[Ron Ramirez]

The frequency stays the same...but most signal generators put out a fairly weak signal which is too low to properly trigger the counter unless the output is set to a high level. So when you have the output control on your generator set low, the counter gives an inaccurate reading.

Best way to overcome this is to study the schematic of your generator, then install an output jack wired into the generator circuitry ahead of the attenuator controls, so that its level remains high. Connect your freq counter to this new jack.