Yes.... MOTs are a rather dangerous choice for one's first SGTC. Here's my MOT-DC coil in action, using a rather inefficient blown 2-element gap (not rotary):
No, you aren't going to be playing music through a Tesla coil of this type! Spark gaps make a lot of noise on their own!
I'd suggest starting out with a Solid State Tesla coil, which can be scaled down to low enough power levels to make it safe to work with on the workbench. And they are much easier to audio modulate. You can probably use your existing secondary and maybe your primary as well. Search for "PLL SSTC" and you'll find a lot of examples. For an even more basic, very low powered type of SSTC, search for "Slayer exciter". Here's the PLL Class E SSTC that I'm currently working on:
Or if you're heart is set on making a SGTC, I'd suggest using a neon sign transformer (NST) as noted above. They are a lot safer than the MOTs due to the current-limiting feature and you can sometimes get them cheaply from used signs, check your local sign shop.
Or you could consider using a flyback transformer from an old CRT TV or monitor as the primary source. A simple ZVS driver for the flyback transformer, the right capacitors and spark gap construction and you have a hybrid SS-SG TC. Here's mine running on 24 VDC from a couple of batteries:
The multiple capacitor bank is commonly used to build up the capacitance and voltage rating needed for your primary tank.