Thanks---the best way I can describe the sound is a "thunk" or "klunk," like someone dropped something heavy and a little metallic. It's not a tapping or rattling noise at all. I notice it only at night, and it seems to be spaced by 2-3 minutes...not sure the spacing is consistent, but frequent enough that when I'm listening for it, I hear it before getting frustrated with waiting. I don't notice it during the day, but that may be because there are other noises and/or because I'm not in the bedroom during the day, and it seems to come from the pipes directly below the bedroom (kitchen and water heater).

Toilet leak to the outside world is fixed (got both a new wax ring and a new flange when we discovered the PO had installed it without one!) though there could still be a leak between tank and bowl (haven't tested recently, but we have dye tablets somewhere). But the noise is definitely not coming from the bathroom---it's from the end of the house with the water heater, associated pipes, and pipes that run to the kitchen, so I think it has to be something in that world.

Any reason a pipe would clunk if the valves it runs to are turned off? That's another possibility, if there's a scenario where that would happen. The kitchen pipes did not have shutoff valves before, and those were added as part of this work---tested fine, then shut off and faucet removed. They have not been on in three weeks, but could there be air or something of that nature in the pipes?

"water hammer" sound doesn't necessarily come from the location of the closing valve but it does always come at the time of the valve closing. Every 2-3 minutes doesn't sound like the toilet. If it was leaking enough to trip the refill every three minutes, I think it would be obvious to you.

Remain suspicious of water heater. Can you say age? Do you have hard water? Crusted-up water heaters can be noisy and make "thunk/clunk" sounds especially if your system is closed and you have no expansion tank there. Wondering if you're listening to sounds of the water heater and/or its deposits expanding and contracting.

Do you have city water? Is there a pressure reducing valve just downstream of the meter?

Thanks---water heater is 12 years old, and was moved recently so we knew that could potentially trigger problems. No hard water that I know of---though we do have city water, and the water district says "between 1 and 7 grains per gallon" so it's an outside possibility. The water heater was fully drained and then refilled while being moved; not sure when that was last done (not on our watch in the last three years!)

Not sure on the pressure reducing valve but can check in the morning to see...

Oh, and I should add---when water heater was moved, new inlet and outlet plumbing was put in, so it would be the heater itself getting crusty if so; pipes are just a few weeks old!

Nothing definite in my thinking but remain suspicious of that of older water-heater especially since you seem to have identified the location of the noise from upstairs as seeming to be where the water heater is located.

If you've got this noise coming at predictable intervals, as you say, I'm thinking the next time you hear it, hop out of bed and go sit next to that water-heater for a while and see what you learn. Will be interested to hear your report if you're willing to interrupt you sleep for a little while. Crusted up water heaters are capable of whole symphonies of various sounds, many of which are definitely in the "thunk/clunk" catagory. Please tell us what you find.

Should have added.....

It's not the pipes themselves, connections or runs. If anything, they merely carry the sound and sometimes amplify it. We're talking about valves (hammer) and water-heater issues, I have no doubt. At present, from your description, I continue to suspect water-heater.

"It's not the pipes themselves, connections or runs. If anything, they merely carry the sound and sometimes amplify it. We're talking about valves (hammer)..."

Water hammer produces noise when the momentum of the water column causes the pipes themselves to move and strike supports.

The pipes themselves move.

It can be reduced by adding more clamping to prevent pipe movement, or using a water hammer arrestor to absorb the momentum of the moving water when a valve closes.

It is the closing of the valve (and faster closing valves are more of a cause) that initiates the hammer.
The water stops flowing out if the valve, but the moving water in the pipes has momentum that needs to be dissipated.

A pressure spike can appear that can be damaging, and the movement of the lines is not very good for them either.

Brickeyee has it right. Thanks for correction.

However, clamping/securing the pipes won't solve the problem, if that's what it is. Need an air-cushion in there for that, as brickeyee said.

Still doubting water-hammer is the issue based on OP's description.

"However, clamping/securing the pipes won't solve the problem, if that's what it is."

Clamping and securing can solve minor water hammer problems, though it is at the expense of small pressure excursions.

For a long time a dead end was left in supply lines, often above the faucet and capped.
Air trapped in the section provided a cushion to reduce water hammer.
The air could eventually be absorbed by the water (more common on hot lines) and the easy fix was then to drain all the hot lines and refill them.
With the air restored in the stubs hammer was eliminated until the air was absorbed again.

Heated water has less dissolved air, so it is more prone to absorbing the air in the arrestor section.

Modern hammer arrestors have a sealed chamber to hold their charge, often nitrogen, and rarely leak it out.

i would agree that the very regularity makes it unlikely to be water hammer.

Water hammer is usually traced to fast acting valves on washers, dishwashers, and other large flow actuated valves.
I have seen it on long runs to single handle faucets.
Slamming the valve closed quickly produced hammer every time.

Without a valve opening and closing the problem is not water hammer.

Thanks! I will try the sitting-by-water-heater solution and see what happens. I also forgot that the water is connected to the washing machine, too (reminded by brickeyee's post!) but nothing has changed there so seems less likely to be the problem. No valve opening or closing (unless something's broken!) in close proximity to the sound---listened last night and it took close to an hour to start after I went to bed, and then was pretty regular thereafter, which seems really odd. Maybe I just missed hearing it before then, but I was listening pretty carefully for it!

Also good to know about the dead end stub---we never had one before, but the guy who replaced our plumbing lines to our kitchen sink put one in (though on the cold water line, if I'm remembering right). Had no idea why, but he said we needed it for our wall-mount faucet and the inspector passed it so I didn't question it. Interesting!

Softener?