Power transformers VERY MUCH care at what frequency they operate! That being said, running them at a lower frequency than designed is usually the cause for failures, rather than higher, and I personally wouldn't lose too much sleep running a 60Hz transformer at 81Hz - as Arthur points out, this isn't a huge difference.
But the other way 'round . . . frequently US-spec equipment that cuts it close on the transformer specification at 60Hz can exhibit failures, or much higher operating temperatures, at 50Hz - the Dynaco amps are famous for this. And if you're re-comissioning old military gear from aircraft or shipboard use - these were frequently run on 400Hz power - the power transformer cans can overheat and explode when run on 60Hz power. This is especially nasty when they're filled with oil containing PCBs . . .
But the other way 'round . . . frequently US-spec equipment that cuts it close on the transformer specification at 60Hz can exhibit failures, or much higher operating temperatures, at 50Hz - the Dynaco amps are famous for this. And if you're re-comissioning old military gear from aircraft or shipboard use - these were frequently run on 400Hz power - the power transformer cans can overheat and explode when run on 60Hz power. This is especially nasty when they're filled with oil containing PCBs . . .