G# and Ab are enharmonic. Therefore:
I. G# major
ii. A#m
iii. B#m
IV. C# major
V. D# major
vi. E#m
vii(b5). F##dim
It's ridiculous to speak in terms of the Key of G# Major because there are not one, not two, not seven...but EIGHT SHARPS in this scale! So, let's rephrase the list to cut down on the amount of sharps:
I. G# major
ii. A#m
iii. Cm
IV. C# major
V. D# major
vi. Fm
vii(b5). Gdim
It's not technically correct to have a natural and sharp/flat of the same letter in the same scale, but it definitely simplifies things memory-wise to deal with only the letter names: C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, and B. It simplifies things even more if you selectively choose a the sharp names over flat names, and vice versa: C, C#, D, Eb, E, F, F#, G, G#, A, Bb, and B. So let's rephrase this again, in a way that mostly guitar players would recognize:
I. G# major
ii. Bbm
iii. Cm
IV. C# major
V. Eb major
vi. Fm
vii(b5). Gdim
It's not technically correct to include flats in a sharp key (and vice versa), but it definitely helps to only have 12 note names instead of 24+ (due to double sharps). Anyhow...
Many, many, many, many chord progressions in popular music contain some permutation of the I-IV-V progression, and since we're talking about the key of G#:
I-IV-V can be replaced by the G#, C#, and Eb major chords.
You can change the order of the chords for some familiar-sounding progressions:
As I-IV-V-IV-V: G#, C#, Eb, C#, and Eb chords.
As I-V-IV-IV: G#, Eb, C#, and C# chords.
As IV-I-V: The C# Lydian-sounding C#, G#, and Eb progression. (Also referred to as I-V-II.)
As V-IV-I: The Eb Mixolydian-sounding Eb, C#, and G# progression. (Also referred to as I-bVII-IV.)
All this looks a lot like high school algebra, but it sounds better than it looks (pun intended).
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