WEBVTT 00:00:00.000 --> 00:00:02.455 align:middle line:90% [SQUEAKING] 00:00:02.455 --> 00:00:04.419 align:middle line:90% [RUSTLING] 00:00:04.419 --> 00:00:05.892 align:middle line:90% [CLICKING] 00:00:05.892 --> 00:00:09.520 align:middle line:90% 00:00:09.520 --> 00:00:11.520 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Let's get started. 00:00:11.520 --> 00:00:12.780 align:middle line:90% Welcome back. 00:00:12.780 --> 00:00:13.610 align:middle line:90% 21M. 00:00:13.610 --> 00:00:16.940 align:middle line:84% 383, Computational Music Theory and Analysis. 00:00:16.940 --> 00:00:20.730 align:middle line:84% We went through probably one of the most slide-heavy, 00:00:20.730 --> 00:00:25.130 align:middle line:84% one of the fastest classes ever on Wednesday 00:00:25.130 --> 00:00:27.330 align:middle line:84% that I'll be doing this semester. 00:00:27.330 --> 00:00:29.010 align:middle line:84% Today, we're going to switch gears. 00:00:29.010 --> 00:00:32.930 align:middle line:84% We're going to do one of the least tech-heavy classes 00:00:32.930 --> 00:00:34.820 align:middle line:84% in this semester, and then we'll probably 00:00:34.820 --> 00:00:36.030 align:middle line:90% keep going back and forth. 00:00:36.030 --> 00:00:39.570 align:middle line:84% This is the only one that in my particular notes, 00:00:39.570 --> 00:00:41.700 align:middle line:90% it's for my lecture. 00:00:41.700 --> 00:00:44.220 align:middle line:90% It says, Mike, don't panic. 00:00:44.220 --> 00:00:47.580 align:middle line:84% There actually is no PowerPoint, because I 00:00:47.580 --> 00:00:49.830 align:middle line:84% was panicking the other day when I was preparing this. 00:00:49.830 --> 00:00:50.760 align:middle line:84% I was like, wait, wait, wait wait. 00:00:50.760 --> 00:00:51.570 align:middle line:90% Did I delete it? 00:00:51.570 --> 00:00:53.780 align:middle line:84% No, there is nothing, because I want 00:00:53.780 --> 00:00:56.900 align:middle line:84% us to step back for a little bit and think about some 00:00:56.900 --> 00:01:00.730 align:middle line:84% of the things and do some work on some of the things 00:01:00.730 --> 00:01:03.320 align:middle line:84% to do with what we mean by music, 00:01:03.320 --> 00:01:05.450 align:middle line:90% because various musical points. 00:01:05.450 --> 00:01:07.450 align:middle line:84% Because there's a lot of things that we 00:01:07.450 --> 00:01:15.821 align:middle line:84% can know that are just sort of intuitively, 00:01:15.821 --> 00:01:17.930 align:middle line:90% we all know what that is. 00:01:17.930 --> 00:01:23.950 align:middle line:84% But then we might not be able to explain it to a computer, 00:01:23.950 --> 00:01:27.320 align:middle line:84% because computers are smart or computers are dumb. 00:01:27.320 --> 00:01:28.600 align:middle line:90% What do you think? 00:01:28.600 --> 00:01:29.480 align:middle line:90% Shout it out. 00:01:29.480 --> 00:01:31.150 align:middle line:90% AUDIENCE: Dumb. 00:01:31.150 --> 00:01:32.240 align:middle line:90% AUDIENCE: Neither? 00:01:32.240 --> 00:01:33.200 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Neither, dumb, neither. 00:01:33.200 --> 00:01:33.880 align:middle line:90% No, no smart? 00:01:33.880 --> 00:01:36.130 align:middle line:84% OK, I think computers are really, really dumb 00:01:36.130 --> 00:01:38.870 align:middle line:84% until we make them smart or something like that. 00:01:38.870 --> 00:01:39.370 align:middle line:90% Great. 00:01:39.370 --> 00:01:41.797 align:middle line:84% There's some people in the back whose names I don't know. 00:01:41.797 --> 00:01:43.130 align:middle line:90% Could you take a sheet of paper? 00:01:43.130 --> 00:01:47.350 align:middle line:84% You can also use your outline to put your name on it, because-- 00:01:47.350 --> 00:01:49.430 align:middle line:90% the outlines for reading later. 00:01:49.430 --> 00:01:52.010 align:middle line:84% And it's kind of nice this way you have it for later. 00:01:52.010 --> 00:01:55.720 align:middle line:84% And this way, you won't sort of get me 00:01:55.720 --> 00:01:57.840 align:middle line:90% if I go out of order, right? 00:01:57.840 --> 00:02:00.000 align:middle line:90% OK. 00:02:00.000 --> 00:02:02.730 align:middle line:84% So I'm seeing here your names are. 00:02:02.730 --> 00:02:04.980 align:middle line:84% Can you take a second and at least 00:02:04.980 --> 00:02:06.390 align:middle line:84% the person you're sharing a table 00:02:06.390 --> 00:02:09.100 align:middle line:84% or sharing the invisible table with, 00:02:09.100 --> 00:02:12.182 align:middle line:84% and introduce yourself if you don't know them? 00:02:12.182 --> 00:02:13.305 align:middle line:90% [SIDE CONVERSATION] 00:02:13.305 --> 00:02:14.680 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK, 00:02:14.680 --> 00:02:20.705 align:middle line:84% now add into your conversation what you think a note is. 00:02:20.705 --> 00:02:22.080 align:middle line:84% You can also keep getting to know 00:02:22.080 --> 00:02:23.247 align:middle line:90% each other at the same time. 00:02:23.247 --> 00:02:24.845 align:middle line:90% But what you think a note is? 00:02:24.845 --> 00:02:26.795 align:middle line:90% [SIDE CONVERSATION] 00:02:26.795 --> 00:02:27.420 align:middle line:90% AUDIENCE: Yeah. 00:02:27.420 --> 00:02:28.962 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK, I'm 00:02:28.962 --> 00:02:32.500 align:middle line:84% going to be asking you for some definitions in a second. 00:02:32.500 --> 00:02:37.950 align:middle line:84% But before we get to that, all I want you to do 00:02:37.950 --> 00:02:39.510 align:middle line:84% is take your definitions-- you've 00:02:39.510 --> 00:02:40.980 align:middle line:84% kind of got them the first thing-- 00:02:40.980 --> 00:02:43.355 align:middle line:84% and you've just got to count notes, OK? 00:02:43.355 --> 00:02:44.730 align:middle line:84% So I'm going to sing some things, 00:02:44.730 --> 00:02:46.800 align:middle line:84% and you tell me how many notes I sing. 00:02:46.800 --> 00:02:52.050 align:middle line:84% So write them down, and then I'll ask them later. 00:02:52.050 --> 00:02:54.330 align:middle line:90% First set. 00:02:54.330 --> 00:02:57.400 align:middle line:90% [SCAT SINGING] 00:02:57.400 --> 00:02:59.000 align:middle line:90% 00:02:59.000 --> 00:03:00.075 align:middle line:90% Pretty easy, right? 00:03:00.075 --> 00:03:02.690 align:middle line:90% 00:03:02.690 --> 00:03:04.190 align:middle line:90% Second one. 00:03:04.190 --> 00:03:06.270 align:middle line:90% [SCAT SINGING] 00:03:06.270 --> 00:03:12.470 align:middle line:90% 00:03:12.470 --> 00:03:14.450 align:middle line:90% Third one. 00:03:14.450 --> 00:03:18.238 align:middle line:90% [SCAT SINGING] 00:03:18.238 --> 00:03:21.590 align:middle line:90% 00:03:21.590 --> 00:03:23.990 align:middle line:90% Fourth one. 00:03:23.990 --> 00:03:27.601 align:middle line:90% [SCAT SINGING] 00:03:27.601 --> 00:03:31.450 align:middle line:90% 00:03:31.450 --> 00:03:33.790 align:middle line:90% And fifth one. 00:03:33.790 --> 00:03:34.660 align:middle line:90% [CLAPS] 00:03:34.660 --> 00:03:35.640 align:middle line:90% 00:03:35.640 --> 00:03:39.560 align:middle line:90% [MELODY PLAYING] 00:03:39.560 --> 00:03:40.550 align:middle line:90% 00:03:40.550 --> 00:03:41.060 align:middle line:90% Great. 00:03:41.060 --> 00:03:45.470 align:middle line:84% Talk with your neighbor and see if you got answers 00:03:45.470 --> 00:03:48.500 align:middle line:90% that line up with each other. 00:03:48.500 --> 00:03:51.866 align:middle line:90% OK, let's come back together. 00:03:51.866 --> 00:03:53.300 align:middle line:90% AUDIENCE: Yeah, [INAUDIBLE]. 00:03:53.300 --> 00:03:55.592 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Let's come back together. 00:03:55.592 --> 00:03:58.720 align:middle line:84% We have-- I believe that the normal distribution of names 00:03:58.720 --> 00:04:02.330 align:middle line:84% in this class is kind of like the letters in the alphabet. 00:04:02.330 --> 00:04:04.370 align:middle line:90% So we'll start with J's. 00:04:04.370 --> 00:04:06.640 align:middle line:84% I'll call on-- who's the alphabetically first J? 00:04:06.640 --> 00:04:08.200 align:middle line:90% Is it Jason? 00:04:08.200 --> 00:04:12.275 align:middle line:84% Jason, something like-- and if I change the things, 00:04:12.275 --> 00:04:14.650 align:middle line:84% I'm doing it accidentally because I don't remember what I 00:04:14.650 --> 00:04:16.700 align:middle line:90% sang, but the first one-- 00:04:16.700 --> 00:04:18.639 align:middle line:90% [SCAT SINGING] 00:04:18.639 --> 00:04:19.383 align:middle line:90% 00:04:19.383 --> 00:04:20.300 align:middle line:90% AUDIENCE: Three notes? 00:04:20.300 --> 00:04:20.720 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Three notes. 00:04:20.720 --> 00:04:21.350 align:middle line:90% How many agree? 00:04:21.350 --> 00:04:22.100 align:middle line:90% How many disagree? 00:04:22.100 --> 00:04:23.710 align:middle line:90% Agrees? 00:04:23.710 --> 00:04:25.480 align:middle line:90% Disagrees? 00:04:25.480 --> 00:04:26.447 align:middle line:90% OK, good. 00:04:26.447 --> 00:04:27.530 align:middle line:90% That was the right answer. 00:04:27.530 --> 00:04:29.060 align:middle line:90% I sang three notes. 00:04:29.060 --> 00:04:29.560 align:middle line:90% Good. 00:04:29.560 --> 00:04:32.840 align:middle line:84% Who's alphabetically next after Jason? 00:04:32.840 --> 00:04:34.510 align:middle line:90% We have Jonathans, Jordans. 00:04:34.510 --> 00:04:35.360 align:middle line:90% We have Jake. 00:04:35.360 --> 00:04:38.240 align:middle line:90% Oh, OK, we went out of order. 00:04:38.240 --> 00:04:39.610 align:middle line:90% Sorry about that, Jake. 00:04:39.610 --> 00:04:42.500 align:middle line:84% No, even if we do Jacob or something, I'm still wrong. 00:04:42.500 --> 00:04:44.830 align:middle line:90% OK, Jake? 00:04:44.830 --> 00:04:46.130 align:middle line:90% This is what I was saying. 00:04:46.130 --> 00:04:48.320 align:middle line:90% [SCAT SINGING] 00:04:48.320 --> 00:04:48.913 align:middle line:90% 00:04:48.913 --> 00:04:50.080 align:middle line:90% AUDIENCE: Probably one more. 00:04:50.080 --> 00:04:51.705 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: One note. 00:04:51.705 --> 00:04:53.270 align:middle line:90% Agree or disagree? 00:04:53.270 --> 00:04:54.780 align:middle line:90% Who agrees? 00:04:54.780 --> 00:04:56.670 align:middle line:90% Who disagrees? 00:04:56.670 --> 00:04:58.060 align:middle line:90% Good, everybody is wrong. 00:04:58.060 --> 00:05:00.480 align:middle line:90% I sang four. 00:05:00.480 --> 00:05:02.700 align:middle line:90% OK, next note. 00:05:02.700 --> 00:05:03.970 align:middle line:90% What's the next one I did? 00:05:03.970 --> 00:05:06.481 align:middle line:90% I went up, right? 00:05:06.481 --> 00:05:09.190 align:middle line:90% [SCAT SINGING] 00:05:09.190 --> 00:05:11.040 align:middle line:90% 00:05:11.040 --> 00:05:15.120 align:middle line:84% Next up alphabetically would be Jonathan comes before John 00:05:15.120 --> 00:05:16.240 align:middle line:90% and comes before Jordan. 00:05:16.240 --> 00:05:18.000 align:middle line:90% So Jonathan. 00:05:18.000 --> 00:05:19.200 align:middle line:90% AUDIENCE: OK. 00:05:19.200 --> 00:05:20.920 align:middle line:90% My impression was two notes. 00:05:20.920 --> 00:05:23.670 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Two notes. 00:05:23.670 --> 00:05:24.570 align:middle line:90% Good. 00:05:24.570 --> 00:05:27.390 align:middle line:90% Who agrees? 00:05:27.390 --> 00:05:29.340 align:middle line:90% OK, we got some agrees. 00:05:29.340 --> 00:05:30.990 align:middle line:90% Who disagrees? 00:05:30.990 --> 00:05:31.870 align:middle line:90% OK, good. 00:05:31.870 --> 00:05:34.000 align:middle line:84% Well, we'll continue with the J's on that. 00:05:34.000 --> 00:05:35.200 align:middle line:90% John, you disagreed. 00:05:35.200 --> 00:05:37.530 align:middle line:84% What's the number that you came up with? 00:05:37.530 --> 00:05:39.700 align:middle line:84% AUDIENCE: I thought because you sang a lot, 00:05:39.700 --> 00:05:41.368 align:middle line:84% I think you sang at least one note. 00:05:41.368 --> 00:05:42.910 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Oh, no. 00:05:42.910 --> 00:05:43.390 align:middle line:90% OK, OK. 00:05:43.390 --> 00:05:44.098 align:middle line:90% Whoa, whoa, whoa! 00:05:44.098 --> 00:05:44.790 align:middle line:90% [LAUGHTER] 00:05:44.790 --> 00:05:47.650 align:middle line:90% Greater than one note. 00:05:47.650 --> 00:05:49.560 align:middle line:84% No, greater than or equal to one note, right? 00:05:49.560 --> 00:05:51.700 align:middle line:90% OK, so that takes a little-- 00:05:51.700 --> 00:05:55.290 align:middle line:84% that's a pretty broad spectrum, I like that. 00:05:55.290 --> 00:05:57.080 align:middle line:90% It's always good. 00:05:57.080 --> 00:06:00.320 align:middle line:84% Who agrees with greater than or equal to one note 00:06:00.320 --> 00:06:02.300 align:middle line:90% or wants more-- 00:06:02.300 --> 00:06:05.040 align:middle line:84% disagree if you want more specificity than that. 00:06:05.040 --> 00:06:07.670 align:middle line:84% Who agrees with greater than or equal to one note? 00:06:07.670 --> 00:06:08.210 align:middle line:90% Good. 00:06:08.210 --> 00:06:09.570 align:middle line:90% Jordan's on your side. 00:06:09.570 --> 00:06:11.070 align:middle line:90% And she's got some people. 00:06:11.070 --> 00:06:11.570 align:middle line:90% Good. 00:06:11.570 --> 00:06:15.090 align:middle line:84% So who disagrees with everything beforehand up till now? 00:06:15.090 --> 00:06:15.590 align:middle line:90% Great. 00:06:15.590 --> 00:06:18.080 align:middle line:90% So I think we have-- 00:06:18.080 --> 00:06:19.825 align:middle line:84% now, Jason, we've already gone through. 00:06:19.825 --> 00:06:21.450 align:middle line:84% Raise your hands again if you disagree. 00:06:21.450 --> 00:06:23.570 align:middle line:84% I want to keep going alphabetically next 00:06:23.570 --> 00:06:24.870 align:middle line:90% among the disagreers. 00:06:24.870 --> 00:06:28.160 align:middle line:90% And that might be a Karima. 00:06:28.160 --> 00:06:28.685 align:middle line:90% Karima? 00:06:28.685 --> 00:06:29.310 align:middle line:90% AUDIENCE: Yeah. 00:06:29.310 --> 00:06:30.727 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Yep. 00:06:30.727 --> 00:06:31.895 align:middle line:90% AUDIENCE: I wrote NASATO 00:06:31.895 --> 00:06:35.600 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: NASATO OK. 00:06:35.600 --> 00:06:38.160 align:middle line:84% We'll make it so that it parses in Python. 00:06:38.160 --> 00:06:39.360 align:middle line:90% Not a number. 00:06:39.360 --> 00:06:40.550 align:middle line:90% Is that OK? 00:06:40.550 --> 00:06:41.890 align:middle line:90% OK, good. 00:06:41.890 --> 00:06:42.390 align:middle line:90% Good. 00:06:42.390 --> 00:06:46.610 align:middle line:84% And anybody still have your number not said? 00:06:46.610 --> 00:06:47.245 align:middle line:90% Adam? 00:06:47.245 --> 00:06:47.870 align:middle line:90% AUDIENCE: Yeah. 00:06:47.870 --> 00:06:49.860 align:middle line:90% I said 14 or 15. 00:06:49.860 --> 00:06:51.990 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 14 or 15. 00:06:51.990 --> 00:06:54.730 align:middle line:90% OK, very, very specific. 00:06:54.730 --> 00:06:56.110 align:middle line:90% What do you base that on? 00:06:56.110 --> 00:06:58.670 align:middle line:84% AUDIENCE: So you went from a C to either a C sharp or a D. 00:06:58.670 --> 00:07:00.790 align:middle line:84% So it's like if you go to all the chromatic notes 00:07:00.790 --> 00:07:02.180 align:middle line:84% and slur them all that's what you get. 00:07:02.180 --> 00:07:02.770 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK. 00:07:02.770 --> 00:07:03.320 align:middle line:90% OK, good. 00:07:03.320 --> 00:07:06.130 align:middle line:90% So we have a range extension. 00:07:06.130 --> 00:07:06.910 align:middle line:90% Good. 00:07:06.910 --> 00:07:10.305 align:middle line:84% Anybody else have a number that hasn't been done yet? 00:07:10.305 --> 00:07:14.305 align:middle line:90% 00:07:14.305 --> 00:07:16.750 align:middle line:90% So that's particularly good. 00:07:16.750 --> 00:07:20.230 align:middle line:90% This one, I went with inf. 00:07:20.230 --> 00:07:22.670 align:middle line:84% Oh, sorry, I wasn't telling you what my numbers were yet. 00:07:22.670 --> 00:07:23.170 align:middle line:90% OK. 00:07:23.170 --> 00:07:25.330 align:middle line:90% Well, that's one I went with. 00:07:25.330 --> 00:07:28.946 align:middle line:90% And then next one. 00:07:28.946 --> 00:07:32.920 align:middle line:90% [SCAT SINGING] 00:07:32.920 --> 00:07:33.520 align:middle line:90% 00:07:33.520 --> 00:07:35.906 align:middle line:90% We have some other-- 00:07:35.906 --> 00:07:38.870 align:middle line:90% [INAUDIBLE] we have a listener. 00:07:38.870 --> 00:07:40.850 align:middle line:84% But do you want to be a participant or also? 00:07:40.850 --> 00:07:41.720 align:middle line:90% Yeah, go ahead. 00:07:41.720 --> 00:07:43.000 align:middle line:90% So with that one. 00:07:43.000 --> 00:07:44.517 align:middle line:90% AUDIENCE: I wrote 6. 00:07:44.517 --> 00:07:45.850 align:middle line:90% MICHAEL SCOTT ASATO CUTHBERT: 6. 00:07:45.850 --> 00:07:47.690 align:middle line:90% Anybody agree? 00:07:47.690 --> 00:07:48.190 align:middle line:90% Yep. 00:07:48.190 --> 00:07:50.060 align:middle line:90% Anybody disagree? 00:07:50.060 --> 00:07:50.560 align:middle line:90% Good. 00:07:50.560 --> 00:07:52.140 align:middle line:90% OK. 00:07:52.140 --> 00:07:55.180 align:middle line:90% And yep. 00:07:55.180 --> 00:07:58.660 align:middle line:84% And now, oh you know I was giving the right numbers. 00:07:58.660 --> 00:08:01.870 align:middle line:84% Yep, so I'm going to say, I did that. 00:08:01.870 --> 00:08:03.150 align:middle line:90% I did that. 00:08:03.150 --> 00:08:04.570 align:middle line:90% Nobody disagreed? 00:08:04.570 --> 00:08:07.710 align:middle line:90% The correct answer there was 2. 00:08:07.710 --> 00:08:09.340 align:middle line:90% And don't worry, don't worry. 00:08:09.340 --> 00:08:11.560 align:middle line:84% This is not frustrating-- be frustrated. 00:08:11.560 --> 00:08:16.690 align:middle line:90% And then who's also around K? 00:08:16.690 --> 00:08:18.301 align:middle line:90% Or do I hear L? 00:08:18.301 --> 00:08:19.263 align:middle line:90% Oh. 00:08:19.263 --> 00:08:20.225 align:middle line:90% L? 00:08:20.225 --> 00:08:21.187 align:middle line:90% AUDIENCE: 0. 00:08:21.187 --> 00:08:22.520 align:middle line:90% MICHAEL SCOTT ASATO CUTHBERT: 0. 00:08:22.520 --> 00:08:25.650 align:middle line:90% 00:08:25.650 --> 00:08:28.020 align:middle line:90% Anybody disagree? 00:08:28.020 --> 00:08:29.080 align:middle line:90% Great. 00:08:29.080 --> 00:08:31.772 align:middle line:84% A person who's disagreed, who has to speak? 00:08:31.772 --> 00:08:32.730 align:middle line:90% AUDIENCE: I just had 1. 00:08:32.730 --> 00:08:34.110 align:middle line:90% MICHAEL SCOTT ASATO CUTHBERT: 1? 00:08:34.110 --> 00:08:34.610 align:middle line:90% Good. 00:08:34.610 --> 00:08:36.030 align:middle line:90% Who agrees with 1? 00:08:36.030 --> 00:08:36.669 align:middle line:90% Good. 00:08:36.669 --> 00:08:40.740 align:middle line:84% How many people have heard neither 0 nor 1? 00:08:40.740 --> 00:08:41.730 align:middle line:90% AUDIENCE: Yep. 00:08:41.730 --> 00:08:43.539 align:middle line:84% So when I was writing a lot of these, 00:08:43.539 --> 00:08:45.820 align:middle line:84% I put two answers to a lot of them, depending on how-- 00:08:45.820 --> 00:08:46.350 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Yeah, OK, but you 00:08:46.350 --> 00:08:47.517 align:middle line:90% can only give one right now. 00:08:47.517 --> 00:08:49.380 align:middle line:84% AUDIENCE: Yeah, well, it's how I notated, 00:08:49.380 --> 00:08:54.005 align:middle line:84% how I'd like pitch-wise, and I was taking it that-- 00:08:54.005 --> 00:08:55.380 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Oh. 00:08:55.380 --> 00:08:56.755 align:middle line:84% AUDIENCE: I was like I was taking 00:08:56.755 --> 00:08:59.005 align:middle line:84% perception of specklegrams and a clap has all of the-- 00:08:59.005 --> 00:09:00.547 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Uh-huh. 00:09:00.547 --> 00:09:01.410 align:middle line:90% So give me a number. 00:09:01.410 --> 00:09:02.910 align:middle line:84% AUDIENCE: That one would also be inf 00:09:02.910 --> 00:09:03.490 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Inf. 00:09:03.490 --> 00:09:04.200 align:middle line:90% OK. 00:09:04.200 --> 00:09:05.940 align:middle line:90% Good. 00:09:05.940 --> 00:09:09.270 align:middle line:84% This one, I'm going to go with 0. 00:09:09.270 --> 00:09:14.430 align:middle line:84% And I will tell you there isn't a single answer on here 00:09:14.430 --> 00:09:18.480 align:middle line:84% that you couldn't argue for and be correct. 00:09:18.480 --> 00:09:22.210 align:middle line:90% So why three notes? 00:09:22.210 --> 00:09:24.270 align:middle line:84% I think we all agreed because I think I sang-- 00:09:24.270 --> 00:09:25.625 align:middle line:90% [SCAT SINGING] 00:09:25.625 --> 00:09:28.150 align:middle line:84% And I count each of those as one note, right? 00:09:28.150 --> 00:09:30.660 align:middle line:90% Second one was 4, because-- 00:09:30.660 --> 00:09:32.850 align:middle line:90% [SCAT SINGING] 00:09:32.850 --> 00:09:33.570 align:middle line:90% 00:09:33.570 --> 00:09:41.910 align:middle line:84% --was a whole note tied to a quarter note tied to a 16th note 00:09:41.910 --> 00:09:44.970 align:middle line:90% tied to a 64th note. 00:09:44.970 --> 00:09:49.280 align:middle line:84% And I do believe that is the closest shortest representation 00:09:49.280 --> 00:09:50.540 align:middle line:90% I can do notationally. 00:09:50.540 --> 00:09:55.070 align:middle line:84% So I was thinking in a notational sphere here. 00:09:55.070 --> 00:09:58.910 align:middle line:84% This time, with the glissando, I was thinking of it 00:09:58.910 --> 00:10:02.650 align:middle line:84% as an infinite number of notes, because if it's continuous, 00:10:02.650 --> 00:10:03.150 align:middle line:90% it could be. 00:10:03.150 --> 00:10:05.930 align:middle line:84% But on the other hand, any of these other ones 00:10:05.930 --> 00:10:06.930 align:middle line:90% could be correct. 00:10:06.930 --> 00:10:09.495 align:middle line:84% Now, let's see if anyone can come up with how from-- 00:10:09.495 --> 00:10:12.170 align:middle line:90% [SCAT SINGING] 00:10:12.170 --> 00:10:13.460 align:middle line:90% --I came up with two. 00:10:13.460 --> 00:10:15.050 align:middle line:90% AUDIENCE: Two Pitches? 00:10:15.050 --> 00:10:16.350 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: There are two different pitches. 00:10:16.350 --> 00:10:17.730 align:middle line:90% That's one good way to do it. 00:10:17.730 --> 00:10:19.920 align:middle line:84% I'm glad I hit the same pitch each time, 00:10:19.920 --> 00:10:21.320 align:middle line:90% maybe something close. 00:10:21.320 --> 00:10:23.400 align:middle line:84% That's not the reason why I was thinking. 00:10:23.400 --> 00:10:23.940 align:middle line:90% Yeah. 00:10:23.940 --> 00:10:25.110 align:middle line:84% AUDIENCE: It's like sort of tremolo. 00:10:25.110 --> 00:10:26.693 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Tremolo. 00:10:26.693 --> 00:10:27.350 align:middle line:90% Yeah. 00:10:27.350 --> 00:10:30.300 align:middle line:84% It was something like, I don't know. 00:10:30.300 --> 00:10:32.640 align:middle line:84% Well, I don't know what thing we're in. 00:10:32.640 --> 00:10:36.560 align:middle line:84% But yeah, I was thinking it as something like that. 00:10:36.560 --> 00:10:38.310 align:middle line:84% Or actually, it would be measured tremolo. 00:10:38.310 --> 00:10:39.433 align:middle line:90% Wouldn't it be like-- 00:10:39.433 --> 00:10:44.480 align:middle line:90% 00:10:44.480 --> 00:10:49.520 align:middle line:84% anyone know this sign, where you have a beamed or no? 00:10:49.520 --> 00:10:50.780 align:middle line:90% Just one beam, right? 00:10:50.780 --> 00:10:52.758 align:middle line:90% Two-beamed dotted half notes. 00:10:52.758 --> 00:10:54.550 align:middle line:84% You see it everywhere every once in a while 00:10:54.550 --> 00:10:57.400 align:middle line:84% when you're playing like Prokofiev 00:10:57.400 --> 00:10:58.765 align:middle line:90% or Schubert or something. 00:10:58.765 --> 00:11:00.890 align:middle line:84% I always like, oh, I have to remember what that is. 00:11:00.890 --> 00:11:04.540 align:middle line:84% But that means fill in the space of one 00:11:04.540 --> 00:11:08.410 align:middle line:84% dotted half note with as many eighth notes 00:11:08.410 --> 00:11:11.710 align:middle line:84% as it takes to fill it in, alternating between the top one 00:11:11.710 --> 00:11:13.130 align:middle line:90% and the bottom one. 00:11:13.130 --> 00:11:15.211 align:middle line:90% AUDIENCE: And clap. 00:11:15.211 --> 00:11:16.836 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: And clap. 00:11:16.836 --> 00:11:17.950 align:middle line:90% AUDIENCE: [CLAPS] 00:11:17.950 --> 00:11:21.220 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: I thought a note to me 00:11:21.220 --> 00:11:26.650 align:middle line:84% had to have some sort of specifiable pitch. 00:11:26.650 --> 00:11:29.020 align:middle line:90% So I count zero. 00:11:29.020 --> 00:11:35.860 align:middle line:84% Now everything that somebody said, a one for this, 00:11:35.860 --> 00:11:39.940 align:middle line:84% or infinite, are all valid definitions 00:11:39.940 --> 00:11:42.820 align:middle line:84% of what we're going to be talking about. 00:11:42.820 --> 00:11:44.300 align:middle line:90% And here's the thing. 00:11:44.300 --> 00:11:47.850 align:middle line:84% 99% of the time when I'm not trying 00:11:47.850 --> 00:11:53.310 align:middle line:84% to set up an example for having fun in the first week of class 00:11:53.310 --> 00:11:56.520 align:middle line:84% with you all, there's no way I would call that second one four 00:11:56.520 --> 00:11:57.100 align:middle line:90% notes, right? 00:11:57.100 --> 00:12:00.150 align:middle line:84% I mean, if I hear it, I'm going to beat one. 00:12:00.150 --> 00:12:03.870 align:middle line:84% So one of the things that's going to come up quite often 00:12:03.870 --> 00:12:08.370 align:middle line:84% is that depending on what purpose you 00:12:08.370 --> 00:12:10.710 align:middle line:84% want to do with something, you're 00:12:10.710 --> 00:12:15.030 align:middle line:84% not going to be able to necessarily even know 00:12:15.030 --> 00:12:17.310 align:middle line:84% how many notes or how many of something 00:12:17.310 --> 00:12:20.760 align:middle line:84% there is, let alone what's the correct spelling of something 00:12:20.760 --> 00:12:23.520 align:middle line:90% or not. 00:12:23.520 --> 00:12:27.060 align:middle line:84% So I think we're just going to be playing around 00:12:27.060 --> 00:12:28.210 align:middle line:90% with something like this. 00:12:28.210 --> 00:12:32.080 align:middle line:84% Now, go back to your definitions of notes that you had before, 00:12:32.080 --> 00:12:35.680 align:middle line:84% and let's grab into groups of four. 00:12:35.680 --> 00:12:38.250 align:middle line:84% So your two groups that are the same joining 00:12:38.250 --> 00:12:39.370 align:middle line:90% with the group behind you. 00:12:39.370 --> 00:12:42.210 align:middle line:84% So we're going to get good at spinning over here. 00:12:42.210 --> 00:12:45.100 align:middle line:84% OK, a group of three here, and three here. 00:12:45.100 --> 00:12:47.690 align:middle line:90% And we'll break up this group. 00:12:47.690 --> 00:12:51.530 align:middle line:84% And talk about what your definitions of the notes 00:12:51.530 --> 00:12:53.490 align:middle line:90% were with the other group. 00:12:53.490 --> 00:12:57.410 align:middle line:84% And then try to figure out, A, if you had correct definitions 00:12:57.410 --> 00:12:59.120 align:middle line:90% or if you had compatible-- 00:12:59.120 --> 00:13:01.730 align:middle line:84% is not a correct definition, compatible definitions 00:13:01.730 --> 00:13:04.830 align:middle line:84% of notes before that with each other's group. 00:13:04.830 --> 00:13:07.790 align:middle line:84% And then also, if you want to change 00:13:07.790 --> 00:13:10.430 align:middle line:84% the definition based on all the weird numbers 00:13:10.430 --> 00:13:12.180 align:middle line:90% that we came up with here. 00:13:12.180 --> 00:13:14.640 align:middle line:84% So go ahead and let's take a couple of minutes to do that. 00:13:14.640 --> 00:13:15.140 align:middle line:90% Great. 00:13:15.140 --> 00:13:18.080 align:middle line:84% Let's all come back together, and-- 00:13:18.080 --> 00:13:21.976 align:middle line:90% [SIDE CONVERSATION] 00:13:21.976 --> 00:13:26.360 align:middle line:90% 00:13:26.360 --> 00:13:29.330 align:middle line:84% There was one word that I just kept 00:13:29.330 --> 00:13:33.770 align:middle line:84% hearing as I was going around, and it begins like this. 00:13:33.770 --> 00:13:36.860 align:middle line:84% When any group use a word that begins 00:13:36.860 --> 00:13:40.040 align:middle line:90% with this in their definition. 00:13:40.040 --> 00:13:40.550 align:middle line:90% Yeah. 00:13:40.550 --> 00:13:41.188 align:middle line:90% John, go ahead. 00:13:41.188 --> 00:13:42.230 align:middle line:90% AUDIENCE: Representation. 00:13:42.230 --> 00:13:45.050 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Representation, yeah. 00:13:45.050 --> 00:13:48.520 align:middle line:90% Presentation. 00:13:48.520 --> 00:13:57.090 align:middle line:84% So we can start with a note is a-- 00:13:57.090 --> 00:14:03.370 align:middle line:84% of-- is anybody's definition completely incompatible 00:14:03.370 --> 00:14:05.410 align:middle line:90% with this opening? 00:14:05.410 --> 00:14:09.280 align:middle line:84% Like, couldn't be put in-- it's no smiles, I think. 00:14:09.280 --> 00:14:15.430 align:middle line:84% OK, so what are some of the ways that your groups could 00:14:15.430 --> 00:14:17.210 align:middle line:90% have done this? 00:14:17.210 --> 00:14:21.050 align:middle line:84% I didn't think I heard, because it's physically difficult, 00:14:21.050 --> 00:14:27.190 align:middle line:84% what Jonathan, Karima, Jordan, and Misha's group came up with. 00:14:27.190 --> 00:14:32.920 align:middle line:84% How would somebody in this group continue that of everybody 00:14:32.920 --> 00:14:35.330 align:middle line:84% has-- oh, you guys are all normally distributed names. 00:14:35.330 --> 00:14:36.860 align:middle line:90% So I've heard from everybody. 00:14:36.860 --> 00:14:38.505 align:middle line:90% So Karima, would you like to-- 00:14:38.505 --> 00:14:39.880 align:middle line:84% AUDIENCE: I think that's anything 00:14:39.880 --> 00:14:40.930 align:middle line:90% with a pitch and duration. 00:14:40.930 --> 00:14:42.347 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: It's 00:14:42.347 --> 00:14:51.347 align:middle line:84% a representation of anything with a pitch and duration. 00:14:51.347 --> 00:14:55.920 align:middle line:90% 00:14:55.920 --> 00:15:00.840 align:middle line:90% And groups disagree with that? 00:15:00.840 --> 00:15:01.560 align:middle line:90% Yeah. 00:15:01.560 --> 00:15:05.100 align:middle line:84% AUDIENCE: So I'm coming at this from the percussion perspective, 00:15:05.100 --> 00:15:07.540 align:middle line:84% where a note doesn't necessarily need a pitch, 00:15:07.540 --> 00:15:09.640 align:middle line:84% and it doesn't necessarily need a duration. 00:15:09.640 --> 00:15:11.015 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK. 00:15:11.015 --> 00:15:14.340 align:middle line:84% So we have not necessarily on that. 00:15:14.340 --> 00:15:16.350 align:middle line:84% So do you have a positive-- did your group 00:15:16.350 --> 00:15:22.097 align:middle line:84% come up with a positive definition from that? 00:15:22.097 --> 00:15:24.305 align:middle line:84% AUDIENCE: I don't think our group came into agreement 00:15:24.305 --> 00:15:24.700 align:middle line:90% [INAUDIBLE]-- 00:15:24.700 --> 00:15:25.240 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Oh, good. 00:15:25.240 --> 00:15:25.948 align:middle line:90% Let's hear some-- 00:15:25.948 --> 00:15:28.650 align:middle line:84% AUDIENCE: --of you is a note as a representation of an instance 00:15:28.650 --> 00:15:30.160 align:middle line:90% of striking something. 00:15:30.160 --> 00:15:31.870 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: An instance of striking something. 00:15:31.870 --> 00:15:32.520 align:middle line:90% OK. 00:15:32.520 --> 00:15:37.690 align:middle line:90% Anybody-- so that's Matthew. 00:15:37.690 --> 00:15:47.280 align:middle line:84% Anybody want to go forward with that, like-- 00:15:47.280 --> 00:15:52.490 align:middle line:84% sorry, I can't talk and write something else at the same time. 00:15:52.490 --> 00:16:01.400 align:middle line:84% Anybody [AUDIO OUT] that's perfect for things-- 00:16:01.400 --> 00:16:04.650 align:middle line:84% while you're speaking, anything with a pitch and a duration. 00:16:04.650 --> 00:16:07.070 align:middle line:84% I think an airplane on an airline flight 00:16:07.070 --> 00:16:10.070 align:middle line:84% has it's pitch and duration, right? 00:16:10.070 --> 00:16:12.420 align:middle line:84% So I'll start calling them notes, too. 00:16:12.420 --> 00:16:13.950 align:middle line:90% No, I'm just having fun. 00:16:13.950 --> 00:16:17.040 align:middle line:84% Just trying to get us to think so we can start making things, 00:16:17.040 --> 00:16:19.200 align:middle line:84% how we're going to make this happen for computer. 00:16:19.200 --> 00:16:20.760 align:middle line:90% I like both of these. 00:16:20.760 --> 00:16:23.210 align:middle line:84% An instance of striking something, so-- 00:16:23.210 --> 00:16:23.940 align:middle line:90% yeah. 00:16:23.940 --> 00:16:25.010 align:middle line:84% AUDIENCE: I feel like that doesn't really 00:16:25.010 --> 00:16:26.218 align:middle line:90% apply to certain instruments. 00:16:26.218 --> 00:16:29.630 align:middle line:84% Like violins, for example, you don't have to strike anything 00:16:29.630 --> 00:16:32.750 align:middle line:90% to issue the next note. 00:16:32.750 --> 00:16:34.310 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Good. 00:16:34.310 --> 00:16:38.010 align:middle line:84% So does somebody who hasn't spoken 00:16:38.010 --> 00:16:41.140 align:middle line:84% want to defend an instance of striking something 00:16:41.140 --> 00:16:43.600 align:middle line:90% as applying to the violin? 00:16:43.600 --> 00:16:45.160 align:middle line:90% Yeah, go ahead, Vanessa. 00:16:45.160 --> 00:16:47.300 align:middle line:84% AUDIENCE: I mean, if you want to be annoying, 00:16:47.300 --> 00:16:50.170 align:middle line:84% you can use a version of striking 00:16:50.170 --> 00:16:51.820 align:middle line:90% in a much more general sense. 00:16:51.820 --> 00:16:53.810 align:middle line:84% So if [INAUDIBLE] like hitting anything, 00:16:53.810 --> 00:16:56.480 align:middle line:84% could just be when you're moving a bow across strings, 00:16:56.480 --> 00:16:58.970 align:middle line:84% you can say that counts as a form of striking, 00:16:58.970 --> 00:17:02.115 align:middle line:84% even if it's not the most straightforward definition. 00:17:02.115 --> 00:17:03.490 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK. 00:17:03.490 --> 00:17:04.700 align:middle line:84% AUDIENCE: Is that a wind instrument? 00:17:04.700 --> 00:17:05.319 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: What about a wind-- 00:17:05.319 --> 00:17:06.569 align:middle line:90% AUDIENCE: [INAUDIBLE] whistle? 00:17:06.569 --> 00:17:07.244 align:middle line:90% [INAUDIBLE] 00:17:07.244 --> 00:17:08.619 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK. 00:17:08.619 --> 00:17:09.536 align:middle line:90% AUDIENCE: [INAUDIBLE]. 00:17:09.536 --> 00:17:10.842 align:middle line:90% AUDIENCE: [LAUGHS] 00:17:10.842 --> 00:17:12.550 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Most of you 00:17:12.550 --> 00:17:14.569 align:middle line:84% are juniors and seniors and things. 00:17:14.569 --> 00:17:18.670 align:middle line:84% So most of you all have gotten through your physics mechanics 00:17:18.670 --> 00:17:20.480 align:middle line:90% general institute requirement. 00:17:20.480 --> 00:17:24.284 align:middle line:84% Anybody want to say how sound's produced? 00:17:24.284 --> 00:17:27.790 align:middle line:90% 00:17:27.790 --> 00:17:29.950 align:middle line:90% Or perceived, maybe? 00:17:29.950 --> 00:17:30.670 align:middle line:90% Moving? 00:17:30.670 --> 00:17:31.610 align:middle line:90% AUDIENCE: Vibrations of air. 00:17:31.610 --> 00:17:32.570 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Vibrations of air. 00:17:32.570 --> 00:17:33.070 align:middle line:90% Good. 00:17:33.070 --> 00:17:37.797 align:middle line:84% And so there's a lot of air vibrating way, 00:17:37.797 --> 00:17:38.630 align:middle line:90% way down the street. 00:17:38.630 --> 00:17:40.275 align:middle line:90% Why do I not hear it? 00:17:40.275 --> 00:17:42.232 align:middle line:90% AUDIENCE: Inverse square law? 00:17:42.232 --> 00:17:44.440 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: The inverse square law. 00:17:44.440 --> 00:17:46.010 align:middle line:90% Yes, that might be. 00:17:46.010 --> 00:17:50.618 align:middle line:84% But what is not happening with the movement of air? 00:17:50.618 --> 00:17:52.160 align:middle line:84% AUDIENCE: It's not reaching our ears. 00:17:52.160 --> 00:17:54.535 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: It's not reaching our ears. 00:17:54.535 --> 00:17:57.490 align:middle line:84% It's not-- what is the one of the first thing it 00:17:57.490 --> 00:17:59.080 align:middle line:90% reaches in our ears? 00:17:59.080 --> 00:17:59.830 align:middle line:90% AUDIENCE: Eardrum? 00:17:59.830 --> 00:18:01.413 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Eardrum. 00:18:01.413 --> 00:18:02.621 align:middle line:90% Oh. 00:18:02.621 --> 00:18:04.190 align:middle line:90% So maybe there is a way. 00:18:04.190 --> 00:18:08.470 align:middle line:84% So we could say an instance of something striking something, 00:18:08.470 --> 00:18:12.765 align:middle line:90% such as air striking a drum. 00:18:12.765 --> 00:18:22.690 align:middle line:90% 00:18:22.690 --> 00:18:26.367 align:middle line:84% Before half an hour of you go, how many of you 00:18:26.367 --> 00:18:27.825 align:middle line:84% would have said that that's a note? 00:18:27.825 --> 00:18:30.850 align:middle line:90% 00:18:30.850 --> 00:18:31.390 align:middle line:90% OK. 00:18:31.390 --> 00:18:32.383 align:middle line:90% What's it striking? 00:18:32.383 --> 00:18:35.753 align:middle line:90% 00:18:35.753 --> 00:18:36.920 align:middle line:90% AUDIENCE: There is a strike. 00:18:36.920 --> 00:18:38.300 align:middle line:84% You said it's a representation of it. 00:18:38.300 --> 00:18:38.960 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Oh, it's 00:18:38.960 --> 00:18:40.790 align:middle line:84% a representation of something striking. 00:18:40.790 --> 00:18:41.290 align:middle line:90% Good. 00:18:41.290 --> 00:18:41.790 align:middle line:90% Good. 00:18:41.790 --> 00:18:42.780 align:middle line:90% OK. 00:18:42.780 --> 00:18:44.900 align:middle line:84% Any other things that we want to do 00:18:44.900 --> 00:18:47.600 align:middle line:84% with confusing, confusing definitions 00:18:47.600 --> 00:18:51.740 align:middle line:84% before we get to one of the points of this class? 00:18:51.740 --> 00:18:56.150 align:middle line:84% Any other really great, beautiful things 00:18:56.150 --> 00:18:57.715 align:middle line:90% that wasn't covered here? 00:18:57.715 --> 00:19:00.470 align:middle line:90% 00:19:00.470 --> 00:19:03.730 align:middle line:84% By the way, I forgot to do this part on there. 00:19:03.730 --> 00:19:06.430 align:middle line:90% 00:19:06.430 --> 00:19:09.286 align:middle line:90% [PLAYS KEY] 00:19:09.286 --> 00:19:10.250 align:middle line:90% 00:19:10.250 --> 00:19:11.230 align:middle line:90% How many notes? 00:19:11.230 --> 00:19:12.703 align:middle line:90% AUDIENCE: Should be three. 00:19:12.703 --> 00:19:13.370 align:middle line:90% AUDIENCE: Three? 00:19:13.370 --> 00:19:14.745 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK, 00:19:14.745 --> 00:19:18.590 align:middle line:84% so if there's something [AUDIO OUT] when you play that, 00:19:18.590 --> 00:19:22.250 align:middle line:84% the three different sounds being done 00:19:22.250 --> 00:19:24.150 align:middle line:84% could be considered three different notes. 00:19:24.150 --> 00:19:29.780 align:middle line:84% So is a chord a note or is a chord a bunch of notes, 00:19:29.780 --> 00:19:31.293 align:middle line:90% or is a chord something else? 00:19:31.293 --> 00:19:34.490 align:middle line:90% 00:19:34.490 --> 00:19:37.390 align:middle line:84% I'd say this because we're going to spend the-- a lot 00:19:37.390 --> 00:19:41.140 align:middle line:84% of the first problem set in the next week is going to be on how 00:19:41.140 --> 00:19:44.020 align:middle line:84% to represent music for the computers-- 00:19:44.020 --> 00:19:47.116 align:middle line:84% for the computers as of the 1960s. 00:19:47.116 --> 00:19:49.520 align:middle line:90% [LAUGHS] For a computer. 00:19:49.520 --> 00:19:58.360 align:middle line:84% So what kinds of choices will lead us into bad places fastest? 00:19:58.360 --> 00:20:01.960 align:middle line:84% And which ones will keep us in good and useful places 00:20:01.960 --> 00:20:03.350 align:middle line:90% for the longest amount of time? 00:20:03.350 --> 00:20:06.650 align:middle line:84% Notice I didn't say which ones will never lead you astray, 00:20:06.650 --> 00:20:09.010 align:middle line:84% because you're always every definition that you're 00:20:09.010 --> 00:20:11.470 align:middle line:84% going to encode into a computer at some point 00:20:11.470 --> 00:20:14.850 align:middle line:84% is going to completely screw up something, for instance. 00:20:14.850 --> 00:20:18.070 align:middle line:90% 00:20:18.070 --> 00:20:21.370 align:middle line:90% We might say one note. 00:20:21.370 --> 00:20:24.220 align:middle line:90% Add a little ornament to it. 00:20:24.220 --> 00:20:26.560 align:middle line:84% It's still one note in some certain senses, but-- 00:20:26.560 --> 00:20:27.790 align:middle line:90% [SCAT SINGING] 00:20:27.790 --> 00:20:31.370 align:middle line:84% --that kind of turn can really change everything. 00:20:31.370 --> 00:20:35.910 align:middle line:84% So those are going to be coming up over and over and over again 00:20:35.910 --> 00:20:39.450 align:middle line:84% how to represent for a computer and whether or not any one 00:20:39.450 --> 00:20:43.650 align:middle line:90% representation is going to work. 00:20:43.650 --> 00:20:47.430 align:middle line:84% Somebody said a note is a representation of anything 00:20:47.430 --> 00:20:51.540 align:middle line:90% with a pitch and a duration. 00:20:51.540 --> 00:20:55.020 align:middle line:84% There are some people who use the term "note" 00:20:55.020 --> 00:20:58.740 align:middle line:84% and the term "pitch" absolutely interchangeably. 00:20:58.740 --> 00:21:00.887 align:middle line:90% And I do it sometimes also. 00:21:00.887 --> 00:21:01.720 align:middle line:90% What pitch was that? 00:21:01.720 --> 00:21:02.220 align:middle line:90% What note? 00:21:02.220 --> 00:21:03.840 align:middle line:90% What note did you play? 00:21:03.840 --> 00:21:13.560 align:middle line:84% And other people use a note to mean the pitch and the duration 00:21:13.560 --> 00:21:16.830 align:middle line:90% as two different entities. 00:21:16.830 --> 00:21:21.310 align:middle line:84% Now, obviously, that also leads to certain contradictions. 00:21:21.310 --> 00:21:26.630 align:middle line:84% I would hope that we think that an eighth note is a note. 00:21:26.630 --> 00:21:27.130 align:middle line:90% Right? 00:21:27.130 --> 00:21:29.230 align:middle line:84% I mean, it has the word note in its name. 00:21:29.230 --> 00:21:32.920 align:middle line:84% We're not talking about quavers in Britain. 00:21:32.920 --> 00:21:34.940 align:middle line:84% I mean, at least here in good old US of A, 00:21:34.940 --> 00:21:37.640 align:middle line:84% we put the word note in our eighth notes. 00:21:37.640 --> 00:21:41.900 align:middle line:84% But by this definition, pitch and duration and eighth note 00:21:41.900 --> 00:21:44.720 align:middle line:90% itself is not a note. 00:21:44.720 --> 00:21:46.170 align:middle line:90% Because it doesn't have a pitch. 00:21:46.170 --> 00:21:47.795 align:middle line:84% So we're going to be finding that we're 00:21:47.795 --> 00:21:50.280 align:middle line:84% going to be going back and forth quite often. 00:21:50.280 --> 00:21:52.970 align:middle line:84% Now, your problem set is going to be dealing 00:21:52.970 --> 00:21:56.820 align:middle line:84% with certain representations of pitch, 00:21:56.820 --> 00:22:00.120 align:middle line:84% at least the non-duration part of something. 00:22:00.120 --> 00:22:04.760 align:middle line:84% I will say I sometimes will pop a head when 00:22:04.760 --> 00:22:08.150 align:middle line:84% the lecture is getting too cerebral and things like that. 00:22:08.150 --> 00:22:11.820 align:middle line:84% In music21, the software we're going to be using quite often. 00:22:11.820 --> 00:22:13.670 align:middle line:90% This is probably the best-- 00:22:13.670 --> 00:22:18.930 align:middle line:84% closest definition to how music21 associates things. 00:22:18.930 --> 00:22:23.150 align:middle line:84% It's something with a conceived of single pitch 00:22:23.150 --> 00:22:26.660 align:middle line:84% and a conceived of single duration. 00:22:26.660 --> 00:22:28.640 align:middle line:84% And that might mean that something 00:22:28.640 --> 00:22:31.893 align:middle line:84% like this is conceived of as having a single pitch, or-- 00:22:31.893 --> 00:22:34.930 align:middle line:90% 00:22:34.930 --> 00:22:38.800 align:middle line:84% this is conceived of as having a single pitch that's 00:22:38.800 --> 00:22:40.360 align:middle line:90% a trill sine. 00:22:40.360 --> 00:22:43.900 align:middle line:84% But there are other times when we don't conceive of something 00:22:43.900 --> 00:22:46.400 align:middle line:90% as a single pitch and duration. 00:22:46.400 --> 00:22:48.860 align:middle line:84% So let's talk about representations of duration. 00:22:48.860 --> 00:22:51.530 align:middle line:84% So we've gone from the trick questions. 00:22:51.530 --> 00:22:56.500 align:middle line:84% And now I hope I haven't ended your faith 00:22:56.500 --> 00:22:57.770 align:middle line:90% in humanity in the class. 00:22:57.770 --> 00:23:01.390 align:middle line:84% Now I want to go to a little bit more 00:23:01.390 --> 00:23:05.020 align:middle line:84% thinking about standard situations, not weird tremolos 00:23:05.020 --> 00:23:07.900 align:middle line:84% and glissandos and all that stuff. 00:23:07.900 --> 00:23:11.860 align:middle line:84% I want to think about, How are some ways you might represent 00:23:11.860 --> 00:23:14.903 align:middle line:90% pitch duration for a computer? 00:23:14.903 --> 00:23:25.060 align:middle line:90% 00:23:25.060 --> 00:23:26.367 align:middle line:90% And we'll say-- 00:23:26.367 --> 00:23:29.440 align:middle line:90% 00:23:29.440 --> 00:23:32.500 align:middle line:84% I'm going to put the term here "musical," 00:23:32.500 --> 00:23:38.220 align:middle line:84% as if somehow there's a different world of time in music 00:23:38.220 --> 00:23:41.110 align:middle line:84% than there is in everywhere else. 00:23:41.110 --> 00:23:44.050 align:middle line:84% There's three kinds of time in the world. 00:23:44.050 --> 00:23:45.318 align:middle line:90% There's the one on your clock. 00:23:45.318 --> 00:23:46.360 align:middle line:90% There's the one on music. 00:23:46.360 --> 00:23:48.600 align:middle line:84% And there's the one they teach you about in relativity class 00:23:48.600 --> 00:23:50.290 align:middle line:84% that you hope you never hear again. 00:23:50.290 --> 00:23:51.790 align:middle line:90% Right? 00:23:51.790 --> 00:23:56.110 align:middle line:84% So thinking about this, what are some ways that you might do it? 00:23:56.110 --> 00:23:57.593 align:middle line:90% I think we've grouped enough. 00:23:57.593 --> 00:23:59.260 align:middle line:84% I think people want to be able to shout. 00:23:59.260 --> 00:24:01.800 align:middle line:84% And some people whose names are toward the beginning 00:24:01.800 --> 00:24:04.450 align:middle line:84% and end of the alphabet might want to be able to say so. 00:24:04.450 --> 00:24:07.110 align:middle line:84% What are some of the things that a musical duration 00:24:07.110 --> 00:24:10.530 align:middle line:90% representation might include? 00:24:10.530 --> 00:24:12.280 align:middle line:84% OK, I think that's a good enough. 00:24:12.280 --> 00:24:15.040 align:middle line:84% I think it's like doing jumping jacks. 00:24:15.040 --> 00:24:18.460 align:middle line:84% You just get the thinking calisthenics going. 00:24:18.460 --> 00:24:21.300 align:middle line:84% So what some of the things that you might 00:24:21.300 --> 00:24:22.540 align:middle line:90% do for representing duration? 00:24:22.540 --> 00:24:23.170 align:middle line:90% Jordan said something. 00:24:23.170 --> 00:24:23.820 align:middle line:90% Yeah. 00:24:23.820 --> 00:24:25.536 align:middle line:84% AUDIENCE: Like seconds or divisions of measures. 00:24:25.536 --> 00:24:25.990 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Seconds. 00:24:25.990 --> 00:24:26.490 align:middle line:90% Good. 00:24:26.490 --> 00:24:29.400 align:middle line:90% Now let's think about it. 00:24:29.400 --> 00:24:32.400 align:middle line:84% We'll make our default assumption for this class 00:24:32.400 --> 00:24:34.840 align:middle line:84% that we're thinking in Python, of course. 00:24:34.840 --> 00:24:37.258 align:middle line:84% Obviously, any halfway decent programming language 00:24:37.258 --> 00:24:38.050 align:middle line:90% can go for another. 00:24:38.050 --> 00:24:40.690 align:middle line:84% So how are we going to represent seconds for a note? 00:24:40.690 --> 00:24:41.410 align:middle line:90% Yeah, go ahead. 00:24:41.410 --> 00:24:42.450 align:middle line:90% Oh, what was that? 00:24:42.450 --> 00:24:45.100 align:middle line:84% AUDIENCE: I guess, typically, don't we use ticks and that sort 00:24:45.100 --> 00:24:45.600 align:middle line:90% of... 00:24:45.600 --> 00:24:47.140 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Well, we'll get to that. 00:24:47.140 --> 00:24:48.550 align:middle line:84% Keep that word there for a second. 00:24:48.550 --> 00:24:49.050 align:middle line:90% Great. 00:24:49.050 --> 00:24:51.060 align:middle line:90% But what kind of-- 00:24:51.060 --> 00:24:54.070 align:middle line:90% is string a good one? 00:24:54.070 --> 00:24:54.570 align:middle line:90% Array? 00:24:54.570 --> 00:24:56.470 align:middle line:84% How are we going to represent seconds? 00:24:56.470 --> 00:24:57.280 align:middle line:90% Yeah, go ahead. 00:24:57.280 --> 00:24:57.880 align:middle line:90% AUDIENCE: Like a float. 00:24:57.880 --> 00:24:58.530 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Float. 00:24:58.530 --> 00:24:59.165 align:middle line:90% OK, good. 00:24:59.165 --> 00:25:01.950 align:middle line:90% 00:25:01.950 --> 00:25:02.945 align:middle line:90% Why not int? 00:25:02.945 --> 00:25:05.230 align:middle line:90% 00:25:05.230 --> 00:25:05.730 align:middle line:90% Yeah. 00:25:05.730 --> 00:25:06.400 align:middle line:90% Just shout out. 00:25:06.400 --> 00:25:07.410 align:middle line:90% Yep, go ahead. 00:25:07.410 --> 00:25:09.060 align:middle line:84% AUDIENCE: Because we can have them between, like-- 00:25:09.060 --> 00:25:09.920 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Good. 00:25:09.920 --> 00:25:10.420 align:middle line:90% Good. 00:25:10.420 --> 00:25:11.410 align:middle line:90% We can have in between. 00:25:11.410 --> 00:25:11.910 align:middle line:90% Great. 00:25:11.910 --> 00:25:13.290 align:middle line:90% Super. 00:25:13.290 --> 00:25:14.640 align:middle line:90% Other things. 00:25:14.640 --> 00:25:17.970 align:middle line:84% I'm going to-- other ways you might 00:25:17.970 --> 00:25:20.880 align:middle line:90% want to represent duration. 00:25:20.880 --> 00:25:21.940 align:middle line:90% Yeah, go ahead Matthew. 00:25:21.940 --> 00:25:22.620 align:middle line:90% AUDIENCE: Fraction? 00:25:22.620 --> 00:25:24.245 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Fraction. 00:25:24.245 --> 00:25:25.500 align:middle line:90% Good. 00:25:25.500 --> 00:25:27.720 align:middle line:90% Seconds as a fraction or-- 00:25:27.720 --> 00:25:31.520 align:middle line:84% AUDIENCE: So I'm thinking both represent seconds 00:25:31.520 --> 00:25:33.000 align:middle line:84% as a fraction instead of a float, 00:25:33.000 --> 00:25:36.170 align:middle line:84% so you don't have the precision issues of a float. 00:25:36.170 --> 00:25:38.750 align:middle line:84% I also think it might make sense to represent it 00:25:38.750 --> 00:25:40.218 align:middle line:90% as a beat and fraction. 00:25:40.218 --> 00:25:41.760 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK, OK. 00:25:41.760 --> 00:25:43.580 align:middle line:90% Well, OK, that's the two things. 00:25:43.580 --> 00:25:44.850 align:middle line:90% We have beat there. 00:25:44.850 --> 00:25:45.630 align:middle line:90% Good, good. 00:25:45.630 --> 00:25:46.860 align:middle line:90% We'll keep going. 00:25:46.860 --> 00:25:49.345 align:middle line:84% What are some other things that we might do-- yeah. 00:25:49.345 --> 00:25:50.970 align:middle line:84% AUDIENCE: I was also thinking fraction, 00:25:50.970 --> 00:25:53.747 align:middle line:84% but fraction of whatever measure you're looking at. 00:25:53.747 --> 00:25:55.830 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Fraction of measure. 00:25:55.830 --> 00:25:59.840 align:middle line:84% AUDIENCE: So if you have like a 3/4 measure, 00:25:59.840 --> 00:26:02.983 align:middle line:84% and you had a half note, that would be 2/3 of the measure. 00:26:02.983 --> 00:26:04.400 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Yep. 00:26:04.400 --> 00:26:04.920 align:middle line:90% OK. 00:26:04.920 --> 00:26:05.420 align:middle line:90% So, good. 00:26:05.420 --> 00:26:06.030 align:middle line:90% 2/3. 00:26:06.030 --> 00:26:08.810 align:middle line:84% That's a particular place where the difference between float 00:26:08.810 --> 00:26:13.560 align:middle line:84% accuracy and fraction can be very, very important. 00:26:13.560 --> 00:26:14.060 align:middle line:90% Good. 00:26:14.060 --> 00:26:20.120 align:middle line:84% Are beat and fraction of measure basically saying the same thing 00:26:20.120 --> 00:26:22.700 align:middle line:90% with reciprocal relationship? 00:26:22.700 --> 00:26:24.450 align:middle line:84% Can somebody come up with a reason not to? 00:26:24.450 --> 00:26:24.985 align:middle line:90% Yeah. 00:26:24.985 --> 00:26:27.110 align:middle line:84% AUDIENCE: I mean, not necessarily because something 00:26:27.110 --> 00:26:31.367 align:middle line:84% could be on the second beat and have a duration of one. 00:26:31.367 --> 00:26:33.700 align:middle line:84% Or it could be a second beat and have a duration of two. 00:26:33.700 --> 00:26:35.300 align:middle line:84% And if it was a fraction of a measure, 00:26:35.300 --> 00:26:36.580 align:middle line:84% their values would be decreasing. 00:26:36.580 --> 00:26:38.205 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK, good. 00:26:38.205 --> 00:26:40.930 align:middle line:84% So we have beat as in what beat is it on? 00:26:40.930 --> 00:26:43.276 align:middle line:84% And that would be very different. 00:26:43.276 --> 00:26:45.850 align:middle line:90% 00:26:45.850 --> 00:26:48.358 align:middle line:84% If we're thinking about, How many beats does it last? 00:26:48.358 --> 00:26:49.400 align:middle line:90% OK, so thank you Vanessa. 00:26:49.400 --> 00:26:51.010 align:middle line:90% That's fantastic. 00:26:51.010 --> 00:26:54.340 align:middle line:84% Is that basically the same as what fraction of the measure 00:26:54.340 --> 00:26:56.530 align:middle line:90% is it? 00:26:56.530 --> 00:26:59.170 align:middle line:84% I think I see Matthew, but I want to get-- 00:26:59.170 --> 00:27:01.820 align:middle line:84% I think I'm going this way because I'm camera shy. 00:27:01.820 --> 00:27:05.590 align:middle line:84% So let me lean in over here, see if there's things-- 00:27:05.590 --> 00:27:11.950 align:middle line:84% anyone want to-- who says it's basically the same thing? 00:27:11.950 --> 00:27:13.540 align:middle line:90% And we can go over. 00:27:13.540 --> 00:27:16.850 align:middle line:84% Who says it could be quite different? 00:27:16.850 --> 00:27:19.750 align:middle line:90% 00:27:19.750 --> 00:27:20.980 align:middle line:90% OK, go ahead. 00:27:20.980 --> 00:27:22.960 align:middle line:90% AUDIENCE: I guess it was like-- 00:27:22.960 --> 00:27:24.920 align:middle line:84% it depends on what you define the beat as. 00:27:24.920 --> 00:27:26.690 align:middle line:84% So if it's like 5, 8 time or something. 00:27:26.690 --> 00:27:28.232 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Oh, OK. 00:27:28.232 --> 00:27:29.170 align:middle line:90% So 5, 8. 00:27:29.170 --> 00:27:31.540 align:middle line:90% We'll say we'll do it as this. 00:27:31.540 --> 00:27:34.500 align:middle line:84% I don't know if people know that symbol. 00:27:34.500 --> 00:27:42.970 align:middle line:90% So how many beats does this get? 00:27:42.970 --> 00:27:44.063 align:middle line:90% AUDIENCE: Two. 00:27:44.063 --> 00:27:45.480 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Two? 00:27:45.480 --> 00:27:46.270 align:middle line:90% In some ways. 00:27:46.270 --> 00:27:47.790 align:middle line:90% And how many this one? 00:27:47.790 --> 00:27:48.390 align:middle line:90% Three. 00:27:48.390 --> 00:27:48.890 align:middle line:90% Good. 00:27:48.890 --> 00:27:50.470 align:middle line:90% And now give me another number. 00:27:50.470 --> 00:27:52.750 align:middle line:84% So we could use instead of that for a lot of 5/8. 00:27:52.750 --> 00:27:53.370 align:middle line:90% Yeah. 00:27:53.370 --> 00:27:54.840 align:middle line:90% AUDIENCE: 10, 16. 00:27:54.840 --> 00:27:55.510 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 10, 16. 00:27:55.510 --> 00:27:56.010 align:middle line:90% Yeah. 00:27:56.010 --> 00:27:57.040 align:middle line:90% We could do any other. 00:27:57.040 --> 00:27:57.540 align:middle line:90% Good, good. 00:27:57.540 --> 00:28:00.940 align:middle line:84% We have an infinite number of non-reduced fractions we can do. 00:28:00.940 --> 00:28:01.440 align:middle line:90% Great. 00:28:01.440 --> 00:28:03.960 align:middle line:90% I love it that. 00:28:03.960 --> 00:28:04.850 align:middle line:90% How about this? 00:28:04.850 --> 00:28:07.770 align:middle line:90% 00:28:07.770 --> 00:28:09.080 align:middle line:90% No, I won't write that yet. 00:28:09.080 --> 00:28:11.730 align:middle line:90% 00:28:11.730 --> 00:28:15.090 align:middle line:90% How many beats does this get? 00:28:15.090 --> 00:28:16.208 align:middle line:90% AUDIENCE: 1, 2, 5. 00:28:16.208 --> 00:28:18.250 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 3 is a good answer. 00:28:18.250 --> 00:28:19.740 align:middle line:90% And there's another good answer. 00:28:19.740 --> 00:28:20.280 align:middle line:90% AUDIENCE: 1. 00:28:20.280 --> 00:28:21.677 align:middle line:90% MICHAEL SCOTT ASATO CUTHBERT: 1. 00:28:21.677 --> 00:28:22.260 align:middle line:90% [SCAT SINGING] 00:28:22.260 --> 00:28:23.170 align:middle line:90% 1. 00:28:23.170 --> 00:28:24.390 align:middle line:90% [SCAT SINGING] 00:28:24.390 --> 00:28:26.120 align:middle line:90% 1, 2. 00:28:26.120 --> 00:28:26.630 align:middle line:90% Right? 00:28:26.630 --> 00:28:28.210 align:middle line:90% So how many beats does this get? 00:28:28.210 --> 00:28:30.830 align:middle line:90% 00:28:30.830 --> 00:28:32.030 align:middle line:90% AUDIENCE: Two beats. 00:28:32.030 --> 00:28:33.570 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: So there are some ways of doing it. 00:28:33.570 --> 00:28:35.420 align:middle line:84% When I put this symbol, I'm saying I'm 00:28:35.420 --> 00:28:39.780 align:middle line:90% going to go 1, 2, 1, 2, 1, 2. 00:28:39.780 --> 00:28:43.070 align:middle line:84% And they're not-- so a beat can actually 00:28:43.070 --> 00:28:48.360 align:middle line:84% change its length during a measure in some representation. 00:28:48.360 --> 00:28:50.330 align:middle line:84% So this is one of the ways I was thinking 00:28:50.330 --> 00:28:53.572 align:middle line:84% not exactly the same thing but pretty close. 00:28:53.572 --> 00:28:56.030 align:middle line:84% Good, let's see what are some other ways we might represent 00:28:56.030 --> 00:28:58.460 align:middle line:90% duration for computer? 00:28:58.460 --> 00:29:01.130 align:middle line:84% I'm going to go back in just a little 00:29:01.130 --> 00:29:07.010 align:middle line:84% bit the names, some of the things I've heard otherwise. 00:29:07.010 --> 00:29:12.050 align:middle line:84% I heard something over here that I think 00:29:12.050 --> 00:29:14.230 align:middle line:90% Adam or one of you, Derek. 00:29:14.230 --> 00:29:17.073 align:middle line:90% 00:29:17.073 --> 00:29:18.240 align:middle line:90% AUDIENCE: Like an attribute. 00:29:18.240 --> 00:29:19.573 align:middle line:90% Like a dot is like an attribute. 00:29:19.573 --> 00:29:21.073 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Great. 00:29:21.073 --> 00:29:22.590 align:middle line:84% So we might keep track of attributes 00:29:22.590 --> 00:29:26.170 align:middle line:84% like, How many dots does it have? 00:29:26.170 --> 00:29:26.810 align:middle line:90% Good. 00:29:26.810 --> 00:29:27.890 align:middle line:90% Anything else like that? 00:29:27.890 --> 00:29:28.900 align:middle line:90% Thank you. 00:29:28.900 --> 00:29:31.040 align:middle line:90% Super. 00:29:31.040 --> 00:29:31.540 align:middle line:90% Yeah. 00:29:31.540 --> 00:29:34.180 align:middle line:84% AUDIENCE: Yeah, you take a number for the n-th node. 00:29:34.180 --> 00:29:35.820 align:middle line:84% So if it's an eighth note, you say 8. 00:29:35.820 --> 00:29:37.585 align:middle line:90% In dots, it'll be an 8 dot. 00:29:37.585 --> 00:29:38.960 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK. 00:29:38.960 --> 00:29:42.700 align:middle line:90% So we can represent it as now-- 00:29:42.700 --> 00:29:45.760 align:middle line:84% 8 dot works pretty well as a float, but is there another way 00:29:45.760 --> 00:29:47.690 align:middle line:84% we might consider that if we're talking-- 00:29:47.690 --> 00:29:49.190 align:middle line:84% AUDIENCE: It works well as a string. 00:29:49.190 --> 00:29:50.390 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: It works better as a string, right? 00:29:50.390 --> 00:29:53.080 align:middle line:84% Because 8 dot dot, suddenly you're 00:29:53.080 --> 00:29:55.300 align:middle line:84% kind of getting a crash error, right? 00:29:55.300 --> 00:29:57.280 align:middle line:84% So that's one way you could do it. 00:29:57.280 --> 00:29:59.150 align:middle line:90% Other ways? 00:29:59.150 --> 00:30:03.110 align:middle line:84% And then so we would say or something like that. 00:30:03.110 --> 00:30:04.040 align:middle line:90% Good, good. 00:30:04.040 --> 00:30:05.590 align:middle line:84% What are other attributes we might 00:30:05.590 --> 00:30:08.400 align:middle line:84% want to represent to talk about the duration of a note? 00:30:08.400 --> 00:30:15.100 align:middle line:90% 00:30:15.100 --> 00:30:18.010 align:middle line:90% Are all notes-- yeah. 00:30:18.010 --> 00:30:20.210 align:middle line:84% AUDIENCE: You could also have these at a triplet. 00:30:20.210 --> 00:30:20.500 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: You 00:30:20.500 --> 00:30:21.792 align:middle line:90% could have things in a triplet. 00:30:21.792 --> 00:30:24.115 align:middle line:90% 00:30:24.115 --> 00:30:24.615 align:middle line:90% Yeah. 00:30:24.615 --> 00:30:30.030 align:middle line:90% 00:30:30.030 --> 00:30:31.650 align:middle line:90% Good. 00:30:31.650 --> 00:30:36.570 align:middle line:84% You could also have things in a quintuplet, right? 00:30:36.570 --> 00:30:40.230 align:middle line:84% Let's see if I can squeeze this in. 00:30:40.230 --> 00:30:49.470 align:middle line:84% And you can also have things in a triplet within a quintuplet. 00:30:49.470 --> 00:30:50.870 align:middle line:90% It's called nested tuplets. 00:30:50.870 --> 00:30:53.640 align:middle line:90% 00:30:53.640 --> 00:31:00.570 align:middle line:84% So I will guarantee you, I have seen at least 20 representations 00:31:00.570 --> 00:31:05.070 align:middle line:84% of notated durations where the tuplet was originally 00:31:05.070 --> 00:31:07.470 align:middle line:84% created as an attribute, and then it 00:31:07.470 --> 00:31:11.880 align:middle line:84% needed to be represented as a list array tuple, something 00:31:11.880 --> 00:31:15.430 align:middle line:84% like that of a tuple of tuplets-- 00:31:15.430 --> 00:31:17.160 align:middle line:90% try to say that 10 times fast-- 00:31:17.160 --> 00:31:20.220 align:middle line:84% for indeterminate number of tuplets 00:31:20.220 --> 00:31:23.100 align:middle line:84% that might be applied to a certain note. 00:31:23.100 --> 00:31:24.870 align:middle line:84% So these might be certain things. 00:31:24.870 --> 00:31:25.760 align:middle line:90% Good. 00:31:25.760 --> 00:31:29.280 align:middle line:84% Anything else that we might use to represent duration? 00:31:29.280 --> 00:31:30.650 align:middle line:90% Yeah, go ahead. 00:31:30.650 --> 00:31:33.072 align:middle line:84% AUDIENCE: Certain markings like staccato or legato? 00:31:33.072 --> 00:31:34.530 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Good. 00:31:34.530 --> 00:31:41.180 align:middle line:84% So we might have modifying, I don't know, 00:31:41.180 --> 00:31:43.890 align:middle line:84% articulations and expressions or markings. 00:31:43.890 --> 00:31:47.400 align:middle line:84% We'll just call them markings because who knows what they are? 00:31:47.400 --> 00:31:50.210 align:middle line:90% Markings. 00:31:50.210 --> 00:31:52.640 align:middle line:84% I'll make a fermata on my I. Good. 00:31:52.640 --> 00:31:58.200 align:middle line:84% So yeah, we have our dots maybe modifying. 00:31:58.200 --> 00:31:58.700 align:middle line:90% Good. 00:31:58.700 --> 00:32:01.950 align:middle line:84% So we can think of tornadoes that those affect the duration. 00:32:01.950 --> 00:32:02.450 align:middle line:90% Great. 00:32:02.450 --> 00:32:08.330 align:middle line:84% Now I want to go towards further on this. 00:32:08.330 --> 00:32:11.870 align:middle line:90% Now our music is on a-- 00:32:11.870 --> 00:32:15.960 align:middle line:84% I was going to use obsolete formats, a CD or streaming. 00:32:15.960 --> 00:32:19.893 align:middle line:84% What are the most useful representations of duration? 00:32:19.893 --> 00:32:23.140 align:middle line:90% 00:32:23.140 --> 00:32:26.230 align:middle line:90% Of notes, let's say. 00:32:26.230 --> 00:32:29.310 align:middle line:84% Or other things, which once these are most useful? 00:32:29.310 --> 00:32:36.233 align:middle line:90% 00:32:36.233 --> 00:32:38.150 align:middle line:84% And I've heard you a couple of times from you. 00:32:38.150 --> 00:32:38.690 align:middle line:90% So great. 00:32:38.690 --> 00:32:39.280 align:middle line:90% Super. 00:32:39.280 --> 00:32:40.340 align:middle line:90% M's got it. 00:32:40.340 --> 00:32:41.400 align:middle line:90% Who else got one? 00:32:41.400 --> 00:32:46.150 align:middle line:90% 00:32:46.150 --> 00:32:50.470 align:middle line:84% Is this a great representation that you're 00:32:50.470 --> 00:32:52.150 align:middle line:84% hearing of the duration of a note 00:32:52.150 --> 00:32:54.600 align:middle line:84% when you're listening to streaming music? 00:32:54.600 --> 00:32:57.670 align:middle line:90% 00:32:57.670 --> 00:33:01.113 align:middle line:84% Maybe not, but boy, that could be useful for other things. 00:33:01.113 --> 00:33:01.905 align:middle line:90% What about seconds? 00:33:01.905 --> 00:33:04.810 align:middle line:90% 00:33:04.810 --> 00:33:07.660 align:middle line:90% That's going to depend on-- 00:33:07.660 --> 00:33:10.930 align:middle line:84% let's say you're listening just for fun. 00:33:10.930 --> 00:33:12.940 align:middle line:90% Seconds very good? 00:33:12.940 --> 00:33:13.840 align:middle line:90% No, maybe not. 00:33:13.840 --> 00:33:16.630 align:middle line:84% I don't usually hear seconds, but who's 00:33:16.630 --> 00:33:19.620 align:middle line:84% somebody who involved in the streaming music 00:33:19.620 --> 00:33:22.115 align:middle line:84% process who might really care about seconds of notes? 00:33:22.115 --> 00:33:24.488 align:middle line:90% 00:33:24.488 --> 00:33:26.280 align:middle line:84% AUDIENCE: I guess the computers in a sense. 00:33:26.280 --> 00:33:28.280 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: The computers way? 00:33:28.280 --> 00:33:30.760 align:middle line:84% Yep, but what kind of human might be really interested? 00:33:30.760 --> 00:33:31.260 align:middle line:90% Yeah. 00:33:31.260 --> 00:33:32.250 align:middle line:90% AUDIENCE: Some editor. 00:33:32.250 --> 00:33:33.958 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: The editor. 00:33:33.958 --> 00:33:36.600 align:middle line:84% Yeah, the person who's doing the recording editing, 00:33:36.600 --> 00:33:38.190 align:middle line:84% they're always going to be thinking 00:33:38.190 --> 00:33:44.160 align:middle line:84% about, OK, let's clip from 22.046 to 22.048 00:33:44.160 --> 00:33:45.430 align:middle line:90% when somebody coughed. 00:33:45.430 --> 00:33:47.270 align:middle line:84% And we'll come up with something, right? 00:33:47.270 --> 00:33:49.920 align:middle line:84% So those types of things come up quite a bit 00:33:49.920 --> 00:33:52.770 align:middle line:90% in that type of world. 00:33:52.770 --> 00:33:56.470 align:middle line:84% Now what if you've written your great piece. 00:33:56.470 --> 00:33:59.140 align:middle line:84% It's already been recorded, performed and things. 00:33:59.140 --> 00:34:02.348 align:middle line:84% And now you've sent it off to your sheet music publisher. 00:34:02.348 --> 00:34:04.640 align:middle line:84% What are the ones they're going to care the most about? 00:34:04.640 --> 00:34:10.409 align:middle line:90% 00:34:10.409 --> 00:34:11.770 align:middle line:90% What's the representation? 00:34:11.770 --> 00:34:12.750 align:middle line:90% Yeah, John. 00:34:12.750 --> 00:34:14.889 align:middle line:90% AUDIENCE: Pitch and duration. 00:34:14.889 --> 00:34:15.850 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: The pitch and the duration. 00:34:15.850 --> 00:34:16.020 align:middle line:90% Good. 00:34:16.020 --> 00:34:18.228 align:middle line:84% And how are they going to be thinking about duration? 00:34:18.228 --> 00:34:19.610 align:middle line:90% How is the engraver? 00:34:19.610 --> 00:34:22.500 align:middle line:84% That's the person who makes musical scores, 00:34:22.500 --> 00:34:23.750 align:middle line:90% the term for that. 00:34:23.750 --> 00:34:25.050 align:middle line:90% What's the engraver? 00:34:25.050 --> 00:34:28.603 align:middle line:84% What's she going to be thinking about in terms of duration? 00:34:28.603 --> 00:34:36.110 align:middle line:90% 00:34:36.110 --> 00:34:37.639 align:middle line:84% What do you think about when you're 00:34:37.639 --> 00:34:38.722 align:middle line:90% looking at musical scores? 00:34:38.722 --> 00:34:39.500 align:middle line:90% Yeah. 00:34:39.500 --> 00:34:41.360 align:middle line:84% AUDIENCE: The beat and then the modifying components? 00:34:41.360 --> 00:34:43.139 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: The beats, the modifiers. 00:34:43.139 --> 00:34:43.770 align:middle line:90% Good. 00:34:43.770 --> 00:34:45.860 align:middle line:90% Good. 00:34:45.860 --> 00:34:47.647 align:middle line:84% What are we going to call something, 00:34:47.647 --> 00:34:49.230 align:middle line:84% the difference between an eighth note, 00:34:49.230 --> 00:34:51.300 align:middle line:84% a quarter note, half note, all that stuff? 00:34:51.300 --> 00:34:53.848 align:middle line:90% What do we want to call that? 00:34:53.848 --> 00:34:56.040 align:middle line:84% We all have been doing music for a very long time. 00:34:56.040 --> 00:34:58.305 align:middle line:84% We all must know the term for that, right? 00:34:58.305 --> 00:35:01.160 align:middle line:90% 00:35:01.160 --> 00:35:03.052 align:middle line:84% There is no generalized term for it. 00:35:03.052 --> 00:35:04.885 align:middle line:84% So what do we want to call it in this class? 00:35:04.885 --> 00:35:10.010 align:middle line:90% 00:35:10.010 --> 00:35:15.030 align:middle line:84% Somebody shout out something, or we'll call it the note animal. 00:35:15.030 --> 00:35:19.640 align:middle line:84% What animal is this note, or what flavor is this note? 00:35:19.640 --> 00:35:20.390 align:middle line:90% That's a good one. 00:35:20.390 --> 00:35:21.973 align:middle line:84% Actually, I wish I had gone with that. 00:35:21.973 --> 00:35:26.830 align:middle line:84% Mhm, mhm, yum, 16th notes are really, really tasty today. 00:35:26.830 --> 00:35:28.740 align:middle line:84% Anybody have a suggestion of a term? 00:35:28.740 --> 00:35:31.360 align:middle line:90% 00:35:31.360 --> 00:35:32.110 align:middle line:90% AUDIENCE: Essence? 00:35:32.110 --> 00:35:32.870 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: The essence. 00:35:32.870 --> 00:35:33.820 align:middle line:90% What essence of note is. 00:35:33.820 --> 00:35:34.320 align:middle line:90% Good. 00:35:34.320 --> 00:35:34.900 align:middle line:90% Good. 00:35:34.900 --> 00:35:39.610 align:middle line:84% I will tell you that essence is better than animal probably 00:35:39.610 --> 00:35:40.220 align:middle line:90% as a term. 00:35:40.220 --> 00:35:41.750 align:middle line:84% It's probably better than flavor. 00:35:41.750 --> 00:35:44.690 align:middle line:84% And it's better than what all the rest of us didn't say. 00:35:44.690 --> 00:35:47.200 align:middle line:84% Because the first thing you have to do 00:35:47.200 --> 00:35:49.330 align:middle line:84% when you're representing for a computer is come up 00:35:49.330 --> 00:35:50.390 align:middle line:90% with a name for everything. 00:35:50.390 --> 00:35:50.973 align:middle line:90% Yeah, Vanessa. 00:35:50.973 --> 00:35:51.910 align:middle line:90% AUDIENCE: [INAUDIBLE]. 00:35:51.910 --> 00:35:52.640 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK. 00:35:52.640 --> 00:35:54.320 align:middle line:90% But come up with a name for it. 00:35:54.320 --> 00:35:55.420 align:middle line:90% AUDIENCE: Duration. 00:35:55.420 --> 00:35:57.212 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: The duration. 00:35:57.212 --> 00:35:59.980 align:middle line:84% OK, so we might have the duration of a duration 00:35:59.980 --> 00:36:01.040 align:middle line:90% is a quarter. 00:36:01.040 --> 00:36:03.650 align:middle line:90% And the number of dots is 2. 00:36:03.650 --> 00:36:06.592 align:middle line:84% A lot of representations do that. 00:36:06.592 --> 00:36:10.310 align:middle line:84% I think MEI calls that part a duration. 00:36:10.310 --> 00:36:11.930 align:middle line:84% So that's a very good term for it. 00:36:11.930 --> 00:36:13.283 align:middle line:90% Other terms. 00:36:13.283 --> 00:36:18.330 align:middle line:90% 00:36:18.330 --> 00:36:20.260 align:middle line:90% Get good at naming things. 00:36:20.260 --> 00:36:22.570 align:middle line:84% Come up with names fast in this class. 00:36:22.570 --> 00:36:26.700 align:middle line:84% So let's just pepper some bad names for it. 00:36:26.700 --> 00:36:28.062 align:middle line:90% Jonathan, what's it? 00:36:28.062 --> 00:36:28.770 align:middle line:90% AUDIENCE: Almond. 00:36:28.770 --> 00:36:29.440 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: The almond. 00:36:29.440 --> 00:36:30.480 align:middle line:90% What almond is it? 00:36:30.480 --> 00:36:33.178 align:middle line:90% Jonathan. 00:36:33.178 --> 00:36:35.220 align:middle line:84% AUDIENCE: I mean, I guess the length [INAUDIBLE]. 00:36:35.220 --> 00:36:36.970 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: What length. 00:36:36.970 --> 00:36:37.620 align:middle line:90% Good. 00:36:37.620 --> 00:36:38.717 align:middle line:90% What length is that note? 00:36:38.717 --> 00:36:39.550 align:middle line:90% It's a quarter note. 00:36:39.550 --> 00:36:40.592 align:middle line:90% What length is that note? 00:36:40.592 --> 00:36:41.460 align:middle line:90% It's an eighth note. 00:36:41.460 --> 00:36:44.190 align:middle line:84% There might be a better term, but that's a pretty good one. 00:36:44.190 --> 00:36:45.190 align:middle line:90% That's good. 00:36:45.190 --> 00:36:45.990 align:middle line:90% Yeah. 00:36:45.990 --> 00:36:47.580 align:middle line:84% AUDIENCE: I feel like spanned is-- 00:36:47.580 --> 00:36:49.247 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: What span? 00:36:49.247 --> 00:36:49.830 align:middle line:90% I like that. 00:36:49.830 --> 00:36:50.790 align:middle line:90% What span? 00:36:50.790 --> 00:36:54.690 align:middle line:84% It might not be so perfect, but it gets us-- 00:36:54.690 --> 00:36:57.120 align:middle line:84% when you think about things, what's 00:36:57.120 --> 00:37:00.970 align:middle line:84% something that spans things that people spend a lot of time, 00:37:00.970 --> 00:37:03.395 align:middle line:84% especially at what course 3 thinking about? 00:37:03.395 --> 00:37:06.265 align:middle line:90% 00:37:06.265 --> 00:37:07.260 align:middle line:90% AUDIENCE: Bridges. 00:37:07.260 --> 00:37:08.070 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Bridges. 00:37:08.070 --> 00:37:08.560 align:middle line:90% Good. 00:37:08.560 --> 00:37:10.740 align:middle line:84% And when you start thinking about bridges, what's something 00:37:10.740 --> 00:37:12.300 align:middle line:84% that we haven't even thought of that 00:37:12.300 --> 00:37:15.895 align:middle line:84% looks like a bridge when we think about durations and notes? 00:37:15.895 --> 00:37:16.820 align:middle line:90% AUDIENCE: Slurs. 00:37:16.820 --> 00:37:18.300 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Slurs, ties. 00:37:18.300 --> 00:37:18.800 align:middle line:90% Good. 00:37:18.800 --> 00:37:19.740 align:middle line:90% Slurs, ties. 00:37:19.740 --> 00:37:21.330 align:middle line:90% I was also thinking of beams. 00:37:21.330 --> 00:37:22.000 align:middle line:90% Any of those? 00:37:22.000 --> 00:37:22.500 align:middle line:90% Good. 00:37:22.500 --> 00:37:25.770 align:middle line:84% So we start when we start thinking of terms like this, 00:37:25.770 --> 00:37:29.720 align:middle line:84% we start thinking of cases who had thought about ties and slurs 00:37:29.720 --> 00:37:31.820 align:middle line:90% in your definition? 00:37:31.820 --> 00:37:34.790 align:middle line:90% Who had thought about beams? 00:37:34.790 --> 00:37:37.200 align:middle line:90% I hadn't thought of ties. 00:37:37.200 --> 00:37:39.300 align:middle line:84% And so when we do these types of things, 00:37:39.300 --> 00:37:43.362 align:middle line:84% suddenly why something is a good name or might not be a good name 00:37:43.362 --> 00:37:45.320 align:middle line:84% can help us think about what other things we're 00:37:45.320 --> 00:37:46.350 align:middle line:90% going to have to represent. 00:37:46.350 --> 00:37:47.250 align:middle line:90% I'm looking at the time. 00:37:47.250 --> 00:37:48.050 align:middle line:84% We're not going to be able to get 00:37:48.050 --> 00:37:50.760 align:middle line:84% through all the different types of representations here, 00:37:50.760 --> 00:37:51.900 align:middle line:90% but good. 00:37:51.900 --> 00:37:55.340 align:middle line:90% Now, what would it take-- 00:37:55.340 --> 00:37:59.623 align:middle line:90% let's say you have this. 00:37:59.623 --> 00:38:02.240 align:middle line:90% 00:38:02.240 --> 00:38:05.460 align:middle line:84% What's it going to take that dotted quarter note? 00:38:05.460 --> 00:38:07.650 align:middle line:90% That's not a trick question. 00:38:07.650 --> 00:38:09.740 align:middle line:84% What's it going to take for you to figure out 00:38:09.740 --> 00:38:11.660 align:middle line:90% how many seconds that is? 00:38:11.660 --> 00:38:14.298 align:middle line:84% Who has performed music from sheet music in class 00:38:14.298 --> 00:38:14.840 align:middle line:90% in real life? 00:38:14.840 --> 00:38:15.340 align:middle line:90% OK. 00:38:15.340 --> 00:38:17.530 align:middle line:90% Basically, everybody. 00:38:17.530 --> 00:38:20.080 align:middle line:84% So when you do that, you have to decide how long you're 00:38:20.080 --> 00:38:21.850 align:middle line:90% going to play that, right? 00:38:21.850 --> 00:38:23.840 align:middle line:84% You might not even be thinking it in your head, 00:38:23.840 --> 00:38:25.600 align:middle line:84% I've never been like, OK, I'm going 00:38:25.600 --> 00:38:31.720 align:middle line:90% to play that for 0.365 seconds. 00:38:31.720 --> 00:38:36.760 align:middle line:84% How do we go from this to a number of seconds? 00:38:36.760 --> 00:38:38.167 align:middle line:90% Yeah, go ahead. 00:38:38.167 --> 00:38:38.750 align:middle line:90% Oh, I'm sorry. 00:38:38.750 --> 00:38:39.708 align:middle line:90% There was two in a row. 00:38:39.708 --> 00:38:41.027 align:middle line:90% We're going behind first. 00:38:41.027 --> 00:38:42.860 align:middle line:84% AUDIENCE: Well, it's based off the template. 00:38:42.860 --> 00:38:43.880 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Based off the tempo. 00:38:43.880 --> 00:38:44.380 align:middle line:90% Good. 00:38:44.380 --> 00:38:46.940 align:middle line:90% Has tempo been included? 00:38:46.940 --> 00:38:50.630 align:middle line:84% I suppose it's almost implicitly included in beat, 00:38:50.630 --> 00:38:52.670 align:middle line:90% but tempo is a particular term. 00:38:52.670 --> 00:38:54.200 align:middle line:90% So we have tempo. 00:38:54.200 --> 00:38:55.970 align:middle line:90% How do we measure tempos? 00:38:55.970 --> 00:38:56.744 align:middle line:90% Tempi. 00:38:56.744 --> 00:38:57.295 align:middle line:90% Tempi. 00:38:57.295 --> 00:38:58.420 align:middle line:90% AUDIENCE: Beats per minute? 00:38:58.420 --> 00:38:59.300 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: What's that? 00:38:59.300 --> 00:38:59.890 align:middle line:90% AUDIENCE: Beat per minute. 00:38:59.890 --> 00:39:01.807 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Beat per minute. 00:39:01.807 --> 00:39:03.130 align:middle line:90% Good. 00:39:03.130 --> 00:39:05.680 align:middle line:90% Beat per minute. 00:39:05.680 --> 00:39:08.680 align:middle line:90% So what do we need to know? 00:39:08.680 --> 00:39:11.830 align:middle line:84% Also, in addition to tempo, in order to figure out how many 00:39:11.830 --> 00:39:12.845 align:middle line:90% beats something is. 00:39:12.845 --> 00:39:15.570 align:middle line:90% 00:39:15.570 --> 00:39:17.130 align:middle line:90% We all think of 4/4, right? 00:39:17.130 --> 00:39:17.860 align:middle line:90% Yeah, Jake. 00:39:17.860 --> 00:39:19.900 align:middle line:84% AUDIENCE: You intentionally say 0.365. 00:39:19.900 --> 00:39:22.383 align:middle line:90% This is 3/8 of [INAUDIBLE] 375. 00:39:22.383 --> 00:39:23.800 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 375. 00:39:23.800 --> 00:39:24.840 align:middle line:90% But yeah, but whatever. 00:39:24.840 --> 00:39:25.600 align:middle line:90% I don't know. 00:39:25.600 --> 00:39:26.800 align:middle line:90% It was something like that. 00:39:26.800 --> 00:39:27.300 align:middle line:90% Yeah. 00:39:27.300 --> 00:39:29.860 align:middle line:84% I very rarely do anything intentionally. 00:39:29.860 --> 00:39:31.130 align:middle line:90% So maybe it's karma. 00:39:31.130 --> 00:39:33.060 align:middle line:90% [LAUGHTER] 00:39:33.060 --> 00:39:36.180 align:middle line:84% What do we need to do to get beats per minute? 00:39:36.180 --> 00:39:38.585 align:middle line:90% How many beats is this? 00:39:38.585 --> 00:39:39.460 align:middle line:90% AUDIENCE: It depends. 00:39:39.460 --> 00:39:40.050 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Depends. 00:39:40.050 --> 00:39:40.550 align:middle line:90% Good. 00:39:40.550 --> 00:39:43.080 align:middle line:84% Depends on the-- everybody, shout it out. 00:39:43.080 --> 00:39:43.840 align:middle line:90% Time signature. 00:39:43.840 --> 00:39:44.340 align:middle line:90% Good. 00:39:44.340 --> 00:39:48.210 align:middle line:84% So suddenly, moving from this representation of notes 00:39:48.210 --> 00:39:52.440 align:middle line:84% to seconds, we need tempo in beats per minute and a time 00:39:52.440 --> 00:39:54.900 align:middle line:90% signature. 00:39:54.900 --> 00:39:56.970 align:middle line:90% Good. 00:39:56.970 --> 00:39:58.330 align:middle line:90% Let me give you another one. 00:39:58.330 --> 00:40:09.000 align:middle line:84% What if I said the tempo here was allegro troppo? 00:40:09.000 --> 00:40:09.888 align:middle line:90% OK, the other thing. 00:40:09.888 --> 00:40:12.430 align:middle line:84% If it gets too much longer than that, the other thing we need 00:40:12.430 --> 00:40:13.763 align:middle line:90% is an Italian dictionary, right? 00:40:13.763 --> 00:40:14.990 align:middle line:90% [LAUGHTER] 00:40:14.990 --> 00:40:15.910 align:middle line:90% 00:40:15.910 --> 00:40:18.200 align:middle line:90% Allegro, but not too allegro. 00:40:18.200 --> 00:40:19.510 align:middle line:90% Not too much. 00:40:19.510 --> 00:40:24.480 align:middle line:84% So what do we need also in order to convert this to seconds? 00:40:24.480 --> 00:40:29.620 align:middle line:90% 00:40:29.620 --> 00:40:31.790 align:middle line:90% Let's take a stab at it. 00:40:31.790 --> 00:40:33.710 align:middle line:84% You guys have all been speaking pretty well. 00:40:33.710 --> 00:40:36.127 align:middle line:84% Hannah, I don't think I've heard from you in a little bit. 00:40:36.127 --> 00:40:39.160 align:middle line:84% What would you say you need in order to convert this to-- 00:40:39.160 --> 00:40:42.175 align:middle line:84% AUDIENCE: I guess a knowledge of what it means? 00:40:42.175 --> 00:40:44.050 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: A knowledge of? 00:40:44.050 --> 00:40:45.760 align:middle line:84% AUDIENCE: What it means in terms of the conversion. 00:40:45.760 --> 00:40:47.843 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Knowledge of-- good. 00:40:47.843 --> 00:40:52.570 align:middle line:90% Knowledge of a conversion. 00:40:52.570 --> 00:40:55.870 align:middle line:84% Can you give me a conversion, maybe what it means? 00:40:55.870 --> 00:40:59.530 align:middle line:90% Conversion to, let's say, BPM. 00:40:59.530 --> 00:41:02.650 align:middle line:90% What would be-- 00:41:02.650 --> 00:41:05.860 align:middle line:84% Hannah, if you want to or pass it along to somebody else. 00:41:05.860 --> 00:41:09.440 align:middle line:84% Take a stab, what are you going to name that? 00:41:09.440 --> 00:41:11.450 align:middle line:90% Allegro approximately? 00:41:11.450 --> 00:41:17.000 align:middle line:90% 00:41:17.000 --> 00:41:17.760 align:middle line:90% 7? 00:41:17.760 --> 00:41:18.410 align:middle line:90% AUDIENCE: Yeah. 00:41:18.410 --> 00:41:19.785 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK. 00:41:19.785 --> 00:41:20.510 align:middle line:90% 2 million. 00:41:20.510 --> 00:41:21.150 align:middle line:90% OK, good. 00:41:21.150 --> 00:41:24.230 align:middle line:90% We're narrowing it down. 00:41:24.230 --> 00:41:26.183 align:middle line:90% AUDIENCE: But you're on 110. 00:41:26.183 --> 00:41:27.600 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 110. 00:41:27.600 --> 00:41:29.660 align:middle line:90% Good. 00:41:29.660 --> 00:41:32.223 align:middle line:84% Anybody want to go higher than 110? 00:41:32.223 --> 00:41:33.390 align:middle line:90% What do you want to go with? 00:41:33.390 --> 00:41:34.100 align:middle line:90% AUDIENCE: 126. 00:41:34.100 --> 00:41:35.600 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 126. 00:41:35.600 --> 00:41:38.270 align:middle line:90% Very specific number. 00:41:38.270 --> 00:41:39.415 align:middle line:90% Anyone want to go lower? 00:41:39.415 --> 00:41:42.140 align:middle line:90% 00:41:42.140 --> 00:41:47.030 align:middle line:84% I'm going to go a little bit lower and say 90. 00:41:47.030 --> 00:41:50.510 align:middle line:84% Because the other thing that you need to know 00:41:50.510 --> 00:41:55.010 align:middle line:90% is the cultural context. 00:41:55.010 --> 00:42:02.310 align:middle line:84% And because each of these things changes so much, 00:42:02.310 --> 00:42:08.540 align:middle line:84% Handel has a tempo marking of allegro adagio. 00:42:08.540 --> 00:42:09.637 align:middle line:90% AUDIENCE: Oh. 00:42:09.637 --> 00:42:11.720 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: What does that mean? 00:42:11.720 --> 00:42:12.970 align:middle line:90% Those are like contradictions. 00:42:12.970 --> 00:42:15.650 align:middle line:84% That's like, How do you like your cereal? 00:42:15.650 --> 00:42:17.170 align:middle line:90% I like it hot cold. 00:42:17.170 --> 00:42:20.020 align:middle line:84% Yeah, but at a particular time, that 00:42:20.020 --> 00:42:23.662 align:middle line:84% is-- so sometimes we ignore quite a lot of these, right? 00:42:23.662 --> 00:42:25.730 align:middle line:90% I know I use-- 00:42:25.730 --> 00:42:27.940 align:middle line:84% and by the way, had a pretty close-- 00:42:27.940 --> 00:42:31.090 align:middle line:84% I think I use 118 in a lookup table 00:42:31.090 --> 00:42:34.420 align:middle line:84% when I have no idea what I want to do from allegro. 00:42:34.420 --> 00:42:36.860 align:middle line:90% Or sometimes I've used 126. 00:42:36.860 --> 00:42:38.410 align:middle line:90% I've used other things, 110s. 00:42:38.410 --> 00:42:41.120 align:middle line:90% 110 I usually use is the-- 00:42:41.120 --> 00:42:42.610 align:middle line:84% it depends on whether or not I have 00:42:42.610 --> 00:42:45.370 align:middle line:84% a conception of the term allegretto, in which case 00:42:45.370 --> 00:42:47.180 align:middle line:90% I need to make room for that. 00:42:47.180 --> 00:42:49.360 align:middle line:90% But yeah, 110 is also very good. 00:42:49.360 --> 00:42:49.870 align:middle line:90% Good. 00:42:49.870 --> 00:42:51.880 align:middle line:84% By the way, every guest that people are doing 00:42:51.880 --> 00:42:54.050 align:middle line:84% has been really, really, really good in this class. 00:42:54.050 --> 00:42:56.320 align:middle line:84% So just keep taking the guess, and when 00:42:56.320 --> 00:42:59.840 align:middle line:84% we start talking too much, then I'll slow it down. 00:42:59.840 --> 00:43:00.560 align:middle line:90% But it's good. 00:43:00.560 --> 00:43:02.140 align:middle line:84% So these are all the various things 00:43:02.140 --> 00:43:05.590 align:middle line:84% that we might do to convert from one to another. 00:43:05.590 --> 00:43:11.730 align:middle line:84% There was one other way that we could measure duration 00:43:11.730 --> 00:43:16.990 align:middle line:84% that I think Marlon said that I was like, not yet, not yet, 00:43:16.990 --> 00:43:18.670 align:middle line:84% not yet, but becomes very important. 00:43:18.670 --> 00:43:19.980 align:middle line:90% Do you remember what we said? 00:43:19.980 --> 00:43:20.600 align:middle line:90% Ticks. 00:43:20.600 --> 00:43:21.100 align:middle line:90% Good. 00:43:21.100 --> 00:43:23.940 align:middle line:84% So you can measure on the number of bugs that get into your hair 00:43:23.940 --> 00:43:25.390 align:middle line:90% when you go hiking, right? 00:43:25.390 --> 00:43:27.400 align:middle line:90% No, what do we mean by ticks? 00:43:27.400 --> 00:43:29.220 align:middle line:84% This has a different meaning than-- 00:43:29.220 --> 00:43:30.553 align:middle line:90% AUDIENCE: From my understanding. 00:43:30.553 --> 00:43:33.570 align:middle line:84% It's how the process, like whatever program or application 00:43:33.570 --> 00:43:35.560 align:middle line:84% you're running and that measures and ticks. 00:43:35.560 --> 00:43:38.220 align:middle line:84% And so that kind of dictates what a second is based on it. 00:43:38.220 --> 00:43:39.720 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Great. 00:43:39.720 --> 00:43:41.850 align:middle line:84% Yeah, so what we can do is we can think 00:43:41.850 --> 00:43:45.930 align:middle line:90% of time as somehow discrete. 00:43:45.930 --> 00:43:48.250 align:middle line:90% That time moves forward. 00:43:48.250 --> 00:43:51.150 align:middle line:84% And by the way, there's some theoretical physicists who have 00:43:51.150 --> 00:43:54.780 align:middle line:84% been trying to study whether time actually is discrete 00:43:54.780 --> 00:43:56.430 align:middle line:84% and moves forward in, I don't know, 00:43:56.430 --> 00:43:59.820 align:middle line:84% 10 to the negative 58th seconds or not. 00:43:59.820 --> 00:44:02.640 align:middle line:84% But that we can think of musical time 00:44:02.640 --> 00:44:07.760 align:middle line:84% as a discrete number of something in a purely computer 00:44:07.760 --> 00:44:17.030 align:middle line:84% world, like ticks, which is both brilliant and a way of just 00:44:17.030 --> 00:44:20.820 align:middle line:84% shuffling later to some other later part of the program, 00:44:20.820 --> 00:44:24.560 align:middle line:84% the actual conversion of this to seconds, or to quarter notes 00:44:24.560 --> 00:44:28.850 align:middle line:84% or to eighth notes or anything like that. 00:44:28.850 --> 00:44:30.600 align:middle line:90% But it's very, very useful. 00:44:30.600 --> 00:44:35.480 align:middle line:84% The one term that you may have heard of before MIDI, the MIDI 00:44:35.480 --> 00:44:37.400 align:middle line:84% file format, the MIDI things MIDI 00:44:37.400 --> 00:44:41.420 align:middle line:84% tends to measure everything in ticks. 00:44:41.420 --> 00:44:43.440 align:middle line:84% There's some things that are not-- 00:44:43.440 --> 00:44:45.480 align:middle line:84% and it's a little bit of a simplification. 00:44:45.480 --> 00:44:52.460 align:middle line:84% So ticks end up being ticks per second or ticks per-- 00:44:52.460 --> 00:44:54.980 align:middle line:84% ticks per second is a pretty good one for tempo. 00:44:54.980 --> 00:45:02.510 align:middle line:84% And the other one ticks per quarter note, 00:45:02.510 --> 00:45:06.730 align:middle line:90% comes up quite a lot. 00:45:06.730 --> 00:45:12.130 align:middle line:84% Intriguingly, because of the problem of 6, 8 and 5, 00:45:12.130 --> 00:45:15.640 align:middle line:84% 8, and these weird things, fundamental measurements 00:45:15.640 --> 00:45:18.550 align:middle line:84% in terms of beats have not primarily 00:45:18.550 --> 00:45:26.720 align:middle line:84% been taken on by people who do musical representation. 00:45:26.720 --> 00:45:30.230 align:middle line:84% It's generally seen as a slightly higher representation, 00:45:30.230 --> 00:45:33.340 align:middle line:84% which is ironic because it's one of our fundamental ones 00:45:33.340 --> 00:45:35.230 align:middle line:90% for as musicians, right? 00:45:35.230 --> 00:45:37.910 align:middle line:84% I mean, you think of that, oh, that last half note, 00:45:37.910 --> 00:45:39.525 align:middle line:90% it lasts two beats, right? 00:45:39.525 --> 00:45:41.900 align:middle line:84% And then somebody reminds you, oh, what about cut timing? 00:45:41.900 --> 00:45:44.360 align:middle line:84% Like, you ruin everything, right? 00:45:44.360 --> 00:45:48.850 align:middle line:84% Because we generally do some things like this. 00:45:48.850 --> 00:45:57.280 align:middle line:84% I will share now what I ended up in my program in music21 decided 00:45:57.280 --> 00:46:01.870 align:middle line:84% that for some reason, the quarter note is 00:46:01.870 --> 00:46:04.410 align:middle line:84% the fundamental measure of everything 00:46:04.410 --> 00:46:08.070 align:middle line:84% else so that everything sends are 00:46:08.070 --> 00:46:13.510 align:middle line:84% measured in quarter lengths, which is a terrible term. 00:46:13.510 --> 00:46:15.780 align:middle line:84% Boy, I wish I had come up with something better. 00:46:15.780 --> 00:46:17.470 align:middle line:90% Essence, that's-- almonds. 00:46:17.470 --> 00:46:20.190 align:middle line:84% I wish I had measured in almonds, because quarter length 00:46:20.190 --> 00:46:24.720 align:middle line:84% takes a very long time to type with a camel case in the middle. 00:46:24.720 --> 00:46:26.380 align:middle line:90% And we didn't have-- 00:46:26.380 --> 00:46:27.120 align:middle line:90% what is it? 00:46:27.120 --> 00:46:31.980 align:middle line:84% GitHub, Autopilot, and things like that. 00:46:31.980 --> 00:46:33.450 align:middle line:84% Yeah, and by the way, I didn't mean 00:46:33.450 --> 00:46:36.160 align:middle line:84% to put no ChatGPT on the syllabus. 00:46:36.160 --> 00:46:38.530 align:middle line:84% I put it on the thing later today. 00:46:38.530 --> 00:46:41.970 align:middle line:84% You have fun with it, but not when we're doing any writing 00:46:41.970 --> 00:46:43.870 align:middle line:84% your essay or anything like that. 00:46:43.870 --> 00:46:47.820 align:middle line:84% But maybe we'll come up with a chat music or something 00:46:47.820 --> 00:46:49.860 align:middle line:84% later on this semester and try to see 00:46:49.860 --> 00:46:52.600 align:middle line:90% how we can do things like that. 00:46:52.600 --> 00:46:55.270 align:middle line:84% But yeah, I wish I had come up with a better thing, 00:46:55.270 --> 00:46:58.750 align:middle line:84% but almost everything measured in quarter lengths. 00:46:58.750 --> 00:47:02.640 align:middle line:84% What's nice about that is how many quarter lengths is 00:47:02.640 --> 00:47:04.057 align:middle line:90% a quarter note? 00:47:04.057 --> 00:47:04.640 align:middle line:90% AUDIENCE: One. 00:47:04.640 --> 00:47:05.050 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: One. 00:47:05.050 --> 00:47:05.900 align:middle line:90% Good, good, good. 00:47:05.900 --> 00:47:07.085 align:middle line:90% We're all still awake. 00:47:07.085 --> 00:47:08.960 align:middle line:84% I know it's Friday late and things, but yeah. 00:47:08.960 --> 00:47:14.697 align:middle line:84% So how many quarter lengths is a quarter note in 6, 8? 00:47:14.697 --> 00:47:15.280 align:middle line:90% AUDIENCE: One. 00:47:15.280 --> 00:47:15.750 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: One. 00:47:15.750 --> 00:47:18.470 align:middle line:84% How many quarter lengths is a quarter note in allegro? 00:47:18.470 --> 00:47:19.080 align:middle line:90% One. 00:47:19.080 --> 00:47:21.950 align:middle line:84% So these things and-- but then how many 00:47:21.950 --> 00:47:24.950 align:middle line:84% seconds is something that's 1.5 quarter lengths? 00:47:24.950 --> 00:47:27.240 align:middle line:84% Ah, now you have to keep up with everything. 00:47:27.240 --> 00:47:30.080 align:middle line:84% So you can think about when you're thinking about-- 00:47:30.080 --> 00:47:32.970 align:middle line:84% now let's get to the first word in this class. 00:47:32.970 --> 00:47:34.770 align:middle line:84% It's not representational music theory. 00:47:34.770 --> 00:47:35.810 align:middle line:90% It's computational. 00:47:35.810 --> 00:47:37.353 align:middle line:84% When you're starting to think about-- 00:47:37.353 --> 00:47:41.090 align:middle line:90% 00:47:41.090 --> 00:47:47.350 align:middle line:84% I'll abbreviate it quite often as ql to sec. 00:47:47.350 --> 00:47:53.480 align:middle line:90% 00:47:53.480 --> 00:47:59.100 align:middle line:84% And maybe we'll say secs or floats in this case. 00:47:59.100 --> 00:48:02.650 align:middle line:84% I've used a lot of typed Python, by the way, where 00:48:02.650 --> 00:48:06.220 align:middle line:84% if you haven't ever seen this, you'll put this in 00:48:06.220 --> 00:48:07.640 align:middle line:90% to say what I expect to do. 00:48:07.640 --> 00:48:13.930 align:middle line:84% So it's sort of all the joys of having to type more 00:48:13.930 --> 00:48:15.820 align:middle line:90% things without type safety. 00:48:15.820 --> 00:48:17.330 align:middle line:90% It's not so good. 00:48:17.330 --> 00:48:21.570 align:middle line:84% But what do we want to put in as our attribute or attributes 00:48:21.570 --> 00:48:22.070 align:middle line:90% here? 00:48:22.070 --> 00:48:25.540 align:middle line:90% We're going to return a float. 00:48:25.540 --> 00:48:28.330 align:middle line:84% What's the first thing that we need? 00:48:28.330 --> 00:48:30.450 align:middle line:90% ql to seconds? 00:48:30.450 --> 00:48:31.450 align:middle line:90% AUDIENCE: How many ql's? 00:48:31.450 --> 00:48:33.283 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: How many ql's. 00:48:33.283 --> 00:48:35.060 align:middle line:90% Yeah, so maybe it'll be ql. 00:48:35.060 --> 00:48:37.360 align:middle line:84% Some people like to do ql in, and that's 00:48:37.360 --> 00:48:39.130 align:middle line:90% going to be measured in-- 00:48:39.130 --> 00:48:42.130 align:middle line:90% what do we want to make that? 00:48:42.130 --> 00:48:43.090 align:middle line:90% AUDIENCE: Floats. 00:48:43.090 --> 00:48:44.952 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Float. 00:48:44.952 --> 00:48:45.565 align:middle line:90% Good. 00:48:45.565 --> 00:48:47.290 align:middle line:90% It could be a float. 00:48:47.290 --> 00:48:48.770 align:middle line:90% It's probably not good enough. 00:48:48.770 --> 00:48:51.670 align:middle line:84% Name something not representational 00:48:51.670 --> 00:48:53.632 align:middle line:90% as an int in quarter lengths. 00:48:53.632 --> 00:48:54.340 align:middle line:90% AUDIENCE: Eighth. 00:48:54.340 --> 00:48:56.090 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Eighth note. 00:48:56.090 --> 00:48:57.220 align:middle line:90% Good, good. 00:48:57.220 --> 00:49:00.730 align:middle line:84% The issue-- I tend to sometimes use the fraction class, 00:49:00.730 --> 00:49:04.650 align:middle line:84% if you haven't ever done that because of the first time 00:49:04.650 --> 00:49:07.780 align:middle line:90% they had three triplets add up. 00:49:07.780 --> 00:49:09.000 align:middle line:90% Actually, triplets work fine. 00:49:09.000 --> 00:49:15.000 align:middle line:84% Five quintuplets adds up to 1.0000124 [MUMBLES] 00:49:15.000 --> 00:49:16.000 align:middle line:90% quarter notes. 00:49:16.000 --> 00:49:17.610 align:middle line:84% That's why I started moving that. 00:49:17.610 --> 00:49:18.610 align:middle line:90% But float's pretty good. 00:49:18.610 --> 00:49:20.290 align:middle line:90% Good. 00:49:20.290 --> 00:49:21.990 align:middle line:90% So that's attribute 1. 00:49:21.990 --> 00:49:23.855 align:middle line:84% Anybody want another attribute in there? 00:49:23.855 --> 00:49:27.420 align:middle line:90% 00:49:27.420 --> 00:49:28.390 align:middle line:90% Quarter length second. 00:49:28.390 --> 00:49:28.890 align:middle line:90% Yes. 00:49:28.890 --> 00:49:29.710 align:middle line:90% AUDIENCE: The tempo? 00:49:29.710 --> 00:49:30.240 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Tempo. 00:49:30.240 --> 00:49:30.740 align:middle line:90% Good. 00:49:30.740 --> 00:49:33.670 align:middle line:90% So we can define a tempo object. 00:49:33.670 --> 00:49:35.520 align:middle line:90% And now we're going to see-- 00:49:35.520 --> 00:49:38.410 align:middle line:90% or struct or some kind of thing. 00:49:38.410 --> 00:49:40.480 align:middle line:84% Well, tempo could be a basic thing. 00:49:40.480 --> 00:49:43.470 align:middle line:90% It could be a float, right? 00:49:43.470 --> 00:49:44.690 align:middle line:90% What else could it be? 00:49:44.690 --> 00:49:47.280 align:middle line:90% 00:49:47.280 --> 00:49:50.550 align:middle line:84% What do we-- if we're not thinking about allegro non 00:49:50.550 --> 00:49:54.720 align:middle line:84% troppo as used by Handel as opposed to Mendelssohn 00:49:54.720 --> 00:49:57.734 align:middle line:84% or something like that, what do we-- 00:49:57.734 --> 00:49:58.335 align:middle line:90% Yeah. 00:49:58.335 --> 00:49:59.460 align:middle line:90% AUDIENCE: Beats per minute. 00:49:59.460 --> 00:50:00.330 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Beats per minute. 00:50:00.330 --> 00:50:01.250 align:middle line:90% OK. 00:50:01.250 --> 00:50:04.200 align:middle line:90% So we have beats per minute. 00:50:04.200 --> 00:50:05.670 align:middle line:84% That's the most common one, right? 00:50:05.670 --> 00:50:06.995 align:middle line:90% So that's going to be-- 00:50:06.995 --> 00:50:08.620 align:middle line:84% how would you measure beats per minute? 00:50:08.620 --> 00:50:13.400 align:middle line:90% 00:50:13.400 --> 00:50:16.200 align:middle line:84% Oh sorry, how do we want to represent it? 00:50:16.200 --> 00:50:16.910 align:middle line:90% AUDIENCE: Float. 00:50:16.910 --> 00:50:18.410 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Float. 00:50:18.410 --> 00:50:19.610 align:middle line:90% Good. 00:50:19.610 --> 00:50:23.940 align:middle line:84% So we pass it in first thing a quarter length. 00:50:23.940 --> 00:50:25.820 align:middle line:90% Second thing, a tempo. 00:50:25.820 --> 00:50:28.190 align:middle line:90% Is that enough? 00:50:28.190 --> 00:50:28.900 align:middle line:90% Why not? 00:50:28.900 --> 00:50:29.942 align:middle line:90% AUDIENCE: Time signature? 00:50:29.942 --> 00:50:31.817 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Time signature. 00:50:31.817 --> 00:50:32.780 align:middle line:90% In order to define-- 00:50:32.780 --> 00:50:35.685 align:middle line:84% what are we defining by the time signature? 00:50:35.685 --> 00:50:37.560 align:middle line:84% AUDIENCE: How many beats a quarter length is? 00:50:37.560 --> 00:50:37.940 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Great. 00:50:37.940 --> 00:50:40.100 align:middle line:90% Beats per quarter length. 00:50:40.100 --> 00:50:47.690 align:middle line:84% So ts will measure in beats per quarter length. 00:50:47.690 --> 00:50:51.024 align:middle line:84% And what do we want to make that also? 00:50:51.024 --> 00:50:52.280 align:middle line:90% AUDIENCE: Float. 00:50:52.280 --> 00:50:53.780 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Float. 00:50:53.780 --> 00:50:55.250 align:middle line:90% Good. 00:50:55.250 --> 00:50:57.660 align:middle line:90% Let's do this. 00:50:57.660 --> 00:50:59.440 align:middle line:90% You don't need any-- 00:50:59.440 --> 00:51:01.640 align:middle line:90% go ahead, grab laptops. 00:51:01.640 --> 00:51:06.940 align:middle line:84% Let's implement quarter length to second. 00:51:06.940 --> 00:51:08.570 align:middle line:84% Let's do it as paired programming, 00:51:08.570 --> 00:51:10.130 align:middle line:90% so we learn from each other. 00:51:10.130 --> 00:51:15.730 align:middle line:84% So the person on the left is the-- who's done 00:51:15.730 --> 00:51:16.570 align:middle line:90% paired programming? 00:51:16.570 --> 00:51:18.410 align:middle line:84% Person on the left is the driver, 00:51:18.410 --> 00:51:21.050 align:middle line:84% unless the person on the left doesn't have the thing. 00:51:21.050 --> 00:51:24.250 align:middle line:84% And that's your left, not my left. 00:51:24.250 --> 00:51:28.210 align:middle line:90% And everybody else will-- 00:51:28.210 --> 00:51:31.010 align:middle line:84% 4:34, we'll take about 10 minutes. 00:51:31.010 --> 00:51:34.722 align:middle line:90% [SIDE CONVERSATION] 00:51:34.722 --> 00:51:35.845 align:middle line:90% 00:51:35.845 --> 00:51:37.220 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: OK. 00:51:37.220 --> 00:51:40.910 align:middle line:84% Just before we continue and start going on with things, 00:51:40.910 --> 00:51:44.115 align:middle line:84% how many people wrote five test cases before you started? 00:51:44.115 --> 00:51:44.920 align:middle line:90% [LAUGHTER] 00:51:44.920 --> 00:51:48.230 align:middle line:84% How many people wrote 10 test cases? 00:51:48.230 --> 00:51:51.040 align:middle line:84% How many people wrote one test case? 00:51:51.040 --> 00:51:51.980 align:middle line:90% One test case? 00:51:51.980 --> 00:51:53.840 align:middle line:84% How many people wrote zero test cases? 00:51:53.840 --> 00:51:57.350 align:middle line:84% OK, you're going to hear this a couple times in the next class 00:51:57.350 --> 00:51:57.850 align:middle line:90% and stuff. 00:51:57.850 --> 00:52:00.680 align:middle line:84% And this is very different-- guys, just one second. 00:52:00.680 --> 00:52:01.930 align:middle line:90% I'm going to get back into it. 00:52:01.930 --> 00:52:05.340 align:middle line:84% Very different from a lot of the especially intro level 00:52:05.340 --> 00:52:06.580 align:middle line:90% CS classes at MIT. 00:52:06.580 --> 00:52:09.850 align:middle line:84% But because this isn't a really big established field, 00:52:09.850 --> 00:52:12.210 align:middle line:84% I told all of you all that you're really-- 00:52:12.210 --> 00:52:15.150 align:middle line:84% this is one of the very few classes like this, right? 00:52:15.150 --> 00:52:19.050 align:middle line:84% One of the really important things is writing test cases 00:52:19.050 --> 00:52:21.460 align:middle line:84% and especially looking at corner cases. 00:52:21.460 --> 00:52:23.320 align:middle line:90% So get in the habit of this. 00:52:23.320 --> 00:52:25.420 align:middle line:84% You're going to-- if I'm feeling nice, 00:52:25.420 --> 00:52:27.570 align:middle line:84% I might give one or two test cases 00:52:27.570 --> 00:52:29.680 align:middle line:90% with correct answers on things. 00:52:29.680 --> 00:52:34.740 align:middle line:84% But a lot of it is sit down and think at 60 beats per minute, 00:52:34.740 --> 00:52:42.180 align:middle line:84% at 4, 4 what's the answer for a quarter note for one? 00:52:42.180 --> 00:52:43.650 align:middle line:90% AUDIENCE: One. 00:52:43.650 --> 00:52:44.140 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: One. 00:52:44.140 --> 00:52:44.670 align:middle line:90% Good. 00:52:44.670 --> 00:52:47.470 align:middle line:84% At least, make sure your code does that before you go on. 00:52:47.470 --> 00:52:48.280 align:middle line:90% So keep going. 00:52:48.280 --> 00:52:50.345 align:middle line:90% Try some running and try some-- 00:52:50.345 --> 00:52:52.420 align:middle line:90% [LAUGHTER] 00:52:52.420 --> 00:52:53.730 align:middle line:90% 00:52:53.730 --> 00:52:56.600 align:middle line:84% OK, let's all come back together for a bit 00:52:56.600 --> 00:52:58.560 align:middle line:84% because this isn't the problem set. 00:52:58.560 --> 00:53:03.410 align:middle line:84% And I want to move on and thinks. 00:53:03.410 --> 00:53:10.770 align:middle line:84% One of the terms I heard a lot was this one. 00:53:10.770 --> 00:53:13.733 align:middle line:84% Let's do a dimensional analysis or things like that. 00:53:13.733 --> 00:53:16.400 align:middle line:84% For somebody who didn't use that term or who doesn't-- we're all 00:53:16.400 --> 00:53:18.330 align:middle line:84% coming from different backgrounds and things. 00:53:18.330 --> 00:53:20.720 align:middle line:90% What's a dimensional analysis? 00:53:20.720 --> 00:53:21.747 align:middle line:90% AUDIENCE: Stoichiometry? 00:53:21.747 --> 00:53:23.580 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Stoichiometry. 00:53:23.580 --> 00:53:26.680 align:middle line:84% Well, thank you for obfuscating further. 00:53:26.680 --> 00:53:31.030 align:middle line:84% [LAUGHS] We'll get you on the call-- what's that called? 00:53:31.030 --> 00:53:32.030 align:middle line:90% AUDIENCE: Stoichiometry. 00:53:32.030 --> 00:53:34.370 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Stoichiometry. 00:53:34.370 --> 00:53:37.430 align:middle line:84% I must have failed trigonometry, so I didn't get to that one. 00:53:37.430 --> 00:53:39.910 align:middle line:90% [LAUGHTER] 00:53:39.910 --> 00:53:40.902 align:middle line:90% 00:53:40.902 --> 00:53:43.880 align:middle line:90% OK, what might that mean? 00:53:43.880 --> 00:53:45.420 align:middle line:84% Honestly, I just learned a new word. 00:53:45.420 --> 00:53:45.780 align:middle line:90% Thank you. 00:53:45.780 --> 00:53:47.370 align:middle line:84% AUDIENCE: Just dimensional analysis for chemistry. 00:53:47.370 --> 00:53:48.470 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: That's just dimensional analysis 00:53:48.470 --> 00:53:49.110 align:middle line:90% for chemistry. 00:53:49.110 --> 00:53:51.230 align:middle line:90% OK, good. 00:53:51.230 --> 00:53:56.680 align:middle line:84% Remember, I was up the river, so we didn't learn these things. 00:53:56.680 --> 00:53:59.585 align:middle line:84% What do we mean when we're talking 00:53:59.585 --> 00:54:00.710 align:middle line:90% about dimensional analysis? 00:54:00.710 --> 00:54:00.940 align:middle line:90% Yeah. 00:54:00.940 --> 00:54:03.020 align:middle line:84% AUDIENCE: It's like a conversion between equivalent units? 00:54:03.020 --> 00:54:03.760 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: A conversion 00:54:03.760 --> 00:54:04.940 align:middle line:90% between equivalent units. 00:54:04.940 --> 00:54:05.440 align:middle line:90% Good. 00:54:05.440 --> 00:54:07.660 align:middle line:84% What are some dimensional analysis things 00:54:07.660 --> 00:54:11.530 align:middle line:90% you've done before this class? 00:54:11.530 --> 00:54:12.140 align:middle line:90% Yeah. 00:54:12.140 --> 00:54:12.890 align:middle line:90% AUDIENCE: Physics? 00:54:12.890 --> 00:54:13.270 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Physics. 00:54:13.270 --> 00:54:14.840 align:middle line:90% So what's a dimension? 00:54:14.840 --> 00:54:16.240 align:middle line:90% What's a kind of-- 00:54:16.240 --> 00:54:19.780 align:middle line:84% AUDIENCE: Trying to convert like-- 00:54:19.780 --> 00:54:23.320 align:middle line:84% um, like trying to convert like you say meters per second 00:54:23.320 --> 00:54:24.410 align:middle line:90% to miles per hour. 00:54:24.410 --> 00:54:24.670 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Great. 00:54:24.670 --> 00:54:26.270 align:middle line:84% Meters per second to miles per hour. 00:54:26.270 --> 00:54:26.920 align:middle line:90% Absolutely. 00:54:26.920 --> 00:54:27.860 align:middle line:90% Thank you. 00:54:27.860 --> 00:54:30.080 align:middle line:84% So we have the particular conversion there. 00:54:30.080 --> 00:54:33.110 align:middle line:84% So we have meters, seconds, miles, hours. 00:54:33.110 --> 00:54:36.850 align:middle line:84% What were some dimensionality things-- 00:54:36.850 --> 00:54:40.030 align:middle line:84% dimensions that you use now that you might not 00:54:40.030 --> 00:54:42.580 align:middle line:90% have used in your past before? 00:54:42.580 --> 00:54:43.840 align:middle line:90% Yeah. 00:54:43.840 --> 00:54:45.200 align:middle line:90% AUDIENCE: Beats quarter lengths. 00:54:45.200 --> 00:54:46.780 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Beats per quarter length. 00:54:46.780 --> 00:54:47.870 align:middle line:90% Quarter length per beat. 00:54:47.870 --> 00:54:48.370 align:middle line:90% Good. 00:54:48.370 --> 00:54:49.580 align:middle line:90% Beats quarter lengths? 00:54:49.580 --> 00:54:51.010 align:middle line:90% Absolutely. 00:54:51.010 --> 00:54:53.690 align:middle line:84% You've probably heard beats per minute. 00:54:53.690 --> 00:54:56.090 align:middle line:84% Not everybody has thought of it as, OK, 00:54:56.090 --> 00:55:03.628 align:middle line:84% then I have to convert to beats per second, which is not 00:55:03.628 --> 00:55:04.670 align:middle line:90% something we think about. 00:55:04.670 --> 00:55:07.045 align:middle line:84% We're very, very good at thinking about beats per minute. 00:55:07.045 --> 00:55:08.560 align:middle line:84% As musicians, we're very, very bad 00:55:08.560 --> 00:55:11.470 align:middle line:84% at think about beats per second or seconds per beat. 00:55:11.470 --> 00:55:13.160 align:middle line:90% And then beats per-- 00:55:13.160 --> 00:55:14.600 align:middle line:90% what was the other thing? 00:55:14.600 --> 00:55:17.530 align:middle line:90% Beats per quarter length. 00:55:17.530 --> 00:55:18.670 align:middle line:90% Awesome. 00:55:18.670 --> 00:55:22.700 align:middle line:84% So that came up quite a bit on things going on. 00:55:22.700 --> 00:55:24.580 align:middle line:84% What were some other things that seemed 00:55:24.580 --> 00:55:29.210 align:middle line:84% to stump or be fun or interesting, 00:55:29.210 --> 00:55:32.410 align:middle line:84% or that you learned from programming this? 00:55:32.410 --> 00:55:36.470 align:middle line:84% I heard a lot of, we don't need the time signature. 00:55:36.470 --> 00:55:39.620 align:middle line:84% I think I heard that allowed at least three or four times. 00:55:39.620 --> 00:55:44.480 align:middle line:84% But what do you do if you have the time signature? 00:55:44.480 --> 00:55:46.030 align:middle line:84% And the problem-- and let's say we're 00:55:46.030 --> 00:55:49.310 align:middle line:84% leaving out that 5, 8 where the beat changes stuff? 00:55:49.310 --> 00:55:55.050 align:middle line:84% How do we convert from time signature-- 00:55:55.050 --> 00:55:59.760 align:middle line:84% think of time signature first as a two tuple 00:55:59.760 --> 00:56:02.446 align:middle line:90% of numerator and denominator. 00:56:02.446 --> 00:56:05.910 align:middle line:90% 00:56:05.910 --> 00:56:08.760 align:middle line:84% How do you convert a numerator and denominator 00:56:08.760 --> 00:56:11.705 align:middle line:90% into beats per quarter length? 00:56:11.705 --> 00:56:15.270 align:middle line:90% 00:56:15.270 --> 00:56:16.450 align:middle line:90% What is 4 4. 00:56:16.450 --> 00:56:18.250 align:middle line:84% How many beats per quarter length? 00:56:18.250 --> 00:56:19.110 align:middle line:90% AUDIENCE: 1. 00:56:19.110 --> 00:56:20.280 align:middle line:90% AUDIENCE: 1 1. 00:56:20.280 --> 00:56:21.738 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Good. 00:56:21.738 --> 00:56:22.620 align:middle line:90% What is 2/2? 00:56:22.620 --> 00:56:23.942 align:middle line:90% AUDIENCE: 1. 00:56:23.942 --> 00:56:25.457 align:middle line:90% [INTERPOSING VOICES] 00:56:25.457 --> 00:56:26.040 align:middle line:90% AUDIENCE: One. 00:56:26.040 --> 00:56:27.970 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: How many beats-- 00:56:27.970 --> 00:56:28.470 align:middle line:90% oh, good. 00:56:28.470 --> 00:56:31.920 align:middle line:84% I did hear it, but I heard a lot of-- 00:56:31.920 --> 00:56:32.647 align:middle line:90% I love it. 00:56:32.647 --> 00:56:34.480 align:middle line:84% This is what I'm hoping to get to his class. 00:56:34.480 --> 00:56:37.900 align:middle line:84% I heard a lot of very loud wrong answers, 00:56:37.900 --> 00:56:39.450 align:middle line:84% and then very, very trickling right 00:56:39.450 --> 00:56:41.560 align:middle line:84% at the end, a little whispered right answer. 00:56:41.560 --> 00:56:47.292 align:middle line:84% How many beats per quarter length for cut time for 2 2. 00:56:47.292 --> 00:56:48.200 align:middle line:90% [INTERPOSING VOICES] 00:56:48.200 --> 00:56:49.110 align:middle line:90% AUDIENCE: 2. 00:56:49.110 --> 00:56:50.527 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 2 2. 00:56:50.527 --> 00:56:52.700 align:middle line:90% And I also heard whispered. 00:56:52.700 --> 00:56:53.550 align:middle line:90% Somebody had-- 00:56:53.550 --> 00:56:56.330 align:middle line:90% 00:56:56.330 --> 00:56:57.920 align:middle line:90% AUDIENCE: 1/2. 00:56:57.920 --> 00:56:59.460 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 1/2. 00:56:59.460 --> 00:57:03.415 align:middle line:84% How many beats does it take to play a quarter note in 2 2? 00:57:03.415 --> 00:57:06.380 align:middle line:90% 00:57:06.380 --> 00:57:09.470 align:middle line:90% How long does each of these-- 00:57:09.470 --> 00:57:10.380 align:middle line:90% is that correct? 00:57:10.380 --> 00:57:11.610 align:middle line:90% Am I wrong this time? 00:57:11.610 --> 00:57:12.620 align:middle line:90% AUDIENCE: Half a beat. 00:57:12.620 --> 00:57:13.680 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Half a beat. 00:57:13.680 --> 00:57:15.680 align:middle line:84% This is half a beat, and it gets a quarter note. 00:57:15.680 --> 00:57:18.110 align:middle line:84% This is half a beat, and it gets a quarter note. 00:57:18.110 --> 00:57:22.028 align:middle line:90% OK, what about in 3 2? 00:57:22.028 --> 00:57:22.820 align:middle line:90% AUDIENCE: It's 1/2. 00:57:22.820 --> 00:57:24.237 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 1/2. 00:57:24.237 --> 00:57:27.120 align:middle line:90% So what part do we not need? 00:57:27.120 --> 00:57:28.310 align:middle line:90% AUDIENCE: The numerator. 00:57:28.310 --> 00:57:30.140 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Numerator. 00:57:30.140 --> 00:57:33.450 align:middle line:84% So for this particular thing, we don't need the numerator. 00:57:33.450 --> 00:57:35.360 align:middle line:84% We would if we're-- yeah, go ahead, Matthew. 00:57:35.360 --> 00:57:37.110 align:middle line:84% AUDIENCE: Do we need the numerator in 6 8? 00:57:37.110 --> 00:57:39.693 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Do we need the numerator in 6 8? 00:57:39.693 --> 00:57:40.370 align:middle line:90% Yes. 00:57:40.370 --> 00:57:43.043 align:middle line:84% So what do we need the numerator for? 00:57:43.043 --> 00:57:47.090 align:middle line:90% 00:57:47.090 --> 00:57:54.430 align:middle line:84% We only need the numerator to do a modulo operation 00:57:54.430 --> 00:57:57.880 align:middle line:90% to compare if it equals 0. 00:57:57.880 --> 00:57:59.150 align:middle line:90% But is that good enough? 00:57:59.150 --> 00:58:04.240 align:middle line:84% Because 6 8, 9 8, 12 8, these all generally default 00:58:04.240 --> 00:58:07.750 align:middle line:84% in most conceptions, not all, but in most conceptions 00:58:07.750 --> 00:58:12.650 align:middle line:84% as the number of beats is divided by 3 on that. 00:58:12.650 --> 00:58:13.670 align:middle line:90% So is that good enough? 00:58:13.670 --> 00:58:16.270 align:middle line:84% Does everyone know modulo notation like the remainder 00:58:16.270 --> 00:58:18.620 align:middle line:90% when divided by 3 equals 0? 00:58:18.620 --> 00:58:20.150 align:middle line:90% So does that work? 00:58:20.150 --> 00:58:20.810 align:middle line:90% 6 8? 00:58:20.810 --> 00:58:22.330 align:middle line:90% Great. 00:58:22.330 --> 00:58:23.270 align:middle line:90% 8 8? 00:58:23.270 --> 00:58:23.800 align:middle line:90% Nope. 00:58:23.800 --> 00:58:25.000 align:middle line:90% That's a normal one. 00:58:25.000 --> 00:58:25.920 align:middle line:90% 9 8, great. 00:58:25.920 --> 00:58:29.560 align:middle line:90% 00:58:29.560 --> 00:58:33.100 align:middle line:90% So 6 4, great. 00:58:33.100 --> 00:58:34.455 align:middle line:90% How many beats does 6 4 have? 00:58:34.455 --> 00:58:38.110 align:middle line:90% 00:58:38.110 --> 00:58:40.580 align:middle line:90% Treated in this way? 00:58:40.580 --> 00:58:41.350 align:middle line:90% AUDIENCE: Two. 00:58:41.350 --> 00:58:41.590 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Two. 00:58:41.590 --> 00:58:42.562 align:middle line:90% Two. 00:58:42.562 --> 00:58:44.006 align:middle line:90% 1, 2. 00:58:44.006 --> 00:58:44.506 align:middle line:90% 1-- 00:58:44.506 --> 00:58:45.470 align:middle line:90% [SCAT SINGING] 00:58:45.470 --> 00:58:45.970 align:middle line:90% 2. 00:58:45.970 --> 00:58:47.060 align:middle line:90% Yeah, I say it has two. 00:58:47.060 --> 00:58:49.690 align:middle line:90% And I mean 1, 2, 3, 4. 00:58:49.690 --> 00:58:51.820 align:middle line:90% But I'm giving you the big one. 00:58:51.820 --> 00:58:53.320 align:middle line:90% Great, so 6 4. 00:58:53.320 --> 00:58:55.950 align:middle line:90% How many does 9 16 have? 00:58:55.950 --> 00:58:56.850 align:middle line:90% AUDIENCE: 2 3? 00:58:56.850 --> 00:58:57.370 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Great. 00:58:57.370 --> 00:58:58.810 align:middle line:90% So this works, right? 00:58:58.810 --> 00:59:02.940 align:middle line:84% We have all our good test cases there? 00:59:02.940 --> 00:59:04.330 align:middle line:90% Yeah, you're smiling big. 00:59:04.330 --> 00:59:05.788 align:middle line:90% Anyone else smiling big? 00:59:05.788 --> 00:59:06.580 align:middle line:90% You're smiling big. 00:59:06.580 --> 00:59:09.027 align:middle line:84% What's the test case we've missed? 00:59:09.027 --> 00:59:09.610 align:middle line:90% AUDIENCE: 3 4? 00:59:09.610 --> 00:59:11.250 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 3 4. 00:59:11.250 --> 00:59:15.370 align:middle line:84% So 3 4 has one beat, because you divide by 3. 00:59:15.370 --> 00:59:16.505 align:middle line:90% So what do we have to do? 00:59:16.505 --> 00:59:21.180 align:middle line:90% 00:59:21.180 --> 00:59:35.105 align:middle line:84% If the numerator modulo 3 equals 0 and num not equals 3, right? 00:59:35.105 --> 00:59:37.020 align:middle line:84% That's assuming we've already done 00:59:37.020 --> 00:59:39.480 align:middle line:84% our assertion that numerator is positive 00:59:39.480 --> 00:59:41.940 align:middle line:90% and all the other things, right? 00:59:41.940 --> 00:59:46.500 align:middle line:84% So these are the algorithms that you already 00:59:46.500 --> 00:59:50.940 align:middle line:84% know in your head for music by being musicians. 00:59:50.940 --> 00:59:55.160 align:middle line:84% But they are not the algorithms that you have been programming 00:59:55.160 --> 00:59:56.130 align:middle line:90% before. 00:59:56.130 --> 01:00:00.260 align:middle line:84% Here's a particular one that I always like to do, 01:00:00.260 --> 01:00:02.760 align:middle line:84% and I think we're going to have time to go through it today, 01:00:02.760 --> 01:00:04.843 align:middle line:84% because you guys have been such great participants 01:00:04.843 --> 01:00:10.340 align:middle line:90% in my terrible ploys and things. 01:00:10.340 --> 01:00:13.812 align:middle line:84% Given a note, given a quarter note, let's say. 01:00:13.812 --> 01:00:16.020 align:middle line:84% We'll keep it really simple because we're already in. 01:00:16.020 --> 01:00:18.620 align:middle line:84% We'll call it quarter note one quarter length, one beat 01:00:18.620 --> 01:00:21.230 align:middle line:90% or something. 01:00:21.230 --> 01:00:24.050 align:middle line:90% Given a dot, how many beats? 01:00:24.050 --> 01:00:24.950 align:middle line:90% AUDIENCE: 155. 01:00:24.950 --> 01:00:26.367 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 155? 01:00:26.367 --> 01:00:27.960 align:middle line:90% Given two dots. 01:00:27.960 --> 01:00:28.585 align:middle line:90% AUDIENCE: 1.73. 01:00:28.585 --> 01:00:30.293 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Three dots. 01:00:30.293 --> 01:00:31.340 align:middle line:90% AUDIENCE: 1.83. 01:00:31.340 --> 01:00:31.940 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Oh, somebody had it. 01:00:31.940 --> 01:00:33.630 align:middle line:90% That will be a trail off. 01:00:33.630 --> 01:00:34.160 align:middle line:90% Good. 01:00:34.160 --> 01:00:37.010 align:middle line:90% n dots. 01:00:37.010 --> 01:00:38.175 align:middle line:90% What is the formula? 01:00:38.175 --> 01:00:38.967 align:middle line:90% AUDIENCE: 2 minus-- 01:00:38.967 --> 01:00:40.400 align:middle line:90% AUDIENCE: 2 to the negative 1. 01:00:40.400 --> 01:00:42.525 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Oh, something-- yeah. 01:00:42.525 --> 01:00:44.520 align:middle line:90% So working this out-- 01:00:44.520 --> 01:00:47.290 align:middle line:84% and if you want, I'll put a link online. 01:00:47.290 --> 01:00:50.230 align:middle line:84% Once, I originally had to write out this formula 01:00:50.230 --> 01:00:51.860 align:middle line:90% because I kind of needed it. 01:00:51.860 --> 01:00:54.970 align:middle line:90% It becomes fun. 01:00:54.970 --> 01:00:56.907 align:middle line:90% Yeah, so it ends up being-- 01:00:56.907 --> 01:00:57.740 align:middle line:90% what do you call it? 01:00:57.740 --> 01:00:59.770 align:middle line:84% These are Mersenne numbers which are not 01:00:59.770 --> 01:01:01.460 align:middle line:90% the same as Mersenne primes. 01:01:01.460 --> 01:01:05.960 align:middle line:90% They end up being n minus 1. 01:01:05.960 --> 01:01:06.460 align:middle line:90% What is it? 01:01:06.460 --> 01:01:09.470 align:middle line:84% 2 to the n minus 1 over 2 to the n. 01:01:09.470 --> 01:01:13.540 align:middle line:84% So you end up 1 and 1/2, slightly under. 01:01:13.540 --> 01:01:16.760 align:middle line:90% 1 and 3/4, 1 and 7/8. 01:01:16.760 --> 01:01:18.770 align:middle line:90% So 2 to the n, whatever. 01:01:18.770 --> 01:01:21.170 align:middle line:90% So you can figure out, OK-- 01:01:21.170 --> 01:01:23.080 align:middle line:90% and hopefully that works. 01:01:23.080 --> 01:01:24.970 align:middle line:90% 2 to the 0. 01:01:24.970 --> 01:01:27.260 align:middle line:90% Sorry, that goes down below. 01:01:27.260 --> 01:01:29.050 align:middle line:90% That's not part of the exponent. 01:01:29.050 --> 01:01:30.310 align:middle line:90% I should make that nicer. 01:01:30.310 --> 01:01:34.460 align:middle line:84% 2 to the n minus 1 over 2 to the n. 01:01:34.460 --> 01:01:36.770 align:middle line:84% Sorry, I haven't been writing on whiteboards in a year, 01:01:36.770 --> 01:01:38.600 align:middle line:90% so my technique's a little low. 01:01:38.600 --> 01:01:40.990 align:middle line:90% So does that work? 01:01:40.990 --> 01:01:42.520 align:middle line:90% Or 1 plus, right? 01:01:42.520 --> 01:01:43.120 align:middle line:90% Yeah. 01:01:43.120 --> 01:01:47.190 align:middle line:90% So does that work for zero dots? 01:01:47.190 --> 01:01:50.220 align:middle line:90% What's 2 to the zeroth? 01:01:50.220 --> 01:01:51.400 align:middle line:90% What's 2 to the zeroth? 01:01:51.400 --> 01:01:51.900 align:middle line:90% AUDIENCE: 1. 01:01:51.900 --> 01:01:53.233 align:middle line:90% MICHAEL SCOTT ASATO CUTHBERT: 1. 01:01:53.233 --> 01:01:54.460 align:middle line:90% Minus 1 is 0. 01:01:54.460 --> 01:01:57.080 align:middle line:84% So that cancels that out as long as that's not 0 there. 01:01:57.080 --> 01:01:57.580 align:middle line:90% Good. 01:01:57.580 --> 01:01:59.040 align:middle line:90% So you get 1. 01:01:59.040 --> 01:02:01.040 align:middle line:84% What happens if you have a negative 1 dot? 01:02:01.040 --> 01:02:05.880 align:middle line:90% 01:02:05.880 --> 01:02:07.600 align:middle line:90% 2 to the negative 1? 01:02:07.600 --> 01:02:08.433 align:middle line:90% AUDIENCE: It is 1/2. 01:02:08.433 --> 01:02:09.850 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: 1/2. 01:02:09.850 --> 01:02:10.742 align:middle line:90% Minus 1? 01:02:10.742 --> 01:02:11.700 align:middle line:90% AUDIENCE: Negative 1/2. 01:02:11.700 --> 01:02:14.370 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Negative 1/2 over 2 01:02:14.370 --> 01:02:16.590 align:middle line:90% to the negative 1? 01:02:16.590 --> 01:02:17.945 align:middle line:90% AUDIENCE: Uh, over 1/2. 01:02:17.945 --> 01:02:19.570 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Over 1/2. 01:02:19.570 --> 01:02:20.670 align:middle line:90% What's that end up? 01:02:20.670 --> 01:02:22.200 align:middle line:90% Negative 1/2 over 1/2? 01:02:22.200 --> 01:02:23.240 align:middle line:90% 1 plus-- 01:02:23.240 --> 01:02:23.740 align:middle line:90% AUDIENCE: 2. 01:02:23.740 --> 01:02:24.420 align:middle line:90% AUDIENCE: Negative 1. 01:02:24.420 --> 01:02:25.680 align:middle line:84% MICHAEL SCOTT ASATO CUTHBERT: Negative 1 equals? 01:02:25.680 --> 01:02:26.580 align:middle line:90% AUDIENCE: 0. 01:02:26.580 --> 01:02:27.913 align:middle line:90% MICHAEL SCOTT ASATO CUTHBERT: 0. 01:02:27.913 --> 01:02:31.020 align:middle line:84% So every time you don't hear any music, 01:02:31.020 --> 01:02:35.810 align:middle line:84% know you're hearing the grand symphony of negative 1 dots. 01:02:35.810 --> 01:02:38.850 align:middle line:90% 01:02:38.850 --> 01:02:42.230 align:middle line:84% I think that's a good place to wrap up. 01:02:42.230 --> 01:02:45.000 align:middle line:90%