I always love the joke in TV shows when someone "invents" more notes in a scale. Hehe.. One I remember vaguely was in Red Dwarf and the computer character created the notes H and I, if I remember correctly. As a young musician I always thought it was possible to simply add more notes but really it is impossible to do that. You could, I suppose, give all the half-tones their own letter of the alphabet but you aren't actually "adding" any notes.. just redefining existing ones. You can add more notes to a scale by including micro-tones (notes between the half-tones) but all you are doing is adding more sharp or flat to existing notes...

It's a strange thing in some ways, Music Theory, in a lot of ways it is quite fixed with hard and fast rules. However, in other ways it is open to debate over how to use those rules.. Music in a lot of ways is a magical/quantum state of affairs.. It has this scientific ON/OFF and also the BOTH ON AND OFF states.. then when you start adding notes together you get harmonic resonances and it gets ever more complex the more you explore it.. yet, at its core it is ever so simple.