The thread rolling machine pictured is sure a beauty and would cost
a fortune, if anyone still makes one:

  http://i55.photobucket.com/albums/g153/fairorgan/DSCF0029640x480.jpg
 

Inexpensive machines are made for rolling the threads of bicycle spokes:

  http://www.amazon.com/HOZAN-TOOL5080-Hozan-Threading-Machine/dp/B000C3F5LY 

They have a few limitations but these might be overcome with some
modifications.  They are made to just thread the end of the wire, not
useful for a great distance from the end.  It might be possible to
drill a hole through the die holder to let the wire pass farther through.

The threads for spokes are rather fine and shallow.  A new set of dies
probably has to be made although there is a diameter adjustment so if
the threads are deep enough, they can probably be rolled on a variety
of wire sizes.  Diameter might also not be right but a custom die will
handle that.

Lastly, this cheap machine does not release the die to allow skipping
over a blank portion.  It just uses a nut to set the depth.  Would have
to fiddle with this nut a lot if you want to do multiple separated
threaded sections.  Might be fine if you just need to make a few
replacements.  Otherwise a more "commercial" machine would be needed.
So this machine is probably (at best) for someone who needs threads
just at the end of a wire and or only needs to make a few replacements
now and then.

I found this link for a cycle thread rolling machine that covers
motorcycle sizes as well.  It still does only the end but it might
cover the musical instrument wire range better with the motorcycle
heads: http://www.jetblackproducts.com/products/W7836 

There is also a much better bicycle spoke threading machine that is
likely to be more adaptable.  It looks like it could be made to put
threads anywhere on a wire.  Might have to modify the device to prevent
it from cutting the wire before threading as it is intended to do this:

  http://www.philwood.com/products/tools/spokemach.php 

Everything made by Phil Wood & Co. is of fabulous quality, as reflected
by the price ($4000).

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