Listen to this first sound.
And now listen to this second sound.
Which one sounds higher?
The first one, right?
But that's really weird.
The first sound was a tone of 440Hz.
The second sound was comprised of a bunch of tones
all of which were 500Hz or above.
And yet, the second sound sounds lower than the first.
That's really strange.
We normally think of pitch as being determined
by the frequency of a sound.
So listen to this.
It's a frequency of 220Hz.
We're going to follow that with a frequency of 330Hz.
So that frequency is higher than the first one.
But look what happens when we put the two together.
The resultant pitch that we perceive is actually lower than either of them.
This phenomenon is called the missing fundamental.
Is it because our brain's playing tricks on us?
Or is something else going on?
Well in order to explore this, we're going to
have to use a little bit of maths to find out.
So you're probably familiar that sound is a kind of wave.
And in this room, the way it works, is that something that
generates a perturbation and creates some anomaly in air pressure,
will move across the room and we will perceive that as sound.
One perturbation might be where we're going to use a violin.
And if we draw a violin bow across the string,
the string vibrates like this
and what happens is that the air around that then gets perturbed.
And the sound pressure waves reaching us
appear as sound and that's what we hear.
Those four different strings, those four notes
are not just pure tones.
They're actually a combination of frequencies.
When a violin string is excited
it vibrates at the fundamental frequency.
The fundamental frequency of the note
is usually what our brains register as the pitch of that note.
It's also usually the loudest.
But as we'll see, it isn't quite that simple.
So, even though the second string on the violin is tuned to an A.
Which has a frequency of 440Hz.
If we analyse the composition of the sound actually generated
we can see it also vibrates at multiples of the fundamental frequency.
At twice the frequency.
Three times the frequency.
These things are called harmonics.
So what we hear is a combination of a load of different frequencies
excited just by one bow scraping across the string.
And if we play the same note on the trumpet,
it's at 440Hz but we can see
that it has a different spectrum of different harmonics.
So the multiples of 440 are the same
but the relative strength of each is different.
And this is one of the significant factors that
determines the tone quality of one instrument versus another.
In other words, why different instruments sound different.
So what's this got to do with the missing fundamental
that we alluded to earlier.
Well, we're going to create a set of digitally formed pure sine waves
of frequencies 110, 220, 330, 440, 550, 660Hz.
What we find, is that the more multiples of the 110 that we add
the tone quality changes.
But the pitch that we hear, a 110, does not.
So now let's listen to what happens
when we remove the fundamental frequency of 110Hz.
We still hear it.
This is the phenomenon of the missing fundamental.
We can explain this if we look at what actually happens
when we add these waves together.
The resulting sound wave is a lot messier.
But it's still has a regular repeating pattern.
And the period, which is the shortest repeating section,
is exactly the same as the fundamental.
This is what determines what we perceive as pitch.
Well let's look at the resultant wave form
having removed the fundamental frequency.
What you'll see is that the shortest repeated section
still has the same period as that of the fundamental frequency.
And therefore even though we've removed it
from the contribution of the tones forming that sound,
we still hear it, because when you combine all of the others,
it is still there.
So this tells us something really interesting
about how we perceive pitch.
So let's consider a set of tones:
220, 440, 660Hz.
When we combine all of those
the pitch that we perceive is the lowest of these - 220Hz.
The 440, 660 are multiples of the fundamental
and they are therefore harmonics.
But something really weird happens
if you add yet a higher frequency of 770Hz.
770Hz adding this results us in perceiving a pitch
that is lower than anything of those waves.
It's a 110Hz that we are perceiving as a new pitch.
So this isn't a case of our brains playing tricks with us
By adding a frequency of 770Hz,
we have changed the waveform
and the pitch of that waveform corresponds to that of 110Hz.
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