Start Here: http://arduino.cc/en/Tutorial/Midi. It may give you ideas on using a standard midi port with the arduino.
From there you can start playing with using the Arduino to receive midi codes from the controller through an analog pin.Look at this Instractable: http://www.instructables.com/id/Send-and-Receive-MIDI-with-Arduino/.
Finally you can write your code that takes the midi codes and values and responds with the correct display ion the led strip.