Kitty84 asked:

"what I'm trying to figure out, assuming I know what key I'm in, is whether I need to change chords just because the melody is hitting a different note, or if I don't have to because the new note is contained in part of the first chord."

Interesting Question. Some of the most moving passages I can think of involve the melody hanging on a single note, while the harmony / accompaniment (chord progression) moves "underneath", transforming the context of that single melodic pitch.

In simplest terms, no, you don't have to change chords just because the melody note changes. Some of the most beautiful music is made up of melodies that "outline" the chords.

Think of the "piano lesson" song from the Meredith Willson's "The Music Man". It starts out with the student playing what sounds like a simple piano exercise, then shifts into "Goodnight My Someone". Most of that gorgeous melody is simply singing the notes of the chords, one after another. Still, the chords do change, in a repeating pattern.

Youtube is your friend!