The fifth of c# is g# and has five sharps (f, c, g, d and a):—
g# a# b c# d# e fx g#
1 2∼3 4 5∼6∪7∼8
The student will notice that in this key, f is double sharped. F is sharped in the signature, but because the subtonic requires raising, f demands a double sharp.
The fifth of g# is d# and has six sharps (f, c, g, d, a and e):—
d# e# f# g# a# b cx d#
1 2∼3 4 5∼6∪7∼8
The fifth of d# is a# and has seven sharps (f, c, g, d, a, e and b):—
a# b# c# d# e# f# gx a#
1 2∼ 3 4 5∼6∪7 ∼8
The minor keys having more than seven sharps should be found by the student and submitted to the teacher for correction. For the sake of brevity, they are not given here, but the student should be thoroughly capable, by this time, of finding them all.
A minor has no flats, the fourth of a is d and has one flat (b):—
d e f g a bb c# d
1 2∼3 4 5∼6∪7∼8