To answer Peace's question: "Modal: Are chords only modal when they are 'less' than a triad? That is, would it be an E chord if the two notes in it were E and C#? Or is the 'modality' dependent on having the first and fifth?"

I was using the term "A modal chord" in the informal way it is often used among folk musicians, meaning playing a configuration containing only a and e notes, the first (tonic) and the fifth, without the third (c or c#). That can be done when playing the long A so the pinky holds down both the first and second strings on the fifth fret, like so: 002255.

Dyad would be the more accurate term than chord. To me, a configuartion of notes with only the dyad of e and b would constitute an "E modal chord" in this informal sense.