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.