I would think that the Thu'um derives its power from Kyne. I don't know if there is a patron deity of sword singing.
Furthermore, there has to be a difference between singing power into tangible form as seen with sword singing and Thu'um and the art of Redguard swordplay which can involve invoking power impossible with a normal blade. Surely this must involve a focusing of power with a physical sword as its apex allowing for powerful effects. Sword singing is the same thing minus the physical sword. In my opinion sword singing is a much easier concept to digest than cutting atoms with a physical blade. There has to be some sort of mental power channeling going on.
Furthermore, there has to be a difference between singing power into tangible form as seen with sword singing and Thu'um and the art of Redguard swordplay which can involve invoking power impossible with a normal blade. Surely this must involve a focusing of power with a physical sword as its apex allowing for powerful effects. Sword singing is the same thing minus the physical sword. In my opinion sword singing is a much easier concept to digest than cutting atoms with a physical blade. There has to be some sort of mental power channeling going on.
So you've got your basic magicks, and then there's thu'um and sword-singing and Redguard reality-bending bladery and whatever else. And it occured to me that there might be precedent, somewhere, for a variety of ability not unlike chi as a subtle inner power. The obvious possible origin would be Akavir (if not Yokuda), maybe nasty life-eating monastic powers certain Tsaesci or other Akaviri might wield.
Is there any reason to believe the equivalent of this sort of ability/power exists (or existed) in TES? I can't think of anything specific that even hints at it, but I haven't read everything either.