The punchline to the old joke is, "... then what's the opposite of 'progress'?"
The opposite of "consonance" is "dissonance." Consonance is agreement, dissonanace is disagreement. Musically, consonance is notes that go together, such as those in a chord, and dissonance is notes that don't.
That doesn't mean they always sound bad together.
Some good music is chock-a-block full of dissonance. Not just the Schoenberg-Berg-Webern-droids of modern classical music, either. Listen to Bulgarian Women's choirs. It's all people singing major seconds -- notes right next to one another, like D and E.
In American dance music, the most persistant dissonance is the banjo. Tuning jokes aside, temporarily, I'm talking about the the fifth string, which is a drone. In the basic banjo lick, it's thumped over and over, every other beat, the final '-ty' in "bump-ti-ty."
Common, double-D tuning is, aDADE. The 'a' is the short, fifth string, and it's sounded in every chord: that's D chord, the I, where it belongs; A chord, the V, where it belongs, and G, the IV, where it really, really doesn't. It's part of what makes a banjo sound like a banjo.
Open-A tuning? aEAC#E. Here, the 'a' belongs in the I and the IV -- the A and D chords -- but not in the V, the E chord. Different dissonance, same, banjo-y goodness.
If it's good enough for the banjo, it's good enough for you.
I like drones on both mando and guitar. On the mando, I'll use my first three fingers on the lowest three strings for a C chord, and then use my pinky on the fifth fret of the E string to play an 'a'. It colors the chord with a note that doesn't belong
