Circle Of Fifth Music Theory

  Imagine if we could find a way to visually represent the all the differentkeys and how they are related to each other. We could find which keys were similar, which keys were further away from each other and find out which sharps and flats were ineach key. We could even use this representation as amap to find our route between different keys. Luckily for us, someone has already done justthat. The Greek philosopher Pythagoras, in fact, he of the triangle fame. Maybe if Pythagoras was around today, rather than calling him a philosopher, we might call him a mathematician. You may ask what mathematics has got to dowith music? Well the answer is: Quite a lot actually! Sound is a very mathematical phenomenon. A violin string vibrates as it is bowed. As it vibrates, the string generates pressurechanges in the air which our ears pick up and interpret as sound. If the violinist were to play the note A abovemiddle C, the string would vibrate at 440 times persecond.  

If he were to play the A an octave above that, the string vibrates 880 times per second, precisely twice the number of vibrations persecond as it did before. Another octave above that, and the string vibrates at 1760 vibrationsper second, again twice the number of vibrations per secondas it did on the previous A and so on. Therefore it is not surprising that someonewith a mathematical mind like Pythagoras might think of turning his hand to music aswell. Having had such success with triangles, when Pythagoras turned his attention to music, he decided that a circle might be the bestshape to use. This circle became known as the circle of5ths. If you count the number of semi-tones in anoctave, you'll find that there are 12 in all, semi-tones includes all the black notes onthe piano too. What Pythagoras did was to lay these twelvenotes around the circle like a clock in a special order. Pythagoras didn't actually call them noteslike the notes we know today. He worked with numbers. What we now call C he called 0 and dividedhis circle into 1,200 pieces or cents. Therefore, each of the 12 positions on hiscircle is 100 cents further round the circle fromthe previous half tone. 

This division into semi-tones and the creationof the circle of fifths lies at the very foundation of western musictheory. Because the circle of fifths acts as a sortof roadmap for western music, it is incredibly useful to refer to when tryingto work out things like, what key you are in. If you are in a major key it helps you findthe relative minor key and visa versa. It tells you what chords are available ineach key. It helps you to transpose your music intoa different key and move between keys within a song. The reason it is called the circle of fifths is because of the way it is laid out. As you move around the circle in a clockwisedirection, the next note you encounter will be a fifthabove the note before it. So for example, starting at the 12 o' clockposition, we have C. Move around to the one o' clock position andwe find G. In the key of C, G is the 5th note of thescale. Move round again to the 2 o' clock positionand we find D. Again D is the 5th note of the G major scale. A more in depth explanation of how the differentscales work and how to find the different degrees of eachscale, like the fifth, can be found in the Podcast Extra. If I play all 12 tones of the circle on the piano, you can hear the melodic progression. C, G, D, A, E, B, F#, Db, Ab, Eb, Bb, F and finally back to C. So how does the circle of fifths help us findout what key we are in? The key of C, has no sharps or flats in it. Notice how it is at the 12 o' clock position or the zero position. The key of G has one sharp in it, notice how G is at the 1 o' clock position. The key of D has 2 sharps in it, notice how the key of D is at the two o' clockposition and so on all the way around to the key of C# at the7 o' clock position with 7 sharps in the key signature. I'm going to stop there just for the moment and now have a look at the keys with flatsin their key signatures. If we go back to C at our 0 position and now instead of going clockwise round thecircle, we go anticlockwise, the key of F has one flat in it's key signature, moving another step anticlockwise, the key of Bb has 2 flats in it, another step and Eb has 3 flats in it and so on. Just as when we were going clockwise roundthe circle assigning key signatures with sharps in them, we stopped at 7 o' clock. If we do the mirror of this now with our flats continuing to move anticlockwise around thecircle, we find that we will stop at the 5 o' clockposition.

 This means that the 3 keys at the bottom ofthe circle can be written with 2 different key signatures either made out of flats or sharps but still sound the same. It all depends on what we want to call ourkey. C# and Db are actually the same note. However, to keep things simple, if we say that we are in the key of C# then we will tend to put sharps in the keysignature and if we say we are in the key of Db, we will tend to put flats in our key signature. So the first thing that the Circle of Fifthstells you is how many sharps or flats are in the key you want your song to be in. But that is only half the story. Say you wanted your song to be in the keyof E major, we know from E's position on the circle at4 o' clock that there will be 4 sharps in the key signature. But which 4 notes are sharpened? To find out we simply start at the 11 o' clockposition and count round the circle in a clockwisedirection writing down each note we encounter until we have the number of notes we knoware sharpened in the key signature. So the key of E major has 4 sharps and theyare: F#, C#, G# and D#. That's all well and good for keys containingsharps in their key signatures, but what about flats. Well the circle is symmetrical so we just work backwards. Say you want to write your song in Ab major, if we start at C, to get to Ab we have to move anticlockwise by 4 steps so we know that Ab has 4 flats in its key signature. Which notes are flattened? Well this time we start not at the 11 o' clockposition but at the 5 o' clock position with B. So counting round 4 flats from B, we have Bb, Eb, Ab, and Db. However, for us as songwriters, the usefulness of the circle doesn't stopthere. Remember, in this podcast, we're talking aboutchords. This circle of Fifths tells us which chordtriads are available to us in each key. So if we are composing a song in the key ofC, we can easily see which chords we can includein our song. Here's how: Looking at C on the circle, well we know that in the key of C major, thechord, C major will be one of the chords available. Now we look at the 2 chords on either sideof C on the circle, these are F and G so F C and G, will be the major chords available in thekey of C. Carrying on round the circle in a clockwisedirection, the next 3 chords, D, A and E will give us all the minor chords availablein the key of C. The 7th and final available chord in the keyof C is the diminished chord of B. So if we now lay those out in pitch orderrather than the order they appear on the circle of fifths the chords available to us in the key of Care: C major, D minor, E minor, F major, G major, A minor and B diminished. The reason that these are the chords availableto us is that they are all made up of notes whichexist in the C major scale, you will notice there are no sharps or flatsin these chords as there are no sharps or flats in the scaleof C major. If we look at another key, say the next key round circle, G major, we simply use the same method to find whichchords are available to us in G major as well. Firstly the major chords which are found by taking the G major chordand the 2 chords surrounding it on the circle, C major and D major, then carrying on around the circle we getthe 3 minor chords, A minor, E minor and B minor and finally the diminished chord of F#. Again all these chords are made up of notes which exist in the G major scale. You can use the same method to find the chordsavailable in whichever key you want to write your song in. So the circle of Fifths helps you to workout the palette of chords you have to work with in your song. But the circle's usefulness doesn't end thereeither. Remember, the circle of Fifths is laid outin such a way that it shows us the relationship between different keys. This is especially useful if you want to transposeyour song into another key. Say you've just finished writing your songin the key of C. Along come your vocal artists and you suddenly discover that C is too lowfor them. They would have preferred it if you had writtenyour song in the key of E. You hold your head in frustration! All that careful chord work and now you have to throw the whole lot away and start again in a new key. Well, don't worry, you'll not be burning the midnight oil onthis one after all as the circle of Fifths gives you a time saving way of easily transposingthe chords you have already written. C is at the 12 o' clock position on the circle and E is on the 4 o' clock position. That means to go from C to E we have movedclockwise around the circle by 4 steps. Each chord in your transposed song thereforedoes exactly the same. An F chord, for example would become A as A is 4 steps clockwise around the circlefrom F. A G chord would become B and so on. Exactly the same is true if you move to a key that is anticlockwisearound the circle from your original key. Simply count the distance between the keys and shift all the chords in the song by thesame distance. Voila in 5 minutes you've transposed all thechords in your song. Talking of transposition, what about changing key in the middle of yoursong? To add interest and variety to your composition. Well there are two ways in which the circlecan help you modulate between different keys in your song. Different keys are said to be closely related if their respective scales share many of thesame notes. The more notes shared by each scale, the closerthey are related. Each major key has what is known as a relativeminor key associated with it. That is a minor key that shares all the samenotes in its scale as the major key. Therefore the closest key to any major key is its relative minor. For example the key A minor shares all the same notes in its scale asC major. There are no sharps or flats in either key. Therefore A minor is C major's relative minor. On the circle of Fifths, each key's relativeminor is written with a small letter on the insideof the circle in the same position as the major key. So C major is written with a capital C at the 12 o' clock position on the outsideof the circle and A minor is written with a small A at the 12 o' clock position on the insideof the circle. So why is this important for us as songwriters? Because it means that modulating between Cmajor and A minor is very easy to do in a song as each key contains the same chords so we can flit back and forth between the2 keys with ease. I can play my tune in the C major: And then repeat it easily in A minor: without having to do too much work to link the two parts of the melody together. But what about something a little more complicated. Could you start off your song in C major and at some point modulate to some other majorkey such as G major? Well the answer is of course yes; with a little work. How much work it takes depends on how closely the two keys you areworking in are related to each other and the circle of fifths tells us exactlythat. C and G are adjacent to each other on thecircle, therefore they are said to be closely related. Their scales share many of the same notes. In fact because the key of G only has onesharp in it and C has no sharps in it, they share all the same notes, apart fromone: F# which exists in the key of G but not in the key of C. In order to modulate cleanly and musicallybetween keys in the middle of your song, at the moment of modulation you have to trick your audience's ear intothinking it could be in either key. We do this by using a chord known as a pivot chord. A pivot chord is a chord that exists in bothkeys. By arriving at the pivot chord in your startingkey and then using it as a pivot to take yourselfoff in a new direction in your new key, you can guide the audience's ear through the modulation into the new key. I go into how exactly to do this in that inmore detail in the podcast extra but for now, I'm going to show you how to use the circleof fifths to find these pivot chords. This is done by using the circle to find whichchords are available in your starting key as we described before, then finding which chords are available inyour new key and seeing which chords are identical in bothkeys. It is easier to modulate between closely relatedkeys as closely related keys will have more chords that exist in both keys i.e. you have more flexibility in choosing on which chord to pivot into your new key. So as we discovered before, in the key of C, the chords available to us are: C major, D minor, E minor, F major, G major, A minor and B diminished. In the key of G the chords available to us are: G major, A minor, B minor, C major, D major, E minor and F# diminished. Matching these chords together, we find that the following chords exist inboth keys: C major, E minor, G major and A minor. Therefore any of these chords could be usedas your pivot chord: In the following example, I'm going to use the A minor chords as mypivot chord. Again I go into this in more detail in thepodcast extra, but just to give you a taster of the end result, here is my little tune with starts off in C major and modulates to G major. Here we are in the key of C, But is that where we really want to be, To add a touch of variety, Perhaps we could modulate to G. In order to do it musically, And to lead the ear into the new key, We pivot on A minor this is he, As he leads us through D7 into G. Now we need a little melody, To confirm that we're in the key of G, Then we return to the tune we played in C, Only now we're in the key of G. This video is part of a larger podcast aboutchords and harmonies called "Striking a Chord" The full podcast can be heard at www.themobilestudio.net/podcast and go to Podcast number 1. You can also gain free access to the podcastextra material by going to this webpage and clicking on the subscribebutton on the right hand side of the page.