Is hand independence something that should be tackled after becoming familiar with the layout of the piano? As in first aiming to be able to instinctively reach for the right notes in a key, and getting good a muscular memory.
For someone who is self teaching, I have no idea how to approach hand independence. I often avoid it, because I feel useless when I try it. If I try something remotely fancy in my left hand while playing independently with my right, I find that I cannot 'think' with my right hand while doing this. If I try to, I find myself even getting to most basic of melodies incorrect.
The annoying thing is that a lot of these rhythm patterns are harder to play slower than to play faster! And they certainly sound boring when they're played slowly.
Here's an example of left hand rhythm (at the start of this video) that looks easy, but is bloody hard. I can't even play what's in the video with practice, let alone being able to improvise something. Some of what is going on in the left hand seems impossible. Of course I've no teacher to tell me what the right way to approach learning something like that would be.https://www.youtube.com/watch?v=RHhq3uU5lZ8
Here's another video that seems to keep a pretty consistent left hand rhythm. Completely different to the above video. It's https://www.youtube.com/watch?v=CVerRlMqY8A