1 00:00:00,000 --> 00:00:00,560 2 00:00:00,560 --> 00:00:02,450 SPEAKER 1: Let's dive into some music. 3 00:00:02,450 --> 00:00:04,370 Before we get working on the actual problems 4 00:00:04,370 --> 00:00:07,245 you'll need to solve as part of this problem set, let's take a moment 5 00:00:07,245 --> 00:00:11,920 and look at some background about music, notes, and how we might represent them. 6 00:00:11,920 --> 00:00:14,930 What we're looking at here is a portion of a piano keyboard. 7 00:00:14,930 --> 00:00:18,490 And you'll notice we have seven different white notes and five 8 00:00:18,490 --> 00:00:19,780 black notes. 9 00:00:19,780 --> 00:00:22,420 And so as you may know, each note is assigned a letter 10 00:00:22,420 --> 00:00:27,370 where we have C on the left side, then D, E, F, G, A, and B, 11 00:00:27,370 --> 00:00:32,630 where the white keys on the piano are each assigned to a different letter. 12 00:00:32,630 --> 00:00:36,440 A semi-tone, as we'll refer to it, is just the interval from one 13 00:00:36,440 --> 00:00:40,490 note to the very next note, including both the white and the black keys 14 00:00:40,490 --> 00:00:41,510 on the keyboard. 15 00:00:41,510 --> 00:00:45,770 So between C and D, that's an interval of two semitones, 16 00:00:45,770 --> 00:00:50,000 because we go from C, first to the black note in between C and D, 17 00:00:50,000 --> 00:00:54,530 and then to D. D and E are also two semitones apart, 18 00:00:54,530 --> 00:00:56,580 because there's a black note in between them. 19 00:00:56,580 --> 00:01:00,450 But E and F are one semi-tone apart, because right next to E, 20 00:01:00,450 --> 00:01:03,410 then immediately following it, is the note F. 21 00:01:03,410 --> 00:01:07,040 So semi-tones are just how we're going to refer to a step of exactly one 22 00:01:07,040 --> 00:01:09,230 note on the piano keyboard. 23 00:01:09,230 --> 00:01:13,010 But how, then, are we going to represent the black keys on the piano keyboard 24 00:01:13,010 --> 00:01:15,260 if the white keys are all assigned to letters? 25 00:01:15,260 --> 00:01:19,160 Well, in order to do that, we'll need to use accidentals. 26 00:01:19,160 --> 00:01:24,170 Accidentals adjust notes up or down by exactly one semi-tone. 27 00:01:24,170 --> 00:01:28,010 So the sharp accidental, represented here by the pound sign, 28 00:01:28,010 --> 00:01:31,010 means we're going to move up one semi-tone. 29 00:01:31,010 --> 00:01:34,490 So these are how the black keys would be represented in terms of sharps. 30 00:01:34,490 --> 00:01:37,610 Up one semi-tone from C is C sharp. 31 00:01:37,610 --> 00:01:41,660 And up one semi-tone from D is D sharp, for example. 32 00:01:41,660 --> 00:01:46,190 Likewise, we can also represent notes as flats, where a flat just 33 00:01:46,190 --> 00:01:48,980 means move it down one semi-tone. 34 00:01:48,980 --> 00:01:54,500 So here, we're looking at D flat, which is one note down from D, 35 00:01:54,500 --> 00:01:58,070 and E flat, which is one semi-tone down from E. 36 00:01:58,070 --> 00:02:01,970 And notice here that there are multiple different ways to name the same note. 37 00:02:01,970 --> 00:02:07,220 That note in between C and D can be represented as either C sharp or D 38 00:02:07,220 --> 00:02:07,790 flat. 39 00:02:07,790 --> 00:02:09,810 And they both mean the same thing. 40 00:02:09,810 --> 00:02:11,600 In fact, it's not just the black keys that 41 00:02:11,600 --> 00:02:14,000 can be referred to as sharps and flats. 42 00:02:14,000 --> 00:02:20,390 Since F is one semitone above E, and likewise E is one semi-tone below F, 43 00:02:20,390 --> 00:02:24,980 we can call F, E sharp, and we can call E, F flat. 44 00:02:24,980 --> 00:02:28,400 And those are totally valid ways of representing those notes. 45 00:02:28,400 --> 00:02:32,320 But as we know, a piano does not just consist of these keys. 46 00:02:32,320 --> 00:02:34,350 It consists of far more. 47 00:02:34,350 --> 00:02:36,680 And what we say is that the piano is divided 48 00:02:36,680 --> 00:02:41,150 into octaves, where an octave is just going to be a sequence of these 12 49 00:02:41,150 --> 00:02:45,830 notes that gets repeated over and over across from the low range of the piano 50 00:02:45,830 --> 00:02:47,420 to the high range of the piano. 51 00:02:47,420 --> 00:02:49,670 And so, generally, the middle of the piano 52 00:02:49,670 --> 00:02:52,369 we'll call octave four or the middle octave. 53 00:02:52,369 --> 00:02:54,910 And you'll see that we have a C there, a D there, an E there, 54 00:02:54,910 --> 00:02:57,500 and all the other nodes that are present in octave four. 55 00:02:57,500 --> 00:03:00,950 But that same pattern of notes repeats again in octave five, 56 00:03:00,950 --> 00:03:04,380 to the right of octave four, where all the notes sound similar, 57 00:03:04,380 --> 00:03:06,740 but are actually at a higher frequency. 58 00:03:06,740 --> 00:03:08,450 More on that later. 59 00:03:08,450 --> 00:03:11,930 We can actually refer to notes not just by what letter they are 60 00:03:11,930 --> 00:03:16,010 and what accidental they have, but also by what octave they're in. 61 00:03:16,010 --> 00:03:21,740 For example, we might call the C that is located in octave four, C4. 62 00:03:21,740 --> 00:03:27,410 And we might call the D sharp that's located in octave five as D sharp 5. 63 00:03:27,410 --> 00:03:30,050 And so what you're looking at here is a representation 64 00:03:30,050 --> 00:03:33,170 of a bunch of notes on the piano and how we would represent them 65 00:03:33,170 --> 00:03:37,460 in terms of what note they are, what accidental they have, if any, 66 00:03:37,460 --> 00:03:40,540 and finally, what octave they're in. 67 00:03:40,540 --> 00:03:42,800 Finally, let's take a look at how we would actually 68 00:03:42,800 --> 00:03:45,290 represent these notes if we were to try to write them down 69 00:03:45,290 --> 00:03:49,110 in sheet music, a conventional way for musicians to write down notes 70 00:03:49,110 --> 00:03:51,560 and how long they last, and what they mean. 71 00:03:51,560 --> 00:03:55,250 This is an example of the treble clef in sheet music, which is just part 72 00:03:55,250 --> 00:03:57,560 of the way that notes are represented. 73 00:03:57,560 --> 00:04:01,130 And each one of these lines or spaces between a line 74 00:04:01,130 --> 00:04:03,170 is a space for an individual note. 75 00:04:03,170 --> 00:04:06,560 And so right below that bottom line, if there were a note there, 76 00:04:06,560 --> 00:04:08,600 that would be the note D4. 77 00:04:08,600 --> 00:04:12,980 And after that, each time you go up one line or space between a line, 78 00:04:12,980 --> 00:04:15,000 you just go up by one letter. 79 00:04:15,000 --> 00:04:19,910 So after D4, this note, which is located on the bottom line, is E4. 80 00:04:19,910 --> 00:04:23,360 And the note immediately above that, located in the space between those two 81 00:04:23,360 --> 00:04:25,460 lines, is F4. 82 00:04:25,460 --> 00:04:28,220 And next is G4. 83 00:04:28,220 --> 00:04:31,520 And remember, after G4, we've run out of letters. 84 00:04:31,520 --> 00:04:36,230 And so we need to go to A4 and loop back around. 85 00:04:36,230 --> 00:04:38,540 And then to B4. 86 00:04:38,540 --> 00:04:42,560 Next would be C4, but if you remember from our picture from earlier, 87 00:04:42,560 --> 00:04:47,270 you'll notice that the octaves change numbers once we get to C. Notice 88 00:04:47,270 --> 00:04:51,260 that we have B3, but the note immediately after that is C4, 89 00:04:51,260 --> 00:04:55,500 because C is generally where we'll call the beginning of the next octave. 90 00:04:55,500 --> 00:04:57,590 So if we take a look at this sheet music again, 91 00:04:57,590 --> 00:05:02,000 we have D, E, F, G, A, and B all in octave four. 92 00:05:02,000 --> 00:05:06,300 But the note immediately after that is actually going to be C5. 93 00:05:06,300 --> 00:05:08,240 And now we're in the fifth octave. 94 00:05:08,240 --> 00:05:10,640 So following that is going to be D5. 95 00:05:10,640 --> 00:05:13,130 And following that is going to be E5. 96 00:05:13,130 --> 00:05:15,530 So every line and every space between a line 97 00:05:15,530 --> 00:05:20,350 gets its own letter and octave number in order to represent it. 98 00:05:20,350 --> 00:05:22,720 So this, for example, is A4. 99 00:05:22,720 --> 00:05:26,190 But how would we represent, for example, A sharp 4, A sharp 100 00:05:26,190 --> 00:05:27,230 in the fourth octave? 101 00:05:27,230 --> 00:05:29,230 Well, if you remember that we represented sharps 102 00:05:29,230 --> 00:05:31,510 as kind of just that pound sign, we can just 103 00:05:31,510 --> 00:05:36,850 draw that symbol to the left of the note, and now this note is A sharp 4. 104 00:05:36,850 --> 00:05:39,510 Likewise, if we wanted to represent a note as flat, 105 00:05:39,510 --> 00:05:42,160 where flat just means down one semi-tone, 106 00:05:42,160 --> 00:05:45,310 we could likewise to the left of the note add the flat symbol. 107 00:05:45,310 --> 00:05:49,360 And now this note that we're looking at here is A flat 4. 108 00:05:49,360 --> 00:05:51,820 And so using that representation, we have the capacity 109 00:05:51,820 --> 00:05:55,600 to represent any note using any accidentals, 110 00:05:55,600 --> 00:05:58,300 just by drawing the notes on the correct line 111 00:05:58,300 --> 00:06:00,520 or space between the line that corresponds 112 00:06:00,520 --> 00:06:03,770 to the right note in the right octave. 113 00:06:03,770 --> 00:06:06,470 Now, not all notes are the same length, though. 114 00:06:06,470 --> 00:06:08,470 So how, in sheet music, would we tell apart 115 00:06:08,470 --> 00:06:12,370 a note that is a short versus a note that is a longer note? 116 00:06:12,370 --> 00:06:14,620 Well, there are a bunch of different lengths of notes, 117 00:06:14,620 --> 00:06:17,080 and the notes look different depending upon their length. 118 00:06:17,080 --> 00:06:19,510 So on your left, we're looking at an eighth note. 119 00:06:19,510 --> 00:06:23,230 And an eighth note, we'll say, lasts the duration of one eighth, 120 00:06:23,230 --> 00:06:27,010 and generally looks like a note with a little curvy tail at the top of it. 121 00:06:27,010 --> 00:06:29,320 Next to that we have a quarter note, which 122 00:06:29,320 --> 00:06:33,279 last twice as long as an eighth note, for a duration of one fourth. 123 00:06:33,279 --> 00:06:35,320 And it looks just like an eighth note but doesn't 124 00:06:35,320 --> 00:06:37,860 have that curvy tail at the top. 125 00:06:37,860 --> 00:06:40,390 Next to that, we have a dotted quarter note, 126 00:06:40,390 --> 00:06:42,900 which is a quarter note with a dot to the right of it. 127 00:06:42,900 --> 00:06:46,020 And that lasts three times as long as an eighth note, 128 00:06:46,020 --> 00:06:49,270 or a duration of three eighths, we might say. 129 00:06:49,270 --> 00:06:51,900 And finally, on the right hand side, we have a half note, 130 00:06:51,900 --> 00:06:55,800 which looks like a quarter note except the center of the note is not filled in 131 00:06:55,800 --> 00:06:56,700 and is hollow. 132 00:06:56,700 --> 00:06:59,790 And a half note lasts the length of four eighth notes, 133 00:06:59,790 --> 00:07:01,910 or a duration of one half. 134 00:07:01,910 --> 00:07:04,410 There are more notes than just these, but these are the ones 135 00:07:04,410 --> 00:07:07,520 that we're going to care about for this particular problem set. 136 00:07:07,520 --> 00:07:11,234 And so using these different symbols for notes that determine their length 137 00:07:11,234 --> 00:07:14,150 and placing them in the right place, we have the ability to represent, 138 00:07:14,150 --> 00:07:17,990 in sheet music, a note, which note it is, what accidental it has, 139 00:07:17,990 --> 00:07:22,230 what octave it is in, and also how long the note lasts. 140 00:07:22,230 --> 00:07:24,360 And so one other thing that you might find 141 00:07:24,360 --> 00:07:27,660 when it comes to the lengths of notes is that sometimes when two eighth notes 142 00:07:27,660 --> 00:07:29,050 are next to each other. 143 00:07:29,050 --> 00:07:31,650 They'll be represented in sheet music as just two 144 00:07:31,650 --> 00:07:34,422 notes that have a little bar that connects the two of them. 145 00:07:34,422 --> 00:07:37,380 So if you ever take a look at that and are confused by what that means, 146 00:07:37,380 --> 00:07:40,829 generally, that symbol on the left just means two eighth notes. 147 00:07:40,829 --> 00:07:42,870 And that's all the background we'll need in order 148 00:07:42,870 --> 00:07:45,360 to be able to dive into the problems here. 149 00:07:45,360 --> 00:07:47,220 So with that in mind, even if music notation 150 00:07:47,220 --> 00:07:51,630 might seem confusing or complicated at first, I'm sure that in no time at all 151 00:07:51,630 --> 00:07:53,480 you'll be a natural. 152 00:07:53,480 --> 00:07:54,838