Instead of reading mudcat yesterday I was at choir practice & in the process looking at the music trying to evaluate the idea of chords in that context. Then tonight there was a musical & I got a chance to briefly quiz the college's resident composer.
My personal conclusion is that context is everything & even the lofty Dr. said as much in 2 different ways. So to the initial question, without fully knowing your context, Ed, we can't answer for you. I seems to be called a power chord by some, I've heard it called an open 5th.
Some of the contexts I was thinking apply are that for a guitar the process of holding down strings in some pattern & strumming would be thought of as playing a chord. If one could pretzel the fingers up (or is it spread them out) and have all 6 strings playing the same note, I think there's a stong sense for the guitarist that they are playing a chord. A unison chord would otherwise certainly an oxymoron, but in the context probably the best that fits. Similarly holding down the strings that in strumming would constitute a chord, but instead of the strumming that plays them all essentially simultaneously, the stings are individually plucked. Does a guitarist still think of it as playing a chord? Or is it something else?
I thought of the finger picking as I looked at an accompaniment that involved a lot of arpeggios in a piano accompaniment. An arpeggio being the production of the tones of a chord in succession and not simultaneously, theorists & composers look at them pretty much the same way as a chord & define them with the same neat numbers. So they are sortof, but not quite chords. We also had a couple of sections where we were singing in 2 parts. Unaccompanied 2 parts are?
In reading Don's composition class & listening to the professor (a cool guy) I can't help focusing in on how immediatly they move from defining a chord into rules of composition. Don's professor allowed that 1-3 was ok but 1-5 was not (some root doubling as well) in a compostion. Don almost, but not quite says that first, because permitted is a chord, while the second is not. My prof. basically said you could get away with 2 notes where the 3rd was implied by the context. I also then was told of pieces he delights to assign for analysis because they don't fit the expected conventions.
When I told him our debate was in regard to folk or popular music his immediate reaction was that, the rules don't necessarily apply. Almost without prompting the 'power chord' came up. It would seem the chord is played in the very low range, which, especially with amplification, ends up creating a whole lot of cool overtones & is exactly the desired effect. It's also flexible because neither major nor minor it can fit into either context.
I am self taught when it comes to theory because what I've cared most about is understanding the Sacred Harp music I sing; & perhaps more, understanding the way other people talk about it. Almost everyone I know who's got the technical musical backgroud gets into relishing how it breaks so many of the rules they learned. This is particularly in the area of open 5ths, parallel 5th, and dissonances that do not properly resolve. (You hear that enough & you have to go learn some theory)
Historically the music of the New England singing masters that is included in the Sacred Harp was utterly disdained by the growing European art music informed music establishment. The music of people like William Billings, Daniel Read, Lewis Edson, etc. did many of the things forbidden by the rules of composition. This music was tremendously popular with the everyday, ordinary singer. I personally am immensely grateful that at least some folks refused to bend to the dictums of taste & kept it alive. If you want more information on that particular period I recommend Music of the highest class : elitism and populism in antebellum Boston / Michael Broyles. New Haven : Yale University Press, c1992. It applies to far more than just Boston. Another interesting book is Lowens, Irving, 1916- Music and musicians in early America. New York, W. W. Norton 
A lot of the later music in the Sacred Harp is of folk origin & was frequently written in just 3 parts. I can't say I pay a lot of attention to what the chords are, but I can assure you that even with added alto parts, there are frequently tunes that begin with no 3rd on the opening note. When the keyer sounds the opening notes we all sure think of it as being the opening "chord" regardless of the 3rd. Yes, if someone doesn't at least sound the 3rd before we start I can get confused on the tonality of the piece, but then I've been known to blow singing straight up a minor scale. The Sacred Harp is not online, but the closely related Southern Harmony is. A couple of tunes (melody on middle line) clearly of folk origin to look at are Indian Convert (Nashville in Sacred Harp with much better words), Sweet Rivers, Green Fields, and New Britain. David's Lamentation, Easter Anthem, Schenectady, & Ocean are all 4 part songs by 18th century northeasterners
I know people who are pretty successful in writing music in this style. Some of these are professional musicians who heard the music, loved it, & used the analysis tools they learned in music theory to understand how the effect they heard is accomplished. Figuring out the 'rules' of Sacred Harp harmonies enabled them the write in the style. There are others who have no formal training, but singing it all their lives have put their hand to it & can write perfectly in the style. I can think of 2 or 3 tunes that were added in the 1991 edition, that I can't belive were not among the first I learned, they are that wonderful & on target.
The library is about to close & I must go. On Wednesday I was mostly bent out of shape because I took the trouble to go 'look it up' & got basically no acknowledgement.