Hi!
One way I found to send MIDI signal from your computer to the arduino is to make a processing program that convert the MIDI message to serial and send it to the arduino.
You can use a Serial-MIDI converter software like this:
I am not sure of exactly what can and can't do this converter but using the MIDIBus library for Processing is a easy way to do it (the converter software is done with it if I am correct).
I am for example able to send MIDI timing clock message from my music software on my computer (I use Ableton Live) to Processing, then to Arduino....and I have blinking LEDs in rythm.
So sending note and velocity information should not be very difficult. But you need to find a music software that can read your MIDI file and send those out.
If you are using Windows, you will need to install a program such as MIDI Yoke: http://www.midiox.com/. This will create MIDI port in your computer from which you will be able to send/receive MIDI messages.
Hope this help!