The REMARKABLE Connection Between INTERVALS And The CIRCLE OF FIFTHS
- Have you heard of the circle of fifths?
- Have you heard of intervals?
If you answered yes to one, both, or neither of those questions (hehe), then I have a very interesting connection between the two that I want to share with you.
Normally, the circle of fifths is made by starting from C (*), and writing additional notes by ordering them in ascending fifths (i.e. instead of writing the notes in alphabetical order, we move up by a fifth with each note).
This is all well and good, but something extremely interesting happens when instead of filling in the circle with note names, we fill it in with the name of the interval between that note and C.
- So, instead of starting the circle with C, G, D, and A...
- ...it would start with 1 (unison), P5 (perfect fifth), M2 (major 2nd) and M6 (major sixth).
When we do this, the circle neatly organizes itself into two distinct halves, and the symmetry of these halves will amaze you.
If you want to see exactly what I’m talking about, check out the video below and you’ll be able to see the incredible symmetry of the circle of fifths.
(*) Or any other note, but for simplicity we choose C.
Is this all just a little too complicated for you? If so, check out this basics of music theory eBook if you want to understand these concepts better!
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Video Transcription
Hello, internet so nice to see you! Today, I want to see with you the magic relationship between intervals and the circle of fifths. So let's start immediately let's draw a circle of fifths. What is a circle of fifths? Well, I'm gonna start this way, I'm gonna put the C note up top here, okay, and then I'm going to move on the right as if I was going around the clock. And every time I move one position, I'm gonna go up a fifth step up a perfect fifth.
So C is my starting note. And then I move one step, right, and I go up a perfect fifth. And they've right a G note, which is a perfect fifth higher than C, then I do that again. And the next note is going to be a D, which is a fifth higher, a perfect fifth higher than G, and then after that, I'm going to write A, then E, then B, then F sharp, which is perfect fifth higher than B, I'm going to stop here for a moment.
And we're going to do the other half of the circle by starting again from the top and this time, rather than going up a fifth, I'm going to go down a fifth. Every time I move on the left, I'm doing this just because it's more convenient to do. And of course going up or going down. Perfect fifth is pretty much the same as going up a perfect fourth. Okay, so starting from here and going on the left down a Perfect Fifth from C and F and down a Perfect Fifth from F it's a B flat, and then E flat, A flat, D flat.
And finally the down here, I'm gonna write G flat, which is an harmonically the same as the F sharp but of course, the name is different. And there are some reason to keep the name different. But for now, we don't care about those for us right now, is that the same note? Great, I just wrote the circle of fifths. These is great. When you talk about for instance, the musical keys. Okay, most people will explain the the circle of fifths to you to talk about the musical keys. Why?
Because the key of C major for instance of as no sharp and no flat, the key of G major is one sharp, the key of D major is to sharp the key of A major 3, sharp and so on and so forth. Go in the opposite direction, the key of C major again has no sharps or flats, but the key of F major as one flat, the key of B flat major is two flats, the key of E flat major is three flats, and so on and so forth. This is all nice and good. But it does not have much to do with intervals yet. So I'm going to change my circle of fifths in this way.
Rather than writing this C note here, I'm just gonna write these are letter that stands for root, this is going to be our central note if you want, okay, and then rather than all the other notes, I'm gonna write the interval that that note makes with our root note C. So for instance, the G is the perfect fifth of C, the D is the major second of C, the A is the major sixth of C, and I'm gonna keep going and do the whole trip around.
So the E is a major third, the B is the major seven, the F sharp is the augmented fourth, the other direction, the F is the perfect fourth, the B flat is the minor seventh, which I remind everybody is conventionally written just with a seven, you don't have to put the m in front, the E flat is the minor third, the A flat is the minor sixth, the D flat is the minor second and the G flat is the diminished fifth and again, diminished fifth and augmented fourth are the same interval, it's a tritone.
Now I'm going to delete all the notes and then left only with the intervals. Now I have the circle of fifths of the intervals, not the one of the keys, not the one of the notes, the one of the intervals. What is special about all that? Well, let's see. One special thing about these is that if you notice all the major intervals are on the right side. And know the minor intervals are on the left side.
These will be even more striking if we did not have the perfect fifth interval here, the perfect fourth interval here, and these augmented fourth and diminished fifth intervals here. Of course, some people would go like okay, that was it. That's just how it happens. It's already remarkable that all the major intervals are on the right side. And all the minor intervals are on the left side, it's already remarkable that all the major intervals are on the side of the sharps and all the minor intervals are on the side of the flat is just like we have, you know, The Dark Side of the Force and the light side of the force here.
Okay, but this is gonna be even more striking. If you remember that some time ago, I was making a video on how those intervals were called in the Baroque era, and at the time, the perfect fifth works was called the major fifth. The perfect fourth was called the minor fourth. The augmented fourth was called the major fourth and the diminished fifth was called the minor fifth Now look at the circle of fifths for a moment, all the right side as major interval all the left side as minor interval.
And when they meet at the bottom, you have two intervals one major and one minor that are and harmonically equivalent. Wow, that is striking. But of course, today we call the fifth and the fourth perfect or augmented or diminished. So I'm gonna keep that, of course, and just saying that A, originally, all the majors were on the right, and all the minors were on the left. And that's striking to me, what else can we do to that?
Well, here's another interesting pattern for the circle of fifths, let's take all the intervals who are on the same horizontal line. So for instance, this perfect fourth and perfect fifth. And let's sum those numbers. What do I mean? Well, the four plus five is nine. So far, so good. Let's take the next line seven plus two is a nine. Next line, three plus six is a nine. Next line six plus three, still a nine. Next line, two plus seven, still a nine, hey, even if I take the bottom, and they call it 1/5, and 1/4, it's still a nine. Interesting.
And, of course, maybe we go, how about the top? Well, the top could be a unison, or an octave. So if I sum those two, it's still a nine. Interesting, it's even more interesting, if you notice that the two intervals on every horizontal line are inversions of each other, meaning the perfect fifths and the perfect foot are one the inverse of the other. If I go from C, up to G is a perfect fifth, if I go from g up to C, it's a perfect fourth. So those intervals are inversion of each other. Same happens for the major second, and the minor seven, those two intervals are inverses of each other, and so on and so forth.
The minor third and the major six inverse of each other, the minor sixth to end the major third inverse of each other, the minor second and the major seventh inverse of each other, the tritone, its inverse of itself. And the sum of that somebody can argue about the top note that maybe the unit zone is an inversion of the octave.
I'm not sure about that point, you guys do whatever you want, we can probably accept it to complete the pattern, but completely up to you here. Notice that these is what explains in a sense, the rule of nine, I made a video some time ago about the rule of nine that if you want to invert an interval, you just take the number of the interval and subtract it from nine. So if I want to invert a Perfect Fifth, I'm taking nine take out the five, nine minus five is four, and they get the inversion.
You see these shows you all the row nine in graphical form if you want, okay, and notice that since I changed aside, all major intervals become minor intervals and vice versa when I invert them. So now everything is very visual and very striking. Okay, so this is the circle of fifths of the intervals. How do you use it? Well, there are many ways to use that because the point of things like that is not to immediately write music, the point of things like that is to understand all the mechanics of intervals and then later of chords, and then use intervals and chords and other stuff to write music.
So it's quite hard to apply this specific thing on writing music immediately, right now, it's more kinda, hey, these things help you orient yourself with the stuff you need to actually write music still is a pretty interesting pattern. Okay, we can go way beyond that with those patterns. And we can understand much more about music.
And it's fascinating. If you guys are interested in understanding way more about harmony and also how to write music and how to make your own music and how to play all this stuff on guitar. Well, I recommend you guys have a look at my course. Complete chord mastery, complete chord mastery.
It's not a book. It's a complete video course that takes you from the basics up. We do everything you need to know about harmony and chords on your guitar. All the theory is done straight on the fret board. There is no theory for the sake of theory here. Everything is immediately practical. And everything is developed through exercises so you know how to apply these immediately on your guitar.
If you have just a minute click on the link on the top right to check out complete chord mastery. If you liked this video, smash that like button and don't forget to subscribe and click on notification otherwise, YouTube will not let you know when I put up a new video. And if you have any comments, feedback, suggestions, write them down in the comment. I enjoy reading from you and they make videos on your suggestions. This is Tommaso Zillio for musictheoryforguitar.com, and until next time, enjoy.