Here is a basic singing arc, based on this Instructable.
It uses a TL494 to switch a MOSFET very rapidly, dumping current into the primary coil of a TV flyback. The air rapidly heats up when the spark is on, and it cools quickly when switched off. This causes the air to vibrate, making sound just like a speaker.
I used a Hitachi flyback (about $10 on eBay) but any flyback with an open primary will work. You can use jumper clips for electrodes (as above), but they will melt eventually. Tungsten electrodes are much better. You can also use anything else that is conductive and will tolerate heat, such as chunks of pyrolytic carbon.
Here it is running in a vase full of argon. This gives you much bigger sparks at the same voltage!
Here is Plasmana's original schematic. Replacing the IRF540 with a bigger MOSFET (such as the FQA16N50) will let you dump more current at higher voltage across the flyback, making even bigger sparks. Adding a gate driver between the TL494 and the MOSFET would also likely help.
A good heat sink is critical to keep the MOSFET from melting. I used a large copper CPU cooler with an integrated fan.