Since you already know quite a bit about intervals by this point,

you can use your knowledge of the previous lessons to solve some of these problems.

So I’m going to write up here dissonant, and these are going to be seconds and sevenths.

Like the consonant intervals, you’re going to have major and minor,

and if you got bigger you’d have augmented, and if you got smaller you’d have diminished.

So what happens if you want to make a minor second down from here?

If we think about it on the keyboard, it seems really easy, so I’ll show you that.

Here’s an F sharp, and we’re wanting to make a minor second down.

That’s easy to play, we know it’s right here, it’s F.

Now the problem with this is, if we’re thinking of this as F sharp and this as F,

those are the same letter names so it can’t be a second, because a second

would have to be an F sharp to some kind of an E.

That’s okay though, we can kind of recreate that E as

let’s call this an E sharp, and now it’s going to work.

Let’s look back up on the board here. Here’s our E.

We know we need some kind of E because it’s says second,

and then minor means that we need one half step.

If we leave it like this, just a plain E natural, we’re actually going to have two half steps.

So minor second, is just the same as a half step.

So, I’m going to put this in front of it.

That’s nice to know that a minor second is the distance of one half step.

If we do it here on the board, I’m going to pick this one, I could do either one,

I’m going to pick this one and I’m going to wrap it around, over this, to the next octave.

I’ll take that away. If we count, we’ve got one, two, three, four, five, six, seven.

And two plus seven is going to add up to nine. It always has to add up to nine.

So now we know this isn’t right anymore.

We had a minor second down, and now we have some kind of a seventh going up.

We also know from before that minor intervals are going to invert to major intervals.

They’re just going to go the opposite way.

Let’s listen to that on the keyboard.

You want to listen to the relationship between that minor second and that major seventh.

We had this, this was our original interval like that, an F sharp down to an E sharp.

Then we took that bottom note and flipped it around

so this note is going to want to go all the way up here.

Notice this is almost an octave, if I did this it would be an octave,

so major sevenths are almost octaves. They’re pretty wide intervals,

and they’re really dissonant. That one has a certain kind of dissonance to it.

That minor second has more of an agitated dissonance because the notes are so close together.

So now we’re going to try a major second.

I’m going to do a B flat, and a major second down from that.

We already know it’s going to be some kind of an A, because we need

to count two letter names or we’re not going to get the right thing.

So some kind of an A.

Now, just from thinking about what the piano keyboard looks like,

I know that B flat down to A is just a half step.

That’s not going to be big enough. I need two half steps to get a major second

because major seconds are going to be like a whole step.

As far as the distance is concerned.

If this isn’t big enough, I’m going to widen it by putting a flat in front of that.

So what I’ll do is just invert that.

Maybe this time I’ll take the top note and flip it around.

Again, I’m just inverting it.

It was a major second down, so it should invert to minor,

second should invert to seventh, like this.

I should have a minor seventh, and let’s look at that on the keyboard again.

Here’s my B flat and I go down to an A flat to get that major second.

I’m going to take that B flat and I’m going to put it down the octave,

and there’s a minor seventh.

It has a more mellow dissonance to it, as does the major second

because they are so related, they are inversions of each other.

It has this special name because it used to really shock people when they heard it,

so they had to come up with their own special name for it.

People abbreviate it like this, this is really common and it looks like pi,

but it’s actually because the two T’s tend to run together.

If you see this, it just stands for tritone.

Let’s try figuring out how we get that. A tritone can be two things,

and I’m going to show you one of them, and then I’ll show the other.

So I mentioned a little bit before about how sometimes B and F

can be troublesome when you’re trying to write perfect intervals.

That’s because when you have either F up to B or B up to F

on the piano keyboard, you automatically get that tritone sound.

Let’s look at how that works. On the keyboard, here we have F up to a B.

It’s just a fourth, one, two, three, four, but this is going to give us that dissonance.

Any other fourth that we’re going to play on the white keys is just going to be perfect.

Here's that dissonant one again, and if we keep going, they're all perfect again.

The same thing is true with fifths. If we make a fifth by going from B to F, same thing as the F to B,

they’re just in different octaves, we’re automatically going to get a tritone.

All the other fifths are all going to be perfect.

Let’s look back up on the board here.

So this has got to be some kind of a fourth, because if we count, we get four.

However, it’s not a perfect fourth because a perfect fourth should

only have five half steps, and tritones always have six half steps.

When you count them on the piano keyboard you’ll see that.

Sometimes I like to think that instead of six half steps, I like to think three whole steps.

Sometimes that’s easier.

I’m going to take this, it was perfect, if I had done something like this it would be perfect,

but since it’s not, perfect intervals, when they get bigger, become augmented.

So, F to B, F natural and B natural becomes an augmented fourth.

You could also write like this, that would be fine. Or even just a four, but I’ll be using this one.

This is an augmented fourth, and of course if we invert it,

we’re going to get four plus five equals nine, so this is a fifth.

When you invert an augmented interval, the opposite of that is diminished.

Now this is kind of an interesting one.

You see we’re inverting these, these are kind of the opposite qualities,

we see four and five adding up to nine. Then, six half steps here.

If the half steps add up to twelve, this is also six half steps.

So any of the other intervals that you invert, you’re going to get different numbers of half steps.

But if you invert a tritone, you’re going to get 6 no matter what.

When we do this, the first thing we’re going to worry about is the number, right there.

I know that fours look like there’s going to be one on a line and one on a space, so this is what a fourth looks like.

I’m not worrying about this part yet. Actually what I want here is a diminished fifth.

Here, they’re both going to be on the same thing, they’re both on a line,

or they're both on a space whenever you’re writing a fifth.

So now all I have to do is make sure I have six half steps in each one.

Like I said before, sometimes it’s easier to think about this being three whole steps.

Maybe we can look at that on the piano.

The first one, we were going to write an augmented fourth up from here.

We have this so far, but this is definitely not augmented yet, it sounds to perfect.

I’m going to count whole steps this time, and I could three of them, one, two, three.

I’m going to need a C sharp, but I’m not going to change my letter name

because I specifically wanted to do a fourth.

I’m going to keep it as a C sharp and not a D flat or anything like that.

Now when we write the diminished fifth down from A,

we’re going to use the same strategy we used over here.

Let’s go over to the piano.

Here’s our A, and we’re going to count three whole steps down.

Here’s one, here’s two, and then three is going to take us here.

On the board originally when we didn’t know what our accidentals were,

we had this, which was actually a perfect fifth.

We’re going to need to sharp that D to get six half steps or three whole steps,

which gives us that diminished fifth. It’s going to look like this.

That’s it for this lesson.