It's the Circle of Fifths
It's the Circle of Fifths
And it moves us all...
Look how thrilled that lion is to talk about the Circle of Fifths.
In my last post, I talked about the Perfect Octave and Perfect Fifth, and how the 12-tone scale was derived. I’d highly suggest reading that one before graduating to this magic circle.
To recap, when you stack Perfect Fifths on top of each other, you move twelve steps, before ultimately ending up back where you began.
In other words, that journey to find all twelve notes makes a circle.
And not just any circle, THE CIRCLE:
Notice the 12 slices? Each stop shows the relationship between notes. It also reveals the difference and similarity between “keys” (closer are more related).
Changing “Keys”
A key is another word for a musical scale. Aka a tonality. It’s what people mean when they say, the song’s in C major. When you change keys (modulation), it’s easier to move one step forward (or backward) on the circle, because they are more related. Related meaning more similar.
More specifically, the keys of C and G have only one note that’s different from each other.
G and D have only one note that’s different from each other. (See how they’re neighbors?)
C and D have two notes that are different from each other, because they’re two stops away from each other on the circle. Can you guess how many notes are different between the keys of C major and A major? Answer.
But wait. What happens if we go backwards on the clock?
The Perfect Fourth (4:3 Ratio)
There’s one final “perfect” interval to consider. We have the octave, the fifth, and now may the fourth be with you.
The reason why these intervals are called perfect, is that their ratios are simple. They’re more in that Pythagorean vibe. The other notes… well they have to fudge the numbers a bit to make them all fit. (Turns out the universe isn’t perfect. 😔)
But the people making early music theory are trying to find God in numbers (Pythagoras) or in all things (early Catholic church). And fancy circles made them feel like there was more order to the universe. Naturally, they built our music system around it. And we still use it today. Not because it’s perfect, but because it’s cultural.
Adding to the “ah-ha” of these math nerds, the Perfect Fourth is the inverse of the Perfect Fifth. Meaning if you go up a Perfect Fifth (C to G), you go down a Perfect Fourth to return (G to C).
So, when you’re going counterclockwise on the Circle of Fifths, it becomes the Circle of Fourths.
C to G is up a Perfect Fifth. G to C is down a Perfect Fourth.
C to D is up two Perfect Fifths. C to Bb is down two Perfect Fourths.
Fun(?) Fact
The Perfect Fourth used to be called the diatessaron, which means “made of four [ingredients].” It also refers to “a harmony of the four [Christian] Gospels edited and arranged into a single connected narrative.” I think that help shows where the music theory’s creators heads were at.
A Solar System of Music
The movements of the notes are related to the movements of the planets. At the same time as the development of music theory, geocentrism was in vogue. The Earth was the center of the universe.
The math looked perfect at the time. But as we got better telescopes, we realized we had to fudge the numbers… a bit… to make it all work. Later, scientists accepted that the cleaner model of revolving around the sun was accurate. But music theorists didn’t get the memo. We’re still fudging the numbers. And that’s okay, because music is cultural.
Sharps and Flats
Have you heard of notes like F# (f sharp)? Those are the black keys on the keyboard.
But when you do the legit Pythagorean math, notes like F# (f sharp) and Gb (g flat) shouldn’t be the same note. They’re a liiiiitle different. So musicians treated them that way for quite awhile. It was all cool if you were playing solo, but as people played music in ensembles, orchestras and big groups, they realized it’d be nice to fudge the numbers a bit and simplify. It helps things sound a bit more together.
So they created a concept. Ready for it? It’s a spicy word. Enharmonic.
Ooo ahh.
That’s the word for making notes equivalent.
Here’s a more accurate keyboard to chew on:
Put another way, without fudging the numbers, without this concept of enharmonic, the Circle of Fifths isn’t a great circle. It’s a spiral:
It just goes off and off and off into oblivion. But like the geocentric universe, we fudge the numbers, make the math work, and are amazed at the beauty of the universe (…that we created).
Next Steps
That’s enough talking about a circle. We can dig into keys and chord changes and modulation in a future post.
But first, let’s hear the circle in action. Don’t worry about the vocab like tritone subs and secondary dominants. We’ll get to that.
Just listen to how they make the circle dance: