Serial Data Input through Microcontroller to Output Voltage
I would suggest doing this in a small FPGA. What you want is clockwork it is more suited to an FPGA than a CPU.  The VHDL for it is trivial.

You can get cheap FPGA dev boards, e.g. From Actel (Igloo Nano) that have all the hardware on board that you need.  You just need to connect a level translator for the MIDI and dot matrix driver, e.g. those given in other answers. The dev board has pins to do that. Instead of a PCB you can even use stripboard. I've connected an LCD matrix display in this way.

Igloo Dev Boar Manual