Ladder of Fourths

Hello and welcome back. Today we're going to learn about building one octave major scales on the ladder of fourths
using our old friend the tetrachord.
You probably remember using tetrachords back in an earlier lesson when we explored the ladder of fifths.
Well, today it's time to discover new kinds of patterns on the ladder of fourths. Let's come to the piano to get started.
First, a real quick review of half steps and whole steps.
Can you point to a half step above this key?
If you're pointing here, you're correct.
Remember, a half step is the distance such that there's no key in between, white or black.
But this on the other hand is a whole step because there is a key in between.
One half step plus another half step equals a whole step.
A quick way to determine a whole step is there will always be exactly one key, black or white, in between.
Here's a whole step and here's a whole step,
because we've got that one key in between.
Now you may recall that a major tetrachord is built on two whole steps. You can see a whole step here.
One came between, another whole step here, one came between, and then a half step at the end.
So together that's whole, whole, half, and that's the formula, if you will or the ingredients, of a major tetrachord.
Now let's try building an E major tetrachord.
Point to a whole step above this E.
If you're pointing here, you're correct. Remember we have to skip over one key white or black.
Now point to another whole step above this F-sharp.
Now it should be right here. Another whole step would bring us to G-sharp.
Now that's a whole, whole. We need to finish with a half.
Point to where we would finish with a half step.
You should be pointing right here. Now we have a whole, whole, half. That makes an E major tetrachord.
Let's use some sign language today to help us remember that pattern of whole and half steps.
So we're going to use W for whole. Can you make this W sign with me?
This is the sign for W, and its whole, whole, and then half. This is the, this is sign language for the letter H.
Try this with me. Just two fingers pointing to the side.
So try this together. Whole, whole, half. Good.
Now let's see if you can figure out this one on your own.
I've given you the first note. This will be F or DO. See if you can figure out the notes of the F major tetrachord.
I'll give you a few seconds to figure it out, and then the correct answer will appear.
This is the correct answer for the F major tetrachord. We have a whole step, whole step, half step. Let's try one more.
Can you figure out the E-flat major tetrachord? Use the formula whole, whole, half to figure it out. The correct answer will appear in a few seconds.
Here's an E-flat major tetrachord: whole step, whole step, finishing with the half step.
Now, let's come back to C major for a second.
Here's our C major tetrachord.
You'll recall that to build a one octave major scale we put two major tetra chords together
joined by one whole step in the middle.
Here's the C major tetrachord, here's the G major tetrachord.
They're one whole step apart. You put this together, and we call this the C major one octave scale.
Now in a previous lesson, we found that when we took our starting note and moved it up a fifth,
every time we went up a fifth we found we had to add one sharp.
A fifth above C is G, and G major has one sharp.
When we went up another fifth to D major, we found we had two sharps, etc.
Well, today we're going to explore what happens when we go up by fourths.
What is a fourth above C?
Well, we count one, two, three, four, a fourth above C is F.
So let's build our F major tetrachord. We have a whole step, whole step, half step,
and that gives us our first tetrachord, then we start our next tetrachord a whole step above that, for whole step, whole step, whole step,
and then we finish with a half step.
So this would be our F major one octave scale.
Let's sing this in solfège together. Go.
DO RE MI FA SO LA TI DO
Now let's sing that in letter names, go. F G A B-flat, whoops knocked that guy off, B-flat C D E F
Now, you notice this time instead of sharps we ended up with a flat, and why did we call this a B-flat?
Well, it's because we altered this B
to the left.
If we had taken this note and moved it here, then we would have called it A-sharp,
but it was the B that was altered down a half step to create this half step between MI and FA, which is why we call it a B-flat.
So we see that when we go from C up a fourth, it added one flat.
Let's draw this on our latter of fourths.
Every major scale we discovered today, we're going to be filling out on this ladder of fourths,
which I encourage you to download from our website so you can fill out your own copy too.
that will be a great thing to have for reference as ...