The Circle of Fifths 3

To use the circle of fifths to show how the flat key signatures relate to one another, you need to move one step around backwards around the circle from C to F, the relationship between these two as modes of C major is this:
C: 1 2 3 4 5 6 7
F: 1 2 3 #4 5 6 7
So the difference between Ionian mode and Lydian mode is one note: the fourth which is a perfect 4 in Ionian and a sharp 4 in Lydian. If we decide to play in the key of C there are no sharps or flats, and in the key of F there is one flat which is produced by taking the sharp 4 of F Lydian (a B natural note) and lowering it a semitone to become the perfect 4 of F Ionian which is a Bb note.

The key signature for F major has one flat and that is indicated on the B bar of the staff (image to come) to show that the key of F major has one flat (Bb) 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 flat note as the perfect 4 note of the new key. So going another step backwards around from F to Bb adds the Eb note to the key signature—we keep the Bb from the previous key (obviously because it becomes the tonic in the new key). The further back around you proceed in steps of a fourth, the more flats get added:

C: no sharp
F: 1 flat  (Bb)
Bb: 2 flats (Bb - Eb)
Eb: 3 flats (Bb - Eb - Ab)
Ab: 4 flats (Bb - Eb - Ab - Db)
Db: 5 flats (Bb - Eb - Ab - Db - Gb)

You'll note that the flats 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 Gb? Well that is a special case which I'll cover in another post.