It’s gone......

Glad I waited several hours before checking my thread. Moderators must have been rolling on the floor.

I'll start by changing the fill valve, and picking a different manufacturer.

OK, have to ask, what the heck is a toilet vent?

This should answer your question..
How To Vent & Plumb A Toilet (Step by Step) - YouTube

Waste system plumbing has a vent to to the highest point in the house or building.

Make sure the water valve is turned wide open. More pressure less noise.

If its an Accor (push pull) valve, there is no adjustment.

Real Plumber here :ohdear:
Just go to Lowes and get a FluidMaster Toilet Fill Valve and replace.
Also, when the Koehler stoppers in the tank go bad replace with the Yellow gaskets.
YouTube explains how all those repairs are done.

I agree, but it doesn't explain how flushing one toilet causes a noise in another toilet in another room.

Simply adjust the water level in the tank by turning the screw on the float.

So true.

I wonder if the whistling has ceased and desisted? I got a kick outta this thread, I'm easily amused!

I simply replaced the noisy fill valve with a new one, and a Korky brand instead of Kohler. Problem solved.

The noise is caused by the inflow valve moderating the inflowing water. Replacing it will fix it, cleaning (by taking it apart) may solve the problem for a few months or a year. Best bet is replacement as many others have said.

Glad things worked out for you. Very Good. :clap2:

My theory on why one toilet is noisy after another one is flushed is that the water pressure changes.

When you flush one toilet, the water pressure drops a little, when that toilet is full and the internal float valve turns off the water, there is a slight momentary water pressure increase. This increase causes the weak valve on the other toilet to be overcome with pressure and it turns on briefly. If the valve is weak on that toilet you will get a slow whistle as the weak valve attempts to close. This would become worse if the float is poorly adjusted or too high, and/or if the toilet has a slight leak that tends to reduce the amount of water in the tank. This can also be caused by not having or having a bad pressure tank on top of the hot water heater. The purpose of that tank is to even out the water pressure surges.

So, basically, the only thing that connects the two toilets is the water line. The only thing that can change in the water line is pressure.