4 levels of the Circle of Fifths

And, an extra special thanks goes to Douglas Lind, Vidad Flowers, Ivan Pang, Waylon Fairbanks, Jon Dye, Austin Russell, Christopher Ryan, Toot & Paul Peijzel, the channel’s Patreon saints! 😇

0:00 Introduction
0:31 key signatures
3:22 related keys
6:07 ToneGym
6:46 chord progressions
9:03 modal brightness
11:29 why the circle of fifths?
12:39 piano outro & Patreon

[ND]

Fun fact:

There’s a mathematical reason why the circle of fifths can exist. The western standard division of notes is 12 tone equal temperament, which gives us (rather obviously) 12 unique tones to work with, which we call the semitones.

A perfect 5th is an interval of 7 semitones. 12 and 7 are coprime, meaning that they don’t share any common factors; here’s where the magic comes in.

Start with 0. Now the rule is to take any number between 1 and 12, and add it to itself consecutively. If the result is bigger than 12, then divide by 12 and write the reminder (or for those mathematicians out there, take the number mod12). Set C as 0, and each number represents a note that many semitones away.

Let’s choose 8, for example.

So we go 0, 8, 4, 0, 8, 4, 0…

Translate this to notes and it’s C, Ab/G#, E, C, Ab/G#, E, C, on and on.

Trying with 3 yields this:

0, 3, 6, 9, 0, 3, 6, 9, 0….

This is the sequence C, Eb/D#, Gb/F#, Bb/A#, C, Eb/D#, Gb/F#, Bb/A#, C…

As you can see, in these cases we only hit some notes before returning to C.

Now let’s try 7

0, 7, 2, 9, 4, 11, 6, 1, 8, 3, 10, 5, 0

Translate that to notes and it’s C, G, D, A, E, B, F#/Gb, C#/Db, G#/Ab, D#/Eb, A#/Bb, F, C

Hey look at that; we hit all 12 notes! How did that happen? Well, it’s because of that nifty fact that I mentioned earlier, that 12 and 7 are coprime. This means that smallest amount of 7s you can add to themselves to get to the closest multiple of 12 is 12. Anything else results in a number either too big or small than a multiple of 12. This is also represented by the fact that 7/12 is the simplest form of that fraction. With the other examples, 3 and 8, if we write 3/12 and 8/12, we can reduce those to 1/4 and 2/3 respectively.

Now, 7 is not the the only number coprime to 12: there are 3 others. These are 1, 5, and 11. What happens when we apply a similar process?

For 1, it’s 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0.

C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, B, C

Otherwise known as our chromatic scale.

5 is just the circle of 5ths in reverse (aka the circle of 4ths); if you look at the number sequence for 7 and go backwards you can see that. This is because 5 + 7 = 12.

11 is the chromatic scale in reverse, because 1 + 11 = 12.

Interestingly enough, while not all of the numbers cover the whole selection of 12 notes, they do cover some aspect of music.

0 = unison
1 = chromatic scale ascending
2 = whole tone scale ascending
3 = fully diminished 7th chord tones ascending
4 = augmented triad chord tones ascending
5 = circle of 4ths
6 = tritones
7 = circle of 5ths
8 = augmented triad chord tones descending
9 = fully diminished 7th chord tones descending
10 = whole tone scale descending
11 = chromatic scale descending
12 = octave

Man, when arranged like this it really shows how symmetrical music can be, huh?

So yeah, that’s your music/mathematics fun fact(s) of the day! Awesome video yet again David! I look forward to the next one!

[lawrencetaylor]

I laughed my whole life and said I was born with two left ears. In Choir class, professors told me from 3rd Primary until 2nd Secondary to just move my lips and not make a noise. But I listened to your videos and at my retirement, bought a piano. And now am trying to make up for lost time.
Merci beaucoup.

[markam]

I love your approach to music theory and how you explain it makes it seem so easy. You always do a great job on these videos!

[Drencromalicious]

I never realised the circle of fifths is a musician's periodic table, untill this video. Thank you!

[briancunning]

Couldn't you have thought of a fifth way?

[smoorej]

Absolutely brilliant presentation of the circle of fifths. This is why I subscribe and support this channel. The topics are presented in the most clear and concise way possible. You are a natural teacher, and if you teach beyond YouTube your students should consider themselves very lucky.

[JeremySpidle]

Related Keys are where I learned about the Circle of Fifths. As an EDM DJ, Mixing in Key can give you a smoother more consonant transition between tracks.

[JamesDean-O]

I’m a stuck-in-a-rut guitar player and I just subscribed to you because it’s like you just handed me batteries that I haven’t had in my flashlight for many years. Now I’m hoping I can find one of your videos that will show me how to turn it on once again.

[StartEnjoyingPianoPractice]

The circle of fifths is always feared at the beginning.... I really like the way you described it. It's really easy to follow!
It's also nice to see the relation between chords and the circle. It's a really fast way to build the circle in your head if you don't remember it.
So, each chord has the fifth. If you know notes of C Major - C E G, then since G is the fifth you know the the next letter on the circle is G. Than G major - G B D, D is the fifth so D is the next letter. etc.
If you don't know the notes of each chord, you can also try to visualise your hand on the piano (the way you play the chord) and try to find notes that way.

[michaelross]

O...M...G...THIS IS SOOOO COOL!!! Seriously, I've never really had music theory so I never realized this kind of thing even existed. Thank you for sharing!

[xblinketx]

There is one more very useful application of a circle of fifths. It tells you which chords in a certain key are major chords (these on 11 o'clock, 12 o'clock and 1 o'clock), minor chords (these on 2 o'clock, 3 o'clock and 4 o'clock) and a half-diminished chord (the one on 5 o'clock).

[xwinglover]

I just had another eureka moment from a David Bennett video of which I have had many. The link between the COFs and modes just hit like a ton of bricks. Another great video David!

[agonist]

Your channel has brought new exciting thoughts, examples, and facts to my 20+ year music knowledge growth. I have a 3 year old now, but as she gets older, we will be going back to binge watch all your videos when I start teaching her about music and theory 😁😁

[emiliya]

As a non-musician, each video feels like some hidden super complex musical knowledge box that i have somehow found access to. Fascinating!

But it's just the basics, of course :)

[yokeshhsekoy]

This condensed so much material I've been trying to absorb about the circle in just one neat cohesive video. Your gift for teaching is something that keeps on giving!

[pathnativejam]

You sir, have given me the sight of music. For that, I am forever grateful.It's almost too much to wrap my music fan brain around and all you hear are the laws and fundamentals of this 15$ diagram like a codex to all your favorite songs!Thank you .

[bingfutch]

I'm at 8:28 and you've just blown my mind with the tri-tone relationships in the circle. That put so much into proper perspective in terms of intervals and how to spot their patterns. Thank you!

[dedrxbbit]

For anyone who might care about it as much as I do, I don’t think The Beetles were thinking Gmaj to Cmaj when they wrote I Wanna Hold Your Hand, but more likely Gmaj to Gmixo. When I hear the Gmaj chord in the switch, it still _feels_ like G is the Tonic, which is why I have this assumption, but I understand where you’re coming from.

[charliejoseph]

If you're looking for any video ideas (and it seems you're in no short supply) I'd love one on songs that use dissonance and why they're still pleasant to listen to.

[bettyswunghole]

It can also help work out chord progressions in any key. For example, the I V vi IV...pick a chord as "I"...the "V" is one clockwise, the "IV" is one anti-clockwise and the "vi" is three clockwise.

(On reflection, I guess this is the same thing as saying you can use the circle of fifths for working out modulations!)