0:03

In the first video in this module, we talked about some fundamental properties

Â of wave forms, particularly amplitude, and frequency, and phase.

Â I posed a question at the end of that video about whether that was enough to

Â describe how we actually hear sound in the real world.

Â and so in this video, we're going to talk about a very brief introduction to the

Â field of Psychoacoustics. Which is about that question exactly.

Â how we hear sound and how that might differ sometimes from how we represent it

Â in the real world or how we measure it. so we're going to talk about loudness as

Â a notion. It's a little bit different from the

Â amplitude that we were talking about in the first video.

Â we'll talk about pitch as something again that's a little bit different from

Â frequency as we talked about it in the first video.

Â and we'll talk about, a few other ways that these, intermingle towards the end

Â of the video. so I'm going to start off with a, a quick

Â question for you. we have here, as you can see, this is

Â actually a sine wave. It's kind of, compressed on the time

Â domain. This is a ten-second-long, sine wave.

Â It's starting at 0 amplitude, and it is getting bigger and bigger over time.

Â Its amplitude envelope is increasing as you can see.

Â until it's at full amplitude, a full negative one to one range at the end.

Â so what I want you to do is listen to this and you can see this is a linear

Â ramp, it's increasing linearly from 0 at the beginning to 1 at the end.

Â So you know listen to this, and and, and, listen to whether you hear it is

Â increasing linearly or not. [NOISE].

Â Okay, so I don't know about you but I don't hear that as increasing linearly.

Â I hear that as much more as increasing kind of like on a curve like that.

Â So it seems like its getting louder really fast at the beginning and then

Â slows down, and slows down, and slows down, and slows down.

Â And the reason for this is we don't hear the linear increase in amplitude

Â linearly. so amplitude goes from negative one to

Â positive one. But we hear is something more that we

Â described as loudness, which has a logarithmic relationship to amplitude.

Â So for every ten, we measure loudness in a unit we call decibels which we

Â abbreviate as dB but to write that out its actually decibels.

Â and for every ten decibels that we increase we get twice as loud.

Â and so this reflects the, what you just heard in the example, that that we're not

Â perceiving this amplitude as increasing linearly.

Â But rather our perception of it is on this logarithmic scale.

Â something I want to emphasize about both amplitude and loudness is the really

Â important point about we're using these terms in this course.

Â And how they get used a lot in music technology.

Â Is that they're relative measures they're not absolute measures of how loud

Â something is in the real world. And there, there's a very important

Â reason for this. if you think about amplitude, you know

Â it's negative one to positive one what? You know an, and the answer is really

Â nothing, we are looking at that way from computer.

Â Because, when computer is playing back the sound we have no idea how, we have no

Â idea how, how different things in the chain after that computer are going to

Â affect the sound. How loud is the amplifier it's hooked up

Â to, how loud are the speakers? how far away are we standing from the

Â speakers, so how much are the sound waves kind of losing their energy as they go

Â from the speakers to us? We don't know any of that, so we can't

Â fix kind of absolute units to amplitude as we look at them on the computer.

Â A sense of relative measure. So we know that plus one is more than

Â plus 0.5 is more than 0.25 and so on and so forth, and the same thing is true of

Â loudness. If you look at a mixer for instance this

Â example on the right here that is a physical mixer like someone might use at

Â a concert or a recording studio. And this example here is from the Reaper

Â Digital Audio Workstation Program a virtual mixer, and it's controlling the,

Â the loudness on the channel. and you can see the units here in this

Â virtual example. We have we have zero here let me switch

Â to different colors so you can actually see this.

Â You have zero there, that's zero decibels.

Â That just means whatever sound is coming in is not making it louder, it's not

Â making it softer. Above that, we have Plus 6, and we have

Â plus 12, and then down here we have minus 6, minus 12, minus 18, minus 24, and so

Â on, and so forth. and so again, this isn't speaking to a

Â particular measure that we can measure in the real world of this sound.

Â it's just saying well the sound is coming in at a certain level.

Â And then I'm either leaving it alone, zero dB, or I'm increasing it by a

Â certain amount or I'm decreasing it by a certain amount.

Â So when we look at mixers, either virtually or in the real world, that's

Â how we tend to think about loudness. And, and we're using decibels here as a

Â measure of loudness rather than amplitude.

Â because then moving these sliders has more of perceptual psychoacoustic

Â relevance to us, because of that logarithmic scale.

Â 5:12

let's move on and talk about pitch for a second.

Â You may remember from the first video I played this chirp sound.

Â It went linearly from 20 Hertz all the way up to 20,000 Hertz with the sign

Â waves. So over ten seconds, it went up from 20

Â Hertz all the way up to 20,000 Hertz. I want you to listen to this again.

Â with a similar question that I asked about that, that amplitude envelope at

Â the beginning of this video. do you hear it as increasing linearly in

Â pitch or do you hear it as as increasing at some other kind of scale?

Â so look, go ahead and listen to this. [SOUND].

Â As you were hearing this the basic idea here is that is was it was not increasing

Â linearly. It seemed like the pitch was very quickly

Â at the beginning and then it got slower and slower and slower and slower as it

Â went on. In other words, that same kind of

Â logarithmic curve. It's leveling out as it gets higher and

Â higher. and that's because unsurprisingly there's

Â different ways that we can think about pitch and pitch relationships.

Â as we we're thinking about frequency, we think about frequency as going up

Â linearly. And there's a There's a key musical

Â contruct that's described. It's called the Harmonic Series.

Â See if we have a bass frequency at say 100 Hertz.

Â Well we can think of integer multiples of that.

Â So 2 times 100 is 200, 3 times would be 300, 4 times 400, and so on, 500, 600 and

Â on and on and on. This Harmonic Series is very important in

Â music. and we can think about these Hertz as

Â representing, if our, if our bass frequency were to be you know to

Â represent this low C. then when we double that frequency we

Â would be in the C an octave above. when we go three times that original

Â frequency, we would be the G above that and if we went four times we would be the

Â C above that. and so we're not always getting C's.

Â We're getting different notes. If we went from there we would get an E

Â and we get a G and then a kind of B flat and so on and so forth.

Â but there's another way to think about pitch which is in terms of octaves.

Â And this is not a linear scale of 1 times, 2 times, 3 times, 4 times anymore.

Â this is a scale of doubling every time. So 100, 200 Hertz, 400 Hertz, 800 Hertz,

Â 1600 Hertz and so on and so forth. And if we go at those frequency ratio,

Â ratios always doubling or rather than always multiplying by some integer

Â multiple. We end up with successive octaves where

Â they're all Cs, from C to C to C to C and so you see we got C, we double it, we get

Â the C the next octave up. We double that, we get the C the next

Â octave up. We double that, we get to see the next

Â octave up. and so again, the way that we hear pitch,

Â is not on this linear frequency scale, when there's logarithmic octave scale.

Â because we hear these Cs as sharing something in common with each other and

Â going from one C to the next is traversing this space of an octave.

Â even though the difference between one 100 and 200 Hertz and between 200 and 400

Â Hertz is different in Hertz space is 100 versus 200.

Â so again there's this difference between how we represent things in frequency and

Â how we hear them in terms of these octaves.

Â These, these, this pitch, this logarithmic relationship.

Â I, I want to go a little bit further than that, because we hear something else

Â that's a little bit more complicated too when we're listening to pitch instead of

Â frequencies. So here are, are two here are two

Â frequencies two sine waves, one is at 440 Hertz, the one on top, and then the one

Â on the bottom is at 880 Hertz. so this is a two to one relationships,

Â they're an octave apart from each other. Now what happens if we actually listen to

Â these? I'm going to switch over to Reaper here

Â for a second so that we can hear this. When I play these together here's my 440

Â Hertz sine wave and here's my 880 Hertz sine wave.

Â I'm going to go ahead and play this and think about how many different pitches

Â you're hearing [NOISE]. Okay, that's enough to get an idea there.

Â So the idea there is unless I'm really really concentrating I'm really just

Â really what I feel like is one note or one pitch.

Â but if I go ahead and play this again and just Play the 440 Hertz one, [NOISE], you

Â hear that very clearly. Or play just the 880 Hertz one, [NOISE],

Â you hear that very clearly. But when I play them together we hear

Â something very different. [NOISE].

Â We find some melding of these because they have this special relationship to

Â one another. and this is something that's more even

Â more evident if we go to real world sounds.

Â So if I come over here this is actually a trombone sound.

Â a low E on the trombone. [NOISE].

Â That you can hear. But we're not actually hearing the

Â original trombone sounds here. We're hearing a bunch of sine waves.

Â I can show you what I mean here. I'm going to just play that lowest sine

Â wave [SOUND] and then I'm going to play the next one up with it [SOUND] and the

Â next one up and the next one up [SOUND]. It start [SOUND] and hearing this

Â individual thing. This is actually a harmonic series.

Â So, it's going up 1 times, 2 times, 3 times the bass, frequency.

Â [SOUND] As I click a few more in here, you'll eventually stop really noticing

Â all the individual ones and start hearing is the trombone.

Â [NOISE]. It's really starting to sound like a

Â trombone now, the more of these I add in. So we're not hearing these as individual

Â sine waves, as individual frequencies anymore, we're hearing them as a

Â composite pitch. [NOISE].

Â and that pitch we're hearing in this case is this, this, this low E.

Â we'll return to that demo again in a later video and, and delve into some of

Â the details about it a bit more. so the point here is that its not just

Â the difference between the linear and logarithmic relationship in terms of

Â frequency pitch. But its also a difference between making

Â out individual frequencies and hearing them melding into some bigger composite

Â results. I want to cover one more thing before we

Â we, we leave our discussion of psychophysics for now.

Â I want to play this chirp one last time for you and this time I want you to focus

Â on how loud it sounds over the course of the chirp from 20 Hertz to 20,000 Hertz.

Â Does it sound like its ever getting louder or softer or does it feel like the

Â loudness is the same the whole time?

Â [NOISE].

Â Okay, so the loudness is obviously changing as that goes from 20 Hertz up to

Â 20,000 Hertz. The amplitude of that sin wave in the

Â file is actually not changing at all. It's using the full negative one to

Â positive one range throughout. but our perception of that is changing

Â based on the frequency of the sin wave. this is explained by this phenomenon

Â called the Fletcher-Munson Loudness Curves.

Â What this shows is that on our y-axis here we have decibels, on our x-axis we

Â have frequency. If we follow one of these contours here,

Â if we're changing our loudness here as we go up.

Â We actually perceive that curve as being the exact same loudness throughout.

Â So in order to get something that sounds like it's equally loud from 20 Hertz all

Â the way up to 20,000 Hertz. We actually have to change it's

Â amplitude, in order to kind of fake our ears into hearing it sound like it's the

Â same. because our ears are more sensitive, so

Â you brought a range of dynamics in this, especially in this particular range here.

Â Around three to 5,000 Hertz. Then they are say at the very low end of

Â the spectrum or even at the very high end.

Â So this is another example about how frequency and loudness come together in

Â our brains as we're hearing sounds. to create effects that are very different

Â from what we might see if we're just looking at a wave form.

Â so to review what we've covered in this video, we talked about psychoacoustics as

Â describing how we perceive sound. And not just how it exists acoustically

Â in the world or how we might represent it as a wave form.

Â we particularly talked about loudness versus amplitude, and we talked about

Â pitch versus frequency. We looked at the Fletcher-Munson Loudness

Â Curves as a really good example of this. what we're going to talk about in the

Â next video, is if we had two sounds that actually have the exact same pitch, and

Â the exact same loudness. But they sound really different from each

Â other. But how do we describe that?

Â So we'll be talking about timbre in the next video.

Â