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If you’re into music composition, you need to know the Circle of Fifths because it shows key signatures and key relations (but not chord relations). In the following image, the major keys are indicated with capital letters, and their relative minors are in lowercase.

Also shown are the number of sharps or flats that you put in the key signature for each key.

If you want understand how it works this site can give some nice explanations. In addition an excellent interactive Circle of Fifths can be found here. The knowledge of Circle of Fifths is very important, here is a good guide. A well done video-guide is available here too.

The Circle of Fifths has its uses, but not for showing pathways to meaningful, coherent chord progressions and harmonic movement. Many musicians mistakenly think that the Circle of Fifths actually has something to do with chord progressions. Even authors of books on songwriting and music theory make this mistake, propagating rubbish and confusing their readers to no end. To be clear: the Circle of Fifths shows key signatures and key relations but not chord relations. Below an example of what happens when you treat the elements around the clock face of the Circle of Fifths as chords instead of keys. Presumably, you would want to progress around the Circle of Fifths as though it's a big circular chord progression. To simplify matters, consider the outer circle only, the elements that would be the major chords if the Circle of Fifths had anything to do with chords.

See picture below:

Start at the top of the Circle of Fifths with the first chord, which is C, the tonic chord in the key of C. Then, moving counter-clockwise around the circle, progress to the next chord, which is F. Now you have a perfectly good two-chord progression in the key of C, namely C progressing to F. So far, so good. However (continuing counter-clockwise), the next chord you progress to is Bb. Now you've got a problem. The chord Bb is not a chord in the key of C. Therefore, at this point you've actually exited the key of C. As you progress the rest of the way round the Circle of Fifths, you do not re-enter the key of C until you get to the chord G. Clearly, then, any notion that the elements of the Circle of Fifths having anything to do with chord progressions is wrong. The Circle of Fifths shows relationships among and between keys, not relationships among and between chords within a given key. To summarize, the Circle of Fifths does not work as a chord progression device. That's the job of the harmonic scale which also happens to be circular in shape, but has no functional relationship with the Circle of Fifths.