:90% Oh, but yeah, it's true. 00:29:35.760 --> 00:29:40.860 align:middle line:90% So various things, but if we-- 00:29:40.860 --> 00:29:47.000 align:middle line:84% so x equals 5, y equals 5, x is y. 00:29:47.000 --> 00:29:50.040 align:middle line:90% 00:29:50.040 --> 00:29:51.570 align:middle line:90% True, actually. 00:29:51.570 --> 00:29:52.860 align:middle line:90% It's very odd. 00:29:52.860 --> 00:29:54.760 align:middle line:84% There's all these weird things that happen. 00:29:54.760 --> 00:30:00.850 align:middle line:84% So you'll find that there are other things that 00:30:00.850 --> 00:30:05.530 align:middle line:84% come up quite often that are all the choice that somebody 00:30:05.530 --> 00:30:08.990 align:middle line:90% made at some point to do it. 00:30:08.990 --> 00:30:18.998 align:middle line:84% So let's do music equivalence ops from Music21 import note. 00:30:18.998 --> 00:30:19.790 align:middle line:90% Is that big enough? 00:30:19.790 --> 00:30:20.640 align:middle line:90% No, it got smaller. 00:30:20.640 --> 00:30:23.380 align:middle line:90% 00:30:23.380 --> 00:30:27.850 align:middle line:84% And here's something that I am going to do when I'm in class. 00:30:27.850 --> 00:30:30.070 align:middle line:90% N equals note dot note. 00:30:30.070 --> 00:30:33.050 align:middle line:90% Capital N equals note dot note. 00:30:33.050 --> 00:30:34.880 align:middle line:90% And notice I'm not calling it. 00:30:34.880 --> 00:30:37.660 align:middle line:84% What I'm saying is the variable capital 00:30:37.660 --> 00:30:42.020 align:middle line:84% N can now be used as the class note dot note, 00:30:42.020 --> 00:30:50.580 align:middle line:84% so I can do things like N, C4, plot show, and same as anything 00:30:50.580 --> 00:30:51.080 align:middle line:90% else. 00:30:51.080 --> 00:30:55.520 align:middle line:84% I probably shouldn't have called it that, and works the same. 00:30:55.520 --> 00:31:02.040 align:middle line:84% So give everybody a second to catch up. 00:31:02.040 --> 00:31:06.400 align:middle line:90% 00:31:06.400 --> 00:31:09.730 align:middle line:84% I'm going to create two of those C4s. 00:31:09.730 --> 00:31:12.073 align:middle line:84% Going to call it C. I'll call it C2. 00:31:12.073 --> 00:31:18.040 align:middle line:90% 00:31:18.040 --> 00:31:22.990 align:middle line:84% And what do you hope that the answer on this is? 00:31:22.990 --> 00:31:24.580 align:middle line:90% True. 00:31:24.580 --> 00:31:28.330 align:middle line:84% By the way, I am running Music21 version 9, 00:31:28.330 --> 00:31:31.360 align:middle line:84% and you all are running version 8.1 or 8.3, 00:31:31.360 --> 00:31:32.420 align:middle line:90% or something like that. 00:31:32.420 --> 00:31:35.320 align:middle line:84% We changed a few equals things, so if something up here is 00:31:35.320 --> 00:31:37.600 align:middle line:84% different from yours, shout out, and I'll 00:31:37.600 --> 00:31:40.002 align:middle line:84% try to remember if that's the place we change it. 00:31:40.002 --> 00:31:41.960 align:middle line:84% But I don't think we'll get too much into that. 00:31:41.960 --> 00:31:42.460 align:middle line:90% Good. 00:31:42.460 --> 00:31:45.890 align:middle line:84% So two notes that are the same are there. 00:31:45.890 --> 00:31:51.520 align:middle line:84% Let's call C3 equals N in the same note an octave higher. 00:31:51.520 --> 00:31:53.055 align:middle line:90% So go and type that. 00:31:53.055 --> 00:32:00.280 align:middle line:90% 00:32:00.280 --> 00:32:00.990 align:middle line:90% Well, we hope. 00:32:00.990 --> 00:32:04.465 align:middle line:90% 00:32:04.465 --> 00:32:09.020 align:middle line:90% If you're ever behind, so false. 00:32:09.020 --> 00:32:13.120 align:middle line:90% They're not the same operation. 00:32:13.120 --> 00:32:15.210 align:middle line:84% Does the duration need to be the same? 00:32:15.210 --> 00:32:19.810 align:middle line:90% 00:32:19.810 --> 00:32:23.860 align:middle line:84% So let's just remember that C is the same as C2. 00:32:23.860 --> 00:32:31.080 align:middle line:84% Let's say C2 duration quarter length equals 4.0. 00:32:31.080 --> 00:32:32.830 align:middle line:84% Anyone remember what's the default quarter 00:32:32.830 --> 00:32:34.390 align:middle line:90% length in Music21? 00:32:34.390 --> 00:32:35.230 align:middle line:90% AUDIENCE: One. 00:32:35.230 --> 00:32:35.870 align:middle line:90% MICHAEL CUTHBERT: One. 00:32:35.870 --> 00:32:37.328 align:middle line:84% That's why it shows a quarter note. 00:32:37.328 --> 00:32:39.940 align:middle line:84% So we'll make it 4, which is what? 00:32:39.940 --> 00:32:40.660 align:middle line:90% AUDIENCE: Whole. 00:32:40.660 --> 00:32:41.020 align:middle line:90% MICHAEL CUTHBERT: Whole note. 00:32:41.020 --> 00:32:41.860 align:middle line:90% Good. 00:32:41.860 --> 00:32:45.940 align:middle line:90% C is the same as C2, false. 00:32:45.940 --> 00:32:47.330 align:middle line:90% So good. 00:32:47.330 --> 00:32:54.092 align:middle line:84% We so a lot of us have the same sort of intuition as each other. 00:32:54.092 --> 00:32:54.800 align:middle line:90% Maybe that's bad. 00:32:54.800 --> 00:32:56.590 align:middle line:90% Maybe that's groupthink. 00:32:56.590 --> 00:32:59.960 align:middle line:84% So does anything make an object the same? 00:32:59.960 --> 00:33:03.280 align:middle line:90% We'll say C4 equals-- 00:33:03.280 --> 00:33:04.840 align:middle line:90% we'll create another. 00:33:04.840 --> 00:33:08.380 align:middle line:90% In this case, C4 is C4. 00:33:08.380 --> 00:33:09.563 align:middle line:90% C equals C4. 00:33:09.563 --> 00:33:12.550 align:middle line:90% 00:33:12.550 --> 00:33:17.998 align:middle line:90% What about C? 00:33:17.998 --> 00:33:19.790 align:middle line:84% Here's something you probably haven't seen. 00:33:19.790 --> 00:33:20.995 align:middle line:90% Lyric equals hello. 00:33:20.995 --> 00:33:25.330 align:middle line:90% 00:33:25.330 --> 00:33:28.060 align:middle line:90% Hopefully, that should work. 00:33:28.060 --> 00:33:31.330 align:middle line:90% And C4's lyric, I don't know. 00:33:31.330 --> 00:33:33.220 align:middle line:90% What's your favorite language? 00:33:33.220 --> 00:33:34.400 align:middle line:90% French will do. 00:33:34.400 --> 00:33:37.180 align:middle line:90% Bonjour. 00:33:37.180 --> 00:33:39.375 align:middle line:90% Does C equals C4 now? 00:33:39.375 --> 00:33:43.120 align:middle line:90% 00:33:43.120 --> 00:33:44.460 align:middle line:90% Is that the same on yours? 00:33:44.460 --> 00:33:47.050 align:middle line:90% 00:33:47.050 --> 00:33:51.560 align:middle line:84% So we've decided that we the Music21 community-- 00:33:51.560 --> 00:33:53.750 align:middle line:84% I can't remember if I decided this one or not, 00:33:53.750 --> 00:33:59.260 align:middle line:84% but I'm living with it-- that the lyric is not 00:33:59.260 --> 00:34:04.180 align:middle line:84% an essential part of the quality of a note. 00:34:04.180 --> 00:34:08.030 align:middle line:84% The two notes can have different lyrics, 00:34:08.030 --> 00:34:12.130 align:middle line:90% but still be the same thing. 00:34:12.130 --> 00:34:14.110 align:middle line:84% Weird Al Yankovic has been working 00:34:14.110 --> 00:34:15.440 align:middle line:90% on that for a very long time. 00:34:15.440 --> 00:34:18.260 align:middle line:84% You can do the same song, different lyrics, 00:34:18.260 --> 00:34:19.453 align:middle line:90% still the same song. 00:34:19.453 --> 00:34:23.290 align:middle line:90% 00:34:23.290 --> 00:34:26.560 align:middle line:90% OK, well, let's do this one. 00:34:26.560 --> 00:34:30.469 align:middle line:90% bs, not for B sharp. 00:34:30.469 --> 00:34:32.560 align:middle line:90% Let's create a sharp. 00:34:32.560 --> 00:34:35.860 align:middle line:84% And oh, if I want the same note, let's 00:34:35.860 --> 00:34:40.520 align:middle line:84% see how anal your music theory teaching was. 00:34:40.520 --> 00:34:43.780 align:middle line:84% If I want the same note as C-sharp 4-- sorry-- 00:34:43.780 --> 00:34:48.460 align:middle line:84% C4 as a B-sharp, what's the octave? 00:34:48.460 --> 00:34:49.150 align:middle line:90% AUDIENCE: Three. 00:34:49.150 --> 00:34:50.270 align:middle line:90% AUDIENCE: Four. 00:34:50.270 --> 00:34:52.230 align:middle line:90% MICHAEL CUTHBERT: Four, three. 00:34:52.230 --> 00:34:55.790 align:middle line:84% Well, first, let's create B-sharp 4. 00:34:55.790 --> 00:34:57.990 align:middle line:84% And by the way, this is one of these things. 00:34:57.990 --> 00:35:00.770 align:middle line:84% I think that there's a lot of consensus on this, 00:35:00.770 --> 00:35:02.220 align:middle line:90% but not unanimity. 00:35:02.220 --> 00:35:04.290 align:middle line:84% So somebody might have taught you something else. 00:35:04.290 --> 00:35:11.340 align:middle line:84% But the octave number refers to the letter name. 00:35:11.340 --> 00:35:15.920 align:middle line:84% And so when you put lots of sharps on it, even though this 00:35:15.920 --> 00:35:18.641 align:middle line:90% is the same note as C-- 00:35:18.641 --> 00:35:19.515 align:middle line:90% AUDIENCE: Five. 00:35:19.515 --> 00:35:22.130 align:middle line:84% MICHAEL CUTHBERT: Five, it's still in octave four 00:35:22.130 --> 00:35:23.820 align:middle line:90% because the B is an octave four. 00:35:23.820 --> 00:35:25.170 align:middle line:90% These are all weird things. 00:35:25.170 --> 00:35:26.780 align:middle line:90% So we want bs-- 00:35:26.780 --> 00:35:32.240 align:middle line:84% well, we can say dot pitch dot octave equals 3. 00:35:32.240 --> 00:35:36.570 align:middle line:90% Now, bs should be the same note. 00:35:36.570 --> 00:35:37.980 align:middle line:90% Ooh, I just slipped. 00:35:37.980 --> 00:35:40.650 align:middle line:84% It should be the same note as C-sharp. 00:35:40.650 --> 00:35:43.250 align:middle line:84% So if it's the same note, or C natural. 00:35:43.250 --> 00:35:47.136 align:middle line:84% So it's the same note, then these two should be equal. 00:35:47.136 --> 00:35:49.640 align:middle line:90% And they are not. 00:35:49.640 --> 00:35:57.120 align:middle line:84% So how do you work in a world where you want this to be equal? 00:35:57.120 --> 00:36:01.370 align:middle line:84% One way you can do this, a nice thing about a lot of languages 00:36:01.370 --> 00:36:04.610 align:middle line:84% like Python is you can do something 00:36:04.610 --> 00:36:06.180 align:middle line:90% called monkey patching. 00:36:06.180 --> 00:36:09.680 align:middle line:84% So we can just create a new equality thing, 00:36:09.680 --> 00:36:14.900 align:middle line:84% return whether or not dot pitch dot MIDI 00:36:14.900 --> 00:36:16.940 align:middle line:90% equals B dot pitch dot MIDI. 00:36:16.940 --> 00:36:23.430 align:middle line:90% Whose idea? 00:36:23.430 --> 00:36:26.510 align:middle line:84% And then we can say that n, which 00:36:26.510 --> 00:36:32.130 align:middle line:84% is the same as note dot notes, it's special thing that you run, 00:36:32.130 --> 00:36:35.120 align:middle line:84% underscore, underscore eq, which is run anytime you 00:36:35.120 --> 00:36:38.130 align:middle line:90% check equality, equals new eq. 00:36:38.130 --> 00:36:41.700 align:middle line:84% So now, anytime there's want to do equality, we can check that. 00:36:41.700 --> 00:36:48.290 align:middle line:84% So this is size I use German when I need to do things. 00:36:48.290 --> 00:36:54.620 align:middle line:84% E-sharp equals that, and F is our normal F. Now 00:36:54.620 --> 00:36:59.180 align:middle line:84% we can see is E-sharp the same as F? 00:36:59.180 --> 00:37:01.640 align:middle line:90% Yes. 00:37:01.640 --> 00:37:06.740 align:middle line:84% Just before I do it, you will create things like this 00:37:06.740 --> 00:37:10.650 align:middle line:84% all the time to deal with your definition of equality. 00:37:10.650 --> 00:37:14.540 align:middle line:84% Do this much less often, because I'm not even sure 00:37:14.540 --> 00:37:17.040 align:middle line:84% if note dot show will work anymore, 00:37:17.040 --> 00:37:18.440 align:middle line:84% or if there's other things there. 00:37:18.440 --> 00:37:19.880 align:middle line:90% Yeah. 00:37:19.880 --> 00:37:27.870 align:middle line:84% AUDIENCE: What did you say about the B-sharp 4 going back to C4? 00:37:27.870 --> 00:37:31.340 align:middle line:84% MICHAEL CUTHBERT: So this definition 00:37:31.340 --> 00:37:34.260 align:middle line:84% of octave, which I used quite a bit, 00:37:34.260 --> 00:37:43.050 align:middle line:84% has the notion that the octave defines a range of staff spaces. 00:37:43.050 --> 00:37:51.590 align:middle line:84% So if we're in treble clef, this is all octave four. 00:37:51.590 --> 00:37:52.680 align:middle line:90% October 4th. 00:37:52.680 --> 00:37:57.050 align:middle line:84% It doesn't matter how many flats or sharps you put down anything. 00:37:57.050 --> 00:38:00.440 align:middle line:84% Anything that's written on those staff spaces in treble clef 00:38:00.440 --> 00:38:02.420 align:middle line:90% will be octave four. 00:38:02.420 --> 00:38:04.070 align:middle line:84% AUDIENCE: So in this case, writing 00:38:04.070 --> 00:38:08.210 align:middle line:84% B-sharp 4 would be pointing outside of the staff. 00:38:08.210 --> 00:38:10.670 align:middle line:84% MICHAEL CUTHBERT: No, so B, you first see, 00:38:10.670 --> 00:38:14.040 align:middle line:84% OK, I want octave four, and then I want the B in octave four, 00:38:14.040 --> 00:38:15.570 align:middle line:90% so it's going to be this one. 00:38:15.570 --> 00:38:21.650 align:middle line:84% So B sharp would be this one, even though the C in octave four 00:38:21.650 --> 00:38:23.210 align:middle line:90% is down here. 00:38:23.210 --> 00:38:25.550 align:middle line:84% AUDIENCE: But if you play the B-sharp 4 in this, 00:38:25.550 --> 00:38:26.390 align:middle line:90% it would still-- 00:38:26.390 --> 00:38:28.040 align:middle line:84% MICHAEL CUTHBERT: Sound the same as-- 00:38:28.040 --> 00:38:28.880 align:middle line:90% AUDIENCE: A C5. 00:38:28.880 --> 00:38:29.880 align:middle line:90% MICHAEL CUTHBERT: A C5. 00:38:29.880 --> 00:38:32.990 align:middle line:90% Yep, great. 00:38:32.990 --> 00:38:36.080 align:middle line:84% Like I said, you could probably find somewhere someone who's 00:38:36.080 --> 00:38:37.500 align:middle line:90% not using that definition. 00:38:37.500 --> 00:38:39.500 align:middle line:84% And you can definitely find a lot of places 00:38:39.500 --> 00:38:44.650 align:middle line:84% where this has not been well defined in lot of textbooks, 00:38:44.650 --> 00:38:45.490 align:middle line:90% but yep. 00:38:45.490 --> 00:38:48.210 align:middle line:90% Any other questions on that? 00:38:48.210 --> 00:38:49.300 align:middle line:90% We can try. 00:38:49.300 --> 00:38:54.430 align:middle line:84% Certain things are meter time signature. 00:38:54.430 --> 00:38:56.400 align:middle line:90% Anyone play this? 00:38:56.400 --> 00:38:59.670 align:middle line:90% Is 3/4 the same as meter-- 00:38:59.670 --> 00:39:03.455 align:middle line:84% this is why I abbreviate these things-- time signature 6/8? 00:39:03.455 --> 00:39:06.270 align:middle line:90% 00:39:06.270 --> 00:39:08.280 align:middle line:90% Copy all that. 00:39:08.280 --> 00:39:09.990 align:middle line:90% Oops. 00:39:09.990 --> 00:39:12.580 align:middle line:84% Yes, it's exactly the same if you don't import meter. 00:39:12.580 --> 00:39:15.300 align:middle line:84% They're both an error from Music21. 00:39:15.300 --> 00:39:18.630 align:middle line:90% Import meter. 00:39:18.630 --> 00:39:23.380 align:middle line:84% Yeah, so it's not just based on the duration of the meter. 00:39:23.380 --> 00:39:25.560 align:middle line:84% You can try to figure out, there's some ways 00:39:25.560 --> 00:39:28.200 align:middle line:84% that you can define time signatures such 00:39:28.200 --> 00:39:32.250 align:middle line:84% that they might look the same but do different. 00:39:32.250 --> 00:39:39.160 align:middle line:84% Is 2/8 plus 3/8 the same as 3/8 plus 2/8 and so on. 00:39:39.160 --> 00:39:42.330 align:middle line:90% Any other questions on-- 00:39:42.330 --> 00:39:45.720 align:middle line:84% oh, and even in this case, by the way, 00:39:45.720 --> 00:39:48.970 align:middle line:84% what we've redefined to be MIDI is here. 00:39:48.970 --> 00:39:52.470 align:middle line:84% I'm going to put this up here so it's next to it. 00:39:52.470 --> 00:39:57.070 align:middle line:90% eis is f, false. 00:39:57.070 --> 00:39:57.900 align:middle line:90% Yep. 00:39:57.900 --> 00:40:00.305 align:middle line:84% AUDIENCE: I actually did 3/4 is equal to 3/4, 00:40:00.305 --> 00:40:01.180 align:middle line:90% and it returns false. 00:40:01.180 --> 00:40:02.730 align:middle line:90% So that's what's happening? 00:40:02.730 --> 00:40:04.230 align:middle line:84% MICHAEL CUTHBERT: I think that might 00:40:04.230 --> 00:40:11.070 align:middle line:84% be one of the places that was fixed in version 8, 00:40:11.070 --> 00:40:12.990 align:middle line:90% in version 9. 00:40:12.990 --> 00:40:15.210 align:middle line:84% Yes, so that was changed in version 9. 00:40:15.210 --> 00:40:21.040 align:middle line:84% I think that I remember that was some time over the holidays. 00:40:21.040 --> 00:40:23.640 align:middle line:84% I got an urgent call from somebody who was like, 00:40:23.640 --> 00:40:25.896 align:middle line:84% I needed this to work, and it didn't. 00:40:25.896 --> 00:40:27.460 align:middle line:90% So that's good. 00:40:27.460 --> 00:40:30.840 align:middle line:84% There's a lot of things that are still up in the air, 00:40:30.840 --> 00:40:33.130 align:middle line:84% and there are all things that people can debate. 00:40:33.130 --> 00:40:38.400 align:middle line:84% So equal's kind of slightly arbitrary in this case. 00:40:38.400 --> 00:40:40.960 align:middle line:90% 00:40:40.960 --> 00:40:45.130 align:middle line:90% But let's do one exercise. 00:40:45.130 --> 00:40:47.220 align:middle line:84% It'll take like five minutes to do. 00:40:47.220 --> 00:40:48.670 align:middle line:90% Either get a blank document. 00:40:48.670 --> 00:40:51.010 align:middle line:84% You can probably just jot it down, also, in the Jupiter, 00:40:51.010 --> 00:40:53.950 align:middle line:84% or it's more fun with a blank sheet of paper or something. 00:40:53.950 --> 00:40:57.750 align:middle line:84% And you're going to hear a chacoan, which is a theme that 00:40:57.750 --> 00:40:59.740 align:middle line:90% repeats over and over. 00:40:59.740 --> 00:41:04.170 align:middle line:84% And what I want you to do is, there'll be some letters. 00:41:04.170 --> 00:41:06.400 align:middle line:84% And maybe don't try to count the number of measures. 00:41:06.400 --> 00:41:09.120 align:middle line:84% Just say just before A or a little bit after A or B, 00:41:09.120 --> 00:41:10.330 align:middle line:90% these rehearsal letters. 00:41:10.330 --> 00:41:13.260 align:middle line:84% And I want to find out where you hear the chacoan 00:41:13.260 --> 00:41:14.400 align:middle line:90% theme each time. 00:41:14.400 --> 00:41:18.070 align:middle line:84% It begins at the beginning, so you all get that as a freebie. 00:41:18.070 --> 00:41:20.080 align:middle line:90% But I want to try to do it. 00:41:20.080 --> 00:41:23.760 align:middle line:84% And then if it's the chacoan theme 00:41:23.760 --> 00:41:29.340 align:middle line:84% but transformed, what's transformed about it? 00:41:29.340 --> 00:41:31.958 align:middle line:90% Anybody know that piece before? 00:41:31.958 --> 00:41:32.500 align:middle line:90% We played it. 00:41:32.500 --> 00:41:33.280 align:middle line:90% A few people? 00:41:33.280 --> 00:41:35.370 align:middle line:90% Anyone playing it right now? 00:41:35.370 --> 00:41:38.800 align:middle line:84% I believe it's on the wind ensembles next concert. 00:41:38.800 --> 00:41:39.760 align:middle line:90% I saw that around. 00:41:39.760 --> 00:41:40.260 align:middle line:90% Great. 00:41:40.260 --> 00:41:43.110 align:middle line:84% So I feel like it's a great piece, one 00:41:43.110 --> 00:41:47.590 align:middle line:84% of Holst's greatest, maybe after the planets and things, 00:41:47.590 --> 00:41:49.720 align:middle line:90% but one of his wonderful pieces. 00:41:49.720 --> 00:41:51.853 align:middle line:84% So about how many did people find? 00:41:51.853 --> 00:41:57.090 align:middle line:90% 00:41:57.090 --> 00:41:58.318 align:middle line:90% Tell me 2.2. 00:41:58.318 --> 00:41:59.235 align:middle line:90% AUDIENCE: Seven or so. 00:41:59.235 --> 00:42:00.960 align:middle line:84% MICHAEL CUTHBERT: Seven or so, about? 00:42:00.960 --> 00:42:02.940 align:middle line:84% AUDIENCE: I was going to say, it was pretty much there 00:42:02.940 --> 00:42:03.490 align:middle line:90% the whole time. 00:42:03.490 --> 00:42:04.660 align:middle line:84% MICHAEL CUTHBERT: It's there the whole time. 00:42:04.660 --> 00:42:05.160 align:middle line:90% Good. 00:42:05.160 --> 00:42:07.484 align:middle line:84% Anyone find a place where it wasn't? 00:42:07.484 --> 00:42:10.872 align:middle line:90% [MUSIC PLAYING] 00:42:10.872 --> 00:42:12.330 align:middle line:90% 00:42:12.330 --> 00:42:15.556 align:middle line:84% What's different on the second entrance? 00:42:15.556 --> 00:42:18.700 align:middle line:90% [MUSIC PLAYING] 00:42:18.700 --> 00:42:19.200 align:middle line:90% 00:42:19.200 --> 00:42:20.030 align:middle line:90% John, go ahead. 00:42:20.030 --> 00:42:21.940 align:middle line:84% AUDIENCE: They harmonize the main thing. 00:42:21.940 --> 00:42:23.690 align:middle line:84% MICHAEL CUTHBERT: So it's been harmonized. 00:42:23.690 --> 00:42:27.820 align:middle line:84% So something can be-- a theme can be the same theme, 00:42:27.820 --> 00:42:29.020 align:middle line:90% but harmonized. 00:42:29.020 --> 00:42:30.045 align:middle line:90% What else is different? 00:42:30.045 --> 00:42:30.545 align:middle line:90% Anybody? 00:42:30.545 --> 00:42:33.600 align:middle line:90% [MUSIC PLAYING] 00:42:33.600 --> 00:42:34.100 align:middle line:90% Yeah. 00:42:34.100 --> 00:42:35.260 align:middle line:84% AUDIENCE: It's the instrument that plays it. 00:42:35.260 --> 00:42:35.930 align:middle line:90% MICHAEL CUTHBERT: It's what? 00:42:35.930 --> 00:42:36.910 align:middle line:84% AUDIENCE: It's the instrument that plays it. 00:42:36.910 --> 00:42:38.150 align:middle line:84% MICHAEL CUTHBERT: The instrument that plays it. 00:42:38.150 --> 00:42:38.800 align:middle line:90% Good. 00:42:38.800 --> 00:42:41.638 align:middle line:90% [MUSIC PLAYING] 00:42:41.638 --> 00:42:42.923 align:middle line:90% 00:42:42.923 --> 00:42:44.590 align:middle line:84% I always think that when the clarinet is 00:42:44.590 --> 00:42:47.300 align:middle line:84% going to enter it, but then somebody, the other one does. 00:42:47.300 --> 00:42:48.805 align:middle line:90% What else has changed? 00:42:48.805 --> 00:42:50.180 align:middle line:84% Do you remember where it started? 00:42:50.180 --> 00:42:50.410 align:middle line:90% Yeah. 00:42:50.410 --> 00:42:50.950 align:middle line:90% AUDIENCE: The dynamics. 00:42:50.950 --> 00:42:52.000 align:middle line:90% MICHAEL CUTHBERT: The dynamics. 00:42:52.000 --> 00:42:52.500 align:middle line:90% Good. 00:42:52.500 --> 00:42:55.715 align:middle line:84% So dynamics we consider something sometimes 00:42:55.715 --> 00:42:58.215 align:middle line:84% to be the same, sometimes not if the dynamics are different. 00:42:58.215 --> 00:43:01.322 align:middle line:90% [MUSIC PLAYING] 00:43:01.322 --> 00:43:03.610 align:middle line:90% 00:43:03.610 --> 00:43:07.000 align:middle line:84% Now we're back to a very low octave, 00:43:07.000 --> 00:43:09.789 align:middle line:90% which we weren't in every time. 00:43:09.789 --> 00:43:13.282 align:middle line:90% [MUSIC PLAYING] 00:43:13.282 --> 00:43:28.780 align:middle line:90% 00:43:28.780 --> 00:43:30.730 align:middle line:90% What's different this time? 00:43:30.730 --> 00:43:31.505 align:middle line:90% AUDIENCE: Duration 00:43:31.505 --> 00:43:32.630 align:middle line:90% MICHAEL CUTHBERT: Duration. 00:43:32.630 --> 00:43:35.560 align:middle line:84% Or we could say spacing between the two, 00:43:35.560 --> 00:43:39.560 align:middle line:84% because the duration hasn't really changed. 00:43:39.560 --> 00:43:42.190 align:middle line:84% So that's another thing that we might think 00:43:42.190 --> 00:43:44.450 align:middle line:90% of as the same but different. 00:43:44.450 --> 00:43:47.162 align:middle line:90% [MUSIC PLAYING] 00:43:47.162 --> 00:43:48.070 align:middle line:90% 00:43:48.070 --> 00:43:49.890 align:middle line:90% Register instrument again. 00:43:49.890 --> 00:43:52.660 align:middle line:90% [MUSIC PLAYING] 00:43:52.660 --> 00:43:55.750 align:middle line:84% So I'm going to fade it out for a little bit 00:43:55.750 --> 00:43:57.410 align:middle line:90% so that we can just talk. 00:43:57.410 --> 00:44:01.810 align:middle line:84% So all of these things that we wouldn't say it's 00:44:01.810 --> 00:44:04.130 align:middle line:90% playing the exact same music. 00:44:04.130 --> 00:44:08.170 align:middle line:84% But we're saying in some sense, they're playing the same thing 00:44:08.170 --> 00:44:09.140 align:middle line:90% as before. 00:44:09.140 --> 00:44:12.525 align:middle line:84% And we'll get one more coming up in just a little bit. 00:44:12.525 --> 00:44:15.270 align:middle line:90% [MUSIC PLAYING] 00:44:15.270 --> 00:44:17.200 align:middle line:90% 00:44:17.200 --> 00:44:18.700 align:middle line:90% This is very beautiful, anyhow. 00:44:18.700 --> 00:44:22.116 align:middle line:90% [MUSIC PLAYING] 00:44:22.116 --> 00:44:28.960 align:middle line:90% 00:44:28.960 --> 00:44:29.670 align:middle line:90% What's here? 00:44:29.670 --> 00:44:32.786 align:middle line:90% [MUSIC PLAYING] 00:44:32.786 --> 00:44:35.560 align:middle line:90% 00:44:35.560 --> 00:44:37.185 align:middle line:90% Does anyone hear the theme now? 00:44:37.185 --> 00:44:40.448 align:middle line:90% [MUSIC PLAYING] 00:44:40.448 --> 00:44:41.410 align:middle line:90% 00:44:41.410 --> 00:44:42.040 align:middle line:90% Nobody? 00:44:42.040 --> 00:44:45.414 align:middle line:90% [MUSIC PLAYING] 00:44:45.414 --> 00:44:48.310 align:middle line:90% 00:44:48.310 --> 00:44:54.100 align:middle line:84% Holst seems to think that the theme is still playing here. 00:44:54.100 --> 00:44:55.560 align:middle line:90% Says he doesn't-- yeah, Sean. 00:44:55.560 --> 00:44:58.060 align:middle line:84% AUDIENCE: It's like the concept of the theme is still there. 00:44:58.060 --> 00:45:01.303 align:middle line:84% It's just kind of a bit more of a major ish. 00:45:01.303 --> 00:45:03.470 align:middle line:84% MICHAEL CUTHBERT: A little bit more major ish theme? 00:45:03.470 --> 00:45:04.340 align:middle line:90% Yep. 00:45:04.340 --> 00:45:05.020 align:middle line:90% Good. 00:45:05.020 --> 00:45:05.810 align:middle line:90% Yeah. 00:45:05.810 --> 00:45:07.120 align:middle line:90% AUDIENCE: It's inverted. 00:45:07.120 --> 00:45:09.340 align:middle line:84% MICHAEL CUTHBERT: Is it inverted? 00:45:09.340 --> 00:45:12.805 align:middle line:90% [SINGING] 00:45:12.805 --> 00:45:14.290 align:middle line:90% 00:45:14.290 --> 00:45:15.680 align:middle line:90% What do we have here? 00:45:15.680 --> 00:45:16.180 align:middle line:90% Instead of-- 00:45:16.180 --> 00:45:18.490 align:middle line:90% [SINGING] 00:45:18.490 --> 00:45:20.900 align:middle line:90% 00:45:20.900 --> 00:45:23.650 align:middle line:90% So it's an inversion. 00:45:23.650 --> 00:45:27.910 align:middle line:84% Is playing something upside down the same as playing it? 00:45:27.910 --> 00:45:28.660 align:middle line:90% AUDIENCE: Depends. 00:45:28.660 --> 00:45:29.410 align:middle line:90% MICHAEL CUTHBERT: Depends. 00:45:29.410 --> 00:45:30.493 align:middle line:90% It really, really depends. 00:45:30.493 --> 00:45:33.050 align:middle line:84% If I say, let's all sing happy birthday-- 00:45:33.050 --> 00:45:38.470 align:middle line:84% let's see if I can do this-- and you all go happy birthday to-- 00:45:38.470 --> 00:45:39.130 align:middle line:90% how's it go? 00:45:39.130 --> 00:45:43.880 align:middle line:84% To you, you'd be like, OK, you just ruined my birthday. 00:45:43.880 --> 00:45:44.380 align:middle line:90% Right? 00:45:44.380 --> 00:45:44.900 align:middle line:90% Right? 00:45:44.900 --> 00:45:46.670 align:middle line:90% So it's not always the same. 00:45:46.670 --> 00:45:50.920 align:middle line:84% Yet there are some cases where composers 00:45:50.920 --> 00:45:53.290 align:middle line:90% think of it as the same. 00:45:53.290 --> 00:45:56.590 align:middle line:84% By the way, if you don't have that, one of the things nobody 00:45:56.590 --> 00:46:00.050 align:middle line:84% said was it's the same when the rhythm is the same, 00:46:00.050 --> 00:46:01.550 align:middle line:90% if nothing else. 00:46:01.550 --> 00:46:04.110 align:middle line:90% [SINGING] 00:46:04.110 --> 00:46:06.890 align:middle line:90% 00:46:06.890 --> 00:46:09.230 align:middle line:84% So it is even still the same rhythm, 00:46:09.230 --> 00:46:13.100 align:middle line:84% even if it wasn't fully inverted. 00:46:13.100 --> 00:46:13.790 align:middle line:90% But yeah. 00:46:13.790 --> 00:46:17.920 align:middle line:84% So things that are sometimes we want to consider the same, 00:46:17.920 --> 00:46:20.260 align:middle line:84% and sometimes we don't, we don't tend 00:46:20.260 --> 00:46:23.360 align:middle line:90% to call them equal very much. 00:46:23.360 --> 00:46:26.450 align:middle line:84% We tend to say that they're equivalent, 00:46:26.450 --> 00:46:29.190 align:middle line:84% and they're equivalent in some way. 00:46:29.190 --> 00:46:30.690 align:middle line:90% Or what we'll often use-- 00:46:30.690 --> 00:46:34.310 align:middle line:84% I'm putting this up so somebody might put this back down-- 00:46:34.310 --> 00:46:37.366 align:middle line:84% is that they're equivalent under something. 00:46:37.366 --> 00:46:45.440 align:middle line:90% 00:46:45.440 --> 00:46:52.580 align:middle line:84% Let me take something that you might know right now, just 00:46:52.580 --> 00:46:53.430 align:middle line:90% looking up there. 00:46:53.430 --> 00:46:54.600 align:middle line:90% It's a very musical-- 00:46:54.600 --> 00:46:56.150 align:middle line:84% we just did a follow of John Cage, 00:46:56.150 --> 00:46:58.345 align:middle line:90% and the time right now is that. 00:46:58.345 --> 00:47:03.140 align:middle line:90% 00:47:03.140 --> 00:47:06.110 align:middle line:90% Anybody prefer that time? 00:47:06.110 --> 00:47:10.820 align:middle line:90% What's the equivalence here? 00:47:10.820 --> 00:47:14.960 align:middle line:84% How is it that some people might say, especially 00:47:14.960 --> 00:47:18.060 align:middle line:84% if I put that on, that these two are equivalent? 00:47:18.060 --> 00:47:19.720 align:middle line:84% But let's get rid of that for now. 00:47:19.720 --> 00:47:22.365 align:middle line:90% 00:47:22.365 --> 00:47:22.865 align:middle line:90% Yeah. 00:47:22.865 --> 00:47:23.428 align:middle line:90% Go ahead. 00:47:23.428 --> 00:47:25.386 align:middle line:84% AUDIENCE: One's using a 12 hour time signature, 00:47:25.386 --> 00:47:27.560 align:middle line:84% and one's using a 24 hour time signature. 00:47:27.560 --> 00:47:29.690 align:middle line:90% MICHAEL CUTHBERT: Yeah. 00:47:29.690 --> 00:47:33.140 align:middle line:90% So 12 hour can-- 00:47:33.140 --> 00:47:39.890 align:middle line:84% each time in a 12 hour in a-- we could call it an AM/PM world-- 00:47:39.890 --> 00:47:43.668 align:middle line:84% has an equivalent in a 24 hour-- you could call it military time, 00:47:43.668 --> 00:47:45.210 align:middle line:84% whatever you want to call it-- world, 00:47:45.210 --> 00:47:49.550 align:middle line:84% so that there is an equivalence that allows the mapping back 00:47:49.550 --> 00:47:50.910 align:middle line:90% and forth between them. 00:47:50.910 --> 00:47:53.390 align:middle line:84% Not all equivalences allow a perfect mapping. 00:47:53.390 --> 00:47:53.960 align:middle line:90% Good. 00:47:53.960 --> 00:48:03.230 align:middle line:84% Mathematically, what do you need to do if you're at 2:05 PM? 00:48:03.230 --> 00:48:06.968 align:middle line:84% What do you do to convert that to a 24 hour time? 00:48:06.968 --> 00:48:07.760 align:middle line:90% AUDIENCE: At 12:00. 00:48:07.760 --> 00:48:08.210 align:middle line:90% MICHAEL CUTHBERT: At 12:00. 00:48:08.210 --> 00:48:08.710 align:middle line:90% Good. 00:48:08.710 --> 00:48:16.080 align:middle line:84% And what do you do if you are at 14:05 PM and you need to do it? 00:48:16.080 --> 00:48:20.520 align:middle line:84% You can subtract 12, or you can think of it as mod. 00:48:20.520 --> 00:48:22.500 align:middle line:90% Yeah, is it mod 12 or mod 24? 00:48:22.500 --> 00:48:24.307 align:middle line:90% AUDIENCE: Both happen to work. 00:48:24.307 --> 00:48:25.890 align:middle line:84% MICHAEL CUTHBERT: Both happen to work. 00:48:25.890 --> 00:48:27.170 align:middle line:90% Do they? 00:48:27.170 --> 00:48:32.242 align:middle line:84% No, mod 24 doesn't work because 23:50. 00:48:32.242 --> 00:48:34.200 align:middle line:84% AUDIENCE: OK, yeah, but in that case, it works. 00:48:34.200 --> 00:48:35.460 align:middle line:84% MICHAEL CUTHBERT: In this case, yes. 00:48:35.460 --> 00:48:36.360 align:middle line:90% In this case, it works. 00:48:36.360 --> 00:48:36.860 align:middle line:90% Yes. 00:48:36.860 --> 00:48:37.440 align:middle line:90% Good. 00:48:37.440 --> 00:48:40.760 align:middle line:84% Always solve for the most specific case you can. 00:48:40.760 --> 00:48:41.910 align:middle line:90% No, of course, we'll know. 00:48:41.910 --> 00:48:43.785 align:middle line:84% We'll try to solve for the most general case. 00:48:43.785 --> 00:48:48.500 align:middle line:84% So mod 12, there's some other little thing that you have to do 00:48:48.500 --> 00:48:59.690 align:middle line:90% on this if you're at 12:05 PM. 00:48:59.690 --> 00:49:00.330 align:middle line:90% Let's see. 00:49:00.330 --> 00:49:02.100 align:middle line:90% Yeah, in that case, no. 00:49:02.100 --> 00:49:02.820 align:middle line:90% I can't remember. 00:49:02.820 --> 00:49:05.820 align:middle line:84% Anyhow, there's something off by one error, so don't follow. 00:49:05.820 --> 00:49:08.000 align:middle line:84% Don't try to figure them off at the-- 00:49:08.000 --> 00:49:11.000 align:middle line:84% there's a particular case where if it equals 0, 00:49:11.000 --> 00:49:12.510 align:middle line:90% you're going to want to add 12. 00:49:12.510 --> 00:49:14.840 align:middle line:90% So it's mod 12 plus-- 00:49:14.840 --> 00:49:16.040 align:middle line:90% I can't remember. 00:49:16.040 --> 00:49:17.065 align:middle line:90% You'll figure it out. 00:49:17.065 --> 00:49:18.690 align:middle line:84% I know how to do it in music and stuff. 00:49:18.690 --> 00:49:23.190 align:middle line:84% So let's think of some musical equivalence classes. 00:49:23.190 --> 00:49:25.830 align:middle line:84% One of the ones that we've put up here, 00:49:25.830 --> 00:49:29.720 align:middle line:84% and so one of the reasons we debate a lot about equals 00:49:29.720 --> 00:49:33.980 align:middle line:84% is that equals is trying to create 00:49:33.980 --> 00:49:36.870 align:middle line:84% a set of equivalence classes once and for all. 00:49:36.870 --> 00:49:37.800 align:middle line:90% This is better. 00:49:37.800 --> 00:49:39.200 align:middle line:84% I'll keep this one in the center. 00:49:39.200 --> 00:49:42.410 align:middle line:90% 00:49:42.410 --> 00:49:52.490 align:middle line:84% So here's a particular thing that we can debate 00:49:52.490 --> 00:49:55.140 align:middle line:90% whether or not they're equal. 00:49:55.140 --> 00:49:57.690 align:middle line:84% Music21 has decided that they are not, 00:49:57.690 --> 00:49:59.070 align:middle line:90% but that could be a debatable. 00:49:59.070 --> 00:50:02.120 align:middle line:84% But I don't think it's debatable that there 00:50:02.120 --> 00:50:05.610 align:middle line:84% is some form of equivalence between these two. 00:50:05.610 --> 00:50:07.365 align:middle line:90% What do we want to call that? 00:50:07.365 --> 00:50:08.240 align:middle line:90% AUDIENCE: Enharmonic? 00:50:08.240 --> 00:50:09.948 align:middle line:84% MICHAEL CUTHBERT: Enharmonic equivalents. 00:50:09.948 --> 00:50:11.450 align:middle line:90% Good. 00:50:11.450 --> 00:50:15.860 align:middle line:90% Enharmonic equivalents. 00:50:15.860 --> 00:50:18.270 align:middle line:84% They are enharmonically equivalent. 00:50:18.270 --> 00:50:20.220 align:middle line:84% Somebody told me if I got my Es and As right. 00:50:20.220 --> 00:50:22.920 align:middle line:90% Yeah, I think this time. 00:50:22.920 --> 00:50:25.020 align:middle line:84% We can also sometimes say they're 00:50:25.020 --> 00:50:30.120 align:middle line:84% equivalent under spelling, under lack of spelling or something 00:50:30.120 --> 00:50:31.600 align:middle line:90% equivalent with spelling. 00:50:31.600 --> 00:50:32.100 align:middle line:90% Good. 00:50:32.100 --> 00:50:34.620 align:middle line:84% What's another equivalence class that-- we're 00:50:34.620 --> 00:50:38.010 align:middle line:84% going to go really fast, so let's start thinking. 00:50:38.010 --> 00:50:39.930 align:middle line:84% What's something else that we might sometimes 00:50:39.930 --> 00:50:41.050 align:middle line:90% think is equivalent? 00:50:41.050 --> 00:50:42.780 align:middle line:90% We said inversion. 00:50:42.780 --> 00:50:45.410 align:middle line:90% Sometimes, but often not. 00:50:45.410 --> 00:50:45.910 align:middle line:90% Good. 00:50:45.910 --> 00:50:48.570 align:middle line:90% What's another? 00:50:48.570 --> 00:50:49.395 align:middle line:90% AUDIENCE: Duration? 00:50:49.395 --> 00:50:50.520 align:middle line:90% MICHAEL CUTHBERT: Duration. 00:50:50.520 --> 00:50:53.070 align:middle line:84% Sometimes we don't care how long two things are. 00:50:53.070 --> 00:50:54.180 align:middle line:90% Good. 00:50:54.180 --> 00:50:54.910 align:middle line:90% John? 00:50:54.910 --> 00:50:55.823 align:middle line:90% AUDIENCE: Key. 00:50:55.823 --> 00:50:56.740 align:middle line:90% MICHAEL CUTHBERT: Key. 00:50:56.740 --> 00:50:57.970 align:middle line:90% Ooh, that'll be good. 00:50:57.970 --> 00:50:58.680 align:middle line:90% Great. 00:50:58.680 --> 00:50:59.830 align:middle line:90% I heard another one. 00:50:59.830 --> 00:51:00.360 align:middle line:90% Just shout. 00:51:00.360 --> 00:51:00.940 align:middle line:90% AUDIENCE: Octave. 00:51:00.940 --> 00:51:01.590 align:middle line:90% MICHAEL CUTHBERT: Octave. 00:51:01.590 --> 00:51:03.540 align:middle line:84% I should have chosen the one without staff lines. 00:51:03.540 --> 00:51:04.450 align:middle line:90% Twice as much space. 00:51:04.450 --> 00:51:06.690 align:middle line:90% Keep going, everybody. 00:51:06.690 --> 00:51:07.458 align:middle line:90% What's that? 00:51:07.458 --> 00:51:08.333 align:middle line:90% AUDIENCE: Instrument? 00:51:08.333 --> 00:51:09.541 align:middle line:90% MICHAEL CUTHBERT: Instrument. 00:51:09.541 --> 00:51:10.320 align:middle line:90% Yeah. 00:51:10.320 --> 00:51:15.910 align:middle line:84% Sometimes it doesn't matter what instrument is playing. 00:51:15.910 --> 00:51:17.470 align:middle line:90% We'd say it's the same thing. 00:51:17.470 --> 00:51:22.110 align:middle line:84% And sometimes when you hire a musician to perform 00:51:22.110 --> 00:51:24.600 align:middle line:84% at your wedding, and they show up 00:51:24.600 --> 00:51:27.820 align:middle line:84% with an accordion and a bagpipe, it's not equivalent. 00:51:27.820 --> 00:51:28.330 align:middle line:90% Right? 00:51:28.330 --> 00:51:28.830 align:middle line:90% Good. 00:51:28.830 --> 00:51:30.750 align:middle line:84% What other things that we might say? 00:51:30.750 --> 00:51:31.500 align:middle line:90% AUDIENCE: Context. 00:51:31.500 --> 00:51:32.190 align:middle line:90% MICHAEL CUTHBERT: What's that? 00:51:32.190 --> 00:51:32.940 align:middle line:90% AUDIENCE: Context. 00:51:32.940 --> 00:51:34.920 align:middle line:90% MICHAEL CUTHBERT: Context. 00:51:34.920 --> 00:51:35.620 align:middle line:90% No, too broad. 00:51:35.620 --> 00:51:36.520 align:middle line:90% Too broad. 00:51:36.520 --> 00:51:38.260 align:middle line:90% Good idea. 00:51:38.260 --> 00:51:40.838 align:middle line:84% Give me one context that might be-- 00:51:40.838 --> 00:51:43.380 align:middle line:84% AUDIENCE: Where you're coming from and where you're going to. 00:51:43.380 --> 00:51:50.220 align:middle line:84% MICHAEL CUTHBERT: Where you're coming from, coming from, going 00:51:50.220 --> 00:51:51.390 align:middle line:90% to. 00:51:51.390 --> 00:51:57.930 align:middle line:84% So the same song is the same under equivalence of car 00:51:57.930 --> 00:52:02.310 align:middle line:90% stereo versus home. 00:52:02.310 --> 00:52:05.610 align:middle line:84% It's interesting that we might think. 00:52:05.610 --> 00:52:07.710 align:middle line:84% Give me a context where listening 00:52:07.710 --> 00:52:12.300 align:middle line:84% to the same song in your recording studio 00:52:12.300 --> 00:52:17.280 align:middle line:84% or at home versus your car might be a difference. 00:52:17.280 --> 00:52:19.840 align:middle line:84% The same song might not be equivalent under that. 00:52:19.840 --> 00:52:21.850 align:middle line:84% AUDIENCE: If the car has police sirens in it? 00:52:21.850 --> 00:52:23.640 align:middle line:84% MICHAEL CUTHBERT: If the car has police sirens in it. 00:52:23.640 --> 00:52:24.140 align:middle line:90% Good. 00:52:24.140 --> 00:52:30.120 align:middle line:84% I was thinking, if you're trying to mix your composition 00:52:30.120 --> 00:52:33.480 align:middle line:84% for submission, does it matter if you're 00:52:33.480 --> 00:52:36.550 align:middle line:84% listening at home in stereo with your very nice headphones? 00:52:36.550 --> 00:52:39.450 align:middle line:84% Is it the same piece as if you were-- 00:52:39.450 --> 00:52:41.413 align:middle line:84% let's hope you're not doing it while driving. 00:52:41.413 --> 00:52:43.080 align:middle line:84% You're in the passenger seat, but you're 00:52:43.080 --> 00:52:44.380 align:middle line:90% doing it on a noisy road. 00:52:44.380 --> 00:52:46.050 align:middle line:84% Yeah, so the amount of background noise 00:52:46.050 --> 00:52:48.300 align:middle line:84% might be a context that changes whether or not 00:52:48.300 --> 00:52:50.050 align:middle line:84% you think this piece of music is the same. 00:52:50.050 --> 00:52:50.190 align:middle line:90% Yeah. 00:52:50.190 --> 00:52:52.600 align:middle line:84% AUDIENCE: I was saying if you're looking at a pitch, what 00:52:52.600 --> 00:52:53.340 align:middle line:90% the chord is coming from. 00:52:53.340 --> 00:52:54.840 align:middle line:84% MICHAEL CUTHBERT: Yeah, I knew that. 00:52:54.840 --> 00:52:55.600 align:middle line:90% I knew that. 00:52:55.600 --> 00:52:58.060 align:middle line:90% I knew you meant that, but yeah. 00:52:58.060 --> 00:53:04.975 align:middle line:90% So preceding versus following. 00:53:04.975 --> 00:53:05.475 align:middle line:90% Good. 00:53:05.475 --> 00:53:08.040 align:middle line:90% 00:53:08.040 --> 00:53:09.330 align:middle line:90% Other things. 00:53:09.330 --> 00:53:12.120 align:middle line:84% This year we've been super great. 00:53:12.120 --> 00:53:12.660 align:middle line:90% Yeah. 00:53:12.660 --> 00:53:13.560 align:middle line:90% AUDIENCE: Articulation. 00:53:13.560 --> 00:53:14.852 align:middle line:90% MICHAEL CUTHBERT: Articulation. 00:53:14.852 --> 00:53:16.020 align:middle line:90% Good. 00:53:16.020 --> 00:53:16.960 align:middle line:90% Articulation. 00:53:16.960 --> 00:53:17.460 align:middle line:90% Good. 00:53:17.460 --> 00:53:18.173 align:middle line:90% Shout some more. 00:53:18.173 --> 00:53:18.840 align:middle line:90% AUDIENCE: Tempo. 00:53:18.840 --> 00:53:21.300 align:middle line:90% MICHAEL CUTHBERT: Tempo. 00:53:21.300 --> 00:53:25.960 align:middle line:84% The same piece is the same piece if you rush through it, 00:53:25.960 --> 00:53:26.460 align:middle line:90% sometimes. 00:53:26.460 --> 00:53:28.360 align:middle line:90% Sometimes not, but yeah, good. 00:53:28.360 --> 00:53:29.700 align:middle line:90% Anything else? 00:53:29.700 --> 00:53:31.360 align:middle line:84% You can keep thinking of some more. 00:53:31.360 --> 00:53:32.860 align:middle line:84% I want to use them all up, because I 00:53:32.860 --> 00:53:36.610 align:middle line:84% think we're going to be asked to come up with at least one. 00:53:36.610 --> 00:53:38.100 align:middle line:90% That's great. 00:53:38.100 --> 00:53:41.320 align:middle line:90% So this is really, really good. 00:53:41.320 --> 00:53:45.630 align:middle line:90% You're going to be reading. 00:53:45.630 --> 00:53:46.440 align:middle line:90% Aha! 00:53:46.440 --> 00:53:49.560 align:middle line:90% You all got to be faster. 00:53:49.560 --> 00:53:52.380 align:middle line:84% You're all going to be reading another section 00:53:52.380 --> 00:53:57.160 align:middle line:84% from this book by Dmitri Tymoczko, a geometry of music, 00:53:57.160 --> 00:54:01.710 align:middle line:84% and a second part of Chapter 2, which you read earlier 00:54:01.710 --> 00:54:05.040 align:middle line:84% when we were talking about those flipped inversions 00:54:05.040 --> 00:54:06.310 align:middle line:90% with the mirrors. 00:54:06.310 --> 00:54:11.230 align:middle line:84% And he defines five points of inversion, 00:54:11.230 --> 00:54:17.770 align:middle line:84% five equivalence classes that we think of quite often in music. 00:54:17.770 --> 00:54:19.240 align:middle line:90% And he gave them. 00:54:19.240 --> 00:54:22.992 align:middle line:84% The ordering isn't the greatest ordering in the world, 00:54:22.992 --> 00:54:24.700 align:middle line:84% except it makes it very easy to remember. 00:54:24.700 --> 00:54:25.900 align:middle line:90% OPTIC. 00:54:25.900 --> 00:54:28.420 align:middle line:84% And I'm going to add a sixth one because I 00:54:28.420 --> 00:54:30.910 align:middle line:90% think it's very important to. 00:54:30.910 --> 00:54:32.180 align:middle line:90% The octave. 00:54:32.180 --> 00:54:34.100 align:middle line:90% Quite often we don't care. 00:54:34.100 --> 00:54:38.590 align:middle line:84% We consider the two musical elements, two chords 00:54:38.590 --> 00:54:43.420 align:middle line:84% to be the same if they're in different octaves. 00:54:43.420 --> 00:54:47.560 align:middle line:84% Or two notes, the same note or equivalent note. 00:54:47.560 --> 00:54:48.592 align:middle line:90% Permutation. 00:54:48.592 --> 00:54:49.800 align:middle line:90% What do you think that means? 00:54:49.800 --> 00:54:54.383 align:middle line:90% 00:54:54.383 --> 00:54:55.243 align:middle line:90% Yeah, Adam. 00:54:55.243 --> 00:54:57.410 align:middle line:84% AUDIENCE: You have a chord and some inversion of it. 00:54:57.410 --> 00:54:59.560 align:middle line:84% Perhaps you want to consider them the same. 00:54:59.560 --> 00:55:02.690 align:middle line:84% MICHAEL CUTHBERT: Yeah, so we have an inversion of a chord. 00:55:02.690 --> 00:55:04.360 align:middle line:90% You might consider it the same. 00:55:04.360 --> 00:55:06.310 align:middle line:90% The order that goes only-- 00:55:06.310 --> 00:55:08.533 align:middle line:84% that would only work if you also have octave. 00:55:08.533 --> 00:55:14.330 align:middle line:90% 00:55:14.330 --> 00:55:17.732 align:middle line:90% [MUSICAL NOTES] 00:55:17.732 --> 00:55:22.120 align:middle line:90% 00:55:22.120 --> 00:55:25.350 align:middle line:84% Is there some way that those are the same? 00:55:25.350 --> 00:55:28.340 align:middle line:90% 00:55:28.340 --> 00:55:30.110 align:middle line:84% If I told you the first note was C, 00:55:30.110 --> 00:55:34.820 align:middle line:84% they're both arpeggiated C major triads. 00:55:34.820 --> 00:55:37.280 align:middle line:90% You can hear that. 00:55:37.280 --> 00:55:38.450 align:middle line:90% Does it matter? 00:55:38.450 --> 00:55:41.350 align:middle line:84% Sometimes it matters if, well, you're arpeggiating it up, 00:55:41.350 --> 00:55:43.040 align:middle line:84% and sometimes it matters if you're arpeggiating it down. 00:55:43.040 --> 00:55:44.630 align:middle line:84% If you're doing your theory analysis, 00:55:44.630 --> 00:55:47.900 align:middle line:84% does that matter if you're trying to hit a chord note? 00:55:47.900 --> 00:55:48.400 align:middle line:90% No. 00:55:48.400 --> 00:55:53.475 align:middle line:84% So sometimes, on the other hand, let's stick with happy birthday, 00:55:53.475 --> 00:55:55.100 align:middle line:84% I'm going to say happy birthday to you. 00:55:55.100 --> 00:55:58.070 align:middle line:84% But I've run it through my Python scramble thing. 00:55:58.070 --> 00:56:02.260 align:middle line:84% I'm going to do every note in a different order. 00:56:02.260 --> 00:56:04.790 align:middle line:84% We would not apply that equivalence class at that place, 00:56:04.790 --> 00:56:08.110 align:middle line:84% so the permutation is something that, quite often, 00:56:08.110 --> 00:56:12.110 align:middle line:84% when we're just analyzing the chordal structure of a measure, 00:56:12.110 --> 00:56:14.523 align:middle line:84% we don't really care what order the notes come in. 00:56:14.523 --> 00:56:16.940 align:middle line:84% We just want to see what are all the notes in the measure, 00:56:16.940 --> 00:56:18.950 align:middle line:84% and then figure out what chord it might be. 00:56:18.950 --> 00:56:21.040 align:middle line:90% So the permutation. 00:56:21.040 --> 00:56:22.540 align:middle line:90% Transposition. 00:56:22.540 --> 00:56:24.410 align:middle line:90% Who shouted key? 00:56:24.410 --> 00:56:25.630 align:middle line:90% Yeah, John. 00:56:25.630 --> 00:56:30.860 align:middle line:84% Were you thinking of the same piece in two different keys? 00:56:30.860 --> 00:56:31.550 align:middle line:90% Could be? 00:56:31.550 --> 00:56:35.080 align:middle line:84% AUDIENCE: Yeah, that and saying, it's 00:56:35.080 --> 00:56:38.330 align:middle line:84% kind of synonymous to enharmonic, 00:56:38.330 --> 00:56:40.155 align:middle line:84% so if you're like G-flat major or F-sharp. 00:56:40.155 --> 00:56:41.030 align:middle line:90% MICHAEL CUTHBERT: OK. 00:56:41.030 --> 00:56:42.010 align:middle line:90% Yep, also. 00:56:42.010 --> 00:56:42.590 align:middle line:90% Great. 00:56:42.590 --> 00:56:46.160 align:middle line:84% But sometimes it doesn't matter actually what key you're in. 00:56:46.160 --> 00:56:48.850 align:middle line:84% If you're a singer and you show up, 00:56:48.850 --> 00:56:51.820 align:middle line:84% and people used to be able to-- pianists accompanists, 00:56:51.820 --> 00:56:54.560 align:middle line:84% collaborators used to really know how to do this and stuff. 00:56:54.560 --> 00:56:58.130 align:middle line:84% You've been practicing all week in G major, 00:56:58.130 --> 00:57:01.930 align:middle line:84% and the singer comes to the concert and says, 00:57:01.930 --> 00:57:04.160 align:middle line:84% I woke up with a scratchy throat. 00:57:04.160 --> 00:57:07.660 align:middle line:90% Can we take it down to F today? 00:57:07.660 --> 00:57:08.510 align:middle line:90% And they play. 00:57:08.510 --> 00:57:10.970 align:middle line:84% And you're still playing in some ways the same piece. 00:57:10.970 --> 00:57:14.900 align:middle line:84% So the transposition might not matter in some cases. 00:57:14.900 --> 00:57:16.360 align:middle line:84% In some cases, it really matters. 00:57:16.360 --> 00:57:19.570 align:middle line:84% One place it really matters is if you're 00:57:19.570 --> 00:57:22.270 align:middle line:84% playing the viola in the orchestra, 00:57:22.270 --> 00:57:24.920 align:middle line:84% and you choose to transpose and nobody else does. 00:57:24.920 --> 00:57:27.002 align:middle line:90% I think people will notice. 00:57:27.002 --> 00:57:30.050 align:middle line:84% So transposition, again, these are all equivalence classes. 00:57:30.050 --> 00:57:33.230 align:middle line:84% I didn't do a good job of this in other years of lecturing. 00:57:33.230 --> 00:57:37.810 align:middle line:84% So I want to say, now, these are things that in certain contexts 00:57:37.810 --> 00:57:41.260 align:middle line:84% make sense to apply, and in certain contexts, 00:57:41.260 --> 00:57:43.250 align:middle line:90% do not make sense to apply. 00:57:43.250 --> 00:57:46.030 align:middle line:84% And so transposition is one here. 00:57:46.030 --> 00:57:47.800 align:middle line:84% Inversion we've already talked about. 00:57:47.800 --> 00:57:50.480 align:middle line:84% In some cases, it makes sense to apply. 00:57:50.480 --> 00:57:52.390 align:middle line:90% In some cases, it doesn't. 00:57:52.390 --> 00:57:55.200 align:middle line:84% Want to say there are two different-- 00:57:55.200 --> 00:57:58.310 align:middle line:84% a number of different definitions of inversion. 00:57:58.310 --> 00:58:01.130 align:middle line:84% And that's actually one of the things that happens. 00:58:01.130 --> 00:58:05.900 align:middle line:84% One is something that we call a tonal inversion, where 00:58:05.900 --> 00:58:12.180 align:middle line:90% you say tonal-- 00:58:12.180 --> 00:58:15.240 align:middle line:84% I'll put it in the key signature-- something like that. 00:58:15.240 --> 00:58:19.880 align:middle line:84% Instead of going up four notes, we go down four notes, 00:58:19.880 --> 00:58:24.260 align:middle line:90% and then go down one more note. 00:58:24.260 --> 00:58:26.040 align:middle line:84% In this case, it's exactly the same. 00:58:26.040 --> 00:58:27.350 align:middle line:90% Let me go. 00:58:27.350 --> 00:58:29.353 align:middle line:90% Let me keep going up here. 00:58:29.353 --> 00:58:32.030 align:middle line:90% 00:58:32.030 --> 00:58:33.810 align:middle line:90% I have to go one more note up. 00:58:33.810 --> 00:58:36.560 align:middle line:90% Assume these go here. 00:58:36.560 --> 00:58:41.600 align:middle line:84% Eventually, you get to a point where this is a half step, 00:58:41.600 --> 00:58:43.486 align:middle line:90% and this is a-- 00:58:43.486 --> 00:58:46.940 align:middle line:84% that was good to do ledger lines-- whole step. 00:58:46.940 --> 00:58:49.190 align:middle line:84% In a tonal inversion, you just care 00:58:49.190 --> 00:58:51.787 align:middle line:84% that you went up a step in one, and you went down 00:58:51.787 --> 00:58:52.620 align:middle line:90% a step in the other. 00:58:52.620 --> 00:58:54.412 align:middle line:84% If you went up four steps, you don't really 00:58:54.412 --> 00:58:56.330 align:middle line:84% care if it's a perfect fourth or whatever. 00:58:56.330 --> 00:59:01.500 align:middle line:84% In an atonal, or post-tonal, or non-tonal thing, 00:59:01.500 --> 00:59:03.950 align:middle line:84% we would really want to make sure that-- 00:59:03.950 --> 00:59:04.920 align:middle line:90% where did I screw up? 00:59:04.920 --> 00:59:09.007 align:middle line:84% There has to be some place, because this is an octave up. 00:59:09.007 --> 00:59:11.090 align:middle line:84% I'm pretty sure if you go up an octave, you end up 00:59:11.090 --> 00:59:12.617 align:middle line:90% going down in octaves. 00:59:12.617 --> 00:59:14.700 align:middle line:84% AUDIENCE: The first series of notes in the second, 00:59:14.700 --> 00:59:15.492 align:middle line:90% the right hand one. 00:59:15.492 --> 00:59:17.620 align:middle line:90% 00:59:17.620 --> 00:59:18.620 align:middle line:90% MICHAEL CUTHBERT: Sorry. 00:59:18.620 --> 00:59:20.300 align:middle line:84% Now I'm in a post-tonal world, so now I 00:59:20.300 --> 00:59:22.040 align:middle line:84% need to write all my accidentals. 00:59:22.040 --> 00:59:23.340 align:middle line:90% Oh, there it is. 00:59:23.340 --> 00:59:25.160 align:middle line:84% That's the whole step, and so that 00:59:25.160 --> 00:59:29.976 align:middle line:84% would have to be the half, whole step, whole step, and there. 00:59:29.976 --> 00:59:34.130 align:middle line:84% Yeah, so those the two kinds of inversion 00:59:34.130 --> 00:59:36.020 align:middle line:90% that he's talking about. 00:59:36.020 --> 00:59:37.675 align:middle line:90% And sometimes it makes sense. 00:59:37.675 --> 00:59:38.550 align:middle line:90% Sometimes it doesn't. 00:59:38.550 --> 00:59:43.370 align:middle line:84% If you listen to the music, the post-tonal music of the early 00:59:43.370 --> 00:59:47.270 align:middle line:84% 20th century, they use inversional symmetry a lot. 00:59:47.270 --> 00:59:49.020 align:middle line:84% And so if you're trying to figure out, oh, 00:59:49.020 --> 00:59:51.600 align:middle line:84% how does this relate to something I've heard before, 00:59:51.600 --> 00:59:55.640 align:middle line:84% almost always try, well, is it the inversion of it? 00:59:55.640 --> 00:59:58.760 align:middle line:84% And there's some cool things that-- 00:59:58.760 --> 01:00:01.650 align:middle line:90% here's four triads. 01:00:01.650 --> 01:00:03.980 align:middle line:90% You might know them by name. 01:00:03.980 --> 01:00:07.622 align:middle line:84% You don't need to know the name, but what type of triad are they. 01:00:07.622 --> 01:00:10.032 align:middle line:90% [MUSICAL NOTES] 01:00:10.032 --> 01:00:11.960 align:middle line:90% Anyone, shout it out. 01:00:11.960 --> 01:00:12.650 align:middle line:90% AUDIENCE: Major. 01:00:12.650 --> 01:00:13.650 align:middle line:90% MICHAEL CUTHBERT: Major. 01:00:13.650 --> 01:00:14.870 align:middle line:90% [MUSICAL NOTES] 01:00:14.870 --> 01:00:15.370 align:middle line:90% Minor. 01:00:15.370 --> 01:00:18.650 align:middle line:90% 01:00:18.650 --> 01:00:19.587 align:middle line:90% [MUSICAL NOTES] 01:00:19.587 --> 01:00:20.420 align:middle line:90% AUDIENCE: Augmented. 01:00:20.420 --> 01:00:21.720 align:middle line:90% MICHAEL CUTHBERT: Augmented. 01:00:21.720 --> 01:00:23.210 align:middle line:90% [MUSICAL NOTES] 01:00:23.210 --> 01:00:24.560 align:middle line:90% Diminished. 01:00:24.560 --> 01:00:26.423 align:middle line:84% So there's four different triads. 01:00:26.423 --> 01:00:31.130 align:middle line:90% 01:00:31.130 --> 01:00:35.880 align:middle line:84% Major, minor, augmented, diminished. 01:00:35.880 --> 01:00:38.810 align:middle line:84% A lot of people think that major and minor 01:00:38.810 --> 01:00:42.480 align:middle line:84% have more, something more in common than the other two, 01:00:42.480 --> 01:00:50.550 align:middle line:84% because this goes what's up a major third, up a minor third. 01:00:50.550 --> 01:00:54.560 align:middle line:84% If you start and instead go the opposite way, and you start here 01:00:54.560 --> 01:00:59.480 align:middle line:84% and you go up a minor third, and then you go up a major third, 01:00:59.480 --> 01:01:00.870 align:middle line:90% you end up with a minor triad. 01:01:00.870 --> 01:01:05.880 align:middle line:84% So the minor triad is the inversion of the major triad. 01:01:05.880 --> 01:01:10.470 align:middle line:84% And therefore, they both have the exact same interval content. 01:01:10.470 --> 01:01:12.810 align:middle line:84% They both have a minor third, a major third, 01:01:12.810 --> 01:01:20.210 align:middle line:84% and a perfect fifth within them, whereas an augmented triad 01:01:20.210 --> 01:01:25.910 align:middle line:84% cannot be inverted to become a diminished triad, 01:01:25.910 --> 01:01:28.770 align:middle line:84% or to become a major or minor triad. 01:01:28.770 --> 01:01:31.890 align:middle line:84% So they don't have an equivalence class between them. 01:01:31.890 --> 01:01:34.070 align:middle line:90% So this comes up often. 01:01:34.070 --> 01:01:40.620 align:middle line:84% Last cardinality, how many notes there are. 01:01:40.620 --> 01:01:42.060 align:middle line:90% Sometimes it matters. 01:01:42.060 --> 01:01:43.010 align:middle line:90% Sometimes it doesn't. 01:01:43.010 --> 01:01:45.710 align:middle line:90% [MUSICAL NOTES] 01:01:45.710 --> 01:01:47.083 align:middle line:90% Versus. 01:01:47.083 --> 01:01:50.370 align:middle line:90% [MUSIC PLAYING] 01:01:50.370 --> 01:01:50.870 align:middle line:90% 01:01:50.870 --> 01:01:53.440 align:middle line:90% In some ways the same? 01:01:53.440 --> 01:01:53.940 align:middle line:90% Yeah. 01:01:53.940 --> 01:01:58.247 align:middle line:84% Also, if you put it together with octave and cardinality-- 01:01:58.247 --> 01:01:59.830 align:middle line:84% I'm not going to run over there again. 01:01:59.830 --> 01:02:04.050 align:middle line:84% I need to put my keyboard here-- a four-note major triad, 01:02:04.050 --> 01:02:07.750 align:middle line:84% C-E-G-C, now you say that octave doesn't matter. 01:02:07.750 --> 01:02:10.930 align:middle line:84% So now it's C-E-G and a second C here. 01:02:10.930 --> 01:02:12.930 align:middle line:84% And now you really want cardinality not 01:02:12.930 --> 01:02:14.970 align:middle line:84% to matter if you want to say, is this the same 01:02:14.970 --> 01:02:18.780 align:middle line:90% as some other C major triad. 01:02:18.780 --> 01:02:22.080 align:middle line:84% And the last one I think is really important. 01:02:22.080 --> 01:02:26.460 align:middle line:84% Dmitri Tymoczko comes from a slightly different practice 01:02:26.460 --> 01:02:27.780 align:middle line:90% world. 01:02:27.780 --> 01:02:31.300 align:middle line:84% He just assumes that spelling is equivalent, 01:02:31.300 --> 01:02:34.030 align:middle line:84% or what we call MIDI equivalent, or enharmonic equivalent. 01:02:34.030 --> 01:02:35.710 align:middle line:84% I should have called it enharmonic, 01:02:35.710 --> 01:02:37.740 align:middle line:84% but I can't figure out a way to make 01:02:37.740 --> 01:02:41.970 align:middle line:90% an E into the optic acronym. 01:02:41.970 --> 01:02:45.880 align:middle line:84% So does enharmonic equivalent, does spelling matter? 01:02:45.880 --> 01:02:49.230 align:middle line:84% And one of the things in his world, which 01:02:49.230 --> 01:02:51.330 align:middle line:84% is very different from Music21, but in problem 01:02:51.330 --> 01:02:52.830 align:middle line:84% set four, you're going to be working 01:02:52.830 --> 01:02:56.010 align:middle line:84% in the world of optic, of geometry, of music, 01:02:56.010 --> 01:03:00.030 align:middle line:84% the spelling equivalence is always assumed. 01:03:00.030 --> 01:03:00.780 align:middle line:90% Yep. 01:03:00.780 --> 01:03:03.300 align:middle line:90% AUDIENCE: Poetic? 01:03:03.300 --> 01:03:05.280 align:middle line:90% P-O-E-T. 01:03:05.280 --> 01:03:07.410 align:middle line:84% MICHAEL CUTHBERT: P-O. Yeah, but then I 01:03:07.410 --> 01:03:08.850 align:middle line:90% would have to rearrange his. 01:03:08.850 --> 01:03:10.420 align:middle line:84% Yeah, no, that's really, really good. 01:03:10.420 --> 01:03:13.630 align:middle line:84% There's another one that we can start putting in. 01:03:13.630 --> 01:03:16.023 align:middle line:84% We can start thinking of timbre equivalents. 01:03:16.023 --> 01:03:17.940 align:middle line:84% We often think of that, all these other things 01:03:17.940 --> 01:03:19.180 align:middle line:90% that you wrote up there. 01:03:19.180 --> 01:03:23.160 align:middle line:84% But these are the ones that will give you the most hard time 01:03:23.160 --> 01:03:26.730 align:middle line:90% on the next problem set. 01:03:26.730 --> 01:03:28.060 align:middle line:90% There's not time. 01:03:28.060 --> 01:03:31.830 align:middle line:84% So we'll end this up, end a little bit early 01:03:31.830 --> 01:03:33.390 align:middle line:90% for the first time in a while. 01:03:33.390 --> 01:03:33.990 align:middle line:90% Cool. 01:03:33.990 --> 01:03:38.250 align:middle line:84% We'll get to working with intervals next class 01:03:38.250 --> 01:03:39.580 align:middle line:90% and filtering streams. 01:03:39.580 --> 01:03:42.180 align:middle line:90% Thanks, everybody. 01:03:42.180 --> 01:03:52.000 align:middle line:90%