I've got some monophonic melodies that I like to play. Monophonic meaning that these tunes are just single melody lines, without accompaniment. I've either written or stolen these. Usually a little bit of both. Now I'd like to make them "polyphonic" by adding a counterpoint harmony line, like a bass-line.
I guess these tunes are what some would call "cantus firmus", meaning: an existing melody used as the basis for a polyphonic composition. I certainly wasn't thinking of harmony or counterpoint when I originally came up with them. Adding a bass-line would be like adding a second tune pitched below the original to create two concurrent yet perceptually distinct lines (integrated yet segregated).
I wouldn't be playing these all at once on the same instrument the way a pianist or some guitarists might do. I'd overdub one part with the next or alternate back and forth. It's actually more of a composition exercise or study, more than anything else. Either way, I don't currently know how to come up with something like this that sounds good with the melody.
From what I understand, Renaissance period composers did not think about harmony in terms of chords. The melodic lines they created using counterpoint were focused on how the melodies interacted. I like that approach because I have always been blissfully unaware of what chords a pianist might choose if playing along with these melodies.
I'm aware that there are a few suggestions or best practices: 3rds and 6ths intervals sound good (produce clear harmonies); avoid parallel fifths (two fifths in a row), octaves are sometimes OK, 2nds and 7ths are dissonant. Use contrary motion - so if one line moves up, the other moves down (creates a sense of melodic independence). If you do move in similar motion try varying up the intervals. More actual hands-on research needs to be done to see if my ears agree with these guideposts.
What I'm thinking of doing could be something as "simple" as what the band Khruangbin does. Their guitarist Mark Speer plays the lead melody and bassist Laura Lee plays a bass-line that supports it, while drummer DJ Johnson provides the beat. Seems pretty straightforward.
Phil Lesh, the bassist for The Grateful Dead, took a unique approach as if he invented the instrument and nobody else played it before him. In Phil's case it was kind of like "Lead Bass", responding to and having a conversation with the lead treble sound of Jerry Garcia's melodic guitar lines. Phil could play it differently every time, partly because he was a gifted improviser and partly because he probably couldn't remember how he played it last time.
Moondog employed a lot of strict counterpoint in his compositions. Listening to his Moondog's music might show the way. Guitarist Jimmy Wyble was an expert at playing two simultaneous melodies on guitar. Maybe I could analyze his arrangements. Stevie Wonder played keyboard bass on some of his recordings.
There's also brass/horn harmony parts to learn from, how an arranger might write for a horn section where a lower pitched horn has one part while a higher pitched instrument like a trumpet plays something else. Studying how these interact might help.
Hopefully it's easier than I'm making it seem. There's a book called Study of Counterpoint by Johann Joseph Fux that looks pretty cool. It was written in 1725.