The circle of fifths was first invented by Nikolai Diletskii back in 1670. The root of the circle, divided into 12 segments comes from the ideas of Pythagoras (Pythagorean circle). The application of the circle of fifths is limitless and this post will cover only cover a handful of important contributions. In this part we will cover the notes on the outer circle (notes written in blue, which are the major keys).
The circle of 5ths can be used to figure what notes are there in a key. Starting from 12 o’clock, the key of C has no sharp or flat. Moving clockwise to the next key, (1 o’clock) which is the key of G and has one sharp. This is a really easy way to remember how many sharps are there in a key. If the note is at 1 o’clock, it has one sharp. If it is at 2 o’clock, it has two sharps and so on. This applies to all the notes, all the way up to 6 o’clock which is F# and that has 6 sharps. The circle of fifths also tells you what note to sharpen. For example, to know what note is sharpened in the key of G, you only need to go two steps counter clockwise (11 o’clock) and that is an F note, and that is the note that is sharpened in the key of G. Same rule applies for D which is at 2 o’clock. So you know there are two sharps and they are F# (coming from the previous key) and C# (going two steps counter clockwise from D).
The circle of 5ths also presents all the diatonic chords in a very efficient way. If you want to know the diatonic chords in a certain key, all you have to do is take the chords one step above and one step lower to that key. For example the diatonic chords in the key of C includes all the chords written at 11,12 and 1 0’clock (including the minors). Therefore the chords in key of C are C Dm Em F G and Am. You will notice that the diminished chord is omitted here.
When you go counter clockwise from C, you get to find the keys with a different number of flats in it. For example, at 11 o’clock, the key of F has one flat. Moving one more step counter clockwise, the key of B flat (at 10 o’clock) has two flats and so on.