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I'm mostly self-taught, so I don't know much in the way of theory beyond the basics. I have heard of G sharp Major a few times. I believe a scale in the key goes as such: G♯, A♯, B♯, C♯, D♯, E♯, Fx, G♯. Is this key real (as in, has it ever been used in a notable piece)? Or, is it a "theoretical" thing? If it is real, does it have any significant relations to G major?

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I'm not sure why you'd have any reason to question why it's real ... it's not really related to G Major though, no more than C# major is related to C Major. It's enharmonically equivalent to A♭ major, just like C# Major = D♭ Major or F# Major = G♭ Major.

As for pieces involving it, Wikipedia mentions some. In general, keys with double-sharps aren't used very commonly because their equivalents are easier to play. With just intonation, however, G# is not actually the same note as A♭, nor are the keys the same. For more information on that see my answer here and the answers on the question it links to.

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Realize first that keys can be, and very often are, "temporary" within a piece. That is, the tonality may modulate to a new key without changing key signatures. Accidentals are used to indicate on notes that are in the tonality of that section.

With that in mind, I could imagine that G♯ Major would be used in a number of works, but not as a key signature. Try looking for works that might modulate to G♯ Major. c♯ minor could certainly do so, for instance, if the more "traditional" approach of modulating to the relative major were replaced by modulating to the dominant. Sometimes, as in Chopin op. 10, no. 4, the composer will choose to write in A♭ Major instead for notational convenience. Compositions in C♯ Major are fewer, but you may be even more likely to find the modulation in question in such a work.

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Here's how it's related to G major: It's a semitone higher.

I don't know about pieces scored in G#, but any time a guitarist puts a capo on the first fret because the singer is finding G too low, that's G#.

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The larger question is why any composer would use a certain key signature rather than its enharmonic equivalent. For instance the choral music composer John Rutter is known for notating songs in C♭ major (with seven flats) rather than in B major (with five sharps). In the equal-tempered system, C♭ major and B major are the same key.

Despite the fact that this frustrates the heck out of piano accompanists, there is actually a good reason for it; C♭ major is the preferred notation for a harp player, due to the way that the harp is tuned and the pedals on the harp are used to transpose pitches. Rutter has written several pieces that may be performed by either harp or piano.

So in this example, the choice of key signature can be influenced by the instrument that the composer is primarily writing for.

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