1:19

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

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

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

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

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

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

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

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

Â rather than what it is.

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

Â something like that.

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

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

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

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

Â 2:07

So the way we're gonna talk about timbre,

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

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

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

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

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

Â What we have here, is a sound spectrum.

Â A visual spectra representation of sounds,

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

Â So what we have on our x-axis here is

Â frequency and our y-axis is decibels.

Â 3:17

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

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

Â So you see a peak at 440 hertz and

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

Â So these are all coming at integer multiples of the fundamental

Â frequency of 400.

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

Â six times and on and on and on.

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

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

Â down and down and down from there.

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

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

Â 4:42

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

Â technology called the Fourier theorem.

Â And what the Fourier theorem says,

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

Â frequencies that are integer multiples of a fundamental frequency.

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

Â And integer multiples are what I was talking about before,

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

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

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

Â If we add those together we can represent any

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

Â Now it is important to emphasis the word periodic here.

Â This is a very important caveat here.

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

Â The cycles don't repeat infinitely and infinitely and

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

Â So the Fourier theorem only works for periodic waveforms.

Â We can add these all together.

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

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

Â 7:24

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

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

Â in time, in that particular frequency space.

Â The reason these sonograms and spectrograms are important are that we

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

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

Â And this is a key component to timbre as well.

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

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

Â But you also have to be able to say,

Â well this is how this stuff is changing over time.

Â So we go back to SPEAR for a second.

Â I'm gonna close up this sawtooth wave and

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

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

Â You notice in the first opening moments of the sound,

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

Â There going up and down,

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

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

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

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

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

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

Â This is really critical and so

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

Â of our understanding of timbre.

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

Â And I have a sawtooth wave here [SOUND].

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

Â [NOISE] Okay, so there were some little hiccups

Â in the moment that I started and stopped the sounds.

Â But in general, in the middle of this,

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

Â according to the Fourier theorem that are never changing.

Â If I opened up more complex sound here,

Â and I did a similar thing [SOUND].

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

Â equally important is that within each of these notes,

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

Â There's things that are growing and shrinking and

Â moving around and they look like real almost drawings or

Â squiggles rather than simple straight lines that are perfect.

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

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

Â And what we need to describe their timbres.

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

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

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

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

Â We talked briefly about the Fourier theorem for periodic sounds and

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

Â particular frequencies in integer multiple relationships to each other.

Â And we talked about two new visual representations of sound.

Â The spectra, which shows a particular moment

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

Â how these frequency components are changing.

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

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

Â all the issues that come up with that.

Â