We now know how to construct key signatures with sharps (♯), and we have a simple rule to figure out what key any sharp key signature represents. Now let’s do the same thing for flats (♭). The flat symbol tells a musician to lower the pitch one half-step.
To so this, we’ll start with the C major scale again. Counting down the scale five notes starting with C brings us to F, the fourth degree of the C major scale. The major scale starting on F follows the same pattern of whole-steps (w) and half-steps (h) as all major scales: w-w-h-w-w-w-h. To match that pattern the fourth degree of the F major scale must be B♭. That B♭ is the only note in the F major scale that is different than in the C major scale. So show this, the F major key signature has one flat on the line representing B.
We can repeat that pattern to find other flat key signatures. The fourth degree of the F major scale is B♭. The B♭ major scale uses same as the notes as the F major scale, except for the fourth degree. Instead of E, that note is E♭ – a half step lower. With that modification the scale starting on B♭ follows the w-w-h-w-w-w-h pattern. So compared to F, the key of B♭ has one more flat in its key signature: E♭. The key signature of B♭ is two flats, B♭ and E♭.
The same pattern works for other flat key scales. The key signatures belows are listed in order of the number of flats.
C Major: 0 flats
F Major: 1 flat
E♭ Major: 3 flats
A♭ Major: 4 flats
D♭ Major: 5 flats
G♭ Major: 6 flats
You can see that each key in the list adds one flat on the fourth scale degree. For example, the key of E♭ adds one flat on the second space from the bottom in the treble clef – the space corresponding to A. Notice that beginning with the key of B ♭, the second-to-last flat in the key signature is always same as the name of the key. Given a flat key signature, second-to-last flat gives the key. For example, if the the second-to-last flat is A♭, then the key is A♭.
That rule does not work for the key of F major since it only has one flat.
Notice that the key of G♭has all the same notes in it as the key of F♯:
- G♭is enharmonically equivalent to F♯
- A♭ is enharmonically equivalent to G♯
- C♭is enharmonically equivalent to B
- F is enharmonically equivalent to E♯
- and so on
So the key of G♭major is enharmonically equivalent to the key of F♯ major.