The Circle of Fifths made clear

Imagine if we could find a way to visually represent the all the different
keys 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 in
each key. We could even use this representation as a
map to find our route between different keys. Luckily for us, someone has already done just
that. 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 do
with 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 pressure
changes in the air which our ears pick up and interpret as sound. If the violinist were to play the note A above
middle C, the string would vibrate at 440 times per
second. If he were to play the A an octave above that, the string vibrates 880 times per second, precisely twice the number of vibrations per
second as it did before. Another octave above that, and the string vibrates at 1760 vibrations
per second, again twice the number of vibrations per second
as it did on the previous A and so on. Therefore it is not surprising that someone
with a mathematical mind like Pythagoras might think of turning his hand to music as
well. Having had such success with triangles, when Pythagoras turned his attention to music, he decided that a circle might be the best
shape to use. This circle became known as the circle of
5ths. If you count the number of semi-tones in an
octave, you’ll find that there are 12 in all, semi-tones includes all the black notes on
the piano too. What Pythagoras did was to lay these twelve
notes around the circle like a clock in a special order. 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 positions on his
circle is 100 cents further round the circle from
the previous half tone. This division into semi-tones and the creation
of the circle of fifths lies at the very foundation of western music
theory. Because the circle of fifths acts as a sort
of roadmap for western music, it is incredibly useful to refer to when trying
to work out things like, what key you are in. If you are in a major key it helps you find
the relative minor key and visa versa. It tells you what chords are available in
each key. It helps you to transpose your music into
a 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 clockwise
direction, the next note you encounter will be a fifth
above the note before it. So for example, starting at the 12 o’ clock
position, we have C. Move around to the one o’ clock position and
we find G. In the key of C, G is the 5th note of the
scale. Move round again to the 2 o’ clock position
and we find D. Again D is the 5th note of the G major scale. A more in depth explanation of how the different
scales work and how to find the different degrees of each
scale, 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 find
out 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’ clock
position and so on all the way around to the key of C# at the
7 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 flats
in their key signatures. If we go back to C at our 0 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 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 round
the 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 the
circle, we find that we will stop at the 5 o’ clock
position. This means that the 3 keys at the bottom of
the 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 our
key. 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 key
signature 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 Fifths
tells 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 key
of E major, we know from E’s position on the circle at
4 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’ 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 has 4 sharps and they
are: F#, C#, G# and D#. That’s all well and good 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 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’ clock
position 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 stop
there. Remember, in this podcast, we’re talking about
chords. This circle of Fifths tells us which chord
triads are available to us in each key. So if we are composing a song in the key of
C, we can easily see which chords we can include
in our song. Here’s how: Looking at C on the circle, well we know that in the key of C major, the
chord, C major will be one of the chords available. Now we look at the 2 chords on either side
of C on the circle, these are F and G so F C and G, will be the major chords available in the
key of C. Carrying on round the circle in a clockwise
direction, the next 3 chords, D, A and E will give us all the minor chords available
in the key of C. The 7th and final available chord in the key
of C is the diminished chord of B. So if we now lay those out in pitch order
rather than 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 all made up of notes which
exist in the C major scale, you will notice there are no sharps or flats
in these chords as there are no sharps or flats in the scale
of C major. If we look at another key, say the next key round circle, G major, we simply use the same method to find which
chords are available to us in G major as well. Firstly the major chords which are found by taking the G major chord
and the 2 chords surrounding it on the circle, C major and D major, then carrying on around the circle we get
the 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 chords
available in whichever key you want to write your song in. So the circle of Fifths helps you to 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 come your vocal artists and you suddenly discover that C is too low
for them. They would have preferred it if you had written
your 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 on
this one after all as 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 on 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 example would become A as A is 4 steps clockwise around the circle
from F. A G chord would become B and so on. Exactly 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 by the
same distance. Voila in 5 minutes you’ve transposed all the
chords in your song. Talking of transposition, what about changing key in the middle of your
song? To add interest and variety to your composition. Well there are two ways in which the circle
can help you modulate between different keys 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 closer
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 in its scale as
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 key’s relative
minor is written with a small letter on the inside
of 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 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 songwriters? Because it means that modulating between C
major 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 the
2 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 major
key 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 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, 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 one
sharp in it and C has no sharps in it, they share all the same notes, apart from
one: F# which exists in the key of G but not in the key of C. In order to modulate cleanly and musically
between keys in the middle of your song, at the moment of modulation you have to trick your audience’s ear into
thinking 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 both
keys. By arriving at the pivot chord in your starting
key and then using it as a pivot to take yourself
off 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 in
more detail in the podcast extra but for now, I’m going to show you how to use the circle
of fifths to find these pivot chords. This is done by using the circle to find which
chords are available in your starting key as we described before, then finding which chords are available in
your new key and seeing which chords are identical in both
keys. It is easier to modulate between closely related
keys 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 in
both keys: C major, E minor, G major and A minor. Therefore any of these chords could be used
as your pivot chord: In the following example, I’m going to use the A minor chords as my
pivot chord. Again I go into this in more detail in the
podcast 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 about
chords and harmonies called “Striking a Chord” The full podcast can be heard at and go to Podcast number 1. You can also gain free access to the podcast
extra material by going to this webpage and clicking on the subscribe
button on the right hand side of the page.

100 thoughts on “The Circle of Fifths made clear”

  1. Even though you illustrated your point well, the song at the end modulates from F Major to C major not C major to G Major. I think your keyboard may have been transposed.

  2. I knew all these things of the circle of fifths, but gradually the memory fades since I haven't done music for a long while. So whenever I saw that there is a video about the circle of fifths I checked it out, but never found one that really went through it all in a good and concise way, until now. This video does it, very nicely. Thanks!

  3. Great explanation, congrats! What's the name of the app used to make this video animation? All the best!

  4. Great video! But to make one think clear, like Plato and Aristotle.Pythagoras was a student at the Temple in man (mystery school), in Alexandria, Ancient Egypt/Kemet. Where the teachings were Alchemy, Matchematics, Science, Astrology, Medicine etc and Music!

  5. Could someone please explain why for a E major did you start at eleven (F) to determine what the sharps are, and why for A flat you start at twelve ?

  6. This is the absolute BEST and most thorough description/definition/explanation of the Circle of Fifths! Thanks so much!

  7. Bravo! Awesome broad demonstration of what can be done with the Circle of Fifths and where it came from. And even the song at the end is not just an entertaining example, but also very educational in itself, exampling not just how to modulate on a pivot chord but mentions a good chord progression ie D7, and the thinking behind wanting to modulate ie I want to entertain my audience with variety, and the thinking behind communicating to the audience clearly that one has modulated ie play a new melody in the modulated key so everybody knows that the compostion has now definitely modulated, and then go back to playing the original melody in the now firmly modulated key. Mr Newman is, in my imagination, what Mr Haydn would have been like if he were alive today and providing us such wonderful insight as this on YouTube. Well done!

  8. I've watched quite a few Circle of Fifths videos. This one is magnitudes better than any other–dare I say the best.

  9. An easier way to remember the order of sharps goes : Father Charles Goes Down And Ends Battle, and for flats, the opposite: Battle Ends And Down Goes Charles Father

  10. Every time he comes in I feel like he's gonna tell me about construction work

    But is still better at explaining the circle of fifths unlike any of one I've ever seen
    Seriously though, thanks cause jesus this is difficult for me

  11. Thank you sooomuch. This is the clearest explanation I have ever heard of this very technical music theory… thank you again..

  12. Change the arrangement of keys so that F is at one o'clock and the Circle of Fifths can teach you everything you need to know about chord progressions in tonal music. For 300 years the circle has always been backwards and just about key signatures. There is more to it than that.

  13. Wrong title it should be Circle of 5ths made confusing . I do not care about sound being mathematical whats that go to do with the video. NOTHING

    F does not have one flat in it ie b flat it has 5. I hate the dam circle of 5th its contradictory and idiot teachers never explain it properly. For example if you use C major scale and count 6 notes ( no one tells u this but what the hell, music teachers are tossers right and expect you to know. No wonder Elvis failed music ). C G D A E. Its logical right C major has no sharps or flats.

    However if you do the same for flats it does not work. Its nuts i know it really does not. F Bb, Eb Ab Db Gb. Nope the nutters say ur wrong. It only has one flat. I SAY WHERE WHERE DOES IT SAY THAT, IT SAYS IT HAS 5 FLATS. i am going to anti clockwise as was shown lol . I hate it the dam thinking its designed to confuse people and only let OTHERS IN THE KNOW. The fact it takes so long to teach you this, it has major problems.

    Furthermore you cannot use the 5ths concept to determined your notes in the scale for F. It never shows this in the video its assumed you know duh. To find the Fbs , you are supposed to guess, iie f, e, d, c, b. Then you have to try the whole thing again and It DOES NOT WORK. Eb, d, c b. Again it does not work. What a crazy system. If you could go from F and to get Eb then the chart again is useless, as it DOES NOT SHOW WHAT THE FLATS ARE. It is a bit like counting on your fingers and this crap is not needed.

    Please get another job and stop posting these stupid videos your note very good at it.

  14. so when did equal temperament come into play? i dont think it was back in the greeks day? A=440lp , i am sure a violinist would tell you the sharp and flat keys are not the same, only a pianist old fashioned thinking and teaching

  15. I hate people who understand so easily things that I find impossible. HULK MUST SMASH. I'm going to have to review this video thousands of times and hope a little bit of the knowledge falls off into my brain each time.

  16. I'm missing one thing. At 6:47 he starts to explain how to get the sharps and flats in the key. We start at 11 for E and 5 for Aflat but why. I'm not seeing a correlation with the key and starting points so how would I figure out other keys?

  17. Does A-440 mean 440 vibrations/sec? Isn't it 440 Hz? i.e. Does Hz relate to seconds that way? I'm not sure. Please advise.

  18. Thank's , this really is a must try and learn fully, for any muso!! a lot of sound knowledge
    here……..,never could get my head around this, ever … just starting to now !

  19. i'm sorry to ask this silly question but, why I can't get 7 sharps with C# ? actually i don't see the mathematical possibility of having 7 sharps in 12 successive keys in one octave. max i can count is 6, which is correct on F#. please help me out of this circle. Thanks a lot !

  20. You forgot to say that, after putting the relative minor chords in the inner part of the circle, the three minor chords below the three major chords of the key are exactly the minor chords of that key. E.g. in C major, you have F major (one position to the left in the circle) and G major (one position to the right). Right below them you'll have A minor (below C), D minor (below F) and E minor (below G), the three minor chords in the C major key. 😉

  21. I doubt some historical details on Pythagoras, but still the video is awesome, accurate and practical. I especially liked the video of the violin string, and the final song.

  22. Omg I cant believe that from this one video I understand it all😂first time someones explained it properly and well

  23. after 30 years i finally solved the whole misteries about chords in my life with this circle of fifth…thankyou brother…

  24. Thank you for an excellent explanation of the Circle Of Fifths and its many uses. Yes, I knew of the connection between music and mathematics and that cool dude from ancient Greece, the philosopher Pythagoras of the "aware on the hypoteneuese, to ight angled triangles etc etc " fame they tortured us girls who hated math at high school with and preferred music. But I had no idea old Pythagoras also invented the Circle Of Fifths and its principles that form the basis of all Western music. To be honest, I never fully understood it and when my mainly rock musicians band leader kept talking about the 'cents' in the Circle Of Fifths, tuning guitars etc it just made no sense to me. I thought he was talking nonsense and that he really ought to be talking more sense. Glad I know what "cents" he meant, now. I tried to explain that, as musos, we are almost invariably always poor, well most of us, anyways and can't even afford fifty cents for a cheap coffee, let alone 100 cents or whatever the Circle Of Fifths he was raving on about involved, but that, yeah, we might have more sense. He explained that if we knew how the Circle Of Fifths worked and what to do with it, we would definitely have more sense, because we would know what it's "cents" refer to. One frustrated rock muso, desperate to make a lot of noise and have fun doing so said he knew exactly what to do with the Circle Of Fifths and threw the diagram into the trash bin and stormed out. But the rest of us tried to figure it all out, though most, including me, could not make head or tail of it, let alone figure out how to use it, though all wanted to compose original music, alter keys etc, to accommodate annoying vocalists, like me, who need music changed into weird keys musicians hate playing, because it is hard enough working out all the new chords, let alone how to finger them. This explanation was very helpful. It is really quite logical, though my musician friends beg to differ with me on the "logic". Well, I explained that old Pythagoras was no fuckwit, when it came to being intelligent, logical… He was a mathematician and philosopher and, I'd say he probably dabbled in a bit of super cool music, back then, since, in ancient Greece, music was a form of philosophy. Well, actually, it still is nowadays, only we don't think of endless creative hedonism, like music, as a form of philosophy. We call it "art" and that destroys it's true meaning because, when you are hell bent on producing"great art" to sell at great profit, you are no longer focussed on the joys of creativity for enhancing life, or making it more bearable if your life happens to be crap.

  25. Wonderful explanation. Just one small thing I didn't quite understand… what is it that determines where we count from when we are trying to find out how many sharps or flats are in a key.
    You started at 11 for one, and from 4 for the other… And I wasn't clear why?

  26. Very good explanation. Thank you. I"m a harmonica player and your video helped me to get a better understanding of the I-IV-V progression in a standard 12 bar blues.

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