The Wonders of the Circle of Fifths

If you play music for a while, you might have realized by now, that the phenomenon of music is governed by physics and mathematics. I should say that “Music is the most beautiful form of MATH!"

WAAIIITT!! Are you really gonna skip this blog just because I say, MATH??

Fine, fine, I won’t say that word anymore. GEEZ…

However you want to deny it, the most beautiful things that we experience in this universe contains patterns that repeat themselves. For example, do you know that a person with a face that is symmetrical and has an attribute of the Golden Ratio, will be seen to be more attractive than people who are not? Well, suit yourself, it’s well documented!

The Golden Ratio itself is a huge topic on its own, that you can dive into and will astonish to no end, WAIT, after this blog though!

All I’m saying is, if you really are curious about what it is that makes music so beautiful, full of bliss and can be all heart-wrenching at the same time, it’s actually easy.

All you have to do is to pay attention to the patterns that emerge.

In music, we have something, a pattern, that acts almost like a golden ratio, and it’s called: The Circle of Fifths!

It’s basically this Diagram right here.

Basically, it’s just a circle that puts all twelve tones in a particular order. And the order is determined by how far they are from each other. How far exactly? They are a perfect fifth away from each other.

Let me show you what it means.

The Circle of Fifths starts with C. And the next note, is a perfect fifth away from C, which is G.

This is how you count it.

D is a second away,

E is a third away,

F is a fourth away,

and finally G is a fifth away.

Another way to find it is by looking for the 5th note in a C major scale. Which, again, is G.

For now, don’t worry about why it is called a Perfect fifth. I’m probably gonna talk about it in the next blog. But that’s basically how you find a perfect fifth.

So, we got C, and G.

And now if we want to find the next note in the Circle of Fifth, we should just look at the fifth note in G major scale, which is D.

How about the next note?

Just look at the, fifth note in D major scale, which is......... exactly! A.

So, if I continue this pattern, I will eventually finish the circle and end up with all the twelve tones. C, Db, D, Eb, E, F, Gb, G, Ab, A, Bb, B, C.

That’s the Circle of Fifth! So, what now? What’s so WONDERFUL about it?

Well, let’s take a step back.

The circle of Fifths.

Fifths.

Five.

The number 5 is a really important number in music. The number 5 is responsible for so many things in music, almost like cement that glues the phenomenon of music as we know it.

Let’s starts with the phenomenon of the Harmonic Series.

Harmonic Series

Has it ever occurred to you? That you were trying to practice, but every time you play one particular note, an object in your room starts buzzing. It could be your ceiling, it could be your music stand, or it could be the phone mount right here.

But notice! The object only makes that buzz when you play that very specific note. It’s so annoying, isn’t it?

Well, you just experienced the phenomenon of the harmonic series. The object is basically in perfect alignment in the harmonic series overtones of that particular note.

Harmonic series is basically a sequence of notes that is produced by a single fundamental note.

If the fundamental note is C, these are the harmonic series.

<INFO>

Now watch:

Did you hear that? You can actually hear G. How is it possible? That’s because this G is in the harmonic series of this C.

But what does it have to do with the number 5? Well, look at this harmonic series of C.

The first harmonic or the fundamental is, of course, C.

The second harmonic is, the C one octave above the fundamental.

But look at the next harmonic.

It’s G! Which happens to be a fifth away from C.

This is actually not a coincidence.

Do you know that back in the day, people used to tune their piano based on pure fifth and octave intervals?

That’s partly because of the basic understanding of the harmonic series. They basically try to tune, C and G, to sound almost like one-note when they are played together.

Because if C and G tuned in the perfect 5th away from each other, it would create this beautiful sonority. Why, because each note is actually reinforcing each other.

Another cool fact.

Sometimes when you listen to singers, and they happened to sing in pure perfect fifths, you could start hearing notes that they don’t actually sing.

Mysterious, right? Guess what are notes that you will likely hear?

Correct! Those that are in the harmonic series overtones. It’s absolutely mind-blowing! But is that it? Not so fast chief!

Let’s look at the first 5 notes in the harmonic series.

<C - G - E>

What do you get? A glorious C major chord.

That’s probably why a major chord is perceived to be a bright and happy chord. Because this is the harmony that nature itself plays for us. The notes in a major chord are vibrating and reinforcing each other every time they are played together. Not only within the instruments, but they also vibrate and reinforce every object in the room that is in the same frequency.

But is that all? uh-uh!

The circle of fifths is also an extremely useful diagram, that contains a lot of informations. If, only we knew how to find it!

The most well-known fact:

That the circle of fifth arrange keys, from the one with 0 sharp or flat to those with the most sharps or flats, in order.

Start with C, C has 0 Sharp or Flat.

G, has 1 Sharp.

D, has 2 sharps.

A, has 3 sharps.

And so on, all the way to, technically E# with a whooping 11 sharps.

But it’s really not practical to write a piece of music in E# Major with 11 sharps,

where you can easily call it F Major with 1 cute flat! This equivalent is called Enharmonic.

Enharmonic

So, if you go clockwise you get to see the order of keys with sharps. If you go counterclockwise, you get the order of keys with flats.

Again, start with C, it has 0 Sharp and Flat.

F, has 1 flat.

Bb, has 2 flats, and so on and so forth.

But this time let’s stop at Gb with 6 flats.

But, it’s still not the end of the story!

Let’s look at the sharps and flats that exist in each key!

G, has F#.

D, has F# and C#.

A, has F#, C#, and G#.

Well, have you seen a pattern here?

<Highlight the Accidental in the Circle>

The additional sharps of the next key are also embedded in the circle of fifths.

Can you guess the additional sharp in the key of E? Sure enough, it’s a perfect fifth away from G#, which is D#.

And so on and so forth.

What about the flat? You can guess it by now, right? That the order of the flat, is for sure hidden inside as well.

Let’s see.

F, has Bb.

Bb, has Bb and Eb,

Eb, has Bb, Eb, and Ab.

And the pattern continues.

The difference is that it moves counterclockwise.

Huft, if this is not fascinating enough, I don’t know what is!

But, there is more. And you wanna see this. Every major scale is actually grouped together in the circle of fifth, in a very profound way.

Take the most obvious one, the C major scale: The notes in C major scale is actually grouped together starting from F all the way to B. But they are not just grouped randomly. If you pay closer attention, the quality of the triad in C major scale is actually also cleverly grouped. According to whether they are major, minor, or diminished.

In C major scale.

F, C, and G will create major triads.

While D, A, and E create minor triads.

And B, the lonesome one at the end of the chain, is a diminished triad.

Sure, you can use this, for any other major scale.

Let’s pick Bb major scale, as an example. To find the notes on Bb Major scale, you can simply go back one step from Bb, which is Eb, and go forward through the next 6 notes ahead. So, it extends from Eb all the way to A, going clockwise. And that will be the notes in Bb Major scale.

The first 3 triads will be major.

The next 3 triads will be minor.

And the last one is diminished.

The circle of fifths is also very useful to determine, how far each Key is, harmonically from each other. Let me ask you this question. Which key is the closest from the key of C?

The key of G or the key B.

Let’s think about it for a second. Don't even think about scrolling down that fast! ;)

The right answer is: G.

The key of G is harmonically closer to C than the key of B. It’s because C has more common notes with G than it has with B.

The only different note between the key of C and

G is F#.

Compared to B that has C#, D#, F#, G# and A#.

5 notes difference versus 1 note difference. So, the key of G is more closely related to C than the key of B. Even though C and B look closer together on the keyboard.

There is another piece of information that you can squeeze from the Circle of Fifths.

Tritone

And that is an exclusive TRITONE relationship between two notes in the Circle of Fifths. Tritone!!! Woww… This is also an eerily fascinating interval. It’s a very unstable yet beautiful interval.

It’s one of the only two symmetrical intervals ever to exist.

Tritone is what makes the harmonic tension-resolution possible.

Think of a tritone like a Sail in harmony. It’s something that moves and also steers the harmony in the direction that you desire. But, we’re gonna talk about it in a future video. Because it’s just too fascinating!

So, how exactly do we find a Tritone pair in the circle of fifths? It’s very easy!

Just look at the note across the note in question.

For example: key of C.

To find the tritone interval of C, just look at the note right across the key of C in the circle. And you will find F#.

Consider this diagram:

How about, hmm, Eb? Well, just look at the note right across the key of Eb. Which is A. Pretty easy, right?

Trust me, to know this is super useful in understanding harmony moving forward. So this trick is a very handy one.

Let’s recap a little bit.

We learned earlier how the harmonic series plays out in our universe and how it is the foundation of harmony in the physics level.

We also have learned how perfect fifths used to be the way people tune their instruments in the past.

After that, we have at least 4 different kinds of information that we can squeeze out of the Circle of Fifths.

From the order of the numbers of the accidentals.

To the order of the accidentals itself.

To how you can find major scale and the quality of the triads - grouped together.

And last we get to find tritone pairs, all using this miraculous Circle of Fifths.

So, what else can we get out of this? Are these all we have. No!

There’s at least one more miracle that you can find in the circle of fifths, which is the ii-V-I progression.

ii-V-I progression

: The foundation of harmony at the musical level.

You actually hear the ii-V-I progression and its derivatives all the time. Across all genres, from classical music, jazz music, to popular music. ii-V-I progression is basically just a movement of chords, whose roots descend in fifth. Therefore it could be represented by looking at the Circle of Fifths in the counterclockwise direction.

Just look at a Turnaround on the famous Chopin Nocturne Op.9 no.2:

Look at the highlighted chords. Those are the ones with the ii-V-I progression or its derivatives.

Or on one of the most beloved jazz standards of all time: All the things you are.

But as I said, it’s also used extensively in pop music. Even though at a decreasing pace.

Let's’ take a look at the chorus of Robbie Williams’ song “Better Man.”

One of the most amazing derivations of ii-V-I progression is: The extended Dominant. Where you can pick any starting chord and any target chord as you like, and use the Circle of Fifths to fill the gaps with a bunch of dominant chords in between these two chords of your choice.

So let’s say you want to start with Eb and you want to arrive at Cmaj7. All you have to do is to spot Eb in the circle of fifths, and go down the path, until you arrive at your target chord, which is C maj7.

Isn’t that cool?

Guys, I'm telling you the Circle of Fifths is an extremely powerful force in music. I will totally vote this to be included as one of the wonders of the world. Because it’s just too fascinating to be ignored.

And I’m glad I get to share these with all of you. And thank you really for staying this far with me. Now I want to turn it over to you. Which of these 7 wonders of the Circle of Fifths, that you have never heard before?

Is it the fact people use to tune their instruments in pure fifths?

Or the practical use of ii-V-I progression?

Let me know by leaving a comment below.

I’m sure you get a fresh new look at the Circle of Fifths, that you might not have already known. Stay tuned! Because in the next video, I’m gonna tell you why the Circle of Fifths actually, SUCKS!! Oh no.

But for now.

Thank you for reading until the end, and see you in the next blog!