Incessant beeping

Beginning to blur at the edges
For more than a week now, I’ve been sitting at my desk to the accompaniment of a faint, persistent beep. It’s about 60 bpm though its rhythm is slightly irregular; sometimes it seems to skip a beat or double up.
I have wandered around the apartment listening carefully and the only place I can really hear it is at my desk. It’s not coming from outside. I’ve checked all the closets and rooms for a mysterious beeping device and found nothing. I stuck my ear up close to all the computers and peripherals and there’s no noise but fan whirs. This lack of source brought me to my recent theory that the old lady next door is on life support.
But that theory was shot down when, in the spirit of thorough investigation, I turned off my computer. The beeping stopped. I turned it back on. After a moment, I heard beeping again. Argh. What can cause a computer to beep at a relatively steady and extraordinarily annoying pace like this?
I’d better take a backup now.