We’ve already talked about how you can notate an interval.

Now what I want to do, is I want to add a little more information about this third.

So the way I’m going to do that is to count the half steps that are within that third.

I’m going to go to the keyboard, and I’m going to look at this third I created.

It was a C and an E. But now what I need to do is count.

There’s one half step, two, three, and four.

So there were four half steps in that third.

But let’s look at a different third and see how many half steps we get, like this one.

E, F, G, one, two, three, so it’s another third.

But this one, we’re going to count one half step, two, three.

So this one only has three half steps. Here’s four, and here’s three.

When you have four half steps, you want to say that your third is major.

Those are all four half steps, all major thirds. And then minor thirds.

They just sound a little bit different but they’re all

in the basic same category of consonant intervals and thirds.

So we’re going to look back up on the board now.

I’m going to add this information. I’m adding a capital M,

and that’s how I write major.

So in general, I’m going to use this abbreviation.

And when I write minor, it gets kind of confusing with of all the M’s,

so I would just write lowercase, and I put this line above it, like that.

That’s my abbreviation for minor, and that’s what I’ll do throughout.

Then the question is, what do you do if you want to notate one of these two different types of thirds?

So let’s try that. Again, it really helps to have

a picture of a piano keyboard in your mind.

So we’re going to try doing – this is my minor third, and I’m going to put up.

I want to write a minor third above that.

So now I’ve got two pieces of information to deal with.

I have the number, and then I have this quality right here.

So I just start with the number, that’s easier.

So I’m just going to count three, and I know it’s up,

so one, two, three, so I know it has to be some kind of a B.

I don’t know what the accidental is yet though.

Then what I want to do is imagine the keyboard in my mind or I can just play it.

I’m going to play three half steps up from that G on the piano.

So there’s my G, and this would just be a plain old B.

One half step, two half steps, so three half steps is actually right there.

When I go back to the board, I need to make sure I put a flat in front of this.

Now the question would be, we know a little about enharmonic equivalence, B flat is actually the same as A sharp.

The problem with this is, if I’m actually trying to write a minor third,

G, A, this is actually going to be some kind of a second.

So it’s actually not going to be what I want right here.

You do have to be careful not to change your letter names all around.

And we’ll just do one more of those.

Let’s say that you do a bass clef, and you want to try a major third,

I’m going to start here with a B flat, and I want to do a major third down.

Here’s my B flat right here, and I go down one half step, one, two, three, four.

If I want a major third, I’m going to have to flat that G to get that major third.

You can think about both pieces of those information when you write your intervals.

Now we’ve talked about thirds, but consonant intervals also include sixths.

I’m going to show you a quicker way than counting intervals to get to your sixths.

We’re going to start with this third, B up to D.

What I’m going to do to invert it is take one of those two pitches,

and I’m going to wrap it around the other one and change the octave.

It needs to cross over where the other note is.

Now I’m going to take this away.

What I did was I just inverted my third and it turned into something else.

I’m going to go back to that same one that I had originally, the same third.

I’m just going to invert it the other direction because now I’m going to keep this the same

and I’m going to move this one around.

I’m going to go like that, bring it up the octave,

and I’ll get rid of this one, and I have just inverted that third again.

So it was B to D before, and it’s really just those same notes,

they’re just in different places. So that’s inversion.

Let’s see why that’s important. If we do this, we’re going to get, in both cases, sixths.

Before, we had a minor third, B up to D, so let’s see what we end up getting with this sixth.

This one, we know it’s a sixth, so we had a minor third.

I’m going to show you what happens on the keyboard here.

I have a really easy way of figuring out if it’s a major or minor sixth.

What I do, is I go back to my third, and I was pretty sure this was a minor third,

but I want to make sure. One, two, three half steps.

Well, the sixth is a major sixth.

We know that without even needing to count.

So if we have major, it’s going to become minor.

Then there was something else that we can summarize up here too.

This of course is also the opposite way.

If we go down here and look at that number, we had a third and it turned into a sixth.

So major becomes minor, and minor becomes major

when you invert an interval, and the numbers add up to nine.

There’s still one more piece of information, that is the half steps.

Maybe the half steps add up to something too, and in fact they do.

So if you have four half steps in your major third, and then you invert it

twelve minus four is eight. So that other interval is going to have eight half steps.

If you have an interval with 6 half steps,

it’s going to invert and become an interval that also has 6 half steps.

Half steps always add up to twelve, the numbers add up to nine, and then these two are going to flip.

Going back to this major third, what happens if we have the same C to E,

those same two letter names, and we add a little bit of an expansion in there?

We could do that, for example, by sharping the E.

So when we do this, we now actually have more than four intervals.

What happens if it shrinks?

Here we have a minor third, what happens if we compress it even more?

I’ll compress it, I’m just going to choose to do this by sharping the C.

I’ve just shrunk it down, so now if this is three half steps,

what I have here is only two half steps, and that’s diminished.

There’s a little circle, and that’s your abbreviation for that.

Since you already know a little bit about inversion,

one more piece to add to that now that we have diminished and augmented here,

if you invert a diminished interval, you’re going to get an augmented interval,

and we’ll look at that on the piano.

Here’s my C to E, and we talk about augmenting that by

raising the E so it looks just like an F on the piano.

That’s you introduction to consonant intervals