Ha, that will teach me to post things when I should be in bed. Sorry about that mistake in the first sentence and thanks for correcting it. As for your extension let me add two points you may wish to memorize:
1) Fine Classic Guitarists Demand Accurate Execution.
2) Be Ever Alert During Guitar Class.
Contrary to what you must be thinking, I have not strayed from the topic. Look at the first letter of each word in sentence 1 and now look at the order of sharps you added from CM through F#M. You will see that they are the same, and music signatures do not go beyond 6 sharps. What you do instead is work backwards from CM, this time adding flats, starting with Bb
(the FM scale) and ending with Cb
M scale) (see sentence 2) for a total of 6 flats. In this way every scale has a single instance of each letter (ABCDEFG) albeit that, with the exception of CM, from one to 6 of those notes being sharp or flat (never a mixture of sharps and flats). This gives a total of (6+6+1=) 13 keys. But wait, there are only 12 notes in the chromatic scale, so how can there be 13 scales?! It is because F#M and Gb
M are enharmonic scales (the same scale named two different ways). Another word to add to your vocabulary is "tetrachord", which refers to the "half scales" we have been talking about. For example, CDEF is a tetrachord as are GABC and F_G_ABb
and so on.
So up to F# your permutations are spot on. The flats will be as follows (note that the flat you just added becomes the next scale in the permutation):
Hopefully I didn't make any mistakes this time