If you've been playing piano for a while, but haven't heard of the circle of 5ths, boy are you missing out. This is gonna me an awesome lesson for you. This will really help you understand your scales, and you're going to love'em. Just bare with me here.
First, you need to know what a 5th is. a 5th is just an interval, the amount of space between two notes. Here's an example
AB = 2nd, AC = 3rd, AD = 4th AE = 5th
If you go past G, you just start over in the alphabet.
FG = 2nd, FA = 3rd, FB = 4th, FC = 5th
That's all a 5th is. Now what happen if you just went up the piano in 5ths? What notes would you have?
C G D A E B F# C# G# D# A# E#(F) B#(C)
And what would happen if you went down by 5ths? GF = 2nd GE = 3rd, etc.
C F Bb Eb Ab Db Gb Cb Fb Bbb(A) Ebb(D) Abb(G)
That's every note on the piano spelled with either sharps or flats using the circle of 5ths. Now, what does that all mean? Well, here's the cool thing
When playing pieces within certain key signatures, you are going to have a number of black keys. If the song is in C major, there are no black keys, if it's in B major, there will be a lot. How do you know how many sharps a particular key signature has? Well, just use the circle of 5ths.
The awesome thing is that when you build major scales a 5th away from each other, each 5th will then add a sharp or flat to that scale depending on if you go up or down.
C major scale has no black keys (no sharps or flats)
G major has 1 sharp (F#)
D major has 2 sharps (F#, C#)
A major has 3 sharps (F#, C#, G#)
COOL TRICK! - the additional sharp will always be 1 step below the new major scale (G major adds an F#, D major adds a C#, etc.)
For flats, you only have to memorize the first flat, and then the additional flat will just be what the next 5th down key signature will be, (the 1st flat is Bb)
C major has no flats
F major has 1 flat (Bb)
Bb major has 2 flats (Bb, Eb)
Eb major has 3 flats (Bb, Eb, Ab)
And so on and so forth. Pretty neat.
So here's the cool thing, let's say you know a piece is in the key of E major, and you don't know how many sharps it has, just go up the circle of 5ths (or down) until you find it.
C, G, D, A, E (that's 4 away, 4 sharps, (add the note below each), F#, C#, G#, D#
What about Db? It's a flat, so you go down the circle of 5ths.
C, F, Bb, Eb, Ab, Db (that's 5 away, 5 flats, (add the next 5th each), Bb, Eb, Ab, Db, Gb
That's one way of figuring out how many sharps or flats any particular major scale or key signature has. Hope this has been helpful.
Below is a picture of the circle. It uses sheet music to describe which notes are sharp or flat, but the formula still applies. (Note: I grabbed this from Wikipedia, hope he doesn't mind)
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