Music Theory – Understanding The Circle of Fifths

– Hi. In this session we’re going to talk about the circle of fifths. Now the circle of fifths is a really wonderful thing that helps us to understand all of our keys. It’s going to tell us about every single major key that we need to know about, every single minor key, and it’s going to tell us exactly what the key signatures are for every key. So it’s really worth it’s weight in gold. As you look at a circle of fifths, you may think it all looks far too complicated.

But hopefully, if we just go through it step by step, you’ll begin to see that there’s great value in this, because the only alternative is to try and remember exactly which sharps and flats you need in every single key.

And by the time you’ve done 12 major keys, 12 harmonic minor keys and 12 melodic minor keys, it’s all a bit too much really. So the circle of fifths is a way of getting us there accurately and quickly. And once you see how the system works, you realise that you don’t have to memorise the circle of fifths, you just have to remember how to put it together. So bear with me while we start constructing the circle of fifths and I’ll explain how it unfolds as we go. Now the first thing to say about the circle of fifths is that in fact it’s not one circle, it’s three circles. One of our circles is going to tell us about major keys. Another circle is going to tell us about minor keys and the third circle is going to tell us which sharps or which flats we need in any of those major or minor keys.

And we’ll see why it’s called the circle of fifths very soon. First of all, we’re going to start with the middle of the three circles. And I’m going to start by putting C at the top of the circle. C for C major because C major is the key that has no sharps and no flats. So it does this. And it follows a pattern for major scales that we’ve learned about in earlier sessions. It goes tone, tone, semitone, tone, tone, tone, semitone. And that’s how we know that C major has got no sharps and no flats because as you work out tone, tone, semitone, tone, tone, tone, semitone, you realise that you don’t need any sharps or flats. So C major is our first major key. No sharps, no flats. What we’re going to do to find a major key that comes after that is we’re going to count up five in just the same way that we did intervals. So if I count C as number one, C, D, E, F, G. So in other words, G is a fifth above C. You might just be beginning to see why this is called the circle of fifths. And I’m going to put G over here. Now as this circle unfolds, you’ll discover that we’re going to have sharp keys on this side of the circle and we’re going to have flat keys on this side of the circle. So C major has got no sharps. G major, which is a fifth above C has got one sharp. This is how it goes and if I go tone, tone and so on according to the major scale pattern, you’ll realise that we’ve got tone, tone, semitone, tone, tone, tone, semitone And you can see on the keyboard that we’ve had to use a black note to make the tones and semitones go. So I’ve used one sharp, it’s F-sharp but we’ll come back to that one later. So C major’s got no sharps. G major, a fifth higher than C, has got one sharp. Okay, let’s carry on. Let’s go up another fifth from G. So G, A, B, C, D. So D major is the next key and if C major’s got no sharps, G major’s got one sharp, D major is going to have two sharps. If I start on D and I go tone, tone, semitone, tone, tone, tone, semitone. You can see that I’ve ended up with two sharps. C major’s got no sharps, G major’s got one sharp, D major’s got two sharps. Hopefully you’re beginning to see how this works. Let’s go up a fifth from D. D, E, F, G, A. So the next key is A major. And A major has three sharps. So you might have noticed there we’ve got these three sharps. Tone, tone, semitone, tone, tone, tone, semitone. Okay, let’s go up another fifth from A major. A, B, C, D, E. So E major is going to have four sharps. Let’s carry on a bit further. E, F, G, A, B. B major is going to have five sharps. Up we go another fifth. B, C, D, E, F. Now I’m going to tell you for nothing at the moment that this isn’t F major. It’s going to be F-sharp major. We’ll come back later to see why that is. Let’s go up another fifth for now. It doesn’t matter that it’s F-sharp or F-flat or anything else for now, it’s F something. So let’s count up a fifth from F. F, G, A, B, C. So this brings us back to C, but it can’t be C major because this was C major up here. This is going to be C-sharp major. And that’s as far as we need to go because by the time you get to C-sharp, believe it or not, everything is sharp. If I start on C-sharp, and I give you a pattern of tones and semitones that we know for the major scale, you’ll find that we’ve got C-sharp, D-sharp, E-sharp, F-sharp, G-sharp, A-sharp, B-sharp, C-sharp. So by the time everything is sharp, there’s no need to go any further. So C major’s got no sharps, G major’s got one sharp, D major’s got two sharps, A major’s got three sharps, E major’s got four sharps, B major’s got five sharps, F-sharp major’s got six sharps and C-sharp major has got seven sharps. And by the time you’ve got to seven, everything’s sharp. So you see we just went up in fifths, starting at C until we came back to C. Now on the left hand side of the circle of fifths, we’re going to discover the keys that use flats. And this time, we’re going to go down in fifths. Now going down in fifths is actually the same as going up in fourths. We’ll have a little think about that in a moment. So if you prefer to go up in fourths, feel free to do that, but as it’s a circle of fifths, for now we’ll count down in fifths. So we’re going to start with C and we’re going to go down. C, B, A, G, F. So F is a fifth below C. And just in case counting backwards is too much and you want to count up in fourths, you’ll see what I mean if I go C, D, E, F. So you can count down a fifth from C and get to F or you can count up a fourth and get to F. Now F major has got one flat. If I start on F and I do the pattern of tones and semitones that we know for a major scale I get this. Tone, tone, semitone, tone, tone, tone, semitone. So in other words, I get F, G, A, B-flat, C, D, E, F. So F major has got one flat. Let’s go down another fifth or go up a fourth if you prefer. F, E, D, C, B. So the next key we’re going to look at is B. Now again for now I’m just going to tell you for nothing that this isn’t B major, it’s B-flat major. It couldn’t really be B major because we already have B major over here. And we learnt that B major’s got five sharps. B-flat major’s got two flats, but don’t worry, I will come back and explain why it’s B-flat later. Let’s carry on going down in fifths. So starting with B, B, A, G, F, E. Everything from now on is going to be a flat key. So it’s E-flat major. F major’s got one flat. B-flat major’s got two flats. E-flat major’s got three flats. We did F major. B-flat with two flats. Tone, tone, semitone, tone, tone, tone, semitone. E-flat major has got three flats. Tone, tone, semitone, tone, tone, tone, semitone. And just in case somebody was looking at that thinking, “That looks as is if it’s got four flats,” one, two, three four, that’s only because you’ve got E-flat at the bottom and E-flat at the top. So that only counts as one flat. There’s one E-flat, even if we’ve got two of them. So those are your three flats. Okay, let’s carry on going down in fifths. We’re on E-flat. Let’s go down another fifth. E, D, C, B, A. So that takes us onto A-flat. So A-flat major will have four flats. Let’s go down another fifth. A, G, F, E, D. D-flat major will have five flats. Let’s go down another fifth. D, C, B, A, G. That tells us that G-flat major has got six flats. And if I go down another fifth, G, F, E, D, C. I come to C-flat major and C-flat major has got seven flats. And by the time I’ve got seven flats, everything is flat so I can’t go any further at all. So I get C-flat, D-flat, E-flat, F-flat, G-flat, A-flat, B-flat, C-flat. And this gives me all of the major scales, all the major scales with sharps on the right hand side. All the major scales with flats on the left hand side. And you notice that we started with C at the top with no sharps, no flats. C-sharp at the bottom where everything is sharp, seven sharps, and C-flat at the bottom here, where everything is flat, seven flats. So that gives me all of the major keys. Now that’s all very well, but I can now tell us that we’ve got keys like A major, must have three sharps. One, two, three. But it’s not much use if you don’t know what those three sharps are. So you could go through what we’ve been doing on the keyboard, going tone, tone, semitone and working it all out. But the circle of fifths is going to show us a quicker route. So let’s go into another colour now and we’re going to do the outer circle. And the outer circle is the circle that tells us which sharps or which flats we need in a particular key. And this is how it works on the sharp side. On the sharp side of the circle of fifths, just ask yourself what is the seventh note of that scale? So if we were in G major, what’s the seventh note? G, A, B, C, D, E, F. So in other words, G major’s got one sharp and that sharp is F-sharp. Now of course, if you think about this, you don’t actually have to count all the way up from one to seven because G, A, B, C, D, E, F, G. So G is number one and G is number eight. So if G is number eight then one back from that is going to be number seven. So you only have to go one back from this key to find that the seventh degree of the scale is F-sharp. So that tells us that in the scale of G major you have to play an F-sharp. Let’s just try that. G, A, B, C, D, E, F-sharp, G. And that puts all our tones and semitones in the right place. Okay, let’s go on. What’s the seventh note in D major? Well, you can count up from D. D, E, F, G, A, B, C. Or you can simply say well D’s number eight, so C must be number seven. So that must mean that it’s got C-sharp. So this is how it works. D major is the key that has two sharps. The first sharp is F-sharp because we had that before, and now we’ve added C-sharp. And where this is also very useful is if you have to write a key signature, it tells you that you must put the sharps and the flats in the right order. Because F-sharp is the first sharp we always put that one first in a key signature and we always put C-sharp as the second one. And you can see how the circle of fifths tells us why that’s the case. Okay, let’s go on. What’s the seventh note in A major? Well the seventh note in A major is G. So in other words, we need a G-sharp there and we now know that A major’s got three sharps and those three sharps are F-sharp, C-sharp and G-sharp. And that’s the order that you put them in the key signature. F-sharp first, C-sharp second, G-sharp third. Let’s move on. The seventh note in E major. Well, if we’re counting one back from E, it must be D. So in E major, you’ve got D-sharp going on the end of the previous sharps. F-sharp, C-sharp, G-sharp, D-sharp. For B major, well, the seventh note there must be A-sharp. So B major’s got five sharps. F-sharp, C-sharp, G-sharp, D-sharp, A-sharp. Let’s just check it out. Here’s B major. B, C-sharp, D-sharp, E, F-sharp, G-sharp, A-sharp, B. So you can see it’s got the five sharps that we’ve identified on the circle of fifths. The seventh note in, F-sharp major must be E-sharp. So F-sharp major’s got six sharps, F-sharp, C-sharp, G-sharp, D-sharp, A-sharp and E-sharp. And the seventh note in C-sharp major is B-sharp. And so there’s C-sharp major with its seven sharps, which means that every single note is sharp. Okay, so do you remember how to do that then? For the major keys, we started with C and we went up in fifths to get the sharp keys. To get the flat keys, we went down in fifths. To get the sharps for the key signatures on the sharp side, we simply said what’s the seventh note of each of these scales so that we can add on the new sharp each time? When it comes to discovering the flats, this time we have to find the fourth note of the scale. The fourth degree of the scale. So seven for the sharps, but four for the flats. Okay, well in F major, what’s the fourth note? F, G, A, B. And because we’re dealing with flats, we’re not going to sharpen anything now. We’ve going to flatten it. So F major has got a key signature of B-flat. What’s the fourth note of B-flat major? B, C, D, E. So that must be E-flat. So B-flat major has two flats, B-flat and E-flat. What’s the fourth note of E-flat major? E, F, G, A. So that’s A-flat. The fourth note of A-flat major. A, B, C, D. So that’s D-flat. The fourth note of D-flat major. D, E, F, G. G-flat. The fourth note of G-flat major. G, A, B, C. C-flat. And the fourth note of C-flat major, C, D, E, F, gives us F-flat. So you can now see the key signatures for every single major scale. So if you want to know how many sharps or flats there are in E major for example, there’s E major. You can say it’s got one, two, three, four sharps. You can tell us what those sharps are. F-sharp, C-sharp, G-sharp and D-sharp. And you can tell us that that’s the order in which those sharps have to come in the key signature. If you wanted to know what the key signature for D-flat major is, you’d find D-flat over here and you’d immediately see that it has five flats. One, two, three, four, five. And you can see what those flats are and you can see the order that you need to put them in the key signature. B-flat, E-flat, A-flat, D-flat, G-flat. So hopefully you’re beginning to see why the circle of fifths is such a valuable tool. It’s also already answering a question we’ve posed earlier, because we said why is this F-sharp major and not F major? Well, back here we introduced F-sharp. And once you’ve introduced F-sharp on this outer ring, you’re telling us that from this point onwards every F you come across is F-sharp. It never becomes F-natural again because it became F-sharp there and it stays F-sharp all the way after that. Because you introduce C-sharp there, then by the time we come around here, this can’t be C major. It will have to be C-sharp major. And the same thing is happening on the flat side. We introduced a B-flat there, so that has to be B-flat major and so on. If you like patterns, you might be beginning to discover a few patterns as well. Like for example, C, G, D, A. You might also notice that the flat for F major is the next key, B-flat major. The flat for B-flat major, E-flat, is the next key, E-flat major and so on. Now all we’ve got to do next is to work out how to do the minor keys. And to do the minor keys you have to count down a third from each of the major keys. Okay, and so we counted up in fifths for the sharp major keys. We counted down in fifths for the flat major keys. We said what’s the seventh note in the scale to get the sharps? We said what’s the fourth note of the scale to get the flats? Now let’s count down three for the minors. So count down three from C. C, B, A. So A minor is called the relative minor of C major. They’re related to each other because they share the same key signature. The key signature of A minor is just the same as C major. No sharps, no flats. If you want to write a harmonic scale or a melodic scale, there are things you’ve got to do to that. But the key signature is the same as it is for C major. If I go down three from G, I come to E minor. So E minor, like G major, has a key signature of F-sharp. E minor is the relative minor of G major. Or you could say G major is the relative major of E minor. Let’s whiz on and just count down in thirds. B is a third below D, so B minor is related to D major, and they both have F-sharp and C-sharp. A third down from A is F, but remember what we said earlier. Because F-sharp is there, this will have to be F-sharp minor. A third down from E is C. Remember, C-sharp here. It’s going to have to be C-sharp minor. A third down from B will be G, but G-sharp is here so it’s G-sharp minor. A third down from F-sharp is going to be D. But it’s going to be D-sharp because we had D-sharp there. A third down from C is A, but it needs to be A-sharp minor because we had A-sharp there. And we do just the same on the flat side. So a third down from F is D. A third down from B-flat is G. A third down from E-flat is C. A third down from A-flat is F. A third down from D-flat is B, but be careful because it must be B-flat minor. A third down from G-flat must be E-flat minor. And a third down from C-flat is A-flat minor. That’s the circle of fifths. I’ve colour coded it so you can see it clearly, so the black circle in the middle there, all your major keys. Start with C, go up in fifths for the majors and the sharps. Go down in fifths for the majors and the flats. To get the key signature all in red on this diagram, seventh degree of each scale for the sharps. Fourth degree of each scale for the flats. Count down three and you get all the relative minors. So any minor has a relative major, any major has a relative minor. A-flat major and F minor, for example, both share the same key signature, B-flat, E-flat, A-flat and D-flat. And I hope at the end of all that you can see how much value we have in this thing we call the circle of fifths. Good luck using that.

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