Understanding the Circle of Fifths
by ReverbLxnd in Saxophone
Understanding the Circle of Fifths
Everything you need to know about mixing music, the mixing process, mixing techniques and mixing engineers in one place.Go to Mixing Blog —
Everything you need to know about the saxophone — saxophone step-by-step guides, fingerings, scales, how-to articles and common FAQs — in one placeGo to Saxophone Blog —
by ReverbLxnd in Saxophone
Understanding the Circle of Fifths
What is the circle of 5ths?
Imagine if we could find a way to visually represent all the different keys and how they are related to each other.
Imagine we could find which keys were similar, which keys were further away from each other, and which sharps and flats were in each key. We could even use this representation as a map to find out the route between different keys.
Luckily for us, someone had done just that—the Greek philosopher Pythagoras, he of the triangle fame.
If Pythagoras was around today, rather than calling him a philosopher, we might call him a mathematician.
What has mathematics got to do with music?
The answer is quite a lot actually.
Sound is a very mathematical phenomenon. A saxophone reed vibrates as it is blown. As it vibrates, the reed generates pressure changes in the air, which our ears pick up and interpret as sound.
If the saxophonist were to play concert A, above middle C, the reed should vibrate at 440 times per second.
If he were to play concert A, an octave above that, the reed vibrates 880 times per second, precisely twice the number of vibrations per second as it did before.
Another octave above that, and the reed vibrates 1760 vibrations per second, again, twice the number of vibrations per second as it did on the previous concert A and so on.
Therefore, it is not suprising that someone with a mathematical mind like Pythagoras might think of turning his hand to music as well.
Having had success with the triangle, when Pythagoras turned his hand to music, he decided that a circle was the best shape to use. This circle became known as the circle of 5ths.
If you count the number of semitones in an octave, you’ll find there are 12 in all. What Pythagoras did was lay this these twelve notes around the circle in a special order, like a clock.
Pythagoras didn’t actually call them notes, like the notes we know today. He worked with numbers.
What we now call C, he called 0, and divided his circle into 1,200 pieces or cents. Therefore each of the 12 position on the circle is 100 cents further round the circle from the previous half note.
This division of semitones and the creation of the circle of fifths lies at the very foundation of wester music theory.
Because the circle of fifths acts as a sort of roadmap for western music, is is incredibly useful to refer to when trying to workout:
The reason it is called the circle of 5ths is because of the way it’s laid out. As you move around the circle in a clockwise direction, the next note you encounter will be a fifth above the note before it.
For instance, starting at the 12 o’clock position, we have C. Moving clockwise to the 1 o’clock position, and we find G. In the key of C, G is the fifth note of the scale.
Move around again to the 2 o’clock position and we find D. Again, D is the 5th note of the G major scale and so on and so forth.
If you play all twelve tones around the circle, you can hear the melodic progression.
So, how does the circle of fifths help us find out what key we’re in?
The key of C has no sharps or flats in it. Notice how it is at the 12 o’clock / 0 position.
The key of G has 1 sharp in it. Notice how G is at the 1 o’clock position.
The key of D has 2 sharps in it. Notice how D is at the 2 o’clock position and so on, all the way around the circle to the key of C♯ at the 7 o’clock position with 7 sharps in the key signature.
Let’s stop there for the moment.
If we go back to C at our O position, and now instead of going clockwise round the circle, we go anticlockwise, the key of F has one flat in it’s key signature.
Moving another step anticlockwise, the key of B♭ has two flats in it. Another step and E♭ has three flats in it and so on.
Just as when we we’re going clockwise, round the circle assigning key signatures with sharps in them, we stopped at the 7 o’clock position, if we do the mirror opposite of this now with our flats, continuing to move anticlockwise around the circle, we find that we will stop at the 5 o’clock position.
This means that three keys at the bottom of the circle can be written with two differentkey signatures either made out of flats, or sharps but still sound the same.
It all depends on what we want to call our key. C♯ and D♭, for example, are actually the same note (enharmonic equivalents).
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 key signature and if we say we are in the key of D♭, we’ll tend to put flats.
So, the first thing the circle of fifths tells you is how many flats or sharps are in the key signature you want your song to be in.
But, that’s only half the story.
Say, you wanted your song to be in the key of E major. We know from E’s position on the circle at 4 o’clock that there are four sharps in the key signature. But which four notes are sharpened?
To find out, we simply start at the 11 o’clock position and count round the circle in a clockwise direction writing down each note we encounter until we have the number of notes we know are sharpened in the key signature.
So the key of E major will have 4 sharps. That is F♯, C♯, G♯ and D♯.
This works for keys containing sharps 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 A♭ major. Starting at C anticlockwise, we move four steps. So we know that A♭ has four flats in its key signature.
Which notes are flattened?
This time, we start not at the 11 o’clock position but at the 5 o’clock position, with B in this case. So counting around 4 flats anticlockwise from B, we have B♭, E♭, A♭, and D♭.
For us as songwriters, the usefulness of the circle doesn’t stop there. There are also chords.
The circle of fifths tells us which chord triads are available to us in each key.
If we are composing our song in the key of C, we can easily see which chords we can include in our song.
Looking at C on the circle, we know that in the key of C major, the chord C major will be one of the chords available. Now we look at two chords, either side of C on the circle. These are F and G.
So F, C and G will be major chords available in the key of C.
Carrying on round the circle in a clockwise direction the next three chords D, A, and E will give us all the minor chords available in the key of C.
The seventh and final available chord in the key of C is the diminished chord of B.
If we played these out in pitch order, rather than in the order they appear on the circle of fifths, the chords available to us in the key of C are C major, D minor, E minor, F major, G major, A minor, and B diminished.
The reason that these are the chords available to us is that they are made up of notes which exist in the C major scale. You will notice there are no sharps or flats in any of these chords, as there are none in the C major scale.
If we look at another key, we simple use the same method to find out which chords are available to us.
The circle of fifths helps you work out the palette of chords you have to work with in your song. But the circle’s usefulness doesn’t end there either.
Remember, the circle of fifths is laid out in such a way that it shows us the relationship between different keys. This is especially useful if you want to transpose your song into another key.
Say you’ve just finished writing your song in the key of C. Along comes your vocal artist and you suddenly discover that C is too low for them. Suppose E is more appropriate for them.
The circle of fifths gives you a time saving way of easily transposing the chords you have already written.
C is at the 12 o’clock position on the circle, and E is at the 4 o’clock position. That means to go from C to E we have moved clockwise around the circle by 4 steps. Each chord in your transposed song therefore does exactly the same.
An F chord for instance will become A, G will become B, and so on and so forth.
The same is true if you move to a key that is anticlockwise around the circle from your original key.
Simply count the distance between the keys and shift all the chords in the song the same distance. In five minutes, you’ll have transposed all the chords in your song.
Different keys are said to be closely related if their respective scales share many of the same notes. The more notes shared by each scale, the more closely they are related.
Each major key has what is known as a relative minor key associated with it. That is a minor key that shares all the same notes 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 with C 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 keys relative minor is written with a small letter on the inside of circle in the same position as the major key.
C major is written with a capital “C” at the 12 o’clock position on the outside of the circle, and A minor is written with a small “a” at the 12 o’clock position on the inside of the circle.
So, why is this important for us as song writers?
Because it means that modulating between C major and A minor is very easy to do in the song as each key contains the same chords so we can flip back and forth between the two keys with ease.
If you want to modulate between two major scales, how much work is takes depends on how closely the two keys you are working in are related to each other and the circle of fifths tells us exactly that.
C and G are adjacent to each other on the circle of fifths, therefore, they are said to be closely related. Their scales share many of the same notes. In fact, the key of only has one sharp in it and C none.
They share all the same notes apart from one F♯ in the key of G.
In order to modulate cleanly and musically between keys in the middle of a song, at the moment of modulation, you have to trick your audiences ear into thinking it could be in either key.
We do this by a chord known as a pivot chord. A pivot chord is a chord tat exists in both keys.
By arriving at the pivot chord in your starting key, and then using it as a pivot to take yourself in the direction of the new key, you can guide the audience’s ear, through the modulation, into the new key.
It is easy to modulate between closely related keys as closely related keys will have more chords that exist in both keys.
That means you have more flexibility in choosing which chord to pivot your new key.
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.
The chords that exist in both keys are C major, E minor, G major, A minor. Any of these chords could be used as a pivot chord.