I've got a real puzzle for you. This one has us stumped.
There is a buzzing noise near the base of the kitchen wall of my cinder block house built around 1950. It is intermittent, sometimes going hours without occurring, but usually occurring every ten to thirty seconds and lasting less than a second. It continues when the main breaker is off, even if left off for days. The home is currently vacant, so the plumbing and heating are not in use. It can be heard overhead from the basement and seems to originate from the sub floor level when listening from the kitchen. The wallboard has been removed in the kitchen where the sound occurs, revealing nothing but cinder block. The exterior wall is stucco, with nothing to vibrate. There are no visible features near the source of the noise. No appliance. No wiring. No plumbing.