1
00:00:00,000 --> 00:00:00,499


2
00:00:00,499 --> 00:00:03,052
BRIAN YU: Finally, let's
take a look at frequency.

3
00:00:03,052 --> 00:00:05,010
Frequency is going to be
a function that you'll

4
00:00:05,010 --> 00:00:10,380
implement in helpers.c that takes as
input a string, which we'll call note,

5
00:00:10,380 --> 00:00:12,270
and output an integer.

6
00:00:12,270 --> 00:00:14,770
So what is that note going to look like?

7
00:00:14,770 --> 00:00:17,190
Well, the note is just going
to be a string that might be

8
00:00:17,190 --> 00:00:19,530
something like A sharp 4, for example.

9
00:00:19,530 --> 00:00:23,280
A note, possibly an accidental,
and then an octave number.

10
00:00:23,280 --> 00:00:28,180
But if there is no accidental, that
note might just be A4, for instance.

11
00:00:28,180 --> 00:00:30,270
So what are you going
to do with that note?

12
00:00:30,270 --> 00:00:34,500
Well first, you're going to parse
the string and figure out its note

13
00:00:34,500 --> 00:00:35,640
and it's octave.

14
00:00:35,640 --> 00:00:39,990
So in the case of the string
A sharp 4, the note is A sharp

15
00:00:39,990 --> 00:00:42,300
and the octave is octave number four.

16
00:00:42,300 --> 00:00:45,150
But you'll need to figure out where
in the string the note part is

17
00:00:45,150 --> 00:00:48,300
and where in the string
the octave part is.

18
00:00:48,300 --> 00:00:52,830
Next, you'll calculate the frequency
of the note in the given octave.

19
00:00:52,830 --> 00:00:57,300
In music, we say that every note has a
different frequency, a different pitch,

20
00:00:57,300 --> 00:00:59,760
that makes each note sound
different from one another.

21
00:00:59,760 --> 00:01:03,870
And those frequencies are generally
represented in a unit called Hertz.

22
00:01:03,870 --> 00:01:05,730
More on that in just a moment.

23
00:01:05,730 --> 00:01:09,960
And finally, you'll return that
frequency as an integer value in Hertz

24
00:01:09,960 --> 00:01:11,980
back to the user.

25
00:01:11,980 --> 00:01:16,080
So how do we figure out what the
frequency is of any given note?

26
00:01:16,080 --> 00:01:19,020
Well, the world is sort of
standardized upon the idea

27
00:01:19,020 --> 00:01:22,650
that the note A4, or A
in the fourth octave,

28
00:01:22,650 --> 00:01:26,050
will have a frequency of 440 Hertz.

29
00:01:26,050 --> 00:01:28,420
So that's something that
you can take for granted.

30
00:01:28,420 --> 00:01:31,270
If the user passes in
A4 into your function,

31
00:01:31,270 --> 00:01:35,490
then the output is just going
to be 440 as the return value.

32
00:01:35,490 --> 00:01:39,360
But what if the note isn't
A4 and it's some other note?

33
00:01:39,360 --> 00:01:43,380
Well, generally when we're talking about
frequency, we can follow these rules.

34
00:01:43,380 --> 00:01:48,960
If A4 is 440 Hertz, then for
every semi-tone up that we move,

35
00:01:48,960 --> 00:01:52,980
remembering that a semi-tone is just
a movement of one key on the piano

36
00:01:52,980 --> 00:01:55,830
keyboard, for every
semi-tone up, we move,

37
00:01:55,830 --> 00:02:01,110
we're going to multiply the
frequency by 2 to the power of 1/12.

38
00:02:01,110 --> 00:02:04,410
And likewise, for every
semi-tone down we move,

39
00:02:04,410 --> 00:02:08,562
we're going to divide the frequency
by 2 to the power of 1/12.

40
00:02:08,562 --> 00:02:11,520
Let's take a look at what that actually
looks like from the perspective

41
00:02:11,520 --> 00:02:13,410
of the piano keyboard.

42
00:02:13,410 --> 00:02:16,140
So we know that A4 is 440 Hertz.

43
00:02:16,140 --> 00:02:17,800
And that's just the standard.

44
00:02:17,800 --> 00:02:22,996
But what about one semi-tone up from
it, A sharp 4, or equivalently B flat 4.

45
00:02:22,996 --> 00:02:24,870
Well, all we're going
to do there is remember

46
00:02:24,870 --> 00:02:28,410
that when we move up one
semi-tone, we take the frequency

47
00:02:28,410 --> 00:02:31,980
and we multiply it by
2 to the power of 1/12.

48
00:02:31,980 --> 00:02:36,630
So if we take 440 and multiply
it by 2 to the power of 1/12,

49
00:02:36,630 --> 00:02:42,440
we get about 466 Hertz as
the frequency for A sharp 4.

50
00:02:42,440 --> 00:02:48,150
What about one more semi-tone up to
B4, the next semi-tone after A sharp 4.

51
00:02:48,150 --> 00:02:53,340
Well, we'll take 466, approximately,
and multiply that by 2

52
00:02:53,340 --> 00:02:57,270
to the power of 1/12, which is
really the same thing as taking

53
00:02:57,270 --> 00:03:03,070
440 and multiplying it by 2
to the power of 1/12, twice,

54
00:03:03,070 --> 00:03:08,010
which is also the same thing as
taking 440 and multiplying it to 2

55
00:03:08,010 --> 00:03:13,950
to the power of 2 over 12, which
would come out to be about 494 Hertz.

56
00:03:13,950 --> 00:03:18,770
Likewise, if we were to move
one semi-tone up from B4 to C5,

57
00:03:18,770 --> 00:03:21,720
remembering that new
octaves always start with C,

58
00:03:21,720 --> 00:03:27,450
we get 440 times 2 to the 3 over
12, which is about 523 Hertz,

59
00:03:27,450 --> 00:03:28,750
and so on and so forth.

60
00:03:28,750 --> 00:03:32,970
The next note is going to be multiplying
440 and by 2 to the 4 over 12,

61
00:03:32,970 --> 00:03:37,630
then 5 over 12, 6, 7, 8, 9, 10, 11.

62
00:03:37,630 --> 00:03:42,720
And finally, when we hit A5,
exactly one octave above A4,

63
00:03:42,720 --> 00:03:47,190
we've now moved 12 semitones
away, or a full octave.

64
00:03:47,190 --> 00:03:55,000
And what we get is 440 times 2 to the
12 over 12, which is just 2 to 1, or 2.

65
00:03:55,000 --> 00:03:59,640
And when we multiply
440 by 2, we get 880.

66
00:03:59,640 --> 00:04:05,400
So notice here that A5, exactly one
octave above A4, all we had to do

67
00:04:05,400 --> 00:04:10,650
is take A4's frequency, 440
Hertz, and multiply it by 2

68
00:04:10,650 --> 00:04:14,220
to get 880 Hertz for A5.

69
00:04:14,220 --> 00:04:17,100
So what does this actually
mean in terms of frequency?

70
00:04:17,100 --> 00:04:21,480
Well, if A4 is 440 Hertz, then
any time we want to take a note

71
00:04:21,480 --> 00:04:25,980
and go up an octave, we multiply
it by 2 to the 12 over 12,

72
00:04:25,980 --> 00:04:28,590
which is just the same thing
as multiplying it by 2.

73
00:04:28,590 --> 00:04:31,770
And likewise to go down an
octave, we just take the frequency

74
00:04:31,770 --> 00:04:33,270
and divide it by 2.

75
00:04:33,270 --> 00:04:36,180
And this doesn't just apply
to A4, given any note,

76
00:04:36,180 --> 00:04:40,020
if you want to move it up an octave,
all you have to do is take its frequency

77
00:04:40,020 --> 00:04:41,580
and multiply it by 2.

78
00:04:41,580 --> 00:04:45,660
And to move it down an octave, you just
take its frequency and divide it by 2.

79
00:04:45,660 --> 00:04:49,680
So now let's think about how we're going
to take a note represented as a string

80
00:04:49,680 --> 00:04:53,790
and figure out what the letter of
the note is, what it's accidental is,

81
00:04:53,790 --> 00:04:55,690
and what it's octave is.

82
00:04:55,690 --> 00:05:00,550
So if we have a note represented as a
string that can take any form of A4,

83
00:05:00,550 --> 00:05:04,550
to B flat 4, to C sharp 5
or anything of the like,

84
00:05:04,550 --> 00:05:06,850
but we know that the note
is going to be a string

85
00:05:06,850 --> 00:05:08,830
and the first character
of the note is always

86
00:05:08,830 --> 00:05:13,390
going to be the letter of the note,
either A, or B, or C, D, E, F, or G.

87
00:05:13,390 --> 00:05:15,160
That much we can rely on.

88
00:05:15,160 --> 00:05:18,910
The second character of the note depends
a little bit upon what note it is.

89
00:05:18,910 --> 00:05:23,150
If the note is a sharp or flat
and has an accidental as a result,

90
00:05:23,150 --> 00:05:27,130
then the second character of that note
string is going to be that accidental.

91
00:05:27,130 --> 00:05:31,360
For example, in the string A
sharp 5, the second character

92
00:05:31,360 --> 00:05:32,950
is that sharp symbol.

93
00:05:32,950 --> 00:05:35,620
On the other hand, if
there is no sharp or flat,

94
00:05:35,620 --> 00:05:39,220
as we might call a natural
note, then the second character

95
00:05:39,220 --> 00:05:41,470
isn't going to be the
sharp or flat symbol,

96
00:05:41,470 --> 00:05:43,150
but it's going to be the octave symbol.

97
00:05:43,150 --> 00:05:47,320
So for instance, if we had the note
C4, where there is no sharp or flat,

98
00:05:47,320 --> 00:05:50,530
C is still the first character, the
letter of the note that we want.

99
00:05:50,530 --> 00:05:55,480
But the second character is going to
be the octave, octave number four.

100
00:05:55,480 --> 00:05:58,870
Finally, if there was an
accidental, sharp or flat,

101
00:05:58,870 --> 00:06:01,030
we still need to figure
out what octave it's in.

102
00:06:01,030 --> 00:06:04,750
So if there was an accidental, then
the third character of the string

103
00:06:04,750 --> 00:06:06,340
is going to be the octave.

104
00:06:06,340 --> 00:06:11,080
So in the case of a note like B
flat 4, B is the first character,

105
00:06:11,080 --> 00:06:12,730
and that's the letter of the note.

106
00:06:12,730 --> 00:06:16,810
Flat, or the represented by the
lowercase b symbol, is the accidental.

107
00:06:16,810 --> 00:06:20,240
That's what's going to show up as
the second character in the string.

108
00:06:20,240 --> 00:06:22,240
And finally, the third
character of the string

109
00:06:22,240 --> 00:06:24,350
is going to be the octave number.

110
00:06:24,350 --> 00:06:27,040
And so now that we understand
how to actually represent a note,

111
00:06:27,040 --> 00:06:28,748
let's walk through
the steps of how we're

112
00:06:28,748 --> 00:06:32,380
going to go from taking an arbitrary
note that could be any note,

113
00:06:32,380 --> 00:06:34,690
and turning it into an actual frequency.

114
00:06:34,690 --> 00:06:36,572
But let's take it step by step.

115
00:06:36,572 --> 00:06:38,530
The first thing that
you'll probably want to do

116
00:06:38,530 --> 00:06:41,230
is to implement different octaves of a.

117
00:06:41,230 --> 00:06:43,840
You know that for A4, you
can just return the number

118
00:06:43,840 --> 00:06:47,290
440 because we've said that
that is the number of Hertz that

119
00:06:47,290 --> 00:06:49,540
represents the note A4.

120
00:06:49,540 --> 00:06:55,480
But what about other octaves of the
note A, like A3, or A2, or A5, or A6.

121
00:06:55,480 --> 00:06:58,810
Well, we know that to change the
octave, we just need to multiply

122
00:06:58,810 --> 00:07:00,850
or divide by some power of 2.

123
00:07:00,850 --> 00:07:05,740
To get from A4 to A5, we take
440 and multiply it by 2.

124
00:07:05,740 --> 00:07:10,750
To get from A4 to A6, we take
440 and multiply it by 2 twice,

125
00:07:10,750 --> 00:07:13,000
or multiply it by 4.

126
00:07:13,000 --> 00:07:17,830
Likewise, to go from A4 to
A3, we'll have to divide by 2

127
00:07:17,830 --> 00:07:20,740
to get 220 Hertz for A3.

128
00:07:20,740 --> 00:07:25,420
And so we can use multiplication
or division by some power of 2

129
00:07:25,420 --> 00:07:29,680
to be able to figure out what the
frequency of some different octave of A

130
00:07:29,680 --> 00:07:30,920
is going to be.

131
00:07:30,920 --> 00:07:33,220
And finally, be sure that
when you do this math,

132
00:07:33,220 --> 00:07:37,470
you're rounding any decimals that
you get to the nearest integer.

133
00:07:37,470 --> 00:07:40,040
So now that we've got
different octaves of A,

134
00:07:40,040 --> 00:07:43,860
let's think about accidentals,
sharps or flats that might modify A,

135
00:07:43,860 --> 00:07:47,880
and how we're going to adjust
for those frequencies as well.

136
00:07:47,880 --> 00:07:52,220
So step two is going to be
supporting A sharp and A flat.

137
00:07:52,220 --> 00:07:56,210
Well, we know that to make a note sharp,
since a sharp just means exactly one

138
00:07:56,210 --> 00:08:00,110
semi-tone ahead of the previous
note, all we have to do

139
00:08:00,110 --> 00:08:05,000
is multiply the original frequency
by 2 to the power of 1 over 12,

140
00:08:05,000 --> 00:08:07,640
remembering that in order
to get from one frequency

141
00:08:07,640 --> 00:08:10,070
to the frequency exactly
one semitone above it,

142
00:08:10,070 --> 00:08:13,400
we just multiply by this 2 to 1 over 12.

143
00:08:13,400 --> 00:08:16,520
Likewise, to make a note
flat, we'll do the opposite,

144
00:08:16,520 --> 00:08:19,790
divide the frequency by 2 to 1 over 12.

145
00:08:19,790 --> 00:08:25,580
So think about, if we have A, and
A is 4 is represented by 440 Hertz,

146
00:08:25,580 --> 00:08:30,140
and we want to represent A sharp
4, example, all we need to do

147
00:08:30,140 --> 00:08:35,090
is take the frequency 440 and
multiply it by 2 to 1 over 12.

148
00:08:35,090 --> 00:08:38,780
And likewise for A flat, we
would take the frequency 440

149
00:08:38,780 --> 00:08:41,760
and divide it by 2 to the 1 over 12.

150
00:08:41,760 --> 00:08:46,310
But as you do this, also make sure to
be able to support A sharp and A flat

151
00:08:46,310 --> 00:08:48,140
in multiple different octaves.

152
00:08:48,140 --> 00:08:55,320
Sure, A sharp 4 is just A4's 440 Hertz
multiplied by 2 to the 1 over 12.

153
00:08:55,320 --> 00:08:58,760
But what about A sharp 5 or A sharp 6?

154
00:08:58,760 --> 00:09:01,130
Well, if you remember that
in order to go up an octave,

155
00:09:01,130 --> 00:09:04,580
you just multiply the frequency
by 2, and to go down an octave

156
00:09:04,580 --> 00:09:08,690
you just divide the frequency by 2,
then if you know what A sharp 4 is,

157
00:09:08,690 --> 00:09:11,870
all you need to do is
multiply that frequency by 2

158
00:09:11,870 --> 00:09:14,300
in order to get A sharp 5.

159
00:09:14,300 --> 00:09:18,140
So you might think about, first,
adjusting for sharps or flats,

160
00:09:18,140 --> 00:09:21,189
and then adjusting
for different octaves.

161
00:09:21,189 --> 00:09:23,480
Or alternatively, you could
do it the other way around.

162
00:09:23,480 --> 00:09:26,240
First adjust for the octave
by multiplying or dividing

163
00:09:26,240 --> 00:09:27,680
by some power of two.

164
00:09:27,680 --> 00:09:31,210
And then adjusting for
a sharp and a flat.

165
00:09:31,210 --> 00:09:35,350
And finally, once we've
supported A, A sharp, and A flat,

166
00:09:35,350 --> 00:09:39,430
the last step is going to be to support
all different kinds of notes, where

167
00:09:39,430 --> 00:09:42,920
we'll use A as our starting point,
and figure out how many semi-tones

168
00:09:42,920 --> 00:09:45,229
away various notes are.

169
00:09:45,229 --> 00:09:47,020
And if you take a look
at a piano keyboard,

170
00:09:47,020 --> 00:09:48,830
you should be able to figure this out.

171
00:09:48,830 --> 00:09:51,040
If you remember which
note has which letter,

172
00:09:51,040 --> 00:09:55,300
you should be able to calculate how
many semitones away B is from A,

173
00:09:55,300 --> 00:09:59,200
how many semitones C is away from A,
and as well for all the other nodes

174
00:09:59,200 --> 00:10:00,970
that appear on the piano keyboard.

175
00:10:00,970 --> 00:10:05,590
An important thing to remember is that
octaves start at C. In other words,

176
00:10:05,590 --> 00:10:09,010
C5 is one semitone above B4.

177
00:10:09,010 --> 00:10:12,190
This becomes clearer if you take a
look at a picture of the piano that

178
00:10:12,190 --> 00:10:14,920
represents all the different notes
and what octaves they belong,

179
00:10:14,920 --> 00:10:19,750
where you'll notice that the fourth
octave ranges from C4 all the way up

180
00:10:19,750 --> 00:10:20,890
to B4.

181
00:10:20,890 --> 00:10:24,910
But as soon as we move from B4 to
the note one semi-tone after that,

182
00:10:24,910 --> 00:10:29,110
we arrive at C5, which is the
beginning of the fifth octave.

183
00:10:29,110 --> 00:10:31,600
So while it may seem a
little bit counterintuitive,

184
00:10:31,600 --> 00:10:35,860
A4 and B4 are actually
higher notes than C4,

185
00:10:35,860 --> 00:10:38,470
even though C comes
later in the alphabet,

186
00:10:38,470 --> 00:10:41,140
because C marks the start of the octave.

187
00:10:41,140 --> 00:10:44,620
And so bearing in mind which
notes belong to which octaves,

188
00:10:44,620 --> 00:10:46,840
and when new octaves are
starting, can help you

189
00:10:46,840 --> 00:10:49,350
out when it comes to
computing the frequency.

190
00:10:49,350 --> 00:10:51,850
So ultimately, the logic that
you're going to want to follow

191
00:10:51,850 --> 00:10:55,600
is to, first, figure out what
the string actually represents,

192
00:10:55,600 --> 00:10:58,420
what the letter of the note
is, what accidental it has,

193
00:10:58,420 --> 00:11:00,010
and what octave it has.

194
00:11:00,010 --> 00:11:06,370
Then using A4 as your baseline, where
you know that A4 is equal to 440 Hertz,

195
00:11:06,370 --> 00:11:07,330
you can adjust.

196
00:11:07,330 --> 00:11:11,840
Any time you move up a semitone,
multiply by 2 to the power of 1/12.

197
00:11:11,840 --> 00:11:16,330
Anytime you move down a semi-tone,
divide by 2 to the power of 1/12.

198
00:11:16,330 --> 00:11:18,640
And if you ever want
to jump a full octave,

199
00:11:18,640 --> 00:11:21,310
remember that to go up an
octave, you just take a frequency

200
00:11:21,310 --> 00:11:22,990
and multiply it by 2.

201
00:11:22,990 --> 00:11:26,620
And any time you want to go down an
octave, you just take the frequency

202
00:11:26,620 --> 00:11:28,660
and you divide it by 2.

203
00:11:28,660 --> 00:11:31,690
At the end, you'll likely end
up with a floating point number

204
00:11:31,690 --> 00:11:33,650
with digits after the decimal point.

205
00:11:33,650 --> 00:11:36,850
But remember that the frequency function
is supposed to return an integer.

206
00:11:36,850 --> 00:11:40,270
So once again, make sure you're rounding
your number to the nearest integer

207
00:11:40,270 --> 00:11:44,270
in order to make sure that your output
matches the desired frequency level.

208
00:11:44,270 --> 00:11:47,530
So those are the steps to figuring
out frequency, after which point

209
00:11:47,530 --> 00:11:50,980
you should be able to hear songs and
listen to them based on the functions

210
00:11:50,980 --> 00:11:53,980
that you've implemented
inside of helpers.c.

211
00:11:53,980 --> 00:11:55,600
On that note, I'll leave you to it.

212
00:11:55,600 --> 00:11:56,290
Good luck.

213
00:11:56,290 --> 00:11:59,850
My name is Brian, and this was music.

214
00:11:59,850 --> 00:12:01,451