It depends on the alloy used. Getting steel hot and quenching it in water is the most reliable way to harden it, so that's not what you want to do if you want it soft. I've found that even letting 1/8" diameter music wire air-cool quenches it fast enough that it hardens, except at the boundary between the hot bits and the cold bits. To anneal steel you need to bring it up to temperature then you need to let it cool slowly. To seriously anneal steel you bring it up to heat and bury it in hot ashes to insulate it, so that it cools down over the space of several hours.
(I'm not sure what the right hardening temperature is for music wire, but in general it's the heat where it glows dull red in a moderately well-lit room, or the heat where it won't attract a magnet any more. The temperature depends on the alloy, so if you have no clue as to the alloy heating it up until it won't attract a magnet anymore is probably smartest).
Part or all of the hardness in music wire is there not because of heat-treating, but from the work-hardening caused by drawing it to size. That's not something that you can duplicate by re-tempering the wire. Moreover, getting a whole bent-wire assembly up to the proper temperature, and then quenching it at the right speed, is going to be a challenge because it'll start to quench just in the trip from the furnace to the water or oil bath. If your need for heat treating is at all critical you may want to get some oil- or air-hardening rod and use that -- even then, you'll probably do best finding someone who has a proper furnace to heat it up with rather than trying to make it work with a torch.
If you don't want it tempered, but just want straight pieces of soft steel wire in common music wire sizes, go to a welding supply shop and get welding rod. They'll want to sell it by the pound, but it's fairly cheap. Alternately, you could go to a real welding shop and see if you can buy or bum a few sticks from them -- not everyone will have it (you'd need to find a place that does TIG or gas welding), but those that do may be helpful. You can even get stainless rod which falls somewhere in between steel welding rod and music wire in hardness, and which looks a lot prettier in an assembly.