The only category that even remotely fits for Tortoise is calling them an Indie Rock band. Beyond that, the definitions become murky as Tortoise was very experimental in nature utilizing anything and everything from Krautrock, Dub and Jazz to make albums that were not found on the traditional Rock or even Independent scene.  The critics do love them and they found a niche fan base, but this has not proven to be the formula for a Rock and Roll Hall of Fame induction.