> More “fake” notes exist than E♯, too; I hear rumor of such nonsense as G𝄪, “G double sharp”, which I would rather call “A”.
It starts making more sense when you're working with harmony and chords. The wikipedia example section on enharmonic equivalents has a nice example of a Shubert sonata that makes use of this [1].
Yes, if you think enharmonic notes are pointless or "fake" you should look into the derivation of diatonic and chromatic scales via "stacking" fifths, and what that implies for modulation along the circle of fifths. Also how sharp and flat are often theoretically conflated with mi and fa, since both proceed by half-step to their neighbor note.
It starts making more sense when you're working with harmony and chords. The wikipedia example section on enharmonic equivalents has a nice example of a Shubert sonata that makes use of this [1].
[1]https://en.wikipedia.org/wiki/Enharmonic