The really old TVs with the knobs on front will usually have a 300 ohm screw down connection for the UHF signal and often a 75 ohm barrel for the VHF. When this is the case, you will find that connecting a jumper to the barrel will give you channel 3, this is because it is in the VHF range.
However, when you try to input channel 60 to the TV, you are attempting to send a UHF channel through a barrel that might be restricted to just the VHF bands. A matching transformer may be necessary here. Just look at the back of the set and find the set of screw downs that are marked UHF and connect the transformer there. In some cases, you will have to move a small metal "staple" that is attached to the back of the TV into the barrel to jump to the 300-ohm terminals.
I hope that this helps.
Re: frequency to channel mappings....
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