Now that you already know how to spell thirds and invert them

the remaining intervals are going to be a lot easier to learn.

Perfect intervals, abbreviated with a P, are going to include fourths,

and fifths, and octaves, and I’ll even put this one down.

A one would be a unison. I can’t play that one the piano

because it’s the same note played twice so you need two different instruments to create unison.

But it’s also considered perfect.

First I’m just going to make a fourth, like this, and you might notice that

it goes from a line to a space when you write a fourth,

or it could be like this, from a space to a line.

They have a really characteristic look on the staff.

This first one, I’m going to keep the C where it is and I’m going to

wrap the G around it and put it in the other octave, like that.

And then I can just take that away. So I had that fourth and I inverted it into a fifth.

So of course, 4 + 5 = 9, and we know that when we invert intervals we get nine.

But what about the perfect part? It was perfect fourth and perfect fifth.

It turns out that if something is perfect and you invert it, it is still perfect, so that’s easy to remember.

So, perfect equals perfect when you invert it.

Now let’s try a couple others that might involve some accidentals.

We’re just going to notate a couple of intervals here.

We’re going to start with a perfect fourth up, like this.

So with this one, you can kind of think back about major thirds.

Major thirds are just one half step smaller than perfect fourths.

That means that if major thirds have four half steps, then perfect fourths must have five.

That also tells you that if you invert a perfect fourth, that’s five half steps,

you’re going to get something with seven half steps because seven and five is twelve.

With four half steps, sometimes people have all kinds of tricks for this.

If you happen to know that F to A is a major third, you could just go up a half step,

like this, a half step up from A is B flat, and that’s going to give you a perfect fourth.

That's one way you can do it. But, you can also do it another way.

You can count, F, G, A, B. So you know it's some kind of a B,

and then you have to check how many half steps you have.

So let's look at the piano. We've got our F, and then one, two, three, four.

So if we just left the notes as they are, we'd get this sound.

Now your ear might tell you that this is a really harsh sound, it doesn't sound like a perfect interval.

That alone could tell you that something is wrong.

Now we're going to go the way I first showed you.

Let's say you happen to know F to A is your major third. I'm going to raise that up half a step.

F to B flat gives me my perfect fourth.

And then we can count. One, two, three, four, five. And there's the five half steps.

We're going to look back up here and try a couple more.

So I'm going to put my flat right here. There's my perfect fourth.

Let's do a fifth. How about this one? We'll do a perfect fifth up

We can start by counting. That gives me a C. Some kind of a C.

Now, when I play this on the piano, it's going to sound very very dissonant.

The nice thing about fifths, is two things. First of all, if one note is on a space, the other one will also be on a space.

If one is on a line, the other one will be on a line.

You'll get to know how they look, just like you know the way fourths look.

I know I have them on the right place in general, but I'm just not sure about the accidentals.

Well the other nice thing about perfect fifths is that they're usually going to have the same accidental.

But not always, so we'll look at an example where that's not true.

Usually they're going to have the same accidental.

Now if you want to verify this to make sure this is actually right, there are a couple ways you can do it.

Back over here on the keyboard, I had F sharp and the first thing I wrote was just a C.

That's that really dissonant sound.

F sharp to just a C natural. That's way too dissonant for a perfect interval.

Then I thought they usually have the same accidental in front of them, right?

F sharp to C sharp. Now we can count, one, two, three, four, five, six, seven.

Seven half steps, and I know that has to be true because a perfect fourth has five

five plus seven is twelve. Let's look at it in one more way.

I'm going to invert this and make sure that it inverts to a perfect fourth.

I'm going to keep my F sharp the way it is,

and I'm going to take that C sharp and move it down to the previous octave.

That sounds like a perfect fourth, but I want to make sure.

One, two, three, four, five. Five half steps.

I'd rather count five half steps than seven half steps.

So if I'm going to count, I'm going to count the inverted interval,

and then invert it back to where it was.

We're going to look at an example where a perfect fifth doesn't have the same accidental

kind of like the perfect fourth over here,with two different accidentals.

Let's try this one.

Now I'm going to try to write a perfect fifth down from F.

It turns out that when you're writing fourths or fifths, and you're using these notes F and B,

you tend to get some funny things that happen.

The reason for that is that the keyboard is not symmetrical.

There are, as you remember on the white keys of the piano, there are half steps between

B an C, and E and F, and all the other ones have whole steps.

That means that even though something might be true in one case, like the two sharps here,

it's not going to be true in every case, because the keyboard is not symmetrical.

Let's look and see what happens here.

I know they're both supposed to be on the line, because that's how perfect fifths look,

so instead of counting, I can just go like this. Skip that line in the middle.

I can always count if I need to verify if that's a fifth, but I know that it is.

Now this one has got a B and an F in it, so when I play it on the keyboard,

because I know about the keyboard, I know it's going to sound really dissonant.

Let's see if that's true.

Here's the F, and if I walk down, one, two, three, four, five,

there it is. So this is not a perfect fifth. It's very dissonant sounding.