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It’s basically a handy way of mapping the relationships between the 12 notes of the chromatic scale and highlighting the patterns of their key signatures.
The first thing you need to know are perfect fifths. A perfect fifth is the note that is 7 semitones above another note. For example, C’s perfect fifth is G. These perfect fifths all form a loop: if you started at C and went up 12 perfect fifths, you’d end up back at (a far higher) C.
Now the order of these perfect fifths all follow a pattern, that goes F C G D A E B. It then repeats with all the sharp notes. The circle of fourths is the pattern backwards (B E A D G C F), with flats instead of sharps.
But because we root a lot of our music stuff in C instead of F, that gets shifted around a bit, and there’s some overlap points (like E♯ is just F). The simplified version is this:
**Circle of fifths (sharps):** C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯, F, C
**Circle of fourths (flats):** C, F, B♭, E♭, A♭, D♭, G♭, B, E, A, D, G, C
If you’re able to memorize these two patterns, it’s a lot of handy mnemonics for figuring out info about key signatures.
For example, how many sharps are in E major? E is 4 perfect fifths above C, so it has 4 sharps. What are those sharps? It follows the pattern, so F♯, C♯, D♯ and A♯.
How many flats are in D♭ major? D♭ is 5 perfect fourths above C, so it has 5 flats. What are those flats? It follows the backwards pattern, so B♭, E♭, A♭, D♭, and G♭.
What about minor keys? To find a major’s corresponding minor chord, count up 3 on the circle of fifths, or down 3 on the circle of fourths. G major has the same number and kind of sharps as E minor. E♭ major has the same number and kind of flats as C minor.
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