The fifth of A# is e# and has eleven sharps (four double sharps, f, c, g and d):—
E# fx gx a# b# cx dx E#
1 2 3∼4 5 6 7∼ 8
The fifth of E# is b# and has twelve sharps (five double sharps, f, c, g, d and a):—
B# cx dx e# fx gx ax B#
1 2 3∼4 5 6 7∼ 8
B# has taken us back to our starting key called by a different name.
All twelve keys have now been named with their sharp signatures. To continue counting five would take us over the same keys called by different names. The student is advised to do a little of this for mental discipline. If this is done beyond fourteen sharps, it will be necessary to add triple sharps. Of course, triple sharps are never used in musical notation and such a research would be entirely arithmetical.
The order of the letters in the sharp signature which follows should be committed to memory:—
F C G D A E B.
All keys having one double sharp or more would be difficult to read, and so instead of using the sharp signatures on such keys, the flat signatures are used. All twelve keys with their flat signatures will now be given.