As shown in the videos, the noise is a rapid, loud, rhythmic beating that can change in tempo, duration (usually 30 seconds or less), and volume. The noise always comes from the same location in the house - it seems to be in the interstitial space between the basement and first floor, roughly near/above (but not in) the water heater, and this happens to be near the spigot at the back of the house.
Before the noise starts, no water is running. None of our toilets are leaking, no faucets are dripping, no sinks are running etc ... In addition it does not correlate with the automatic ice maker so far as I can tell.
Having said that, once the noise does start, if any water valve is opened (faucet, back spigot, toilet etc) the noise stops instantly. Some times it comes back in a few minutes, some times it doesn't start again for hours. Usually we hear it at least once a day, but that depends on how much we are home.
Things I have tried include flushing the water heater (although I don't think it is minerals in the water heater) and draining all of the water from the house in case this was a water hammer issue (both plumbers didn't think it was this). I've tried each several times, but neither has helped alleviate the problem.
The most recent thing we have tried came at the suggestion of one plumber. On his advice we asked the county to give us a new water meeter. They claim to have done this, but the noise is still there.
Here are two videos of the noise:
So I'm hoping someone might have an idea or two about what is causing this noise. I can call another plumber but paying some money to have someone come out and say "I don't know" doesn't seem productive.
Thank you for the help