This is not the sort of project where sharing a simple schematic is useful - it wouldn't cover the most important and difficult parts of construction and the key is understanding rather than blindly copying. Exposed voltages _start_ at mains potential (though that is the most dangerous), currents can easily be in the kA region and you can blow up all sorts of electronics if you're not careful, so it ain't a beginner project.
That said, there is a lot of info out there on how they work and how to build one. Gao Guangyan sets a high standard for write-ups here:
http://www.loneoceans.com/labs/#, for english language forums I'd check out
http://4hv.org/e107_plugins/forum/forum.php and
http://highvoltageforum.net, and there is a work-in-progress design guide on Mads Barnkob's site here:
http://kaizerpowerelectronics.dk/tesla-coils/drsstc-design-guide/.In general a DRSSTC will normally involve a handheld controller sending pulses via an optical fibre to a IGBT driver at the base of the coil, the most popular design of which is probably the 74HC based UD2.x series originally designed by Steve Ward (
https://www.stevehv.4hv.org/SSTCindex.htm). This driver uses primary current feedback (zero current switching) to switch an IGBT bridge at the resonant frequency (10s to 100s of kHz) of the primary LC circuit, which is magnetically coupled to the secondary coil and toroid (another LC circuit with a similar resonant frequency), eventually building up enough to start forming an arc channel in the air. By turning on the drive to the IGBT bridge drive via the controller for a few tens-hundreds of microseconds at a time at a pulse rate of a few tens of Hz to low kHz the arc channel can grow into a long "streamer" or hit and earthed object in a "ground strike". To make music the pulse rate can be changed, making different audio frequencies, and the volume adjusted (a little) with different pulse-lengths, normally via a MIDI decoder. This is how Phoenix's coil will be controlled for the Pirates of the Caribbean music, probably with 2 notes simultaneously mixed/multiplexed onto the single fibre optic drive signal.
Phoenix's coil looks like a rather tidy and nice example of a mid-sized DRSSTC, and is probably similar in performance to my own coil which can make arcs a little over 2m long. They get a _LOT_ bigger than this too (search "Gigantor Tesla" on youtube), as well as smaller as seen in the oneTesla kits etc. There are also more complicated DRSSTC drive methods which can make arcs which behave very differently (e.g. QCW coils), and the classic spark gap, vacuum tube and single-resonant solid state coils that have been around for decades to over a century (Tesla's patent is from 1891 according to wikipedia). Finally all a Tesla coil is good for is turning electricity into exciting and rather noisy sparks (along with occasional semiconductor shrapnel when you get things wrong) - it's not the key to worldwide wireless or free energy like a lot of nutters unfortunately associate with them.