The tip of your probe has internal capacitance to its ground clip. This will tend to pull the frequency of a crystal downwards, as if you had soldered a 10pf (or so) disc cap to the same spot in the circuit. Textbook name for this is 'circuit loading'.
That's why moving the ground connection changes your reading. The ground clip of the probe is in series with the capacitance of the tip. Since capacitors in series reduce the total capacitance, leaving the ground clip loose reduces the "loading" capacitance of the probe tip on the crystal. Not all counters are sensitive enough to give you a stable reading this way.
The "floating" reading you got will be the most accurate. Looks as if you're chasing a problem that was caused by your measurement method, not by a fault in the radio.
This is what caused us to stop using frequency counters for setting crystal frequencies. A communications service monitor has both an accurate frequency reference and a receiver input. The probe tip becomes an antenna and only has to "sniff" the signal from alongside a crystal without touching any part of the circuit. The trimmer gets set to zero beat with the monitor's setting.
But a counter is more accessible than a service monitor. Cheaper, too. They work best when you can probe to a point in the circuit that's "downstream" from the crystal itself. Some PLL chips like the MC145106 found in many RCI-made radios have a pin that puts out half the 10.24 crystal's frequency. This pin is not connected to the crystal itself, and the probe won't disturb the crystal if you use that pin to make this check. No trick to double the frequency error you see on the 5.12 MHz reading you'll get.
And if your counter is sensitive enough to show a stable reading with the ground clip loose, that's the simplest solution to the loading problem.
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That's why moving the ground connection changes your reading. The ground clip of the probe is in series with the capacitance of the tip. Since capacitors in series reduce the total capacitance, leaving the ground clip loose reduces the "loading" capacitance of the probe tip on the crystal. Not all counters are sensitive enough to give you a stable reading this way.
The "floating" reading you got will be the most accurate. Looks as if you're chasing a problem that was caused by your measurement method, not by a fault in the radio.
This is what caused us to stop using frequency counters for setting crystal frequencies. A communications service monitor has both an accurate frequency reference and a receiver input. The probe tip becomes an antenna and only has to "sniff" the signal from alongside a crystal without touching any part of the circuit. The trimmer gets set to zero beat with the monitor's setting.
But a counter is more accessible than a service monitor. Cheaper, too. They work best when you can probe to a point in the circuit that's "downstream" from the crystal itself. Some PLL chips like the MC145106 found in many RCI-made radios have a pin that puts out half the 10.24 crystal's frequency. This pin is not connected to the crystal itself, and the probe won't disturb the crystal if you use that pin to make this check. No trick to double the frequency error you see on the 5.12 MHz reading you'll get.
And if your counter is sensitive enough to show a stable reading with the ground clip loose, that's the simplest solution to the loading problem.
73