If so ,THAT would be a fair indication that the wave form is not a near pure sine wave as claimed.
Perhaps not as bad as MSW [modified SQUARE wave] but still with noticable steps & resultant spikes with some inductive loads,so not PURE sine wave
Have you tried it with a pure resistive load[elecric element, such as 3way fridge,elecric kettle /jug etc??
I know one particular brand of claimed PSW inverter genny has a very poor wave form [not much better than a MSW]
edit
I see that while I was posting you came up with the answer , that on a pure resistive load it did operate around 50Hz
The steps in the sine wave ouput [not smooth curve] are causing inductive spikes when connected to inductive loads
Some instruments will pick up those spikes more than others which is why you see the great variations.
They can actualy be harmonics of the original steps.[the hundreds]
Such are unlikely to have sufficient energy to affect most gear,such as motors & certainly not resistive loads
But could give operation problems with some electronic equipment AND highly inductive loads[ such as ballasted fluoro lights
Actual damage is unlikely
It would be interesting to know if this is typical of Honda Inverter gennys
It is of another brand!
Cannot name but begins with an E
Peter
