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You need to be able to play the melody and bass together to make sure it sounds good. Once you can do this, add chord tones between the
bass line and the melody. Here is where the work begins.
You can literally use any chords you find that sound good to you. Many chords won’t sound good (or may even sound downright bad). Finding
the good ones gets easier with experience and once you have done this with a few tunes, you’ll come to learn what works and what doesn’t.
You can try any kind of chord at all and you don’t have to stay in any particular key or tonality. This is why you must use a symmetrical bass line.
It produces order in what could be an otherwise chaotic chord progression. The symmetry makes it all come together.
Other ideas for symmetrical bass lines could include all whole steps, all half steps, minor 3rd up and a half step back repeated over and over,
4ths, alternating whole and half steps and anything else you can dream up. Here is a completed reharmonization of Jazz n’ Java.
Jazz’n Java With Reharmonization