G# minor is the relative minor to B Major, they share the same key signature of 5 sharps -- F#,C#,G#,D#,A#Every scale will have only one representation (in the form of natural, sharped or flatted) of each letter of the musical alphabet. G# natural minor looks like this : G# A# B C# D# E F# G#Your example above includes a G natural, as well as a G# and there is no representation of an F. You won't have both kinds of G's in the scale (at least they won't be called that) and since the name of the scale is G#, the G natural has to go. If you would like to build a harmonic minor scale, which means the same scale as the natural minor scale but with a raised 7th scale degree (an 'F' of some sort in this case), you would sharp the 7th scale degree, which in this case is F#. Since the F is already sharped, raising it would turn it into an F double sharp, which can be spelled enharmonically as 'G', but it is more harmonically correct to spell it as an F double sharp (Fx), so as to have each member of the musical alphabet represented.So, in a way what you wrote IS the scale (G# harmonic minor), but it's not entirely accurate since the G should be spelled as an Fx instead. Hope that helps !
So - in short - G natural minor is G#, A#, B, C#, D#, E, F#, G# (because the natural doesn't have the raised 7th)However the harmonic minor ir G#, A#, B, C#, D#, E, Fx, G# (with x being the symbol for double sharp).But K is correct.