Greetings,  There are sure to be modern solutions and maybe even ones
that are not terribly expensive, but for running even a 1/4 HP motor,
you do need a pretty big device to handle the inductive load and the
starting kick.  Fortunately, mechanical music devices usually start
under light load before the vacuum builds.  Here are some
possibilities.

It is possible that a cheap high-frequency inverter type device is
being marketed by now, since this sort of thing could be made very
cheaply if there were a big enough market.  A lightweight little box
with a few power components, a tiny transformer and minimal electronics
could convert 110V 60 HZ into 220V 50 HZ with no problem at all, even
with an inductive load.  The problem is that it is more likely to be an
expensive piece of industrial equipment costing thousands, even though
my $300 Chinese-made inverter is the same thing except for the details.

Buy an over-priced transformer and change a pulley to make up the speed
difference.  It should be no problem for a 50 Hz motor to run on 60 Hz.
It is more likely to be a problem the other way around.

Store the original motor and put in a replacement, with a tag on it
telling the next owner where to find the original motor.

Or do what I have been doing for years at almost no cost at all: use
surplus junk.  There are plenty of industrial transformers that were
used in factories for matching voltages.  (Watch out for ones that have
PCBs in them if this worries you; even if it doesn't worry you, you are
maybe in for a big surprise if you ever have to dispose of it.)  They
are either multitap autotransformers or two winding [primary/secondary]
transformers.  Either type will do for upping the voltage if the ratios
are right.

I have one that I use when the commercial power fails to run all of my
220V stuff from the 110V generator.  (Can't do without the hot tub when
it is snowing, this being California!)  It is something like a 12.5 KVA
monster and it cost me about $15 from the junk seller who was glad to
see it go after moving it a hundred times.

This kind of transformer is being yanked out of sawmills and machine
shops all the time and there is not much of a market for it so it goes
real cheap.  It is too much of a mix of metals and tough cases to be
of much recycling value either.  Check it for shorts and bad external
insulation before you plug it in, and make sure the circuit breaker is
right for it.  Not much can go wrong with a transformer but you will
know when it does.  You still have to change a motor pulley to get the
speed right.

Best regards,
Spencer Chase
Garberville, CA
http://www.spencerserolls.com/