I am trying to self learn piano. I can play some melody (right hand), can play some chords (left hand) and can play some melody with chords (right + left) with right doing all the complex finger movements for the melody and left just pressing the chord keys once at each change.
I am trying to play something more complex with left hand and interleave the notes with those on the right hand melody. But I do not know how to come-up with the rhythm parts. I try arpeggiating the chords instead of "playing" them but result does not fit in and sounds muddy. Also been trying a few other patterns for a while now, but nothing seems to stick.
My question: are there some patterns (rule of thumb etc.) for coming up with rhythm patterns given a melody? For example, in case of chords, one can rarely go wrong playing the chord for the root note of the melody and a progression thereof.
PS: Not sure if this is classified as "improvisation", but tagging it so.