People from all cultures can and do use notes from outside those twelve tones in music. In western music, sometimes you’ll notice (check out King Gizzard and the Lizard Wizard[1]), and sometimes you probably won’t (that “raspiness” in blues music is usually because they’re singing/playing a note slightly “out of tune” aka “microtonally”).
Music and “what sounds good” is a cultural construct, and I’d encourage you to check out music from around the world as well experimental microtonal artists if you’re interested in hearing what happens when you aren’t tied to the idea of twelve notes in an octave.