0:03

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

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

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

describe how we actually hear sound in the real world.

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

field of Psychoacoustics. Which is about that question exactly.

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

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

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

amplitude that we were talking about in the first video.

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

frequency as we talked about it in the first video.

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

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

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

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

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

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

Its amplitude envelope is increasing as you can see.

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

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

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

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

increasing linearly or not. [NOISE].

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

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

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

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

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

linearly. so amplitude goes from negative one to

positive one. But we hear is something more that we

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

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

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

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

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

perceiving this amplitude as increasing linearly.

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

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

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

And how they get used a lot in music technology.

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

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

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

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

nothing, we are looking at that way from computer.

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

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

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

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

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

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

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

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

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

loudness. If you look at a mixer for instance this

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

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

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

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

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

to different colors so you can actually see this.

You have zero there, that's zero decibels.

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

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

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

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

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

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

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

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

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

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

measure of loudness rather than amplitude.

because then moving these sliders has more of perceptual psychoacoustic

relevance to us, because of that logarithmic scale.

5:12

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

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

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

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

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

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

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

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

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

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

linearly. It seemed like the pitch was very quickly

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

went on. In other words, that same kind of

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

higher. and that's because unsurprisingly there's

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

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

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

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

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

Well we can think of integer multiples of that.

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

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

music. and we can think about these Hertz as

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

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

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

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

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

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

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

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

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

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

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

ratios always doubling or rather than always multiplying by some integer

multiple. We end up with successive octaves where

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

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

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

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

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

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

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

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

Hertz is different in Hertz space is 100 versus 200.

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

how we hear them in terms of these octaves.

These, these, this pitch, this logarithmic relationship.

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

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

frequencies. So here are, are two here are two

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

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

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

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

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

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

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

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

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

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

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

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

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

something very different. [NOISE].

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

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

more evident if we go to real world sounds.

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

a low E on the trombone. [NOISE].

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

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

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

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

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

individual thing. This is actually a harmonic series.

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

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

all the individual ones and start hearing is the trombone.

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

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

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

composite pitch. [NOISE].

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

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

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

the difference between the linear and logarithmic relationship in terms of

frequency pitch. But its also a difference between making

out individual frequencies and hearing them melding into some bigger composite

results. I want to cover one more thing before we

we, we leave our discussion of psychophysics for now.

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

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

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

loudness is the same the whole time?

[NOISE].

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

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

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

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

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

called the Fletcher-Munson Loudness Curves.

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

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

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

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

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

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

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

same. because our ears are more sensitive, so

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

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

the spectrum or even at the very high end.

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

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

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

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

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

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

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

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

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

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

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

other. But how do we describe that?

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