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The notes of the G-sharp major scale are: G#, A#, B#, C#, D#, E#, Fx, G#. The x you see is called a double sharp. (Double sharps raise a note higher by 1 whole step. Fx is actually G.) However, because of the simpler enharmonic equivalent of Ab major, which has 4 flats, Ab major is used a lot more than G# major ever is.
G''' (1/5 of length; two octaves and a third up; 410 Hz; 13.2cm; touching the string here suppresses the fourth harmonic so you hear this pitch; in fact a tempered G''' is 415.305 Hz, so the tuner will register this note as sharp if you touch the string right above the fret).