Empathy is a little-taught skill that's critical to, among other things, teaching, storytelling, and music. When you're comping, you want to be sure the listener (and the soloist) know where they are in the song, without getting in the way. Doing it right requires listening closely, because you want your dynamics (generally) to mirror the soloist's, you want to anticipate when he'll go slow or take a breath because those are the best times to say something. As an accompanist your rhythm should be simpler than the drummer's or the soloist's, but should also (or rather, it often sounds good if you do) reflect any temporary motifs they introduce. If the bass is playing a pedal tone rather than the root, you might consider including the root more important than it would be otherwise (it's common otherwise to play the third and seventh, since the audience can typically infer the fifth even if it's not in the bassline).

These skills, which are often called "taste", are quite temperament-agnostic. They would apply equally to music with 13 notes per octave.