Measured variable frequency converter without any magnetic core from few uH up to 10 mH. Ten mH inductors are larger but still bendable. Inductance depends on number of turns. Adding magnetic core adds cost. We produced laminated, 3% Si steel for 60Hz and ferrite core suitable to 13.56 MHz. Around 50Hz, we could apply 25 microns thin amorphous steel core. Too many types of frequency converter can be used. We produced composite magnetic core consisting of both ferrite plus amorphous steel. I prefer no magnetic core: easier, simpler, cheaper. Designers could specify custom inductors and then trim/tune to exact value for
converting 60Hz to 50Hz. It is unlikey you will get an efficient system by that arrangement like in this analogy: an arrangement of a motor converter interconnected with a shaft and electrical output of the generator connected back to the driving motor. It does'nt work that way.
Near field radiation pattern needs to be characterized. I designed different shielding. An application maybe using inductors to shield against conducted and possibly radiated
50Hz 60Hz frequency converter. Variable frequency converters are not sold like variable resistors. There are reasons? We can produce variable inductors having wide trim down to -90% or adjust higher to +150%. Or design our variable inductors with tighter adjust range to application. However, why bother if fixed inductors are all that are needed... Inductors have different properties depending upon measurement frequency: 50Hz up to 60Hz.