First of all, it makes no difference whether you use AC or DC. There are no special, magical properties of DC. All you're doing is heating a piece of wire, and either will do just fine.
Having said that, let me propose something I've done that's really quick and easy.
The problem you're facing is the Goldilocks problem: you want the current flowing through your wire to be just right. Too little, no burning: too much, the wire melts.
I made myself a resistance-soldering rig several years ago out of readily-available components that works very well. (Same principle, heating metal by putting current through it.) My rig consists of a step-down transformer (I think I used the 12-volt secondary of a multi-tap transformer) with a light dimmer on the input (AC line) side.
Now, before I hear a chorus of replies saying "You can't do that! Dimmers are only supposed to be used on resistive loads! You can't use them with inductive loads like a transformer!", let me reassure you:
it works fine. You can use the dimmer to fine-tune the voltage (and therefore the current) flowing though your wire so that it's just right. For a single piece of wire, I'm guessing you're going to need something like a 12 volt transformer that can deliver5-6 amps. (It might draw even less, but you want to confine your smoke to the wire, not the transformer!)
It would be a Good Idea to experiment to find out how much current you actually need. Couple ways of doing this:
- Measure the resistance of the wire:
Theoretically sound, but very difficult to measure small resistances like this unless one has expensive test equipment.
- Measure the current:
This is what I'd do. Get ahold of an AC ammeter that measures at least 10 amps, and put it in the circuit, and see how much current you need.
I suppose you could look up the resistance of your gauge of music wire and use that as at least a rough guide. Anyone have that info handy?