Thinking strictly from a "piano" point of view, there's only 12 major signatures, not 15. Why? There's only 12 notes on the piano.
The 11 key signatures that are used are comprised of:
1 through 5 sharps, 1 through 5 flats, and 1 with no accidentals. (Notice how neat that works out, since there are only 5 black notes on the piano).
If you start in the key of C, and then move up 7 half-steps at a time (the cycle of fifths), you move from no accidentals, to key signatures requiring 1 sharp, 2 sharps, etc. up to 5 sharps.
Thus,
key of C - no accidentals
key of G - one sharp
key of D - two sharps
key of A - three sharps
key of E - four sharps
key of B - five sharps
Starting at C and counting DOWN 7 half-steps at a time (reverse cycle of fifths), you move from 1 flat to 5 flats.
Thus,
key of F - 1 flat
key of Bb - 2 flats
key of Eb - 3 flats
key of Ab - 4 flats
key of Db - 5 flats
If you were to count UP seven half-steps from B, or DOWN seven half-steps, you end up with the "bastard" key of F#/Gb. I suppose in the key signature you could show the E's to be sharpened (written in the key of F#), or the C to be flattened (written in the key of Gb) -- but I've never seen that done. I guess it's because there's not a "black key" corresponding to those notes.
So, why would I prefer to call it the key of Gb? I guess because all of the other keys are either written without accidentals, or with flats in the names.
On the other hand, maybe I should feel pity on the sharps, and at least call ONE key a name that has the word "sharp" in it.

Now my head hurts again.

Oh, and what happened to those missing 3 keys? They must correspond to one of the keys already mentioned. I'll leave it as an exercise for someobody to figure it out.

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The Unofficial Photographer of The Wilkinsons
<FONT SIZE=1 COLOR="#8e236b"><p align=CENTER>[This message was edited by David Pennybaker on 10 September 2001 at 02:50 PM.]</p></FONT>
