The Circle of Fifths
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Posted 14 September 2006 - 05:25 PM
The circle of fifths is a useful teaching aid designed to show how closely keys are related to each other in terms of the number of notes that they have in common.
It shows keys arranged in a circle, (with their associated scales) each key separated from its neighbour by the interval of a 'perfect fifth'. (5 scale degrees). The interval of a perfect fifth is used because keys separated by this interval (or its inversion: a perfect fourth) are more closely related than keys separated by any other interval. If you're not sure about intervals you can learn about them here.
Starting from the key of C major at the top of the circle and moving along in a clockwise direction, the keys become increasingly distant as each stage (a fifth higher) introduces a key with one sharped note that is foreign to the preceding key. When we get to the opposite end of the circle, we are as far as we can get in terms of the keys being related to each other. We could continue adding more sharps after we reach the key of F# major but it makes more sense to use what's known as the 'enharmonic equivalent' flat key. Instead of calling the key F# major, which has six sharp notes, we can call it Gb major, which sounds exactly the same, but calls the notes by their flat name (enharmonic) equivalents (e.g., Gb instead of F#). Now if we continue going round and adding sharps, it will have the effect of cancelling those flats one by one until, eventually, they are all cancelled and we arrive back at the key with no sharps or flats: C major
The relative minor keys
Every major key has an associated relative minor key (a minor third lower) with which it shares exactly the same arrangement of sharps or flats (or key signature). These are shown inside the circle, with the natural form of the minor scales.
As we said, keys separated by the interval of a fifth (or fourth) are more closely related than any others. For example, the key of C major is more closely related to the key of G major than it is to its alphabetical neighbours B major or D major.
C major = C D E F G A B
G major = G A B C D E F#
B major = B C# D# E F# G# A#
From the above you can see that the key of C major shares almost every note with the key of G major. Only one note is different: C major contains the note F and G major contains the note F#.
Contrast that with the key of B major. If we compare C major and B major , we can see that they have only two notes in common: B and E. Although they are next to each other in the alphabet and in pitch, they have very little in common with each other.
So what's the practical value of this?
If you are trying to work out the chords of a song in the key of C major, for example, the chords that are most likely to be used will be the major chords corresponding to the keys on either side.
That means the major chords most likely to be found in a song in the key of C major will be G major and F major. The chord B major will rarely be found in the key of C major because, as the circle shows us, B major is very distantly related to the key of C major.
As for the minor chords most likely to be used in the key of C major, just look inside the circle. The most likely chords will correspond with the inner circle of 'relative minor keys, i.e., A minor and its two neighbours: E minor and D minor.
A song in the key of C major
Most likely major chords = C major, G major and F major
Most likely minor chords = A minor, D minor and E minor
A song in the Key of E major
Most likely major chords = E major, A major and B major
Most likey minor chords = C# minor, F# minor and G# minor
It works just as well with the inner circle of minor keys, with a couple of possible alterations.
A song in the key of D minor
Most likely minor chords = D minor, G minor and A minor (often altered to A major)
Most likely major chords = F major, C major and Bb major
The alterations that often occur in minor keys are, with the exception of the main key chord (in this case D minor), that the other minor chords may be transformed into major chords. This happens as a result of the minor scales having a couple of different forms known as the harmonic and melodic minor scales. So, music written in the key of A minor, for example, and making use of the altered forms of the minor scale, may sometimes include the chord G# diminished (G#BD) instead of G major, (GBD) and will very probably include E major (EG#B)rather than E minor (EGB).
Changing key within a song
Another practical use concerns changing key within a song. The more complex a song is, the more likely it is to change key, even very briefly. The keys that a song will most likely change to are the neighbouring keys on the circle of fifths diagram. If you are writing a song, the keys that you can change (modulate) to most naturally are those on either side of the main key as they are the keys that are most closely related to your starting key. If you are improvising to a song by ear, you will know that if a change of key occurs, which keys the music will most likely modulate to, so, hopefully, they won't take you completely by surprise.
As you can see, the only difference between the keys of C major and G major is that G major has the note F#, whereas C major has just F. All we need to do, if we want to modulate painlessly to the key of G major, is introduce the note F#, followed by the 'new key' chord of G major. There are good, musical ways to do this as explained by Tekker in his modulation lesson.
In summary, the circle of fifths is a simple but very useful tool that makes it easy to visualise the ways that keys are related to each other musically, rather than simply in order of pitch as scales are arranged. It's very useful to know the keys in this order as it will give you a solid understanding of how the western diatonic system of music is structured.
Test your knowledge of the circle of fifths with some quizzes at Circle-of-Fifths.net
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