# Key Signatures Explained

author: chris flatley date: 12/03/2009 category: the basics
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```KEYNo. of sharps
C0
G1 (F)
D2 (F, C)
A3 (F, C, G)
E4 (F, C, G, D)
B5 (F, C, G, D, A)
F#6 (F, C, G, D, A, E)```
At this point I'm going to substitute F# for Gb and continue moving up in fifths.
```KEYNo of  flats
Gb6 (B, E, A, D, G, C)
Db5 (B, E, A, D, G)
Ab4 (B, E, A, D)
Eb3 (B, E, A)
Bb2 (B, E)
F1 (B)
C0```
So we began with C containing no sharps, and we moved through the key signatures in such a way as to arrive back at C, which also contains no flats. A perfect circle. And isn't it a beautiful thing? Look at the symmetry. Not only do we move up in fifths to discover that the next key contains one more sharp, but we also move up in fifths to find out which sharp it is. F up to C, up to G etc. Adversely, if we start at C containing no flats and move DOWN in fifths, not only do we discover that the next key contains one more flat, but by moving down in fifths we also discover which flat it is. B down to E, Down to A etc. Wonderful! So now we can see why we write in Bb and not A#. If, instead of substituting F# for Gb, we were to continue on with the first table, we'd find that C# was the next key. And using the formula established by the previous keys we'd also find that it contains 7 sharps, and they are: F, C, G, D, A, E, B. So now as well as an E#, we now have a B#. Double trouble! But we talked about A# so we have to journey further up the ladder of insanity. The next key would be G#, which according to our formula must contain 8 sharps. But there are only 7 scale degrees, and we sharpened all 7 for C#. And if we look at the fifths: F, C, G, D, A, E, B, the next one is F again. So what's going on. The fact is that the seventh scale degree is always a semitone below the root. So in the case of G#, this means that F's are double sharp ##. Hey Presto! 8 sharps! You can continue alone if you want to move through D# and onto A# if you like. I'm bailing out here. Hopefully that cleared a few things up.
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