Ursula, by George I think you've got it! Except for the square shape, as you say, but your plants and mine both have that "too-tight belt" around the pseudobulbs! I am so excited to see what species of Dendrobium it turns out to be, and found several other yellowish bumps on pseudobulbs on the other side of the plant!
Now to keep from killing it with kindness (overwatering, mainly). When I think that it has been hanging in the window for more than 7 years! I'm awfully glad I asked in this forum: it wouldn't have occurred to me to put it, or anything other than Cymbidiums, in full sun.
Kate, can you believe that it is hanging in a south facing window, no curtains, no trees or shrubs outside (luckily, no neighbors). I am thinking of getting some type of artificial light because that is as much natural light as I can get, we have not seen bright sunlight for weeks now, or at least that's how It seems.