Sergey Malov, who plays all six cello suites on his violoncello da spalla (shoulder cello), gives us the inspiration to look at the suites in a new way. They "transcend" the instrument itself, as by the last one, it's clear that you are meant to be using an instrument with a higher fifth string. The allemande of the sixth suite also transcends its simple dance roots and flows out of its bounds.

Thanks to listener H.G. for the suggestion of the Allemande moment. 

https://www.youtube.com/watch?v=wbH3JYfRjOQ&t=265s