Partial chords can mean two things. It can mean playing the notes that make up a chord, but not doubling them up, so that with a standard major or minor that's just three strings played, and three left alone.
Or it can mean only playing some of the notes, but doubling them up and maybe using all six strings in guitar for example. Play just the C and G like Don started the thread with, and that's a C diad. I like diads, especially with the notes doubled up so all the strings are available. (Nobody ever seems agreed whether it's correct to call them chords or not. On some definitions of chords they aren't included. No matter, I think they often sound better.)
One of the nicest diads I know is the G you get if you play an F with the thumb fretting the E string, but slide it up two frets, and lift the second finger so you get an open G.
And then if you slide it up five more frets, and keep the same fingering you get a C diad, and they do well together, with a D chord to make up the Three.
I haven't been able to work out an easy D diad with standard tuning to allow a Three Diad trick. If anyone's got any suggestions, I'd be grateful if you'd post them here.