Do you have any examples of "a single note for minutes and get it to sound amazing"? I'm finding this difficult to imagine. A lead voice doing this while some accompaniment is changing chords underneath makes sense to me, but then you're back to harmonic relationships.
I can only think of examples which as you describe have accompaniment moving underneath. Neil Young's solo in Cinnamon Girl is one example. Another is Bob Dylan's Like a Rolling Stone in which he sings one note as the chords run up C Dm Em F and only breaks on the G.
Adam Neely has an interesting video about one-note muisc, with some good (and bad) examples: https://www.youtube.com/watch?v=eSuK_5zW2iM
Chariots of Fire is pretty dope.
I'm finding this difficult to imagine
Maybe go on Youtube and listen to music that you might not be familiar with?
Cage, Schaffer, Stockhousen, Boulez are some composers in the tradition of European classical music.
If you go outside that tradition, there’s even more. Endlessly more.
Half joking, but Berlin techno :)
You can have a whole set developing motifs, then multiple minutes of a single note being played in the middle, and somehow that sounds awesome (if you’re into it)