[R-390] Another (perhaps) silly ballast question

[Barry]

I'm not trying to be silly or attempt any cruelty to a dead horse, but I do
have another (perhaps weird) question.

What is the effect of running a transformer's primary at less than its rated
voltage?  If I connect a transformer whose primary is designed to run at
120V to 100V, 75V, 50V, etc, what effect does it have on the secondary?  I
realize the secondary voltage will drop at the same (or approximately same)
ratio as the primary's voltage is dropped, but what about current (or VA)
rating?

In other words, if I have a 120V-PRI/60V-SEC transformer and connect the
primary to a 60V source, the secondary should now be 30V.  Is the
transformer's efficiency compromised?  If the secondary was capable of 1A
when the primary is connected to 120V, does the current rating go down as
the primary voltage is decreased?

I assume these aren't simple questions with simple answers, but I'm
wondering about this for a specific reason.

Thanks!

Barry - N4BUQ