I don't know much about chords and scales, so sorry if this question sounds misinformed. This just seems like witchcraft to me. Here's playable sheet music for this 1848 composition by Charles-Valentin Alkan: https://musescore.com/user/1795986/scores/731721
As you can see, the composition is mostly scale runs in octaves. Very Alkan!
He never modulates anywhere, that I can tell. And yet there is not a single B flat in the entire piece. And doesn't just dodge them; all of his B's get naturals. This entire etude could have had a C major or A minor signature. Yet, the melody naturally lands on the F major chord, and I never get the feeling that something funky is going on harmonically. It is especially apparent in the final bar, where the right hand just plays every white key in a row - yet it ends on the F, and it sounds right!
Is there a name for this "fake F major" key? Or a technique that is consistently being used to avoid having to use a black key? I would love to know how this works.