Key Signatures and the Ladder of Fifths: Part 2

Hello and welcome back. I'm Joseph Hoffman.
Today we're going to finish our climb up the ladder of fifths.
So let's take a look at the ladder of fifths and pick up where we last left off.
If you recall, we made it all the way from C major with zero sharps, up to E major with four sharps.
And before we go up to the next key, let's take a moment to notice an interesting pattern.
Have you noticed that the new sharp is always
just one step away,
one half step away actually, from the key that we're in?
When we're in E major,
that new sharp was D-sharp, when we were in A major, the new sharp was G-sharp. Always just a half step below.
Now it's time to figure out the next key another fifth up on the ladder.
and a fifth above E is B,
which from our pattern of sharps we know will have five sharps.
With the new sharp being just a half step below B.
So, press pause and see if you can play the key of B major on your own
using two tetrachords, one tetrachord in each hand, then press play to try it along with me.
Here are the two tetrachords you need for B major.
We had to sharp both of these to get a whole step, whole step, half step, in this bottom tetrachord,
and then we had to sharp all three of these keys to get the half step here,
and then we needed two whole steps here
for this kind of crazy key of B major where we're using all five possible black keys,
and only these white keys left.
That's B major. Let's try to play it.
So covering up B C-sharp D-sharp E with the left hand leaving out your thumb of course,
and then covering up F-sharp G-sharp A-sharp B
with the right hand. Let's try to play it,
and say the letter names. Ready, go.
B C-sharp D-sharp E F-sharp G-sharp A-sharp B
Now can you try that by yourself once?
Play each note and say the letter names, ready go.
Good, now let's try to play "Follow Me" in this position.
Can you sing the words with me?
And we will play, ready go.
♫Follow, follow, follow, follow me♫
♫Let's make a line for all to see♫
You know there's another song you can play using two tetrachords in this one octave scale.
If you know the song ♫Joy to the world, the lord is come♫
♫Let earth receive her king♫
That's another fun one to do in tetrachords.
So press pause and try playing either "Follow Me" or "Joy to the World", just that first line that I demonstrated.
You can figure it out by ear. Go ahead and challenge yourself.
And then press play when you're ready to go on.
All right, let's fill in the sharps for B major. We had an F-sharp, C-sharp,
G-sharp,
D-sharp,
and the new sharp was A-sharp.
So our key signature:
F-sharp, C-sharp, G-sharp, D-sharp,
and then A-sharp, hold on that doesn't quite look like a D-sharp. Let's get it centered on the line and then A-sharp down here
for five total sharps.
Now here's where things get a little bit crazy.
What would be a fifth above B?
You might be saying F,
and in a way you'd be right, but remember that F is sharped.
And so technically a perfect fifth above B
is F-sharp
because of where we are on the ladder.
B to just F would be what's called a diminished fifth, not quite right for the fifth we're talking about. These are all perfect fifths,
which means we have to take into account the key signature.
So, a fifth above B is F-sharp,
and as you can tell from this pattern we're going to have six sharps now.
Let's come to the piano keys and see how that works.
Okay, here is the crazy key of F-sharp major. We are getting super advanced now.
Remember, we have to have a whole step, then a whole step, then a half step.
So we're on this black key F-sharp to start, whole step, whole step, half step,
then we have to go up a whole step to start the blue tetrachord.
We need a whole step, whole step, and then finish with this half step.
So this is the key of F-sharp major.
Now, you might be thinking well where's the new sharp we still have these
five black keys in F-sharp major. We should have six sharps.
Well, let's figure it out by naming each note and we'll discover the hidden mystery sharp. Can you name them with me? We have F-sharp, G-sharp, A-sharp,
B, then C-sharp, D-sharp.
Now wait a minute.
The next letter in the alphabet should be E because we just had C-sharp, D-sharp,
but this looks like an F,
and then F-sharp?
Ah ha.
Now, this should be a clue to you: when you have an F, F-sharp, but no E.
Well, you see what happened is E became E-sharp, which looks like F,
but in a scale we're supposed to have one of every letter,
and because we skip from D-sharp to F, I knew that something was wrong.
It should go C-sharp, D-sharp, then E something,
and if we're actually here, this is E-sharp.
which ...