I did not know this piece. From the look of it, it's quite a fearsome left hand etude ! The murky sound makes it hard to hear everything clearly, but it seems you are doing a smooth job. I think I heard a couple of little slips but could even be wrong about that. It sounds fluent and confident.
Alkan's pedaling indications would not be clear to me ... the writes Ped: at the start of some bars and sections and then you go figure out until when. How did you handle that ? I was wondering if you were using too much pedal in places - but that could just as well be the swimmy recording.
Anyway, good work.
My pedaling could be improved, and in general, the piece could be more solid (this is four day's progress! I'll repost a new video in a couple weeks or so). His pedal instructions are a little odd, but they should definitely change at least on harmony changes.
The left hand is tricky, but it's nowhere near the difficulty that many believe Alkan's music to be (which, the perceived difficulty of almost all of his larger works is also a little overblown). It's a good study for the left hand, while having to focus on shaping the melody very beautifully in the right hand.
Thanks for your comments! The Chants are gems, and many of them are definitely a couple steps up in difficulty from most of the Preludes and Esquisses.