I feel like genius -- such as it exists -- necessitates that someone is able to pull together concepts from a variety of experiences and is able to create and organize on terms that go beyond the single dimension of artistic output. In other words, a musical genius could very easily transliterate their creations into other fields, and those connections should be easy to see.
In this music I think of Duke Ellington, Charlie Parker, Thelonious Monk, Charles Mingus, Ornette Coleman, Cecil Taylor, Bill Dixon, Misha Mengelberg, Bengt Nordström, François Tusques, Derek Bailey, Evan Parker, John Stevens, Tony Oxley, Anthony Braxton, Roscoe Mitchell...