I posed this question first on the BG side, but remembered that I tend to get better answers to these sorts of questions here. I've tried some different methods of learning tunes, but all of them more or less stem from scale or arpeggio exercises. How about a method that stems from the melody, and embellishes, or builds off this melody in some sort of systematic way that could be turned into an exercise? Yes I know this would be more of a soloistic way of learning a tune and less of a comping approach. I'm curious what ideas are out there. i guess this could either be a way of learning a tune, or perhaps a more general improvisation exercise centered around the melody of a tune.
You can use the exercises in this thread (originated by our wonderful @Ed Fuqua): REALLY Learning a tune
Well, transcribe the melody first then. Learn to sing it, play it, embellish it, and pretty soon you'll have a feeling for what chords could work too, yeah. Learning the melody is a great way to prevent getting lost in the changes.
Once you know the melody well (and can play it), a useful exercise is to, in a sense, invert it. Where a melody line goes up, take it down. This can be done both harmonically and rhythmically.
Lee Konitz was all about this. It's a main reason his playing is so fresh and cliche free.I'm not sure it's an ideal approach for a bassist because others rely on us for harmonic info, but what do I know. I'm sure a internet search for Lee Konitz improv advice or transcriptions of his solos will turn up some of what you're looking for. Brilliant guy. The book Lee Konitz: Conversations on the Improvisors Art is great.