The valves open and shut at an abrupt rate; and do make a open and close noise.
however that is not the type of noise that you can easily hear on a running engine.
The sound that you are referring to maybe because of two reasons
a. The valve clearance is messed up
b. you have screwed up the valve stems.
See this figure
The valve clearance used on old engines is to allow for the valves to open enough and allow either the intake operation to complete or the exhaust stroke to complete.
When people F up with the clearance beyond the manufacturer's specs, what they are doing is increasing intake time and reducing exhaust or vice versa.
Over a period of time, this just destroys all the precision components and the worn out loose valve stems make a metallic clicking noise.
The symptoms you have described are in line with this diagnosis.
Now, have a look at this figure
This is a M119 engine that I mostly work with; notice that there is no rocker arms or the traditional "Tappets".
Under the cam lobe you can spot a smooth cylindrical piece of metal ( also called bucket Tappets ).
These are precision cut to FIX the valve clearance issue and not allow mechanics to F around.
If your particular car's engine has those, you may need to replace them.
They look like this
Get the originals, and don't let anyone modify them, or use any abrasive at all.
If you cam is beyond specs, change that too.
You will notice that Hamony will come back, and the engine will get a huge power boost !
Lastly, always use the manufacturer spec oils ONLY ( there is a reason they make those specifications )