# Venn Circle Of Fifths

Here’s a spin on the classic Circle Of Fifths from music theory.  The circle is usually presented with note names and key signatures for the 12 major (and corresponding relative minor) keys in the diatonic system, arranged clockwise in ascending perfect fifths.  What I’ve done here is to create a Venn diagram showing the relationship between any three adjacent keys in the Circle of Fifths, with special attention to the pentatonic subsets of each key.  As a musician, I’ve been working with the Circle of Fifths for a long time, but this diagram shows some aspects of the circle that only just dawned on me–I hope this way of seeing things might be interesting to others too.

All notes are labeled with respect to an arbitrary major key that we’ll treat as the home key or I.  Its notes are 1, 2, 3, 4, 5, 6, 7.  Stepping counterclockwise in the Circle of Fifths would take us to IV and stepping clockwise would take us to V.  To label the notes of those keys with respect to the home key, we also need b7 (flat seven) and #4.  You’ll see that the notes of all three keys appear in the diagram, left to right, in ascending fifths: b7, 4, 1, 5, 2, 6, 3, 7, #4.

Notice that all the notes of the home key appear inside the large blue oval (it contains everything but b7 and #4).  Within that oval, there are three circles representing the three major pentatonic scales based on IV, I and V.  The yellow circle on the left, containing {4, 1, 5, 2, 6}, represents IV-pentatonic.  (To play these notes as a pentatonic scale, you’d order them as 4, 5, 6, 1, 2.)  The red circle on the right, containing {5, 2, 6, 3, 7}, represents V-pentatonic (which you’d order as 5, 6, 7, 2, 3).  The circle wedged between the yellow and blue circles contains {1, 5, 2, 6, 3}: this is I-pentatonic, which you’d play as 1, 2, 3, 5, 6.

That’s a bunch of facts I just hadn’t realized before drawing this diagram: if you take C major as your home key, you can find the notes of F-pentatonic and G-pentatonic within it.  In fact, C major can be seen as the union of F- and G-pentatonic.  (Another way to say this is that if you take the pentatonics based on any two keys a whole tone apart, their union gives you the major key that falls right in between them on the Circle of Fifths.)  Why is that interesting?  Well, for one thing, it shows that if you stick to pentatonic scales, you can modulate between F, C, and G, all while staying within the seven notes of C major.  When I hear “modulation” I usually think either “accidentals” or “change of key signature,” but if we’re modulating between closely related pentatonics we can do it all inside the confines of one seven-note major scale.  How do you modulate between I-pentatonic and V-pentatonic?  Look at the diagram: you’re moving from the middle circle to the red circle on the right.  Just stop playing 1 and start playing 7.  Another way to say this is that shifting the root of a major pentatonic scale down a semitone gives you new pentatonic rooted a fifth above the original root. (In the seven note world, you modulate up a fifth by raising 4 to #4, which becomes the leading tone of the new key.  In the pentatonic world, there are no leading tones!  You modulate up a fifth by lowering the root!)

The full seven-note major keys based on IV and V are represented by the two large gray circles in the diagram.  The gray circle on the left represents IV and contains the yellow circle as its pentatonic subset–its two additional notes are the tritone b7-3.  The large gray circle on the right represents V and contains the red circle as its pentatonic subset–its two additional notes are the tritone 1-#4.  Notice that the small middle circle encloses all the notes in the intersection of the two large gray circles: {1, 5, 2, 6, 3}. What this means is that I-pentatonic consists of the notes in common between the two heptatonic major scales at IV and V.

It’s also interesting to observe that the notes 5, 2, and 6 (which we could interpret as a quartal chord on 6, or a sus2 chord on 5, or a sus4 chord on 2) are the most extensively shared notes in the diagram, being the intersection of I-pentatonic, IV-pentatonic, and V-pentatonic.

Here’s a look at some of the pieces you’ll find in the full diagram.  You can think of this as F major on the left, with its pentatonic in yellow; G major on the right, with its pentatonic in red, and C major in the middle, shown as the union of F-pentatonic and G-pentatonic–all labeled from the perspective of C.

Here’s the main diagram again, with each circle labeled as Heptatonic or Pentatonic: