So here's the thing, a lot of the patterns actually require the same movement and it's a case of knowing when to apply your knowledge move-set to that particular pattern. There's a few with the left-right-left (or vice-versa) movement. That said, Hyper Hexagonest does have a new pattern that rarely shows up in the other Hypers, that requires you to, I think, go one direction twice, then the other way once. I can't do it yet, it's super quick and super hard.
And Hexagonest's tune is clearly the best!