Sorry to learn you were sick, Matt. I'd have nursed you myself if I'd only known.

Thank you for your help in guiding the adult students to better understand theory. Your dusty, wooden examples are just great. Actually, Good King Wenceslaus rocks!

p.s. - I stole your whip. You can stop looking for it now.

For want of a better term, I would call them "ambiguous" in most contexts. Generally, it is the third above the root of a triad that is the determining tone in whether the triad is major or minor. An open 5th with no intervening 3rd is ambiguous. It could be used in a number of places where one wanted to keep the harmony ambiguous, but for the most part that would have been considered a non-standard usage.

As for calling them "power chords," this is a terminology (and technique) originally used by guitar players, who wanted to make their part in an ensemble more prominent. By using only the root and fifth of the chord, they get more volume (and strangely enough, even on the piano, you'll get overtones that suggest a major chord).
OK, don't get too worked up over this particular one. A fairly common voicing for a chord could just be the root and the third (recall what I just said about it being the determinant interval), often with the root tripled. In fact, this is such a common resolution for a dominant (well, looky there, that's what precedes it!) that it is given special consideration.

Ah, yes, well, isn't g minor the relative minor to Bb Major? Actually, even if one were to ignore the triple-root idea presented just above, the resolution from the dominant to the submediant is very commonly referred to as a deceptive resolution (see what I wrote above about this), which also underscores the whole Major/relative minor relationship.

Here's a handy hint for deciphering weird chords: rearrange them so you can stack them in thirds (all lines or all spaces). When dealing with extended harmonies, it is common to leave many of the notes out of the stack. So your first chord (FGDA) stacks D F A (C) (Eb) G, an 11th chord. 11th chords are usually just suspensions, though. Check the harmony just prior: is there a G that appears to be held over?

The second (FDGD) stacks G (Bb) D F; a 7th chord. Wait, no third??? OK, let's see what follows: a c minor chord. Hmm, sounds like a secondary dominant (or if you're going to c minor, then the dominant in c minor). Why no third? Sometimes voice leading can lead you into a strange spelling for a chord. It happens.

Actually no, this is not really any particular technique. A composer will make lots of decisions on voicing harmonies in deference to voice leading (making the inner voices smoother with mostly stepwise motion) or playability, especially for keyboard instruments. In this particular case, it was apparently felt acceptable that the third be omitted in favor of, most likely, one or the other of the above.

As an extra-added aid in understanding some of the concepts I've presented in this lesson, I'd like you to take a look at this cool little gadget that Frank B. is making available at his pianosupplies.com site: the Circle of Fifths Clock ! Even if you don't buy one, print a copy of the clock face; it's a much better visual than I can possibly render here by typing.

I thought it would be some type of bondage device, after reading the leader in 'Today's Active Topics'.

Seriously, I am looking forward to personally understanding what we are talking about. I AM studying but I am afraid I suffer from Fifth's Disorder.

I bought one of those Circle-of-Fifths clocks for my oldest son when he first went off to college, but I screwed up the order and got the one with a digital readout by mistake. (You have to be really good at theory to read THAT puppy!

Thanks for the feedback on my questions, Matt. I'll have to look more closely at the score when I get home to check for that held-over G.