The Circle of Fifths 2

One of the many interesting things about the circle of fifths is that it can be used to show how all the key signatures relate to one another. If you move one step around the circle from C to G, the relationship between these two as modes of C major, the Ionian mode (with a root of C in C major) and the Mixolydian mode (with a root of G in C major) is this:
C: 1 2 3 4 5 6 7
G: 1 2 3 4 5 6 b7
Looking at just the intervals in these two modes the difference is one note: the seventh which is a major 7 in the Ionian mode and a flat 7 in the Mixolydian mode. If we decide to play in the key of C major there are no sharps or flats, and in the key of G major there is one sharp which is produced by taking the flat 7 of G Mixolydian (an F natural note) and raising it a semitone to become the natural 7 of G major (Ionian) which is a F# note.

The key signature for G major has one sharp and that is indicated on the F bar of the staff (image to come) to show that the key of G major has one sharp (F#) and all the other notes are natural. This works the same way as the keys progress around the circle of fifths: each successive key signature adds a sharp note as the major 7 note of the new key. So going another step around from G to D adds the C# note to the key signature—we keep the F# from the previous key because it becomes the major 3rd note in the new key. The further around we go in steps of a fifth, the more sharps get added:

C: no sharp
G: 1 sharp  (F#)
D: 2 sharps (F# - C#)
A: 3 sharps (F# - C# - G#)
E: 4 sharps (F# - C# - G# - D#)
B: 5 sharps (F# - C# - G# - D# - A#)

You'll note that the sharps shown above in the order they appear on the staff in a key signature are all mapped out in the same order in the circle of fifths (image to come).

So what happens with the key of F#? Well that is a special case which I'll cover in another post. But for the very next post I'll show how the above process works to produce the key signatures that contain flats by going the other way around the circle in fourth intervals.

The Circle of Fifths 1

It will take a couple of posts to cover this I guess—not that it's that complex, but for me the explanation is a work in progress so I'll take my time with it. I also need to develop some images to show what it's all about, and it will take a bit of time to do that. So, what is the Circle of Fifths?

If you start on a given note then go to the next note a fifth interval away, and keep repeating that you will eventually play all twelve notes and end up back at the note you started with, hence the circle of fifths. You can use fourths too seeing as they're related intervals as a kind of reciprocal—but that's a topic for another post.



So usually the circle of fifths is taught starting from C, which is important when covering key signatures, but here's a tip: it's a tiny bit easier to remember if you start a fourth away from C on F:

F C G D A E B F# C# G# D# A# F

Rearranging this into two rows, you will observe that once we get to B the sequence of notes repeats as sharps:

F  C  G  D  A  E  B
F# C# G# D# A#

Starting on F gives us all the natural notes, then the first 5 repeated as sharps covering all 12 notes quite neatly and in a way that is easier to remember.

Back-cycling is the term that is often used to describe traversing the circle of fifths in the other direction, which is in fourths. For reasons that will be made clear in a future post on the circle of fifths, the accidentals are described using flats rather than sharps when back-cycling.


Again when taken from C it is used for describing a logical progression of key signatures, but it is a bit easier to remember the sequence starting two fourth intervals around on B flat:

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

Again the reason this is easier to remember is that once we've covered the 5 flats we get the same sequence of notes as natural notes:

Bb Eb Ab Db Gb
B  E  A  D  G  C  F

You will find it very valuable to be familiar with the Circle of Fifths no matter what the starting note is, proceeding in fifths or fourths, and using both sharps and flats.