Whatever it is, it’s grinding or cutting something, and whatever that something is, it isn’t uniform or smooth, but varied in texture and hardness, which is why the pitch goes up and down- the blade is encountering more and less resistance. I’d say it sounds like a saw cutting a truly lousy piece of OSB (a cheap plywood substitute) that’s been soaked unevenly and dried, creating varied textures. But I’m sure that’s not it. Maybe a coffee grinder?
Could be a kitchenaid mixing something, or a blender.
The suggestion that rings truest for me is paper shredder.
I’m in an apartment building and the layout of the apartments is roughly identical: entrance foyer (narrow little area) widens out to the area with the closets (several electrical outlets, we use ours for our computer area), then widens out significantly (in studio apt configs, the living room; in 1-and 2 br apt configurations the kitchen bisects this); then in back the bathroom (and for studio apts, also the kitchen; for the others, the bedroom(s)).
I’m pretty sold on the idea that it’s a paper shredder. It just fits.
The sound is coming from the area with the closets / elecrical outlets where our computers are. There’s no plumbing in this section of the other apartments, nor would there be room for refrigerators. And one normally places a blender up on a counter top to use it. A home office type paper shredder, on the other hand, would most likely be mounted atop a trash can, which in turn would be sitting directly on the floor.
Yeah that’s the kind of tool that kept coming to mind, but it never made sense that they’d run such a tool for 30-40 seconds and then be done for the day, only to do it again a couple days later, etc etc etc… now think of a paper shredder. The little cheap ones like you get a Staples for home office use. They do make that rapid cycling “yih-yih-yih-yih-yih” sound as the electric motor pulls in the envelopes & papers and slices through them, and they do vary in pitch when they hit something a bit harder (like a sample credit card for example) and with the trash-can mounted unit sitting on the floor the sound would come through the ceiling pretty strongly (unlike a blender on a countertop). And it would be something you’d perhaps use once every other day, + or -, shredding a small stack of 5-6 bills / junkmails, which would take about that long to be pulled through and then you would indeed be done for the day.
Automatic kitty litter scooper thing? http://www.youtube.com/watch?v=9BKvuGHrhGk&feature=related
I just had my wife run our paper shredder from upstairs, and that is exactly what it sounds like.
Another vote for the paper shredder.
Doesn’t sound at ALL like a vibrator, though I will mention that ‘no vocalizations’ is not at all a good reason to rule that out. Down and dirty O-time doesn’t necessarily produce audible tells. 
I can cite porn that says otherwise. 
Another vote for paper shredder. You can hear the variations in tone between when the machine is simply on and when paper is actively being shredded. I’d bet she shreds her mail daily.
Garbage disposal (garburator), maybe. I used to live in a place with one and it drove the neighbor crazy.
Another vote for paper shredder.
It sounds like a mixer to me too.
It’s a shredder. Here’s the question: does it occasionally stop abruptly, continuing in fits and starts as she fights to get some items to shred properly? If not, it’s a GOOD shredder.
I’m going with blender. It sounds pretty much like mine…and it could be on a counter that acts as a sound box to your ceiling.
Whatever it is, your neighbour could reduce the sound for a few bucks and a few minutes of her time by putting a real rubber mat beneath the device. Available in shops that sell speakers (to put under a speaker on the floor). Or available at home depot, teady made to put under a washer.
You might ask the landlord to give them out to all renters, if the building is so sound-sensitive.
If it’s a paper shredder, there’s no hint in that clip that it’s actually shredding anything at that time. That sounds like one running with no load. Similarly for the mixer/blender theories, you’d surely hear the ka-chunk sounds as something solid got blended up. It sounds too low speed to be a milkshake maker or anything like that.
Is it at any particular time of day? Particular days of the week? What does she do for a living?
How about an electric pencil sharpener, automated shoe polisher or a sweater depiller ?
A blender blending ice and frozen fruit? That’s what mine sounds like, at least at close range, I’m not sure what it sounds like to the downstairs neighbors.
Maybe not in your world. 
Paper shredder with an over-ful basket. She feeds a document into the shredder. Shreds from the basket stick up into bottom of the shredder and trigger the unit to keep running after the document is shredded, hence the motor sounds without paper-munching noises.
I vote for shredder - it makes sense it would be in the foyer; and that she would use it once a day for 30 seconds (shredding her junk mail when it comes in the post).
Aw, I was thinking I was clever for listening to the clip and knowing it was a shredder, until I read the thread. I know I’m only adding to a consensus now, but it sounds exactly the same as mine.