1:19

This is how it goes, it says, that attribute of sensation in terms of which

a listener can judge two sounds having the same loudness and pitch are dissimilar.

So the language is a little fancy there, but basically what it is saying is if

they've got the same loudness and they've got the same pitch but

they still sound different to you, well that's timbre.

So basically, it's just a grab bag of everything else about a sound

that can't be described by its loudness and pitch.

That's not a really good definition cuz that's really just saying what it's not

rather than what it is.

Colloquially, we tend to define timbre as the color or the tone or

something like that.

And that's fine, it gives us a general sense of what we're talking about with

timbre, but it doesn't get into any specifics.

It's really just a metaphor to explain again, in this vague way, well,

it's this other stuff that we don't really have a good way to describe.

2:07

So the way we're gonna talk about timbre,

in this course, is in terms of two key components, spectra and envelope.

So we're gonna talk about those in a little bit more detail now.

In order to do that we really need to look at visual representations of sounds.

So up to now, we have been doing the wave form representation of sound,

where our x-axis is time, and our y-axis is amplitude.

What we have here, is a sound spectrum.

A visual spectra representation of sounds,

which is basically showing where there's energy in different frequencies.

So what we have on our x-axis here is

frequency and our y-axis is decibels.

3:17

[SOUND] The same sign wave we know and love at this point.

Over here we have a sawtooth wave, so you see a number of peaks here.

So you see a peak at 440 hertz and

another one at 880 and at 1320 and 1760 and so on and so forth.

So these are all coming at integer multiples of the fundamental

frequency of 400.

So we're at one times, two times, three times, four times, five times,,

six times and on and on and on.

And you can notice, each one is at a lower decibels than the one that came before it,

so our most energy here is at 440 and it goes down and

down and down and down from there.

Now, this recording might be a little bit loud, so watch the volume on your

headphones or your speakers but this is the soft tooth wave.

4:42

And the way we can understand this, is through a very important theorem in music

technology called the Fourier theorem.

And what the Fourier theorem says,

is that any periodic wave form can be represented as the sum of sine waves at

frequencies that are integer multiples of a fundamental frequency.

So our fundamental frequency, in this case, was 440 hertz.

And integer multiples are what I was talking about before,

1 times 440, 2 times 440, 3 times 440, and so on and so forth.

And what we're looking at is at each of those integer multiples,

we have a sine wave at some particular frequency, amplitude, and phase.

If we add those together we can represent any

periodic wave form like a soft tooth wave or a triangle wave or something like that.

Now it is important to emphasis the word periodic here.

This is a very important caveat here.

Cuz in the real world, like a wave form recording of me talking is not periodic.

The cycles don't repeat infinitely and infinitely and

infinitely the way that a sine wave would, or sawtooth wave, or something like that.

So the Fourier theorem only works for periodic waveforms.

We can add these all together.

We'll talk as we move on in this module about some ways we can kind of get

around that periodic limitation, but for now we kind of have to deal with that.

7:24

that's a particular moment in time and a particular place in frequency space.

And the color is an indication of the decibels at that particular moment

in time, in that particular frequency space.

The reason these sonograms and spectrograms are important are that we

obviously have sounds in the real world, like I was saying, that aren't sine waves,

or sawtooth waves, or square waves, that change a lot over the course of the sound.

And this is a key component to timbre as well.

It's not just enough to say, well this is how the frequencies are distributed,

and this is where the energy is across the frequency space.

But you also have to be able to say,

well this is how this stuff is changing over time.

So we go back to SPEAR for a second.

I'm gonna close up this sawtooth wave and

go back to this trombone sound that we've been looking at.

It's very important, especially in the beginning here.

You notice in the first opening moments of the sound,

there's a lot of change in a bunch of these frequency components.

There going up and down,

there changing in amplitude, all kinds of things are happening.

Then it reaches a little bit more of a steady state in the middle.

But it would not be enough just to list a bunch of frequencies and their amplitudes

and phases in order to describe this trombone sound cause we had to describe

how its changing at this beginning part, at the attack portion in the sound.

We had to describe its envelope, how its changing over time.

This is really critical and so

that's why spectra and envelope together are such an important part of timbre and

of our understanding of timbre.

I want to show you one more thing here, which is to go over to Reaper again here.

And I have a sawtooth wave here [SOUND].

And I'm going to open up a live sonogram view of this, as I'm playing it back.

[NOISE] Okay, so there were some little hiccups

in the moment that I started and stopped the sounds.

But in general, in the middle of this,

you can see that it's just these straight lines, these frequency components

according to the Fourier theorem that are never changing.

If I opened up more complex sound here,

and I did a similar thing [SOUND].

Now this is obviously changing because the pitches are changing, but

equally important is that within each of these notes,

you can see they're not just static lines here.

There's things that are growing and shrinking and

moving around and they look like real almost drawings or

squiggles rather than simple straight lines that are perfect.

So this is how, there's a difference between the sounds that we work with in

real life as opposed to these test tones, these sawtooth waves, these oscillators.

And what we need to describe their timbres.

Here is not enough to just say what the vertical, the frequency component is, but

you need to describe the horizontal, as well, how it's changing over time.

So to review this unit that we've done on timbre here,

we've talked about timbre as consisting of two components, a spectra and envelope.

We talked briefly about the Fourier theorem for periodic sounds and

how that describes them as consisting of a series of sine waves,

particular frequencies in integer multiple relationships to each other.

And we talked about two new visual representations of sound.

The spectra, which shows a particular moment

of what the frequency content is and a sonogram which shows over time,

how these frequency components are changing.

In the next several videos now, we're going to shift gears a little bit and

focus on how we represent sound digitally on a computer, and

all the issues that come up with that.